land

Article

Fire Data as Proxy for Anthropogenic LandscapeChange in the Yucataacuten

Marco Millones 1 John Rogan 2 BL Turner II 3 Benoit Parmentier 4 Robert Clary Harris 5 andDaniel A Griffith 6

1 Department of Geography University of Mary Washington 1301 College AveFredericksburg VA 23219 USA

2 Graduate School of Geography Clark University 950 Main St Worcester MA 01610 USAjroganclarkuedu

3 School of Geographical Sciences and Urban Planning and School of Sustainability Arizona State UniversityTempe AZ 88281-5302 USA BillieLTurnerasuedu

4 Sustainability Solutions Initiative Mitchell Center 5710 Norman Smith Hall University of MaineOrono ME 04469 USA benoitparmentiermaineedu

5 Independent Scholar clayharriscgcidorg6 School of Economic Political and Policy Sciences University of Texas at Dallas 800 W Campbell Rd

Richardson TX 75080 USA dagriffithutdedu Correspondence mmilloneumwedu Tel +1-305-298-8542

Received 14 August 2017 Accepted 8 September 2017 Published 12 September 2017

Abstract Fire is one of the earliest and most common tools used by humans to modify the earthsurface Landscapes in the Yucataacuten Peninsula are composed of a mosaic of old growth subtropicalforest secondary vegetation grasslands and agricultural land that represent a well-documentedexample of anthropogenic intervention much of which involves the use of fire This researchcharacterizes land use systems and land cover changes in the Yucataacuten during the 2000ndash2010 timeperiod We used an active fire remotely sensed data time series from the Moderate ResolutionImaging Spectroradiometer (MODIS) in combination with forest loss and anthrome map sourcesto (1) establish the association between fire and land use change in the region and (2) explore linksbetween the spatial and temporal patterns of fire and specific types of land use practices includingwithin- and between-anthromes variability A spatial multinomial logit model was constructedusing fire landscape configuration and a set of commonly used control variables to estimate forestpersistence non-forest persistence and change Cross-tabulations and descriptive statistics wereused to explore the relationships between fire occurrence location and timing with respect to thegeography of land use We also compared fire frequencies within and between anthrome groupsusing a negative binomial model and Tukey pairwise comparisons Results show that fire databroadly reproduce the geography and timing of anthropogenic land change Findings indicate thatfire and landscape configuration is useful in explaining forest change and non-forest persistenceespecially in fragmented (mosaicked) landscapes Absence of fire occurrence is related usefully to thepersistence of spatially continuous core areas of older growth forest Fire has a positive relationshipwith forest to non-forest change and a negative relationship with forest persistence Fire is also agood indicator to distinguish between anthrome groups (eg croplands and villages) Our studysuggests that active fire data series are a reasonable proxy for anthropogenic land persistencechangein the context of the Yucataacuten and are useful to differentiate quantitatively and qualitatively betweenand within anthromes

Keywords tropical fire land useland cover change MODIS anthrome Yucataacuten Peninsulaspatial model

Land 2017 6 61 doi103390land6030061 wwwmdpicomjournalland

Land 2017 6 61 2 of 19

1 Introduction

This study examines anthropogenic land cover change and persistence across the YucataacutenPeninsula of Mexico by incorporating fire occurrence as a geographic context-specific indicator ofhuman land practices Land use and land cover change (ie land change) is an International Councilfor Science (ICSU) millennial research challenge [1] and has been addressed by various researchcommunities [2ndash5] A consensus has emerged that human-induced land changes have increased atunprecedented rates throughout the last century [5ndash7] to such an extent that the long-term well-beingof human-environment relationships now requires more sustainable management of land uses [89]Without disagreeing with the previous assertion other researchers have argued that humans havealtered ecosystems to such a degree that present landscapes would be best characterized in termsof anthropogenic biomes or anthromes as they occupy the largest portion of the terrestrial landsurface [10] These concerns have guided numerous efforts to detect map and monitor land changeespecially with the aid of remote sensing technology (eg [1112]) Complementary mapping effortshave been undertaken to understand the level of direct human influence as well as efforts to modelthe causes constraints mechanisms and trajectories of land change and persistence (eg [21013ndash16])

While much has been learned from these research efforts certain research challenges remainunaddressed [41617] Two of these challenges are pertinent for highly dynamic and spatiallyheterogeneous mosaicked humanized landscapes the need for additional explicit studies seeking tountangle region-specific human-environment interactions and the need to incorporate context andtemporal information from satellite data sources into the analysis [416ndash18]

The accuracy and spatial explicitness of land use and land cover maps has improved inthe past 20 years with the refinement of the spatial and spectral resolution of remotely senseddata [121619] For local-to-regional scale mapping land change research has relied heavily oncross-sectional assessments (eg two or three map dates [20]) Although valuable cross-sectionalapproaches often overlook high frequency land dynamics occurring between land cover map dates [21]and can potentially misrepresent recurrent changes as unidirectional trends leading to over- orunder-estimation of change [22] In the last decade high temporal frequency remotely sensed datasetshaving1 km spatial resolution and improved calibration such as the Advanced Very High ResolutionRadiometer (AVHRR) the Global Inventory Modeling and Mapping Studies (GIMMS) NDVI dataand the MODIS data product suite [23] have been made available While AVHRR and GIMMSdata are ideal for monitoring dynamic long-term environmental processes at continental and globalscales [11182425] their application is limited at sub-national scales [20] The MODIS product suite incontrast although limited by its shorter time-span offers not only better or equivalent spatial spectraland temporal capacity [26] but also the potential use of the MODIS archive of derived products(eg sea ice active fire) as ancillary data to yield improvements in land cover mapping and changedetection (eg [2728])

In addition to improvements in spatial and temporal details of land cover mapping researchershave made significant progress to specify and even re-conceptualize traditional land coverlanduse categories Specifically the re-framing of categories in terms anthropogenic land use intensity(eg anthromes) places the focus on human activities Many of these efforts have relied on populationdensity to characterize differences between areas that are highly or sparsely intervened by humansHeterogeneity is another criterion commonly used to characterize anthropogenic landscapes In thoseinstances landscapes are often measured on a homogeneity continuum from highly heterogeneousareas of ldquobuiltrdquo landscapes combining many different land uses in relatively small areas to otherspresenting large swaths of homogenous features [10]

Fire is one of the earliest and most significant tools used by humans to modify landscapesand to extract benefits from ecosystem goods and services (eg land clearing for agriculture orurban development forest thinning) At the same time human land use and management (eg fuelload quantity and distribution regulation and ignition sources) have altered naturally occurringfire regimes [29ndash31] The ldquopyric transitionrdquo model has been proposed to describe the relationship

Land 2017 6 61 3 of 19

between human intervention and the intensity of fire use across time and space (eg none in denseurban contexts high in agricultural extensive systems low or background in relatively ldquountouchedrdquoecosystems) [29] This relationship however is highly context-specific in terms of the biophysical andthe cultural characteristics of a region

The present study takes advantage of that potential by using MODIS active fire data time-series incombination with categorical land coveruse maps to examine the link between land change humanactivities and fire in the Yucataacuten Peninsula

2 Study Area

The Yucataacuten Peninsula (henceforth the Yucatan) defined in this study by the Mexican states ofCampeche Quintana Roo and Yucataacuten (Figure 1) is a region characterized by a mostly flat karsticquaternary plain The region is a highly dynamic and complex mosaic of subtropical dry forest indifferent states of ecological succession driven by human and environmental disturbance (eg firetropical storms agriculture) [32ndash35] Unless interrupted by specific disturbances such as fire-friendlyplant invasion or management practices post-fire vegetation grows back at a rapid rate after a burnIn much of the Yucataacuten Peninsula secondary vegetation can reach a height of 10 m within-five years ofclearing [36ndash38] As a consequence there is typically only a short window of time to detect land change

Land 2017 6 61 3 of 19

ecosystems) [29] This relationship however is highly context-specific in terms of the biophysical and the cultural characteristics of a region

The present study takes advantage of that potential by using MODIS active fire data time-series in combination with categorical land coveruse maps to examine the link between land change human activities and fire in the Yucataacuten Peninsula

2 Study Area

The Yucataacuten Peninsula (henceforth the Yucatan) defined in this study by the Mexican states of Campeche Quintana Roo and Yucataacuten (Figure 1) is a region characterized by a mostly flat karstic quaternary plain The region is a highly dynamic and complex mosaic of subtropical dry forest in different states of ecological succession driven by human and environmental disturbance (eg fire tropical storms agriculture) [32ndash35] Unless interrupted by specific disturbances such as fire-friendly plant invasion or management practices post-fire vegetation grows back at a rapid rate after a burn In much of the Yucataacuten Peninsula secondary vegetation can reach a height of 10 m within-five years of clearing [36ndash38] As a consequence there is typically only a short window of time to detect land change

Figure 1 Study Area Mexicorsquos Yucataacuten Peninsula Major federal roads main cities and towns state boundaries and protected areas

Fire in the Yucataacuten is not only an environmental disturbance but also the main land-clearing tool in the region It precedes most land conversion (eg urbanization clear-cut deforestation) and land modification events such as shifting cultivation pasture maintenance and secondary vegetation regrowth [3237ndash40] Persistence and maintenance of non-forest land cover types (eg pasture various crops early secondary vegetation) are also controlled by fire In the Yucataacuten two types of fire are commonly distinguished by local population and regulation quemas and incendios Quemas (~agricultural burns) are in theory legally registered and strictly regulated and scheduled for the purpose of swidden (slash-and-burn) agriculture This includes subsistence maize-based cropping (milpa) pasture maintenance and mechanized agriculture (eg sugar cane commercial corn) Incendios forestales (wildfires) are in theory accidental fires that are ignited by cigarette butts broken glass or lightning They typically occur during the dry season (MarchndashMay) can affect large areas and last for several days These fires if a consequence of human action are illegal and usually generate government agency response especially if they grow out of control and affect farming forest extraction and natural protected areas (NPA) [4041] Although the distinction can be easily

Figure 1 Study Area Mexicorsquos Yucataacuten Peninsula Major federal roads main cities and towns stateboundaries and protected areas

Fire in the Yucataacuten is not only an environmental disturbance but also the main land-clearingtool in the region It precedes most land conversion (eg urbanization clear-cut deforestation) andland modification events such as shifting cultivation pasture maintenance and secondary vegetationregrowth [3237ndash40] Persistence and maintenance of non-forest land cover types (eg pasture variouscrops early secondary vegetation) are also controlled by fire In the Yucataacuten two types of fireare commonly distinguished by local population and regulation quemas and incendios Quemas(~agricultural burns) are in theory legally registered and strictly regulated and scheduled for thepurpose of swidden (slash-and-burn) agriculture This includes subsistence maize-based cropping(milpa) pasture maintenance and mechanized agriculture (eg sugar cane commercial corn) Incendiosforestales (wildfires) are in theory accidental fires that are ignited by cigarette butts broken glassor lightning They typically occur during the dry season (MarchndashMay) can affect large areas and

Land 2017 6 61 4 of 19

last for several days These fires if a consequence of human action are illegal and usually generategovernment agency response especially if they grow out of control and affect farming forest extractionand natural protected areas (NPA) [4041] Although the distinction can be easily blurred (eg escapedburns) quemas tend to be more ubiquitous in the region are smaller in area and shorter in durationthan incendios In contrast incendios are less frequent cover large areas and temporally discrete eventsthat are often amplified in contact with hurricane blow downs [42]

Given the previously described links between various human activities and fire practices weexpect that the spatio-temporal pattern of fire can serve as a proxy for certain anthropogenic land usepractices in the Yucataacuten (eg milpa mechanized agriculture sugar cane cultivation and new urbandevelopment) Naturally occurring wild fires are less frequent in this region than fire of anthropogenicorigin This characteristic represents an opportunity to evaluate fire as a proxy for various land usesand land cover changes in the region

The primary goal of this study is to assess land cover change and persistence across theYucataacuten Peninsula by incorporating MODIS active fire occurrence data as a site-specific indicator ofhuman-induced land change The specific objectives are to (a) describe the spatio-temporal dynamicsof fire and its association with land use practices and land change (b) determine the importance offire presence to explain types of land persistence and change using a spatial multinomial logit modeland (c) explore the ability of fire frequency to discriminate between anthropogenic landscape types(anthropogenic biomes or anthromes)

Beside the specific goal stated lessons learned in this study may be of wider interest in otherregions of the world Spatial driver variables used for land-change modeling and prediction aretypically expensive to produce or not frequently updated as most countries and regions do not possesssuch information at the level of detail required Similarly land cover maps are rarely producedannually Most land cover maps are commonly produced using a census like approach with 5ndash10 yearsgaps at the country or regional levels For an increasing number of applications mapping rapidchanges within-these temporal gaps across countries boundaries may be crucial It is in this contextthat active fire data becomes useful as a predictor It has both high temporal frequency and is readilyavailable worldwide To evaluate the usefulness of fire as predictor in both data poor and rich areaswe modeled land change with and without the presence of additional spatial drivers Results reportedin this specific study should therefore be of potential interest to a wider audience of researchers andland management practitioners

3 Methodological Approach

31 Data

A comprehensive active fire dataset was constructed using NASArsquos 1 km MOD14A2 (fromTERRA) and MYD14A2 (from AQUA) 8-day composite product using various time ranges within-thetime period 2000ndash2010 [43] in order to match fire data and land cover data availability Both dataproducts provide detection confidence levels [44] of which only high and medium were used in orderto minimize potential false positive detections [2745] (Figure 2) The 1 km fire grid cell locations wereconverted to centroid points to match and extract the 30 m grid cell land cover attributes [42]

Land changepersistence information was obtained from Southern Mexico Forest Cover andClearance from c 1990 to c 2000 and to c 2007 digital maps developed by the Center for AppliedBiodiversity Science (CABS) at Conservation International [46] The original maps are based on theinterpretation of (~30 m resolution) Landsat-5 Thematic Mapper satellite imagery and are composedof five categories forest non-forest mangrove water and cloudshadow Forest cover is defined asmature forest gt3 m closed canopy [44] Thematic map accuracy was reported to have a Kappa indexof 86 with an error of commission of 1127 and an error of omission of 486 for the dominanttropical dry forest class prevalent in the study area [44] Forest and mangrove classes were mergedwhereas water clouds and shadow pixels were masked and removed from further analysis to produce

Land 2017 6 61 5 of 19

a map of land persistence and change for 2000ndash2007 with three resulting categories forest persistence(FP) non-forest persistence (NFP) and forest-to-non-forest (CH) (Figure 3) It must be noted thatin contrast with FP (ldquoold growthrdquo forest persistence) NFP by definition allows for land changesbetween sub-classes within-a broad non-forest category For example a transition from agriculture topasture or from pasture to secondary forests would be included in NFP Although lacking detailedland categories the resulting three-category map has the advantage of being more consistent thanmost multi-temporal assessments because it was produced using a consistent methodology by thesame research team explicitly for the purpose of forest change mapping [4647]

Land 2017 6 61 5 of 19

lacking detailed land categories the resulting three-category map has the advantage of being more consistent than most multi-temporal assessments because it was produced using a consistent methodology by the same research team explicitly for the purpose of forest change mapping [4647]

Figure 2 Fire frequency map 2000ndash2010 MODIS TERRA-only series Significant Getis-Ord Gi statistic (005 level) hot spots and LISA-based clusters are shown in inset (upper left) 1 = 2006 post-hurricane Wilma fires and urban development related fires 2 and 5 = Mennonite land clearing for commercial maize cultivation 3 = PEMEX oil processing plant and 4 and 6 = high yield commercial corn and bean cultivation

Figure 3 Land changepersistence classes based on the CABS (2009) land cover maps

Figure 2 Fire frequency map 2000ndash2010 MODIS TERRA-only series Significant Getis-Ord Gi statistic(005 level) hot spots and LISA-based clusters are shown in inset (upper left) 1 = 2006 post-hurricaneWilma fires and urban development related fires 2 and 5 = Mennonite land clearing for commercialmaize cultivation 3 = PEMEX oil processing plant and 4 and 6 = high yield commercial corn andbean cultivation

Anthrome map data corresponding to time interval 2001ndash2006 were obtained from the SEDACwebsite [48]) in GeoTIFF format We cropped and match the dataset to the Yucataacuten region andaggregated the original 21 anthrome categories using the six anthrome group classification Densesettlements villages croplands rangelands forested wildlands In order to match the temporal andspatial resolutions an additional fire variable was created from the MODIS time series by aggregatingyears (2001ndash2008) matching projection and coarsening the cell size This resulted in a 10 times 10 km firefrequency map used for the anthrome analysis

Additional variables commonly used in land-change modeling were included in the analysisto control for environmental and socio-economic factors Elevation and slope were derived from a90 m SRTM digital elevation model Precipitation data were derived from Tropical Rainfall MeasuringMission (TRMM) Protected Areas from CONANP (Mexican Natural Protected Area Commission)were processed to match the study area Communal property lands (ejidos) population density changeas well as the distance to road variable were derived from the Mexican Census Bureau [49] Cattledensity by municipality was obtained from the 2007 Censo Agropecuario [49]

Land 2017 6 61 6 of 19

Land 2017 6 61 5 of 19

lacking detailed land categories the resulting three-category map has the advantage of being more consistent than most multi-temporal assessments because it was produced using a consistent methodology by the same research team explicitly for the purpose of forest change mapping [4647]

Figure 2 Fire frequency map 2000ndash2010 MODIS TERRA-only series Significant Getis-Ord Gi statistic (005 level) hot spots and LISA-based clusters are shown in inset (upper left) 1 = 2006 post-hurricane Wilma fires and urban development related fires 2 and 5 = Mennonite land clearing for commercial maize cultivation 3 = PEMEX oil processing plant and 4 and 6 = high yield commercial corn and bean cultivation

Figure 3 Land changepersistence classes based on the CABS (2009) land cover maps Figure 3 Land changepersistence classes based on the CABS (2009) land cover maps

Even though MODIS fire data are constantly updated in this study we only include data to theyear 2010 We consider the 2000ndash2010 ten-year period sufficient to describe the salient points about thespatio-temporal patterns of a fire in the region More importantly the land cover data and anthromedata that we use do not go beyond 2007 and 2008 respectively For this same reason the multinomialmodeling component of this study does not use any fire data from after 2007 (see methods section)

32 Methods

The methodology has three components (a) a characterization of the spatio-temporal patternsand co-location of land changepersistence and fire (b) an assessment of the effect of fire presencelandscape patch size and other covariates land-change outcomes (FP NFP and CH) using a spatialmultinomial logit model for the period 2000ndash2007 and (c) an exploration of the ability of fire frequencyto distinguish human landscape categories defined in anthrome groups and anthrome classes

33 Characterization of Land Change and Fire Patterns

A cross-tabulation-based change analysis was performed on the simplified CABS land covermap pairs 1990ndash2000 and 2000ndash2007 resulting in one map with two persistence classes (FP and NFP)and one change class (CH) (Figure 3) Spatio-temporal dynamics of fire occurrence were derivedby manipulating the MODIS fire archive via map algebra operations (eg overlay reclassification)into map and graph summaries of annual and multi-year fire frequency After accounting for thedifferent time-spans of the TERRA and AQUA series and adjusting for double counting three separatefire occurrence sets were created a TERRA ten-year summary map (2000ndash2010) (Figure 2) and aTERRA-AQUA combined annual time-series graph (2000ndash2009) (Figure 4) Global (MoranrsquoI) and local(Getis-Ord Gi and LISA) measures of spatial autocorrelation were calculated for all sets of maps [50ndash52]Finally a second cross-tabulation analysis was performed for the land changepersistence map (FPNFP and CH) (Figure 3) and the binary fire (reclassification of Figure 2) maps in order to describe andexplore the spatial correspondence between them and the relationship between fire occurrence and thedifferent land cover categories The result of this cross-tabulation map is shown in Figure 5

Land 2017 6 61 7 of 19

Land 2017 6 61 7 of 19

Figure 4 Cumulative annual and 8-day frequency (counts) of fire occurrence (FIRE) 2000ndash2009 in the three-state Yucataacuten Peninsula blue = morning purple = afternoon Inset shows detail of intra-annual fire season for 2005

Figure 5 Cross-tabulation of land changepersistence classes (Figure 1) and fire frequency (Figure 2)

34 Effect of Fire and Patch Size on Land ChangePersistence A Spatial Multinomial Logit Model

A spatial multinomial logit model using 2003ndash2007 fire ldquodensityrdquo or ldquointensityrdquo (fire countfive years) as independent variable (FIRE) and 7 control variables was performed This model specification is used in the literature (eg [5354]) and is preferred because the dependent variable consists of three possible outcomes that are categoricalnominal in nature [55ndash57] To account for the positive spatial autocorrelation present in remotely sensed data [5859] spatial lags variables based on rook-case adjacency were calculated This was done by generating for each observation the

4000

5000

10000

15000

20000

25000

2000 2001 2002 2003 2004 2005 2006 2007 2008 2009

Terraannual

Aquaannual

Terra 8-day

r December February April June August Octoberr December February April June August October

2000

Fire Season2005

Annual

8-day

4000

5000

10000

15000

20000

25000

2000 2001 2002 2003 2004 2005 2006 2007 2008 2009

Terraannual

Aquaannual

Terra 8-day

r December February April June August Octoberr December February April June August October

2000

Fire Season2005

Annual

8-day

Figure 4 Cumulative annual and 8-day frequency (counts) of fire occurrence (FIRE) 2000ndash2009 in thethree-state Yucataacuten Peninsula blue = morning purple = afternoon Inset shows detail of intra-annualfire season for 2005

Land 2017 6 61 7 of 19

Figure 4 Cumulative annual and 8-day frequency (counts) of fire occurrence (FIRE) 2000ndash2009 in the three-state Yucataacuten Peninsula blue = morning purple = afternoon Inset shows detail of intra-annual fire season for 2005

Figure 5 Cross-tabulation of land changepersistence classes (Figure 1) and fire frequency (Figure 2)

34 Effect of Fire and Patch Size on Land ChangePersistence A Spatial Multinomial Logit Model

A spatial multinomial logit model using 2003ndash2007 fire ldquodensityrdquo or ldquointensityrdquo (fire countfive years) as independent variable (FIRE) and 7 control variables was performed This model specification is used in the literature (eg [5354]) and is preferred because the dependent variable consists of three possible outcomes that are categoricalnominal in nature [55ndash57] To account for the positive spatial autocorrelation present in remotely sensed data [5859] spatial lags variables based on rook-case adjacency were calculated This was done by generating for each observation the

4000

5000

10000

15000

20000

25000

2000 2001 2002 2003 2004 2005 2006 2007 2008 2009

Terraannual

Aquaannual

Terra 8-day

r December February April June August Octoberr December February April June August October

2000

Fire Season2005

Annual

8-day

4000

5000

10000

15000

20000

25000

2000 2001 2002 2003 2004 2005 2006 2007 2008 2009

Terraannual

Aquaannual

Terra 8-day

r December February April June August Octoberr December February April June August October

2000

Fire Season2005

Annual

8-day

Figure 5 Cross-tabulation of land changepersistence classes (Figure 1) and fire frequency (Figure 2)

34 Effect of Fire and Patch Size on Land ChangePersistence A Spatial Multinomial Logit Model

A spatial multinomial logit model using 2003ndash2007 fire ldquodensityrdquo or ldquointensityrdquo (fire countfiveyears) as independent variable (FIRE) and 7 control variables was performed This model specificationis used in the literature (eg [5354]) and is preferred because the dependent variable consists of

Land 2017 6 61 8 of 19

three possible outcomes that are categoricalnominal in nature [55ndash57] To account for the positivespatial autocorrelation present in remotely sensed data [5859] spatial lags variables based on rook-caseadjacency were calculated This was done by generating for each observation the average sum of itsneighbors of the same class (CFP CNFP and CCH) and including the lag variable in the model (seeEquation (1)) [5960] Lag values range from 0 (no like neighbors) to 1 (all four like neighbors) whileaverage Moranrsquos I values range from virtually random for CCH (00035) to weak-moderate positivefor CNFP (0392) and CFP (0391) In this particular case spatial lags also serve as an indicator oflandscape configuration and heterogeneity (ie similar to patch size and cohesion)

Pseudo-likelihood estimates were calculated for the main effects and spatial lag parameters of themultinomial model as follows (Equation (1))

Log(πhijπhir) = αj + xprimehi βj (1)

where πhij is the probability that a pixel h in the map of any class i for which fire has been detected willbecome one of land changepersistence category j (FP NFP or CH) j 6= r with land changepersistencecategory r being the reference category There are separate sets of intercept parameters αj and regressionparameters βj for each of the logit models The matrix xprimehi is the set of explanatory variables spatiallag (CY) fire (FIRE) and the commonly used control variables described Two logits equations aremodeled for each FIRE and CY population the logit comparing non-forest persistence (NFP) to forestpersistence (FP) and the logit comparing change (CH) to forest persistence (FP) [56]

35 Fire Frequency and Anthromes Characterization

Anthromes map datasets were processed to match them to the study area and temporal firecount data were aggregated to generate a fire frequency variable (Figure 6) In order to explore theassociation between fire counts and anthrome groups graphically we used boxplots of mean firefrequency by each category present in the study area dense settlements villages (in effect village andsurrounding areas) croplands rangelands forested wildlands We measured the differences in meanfire frequency across anthromes using a negative binomial model and a Tukey pairwise comparisonA binomial model was preferred over Poisson model because the overall (as well as per category) meanand variance are noticeably different (by a factor 100) which suggests over-dispersion in the Poissonparameter We also conducted Tukey comparisons for fire frequency within the cropland anthromesgroup to assess the potential of using fire count for finer definition of the human imprint of landscape

Land 2017 6 61 8 of 19

average sum of its neighbors of the same class (CFP CNFP and CCH) and including the lag variable in the model (see Equation (1)) [5960] Lag values range from 0 (no like neighbors) to 1 (all four like neighbors) while average Moranrsquos I values range from virtually random for CCH (00035) to weak-moderate positive for CNFP (0392) and CFP (0391) In this particular case spatial lags also serve as an indicator of landscape configuration and heterogeneity (ie similar to patch size and cohesion)

Pseudo-likelihood estimates were calculated for the main effects and spatial lag parameters of the multinomial model as follows (Equation (1))

Log(πhijπhir) = αj + xprimehi βj (1)

where πhij is the probability that a pixel h in the map of any class i for which fire has been detected will become one of land changepersistence category j (FP NFP or CH) j ne r with land changepersistence category r being the reference category There are separate sets of intercept parameters αj and regression parameters βj for each of the logit models The matrix xprimehi is the set of explanatory variables spatial lag (CY) fire (FIRE) and the commonly used control variables described Two logits equations are modeled for each FIRE and CY population the logit comparing non-forest persistence (NFP) to forest persistence (FP) and the logit comparing change (CH) to forest persistence (FP) [56]

35 Fire Frequency and Anthromes Characterization

Anthromes map datasets were processed to match them to the study area and temporal fire count data were aggregated to generate a fire frequency variable (Figure 6) In order to explore the association between fire counts and anthrome groups graphically we used boxplots of mean fire frequency by each category present in the study area dense settlements villages (in effect village and surrounding areas) croplands rangelands forested wildlands We measured the differences in mean fire frequency across anthromes using a negative binomial model and a Tukey pairwise comparison A binomial model was preferred over Poisson model because the overall (as well as per category) mean and variance are noticeably different (by a factor 100) which suggests over-dispersion in the Poisson parameter We also conducted Tukey comparisons for fire frequency within the cropland anthromes group to assess the potential of using fire count for finer definition of the human imprint of landscape

For the data processing we used the raster (version 25-8) sp (version 12-4) and rgdal (version 12-7) packages to perform some of the preprocessing for the spatial inputs The raster package was also used for aggregation of the fire occurrences cropping and reclassification of anthromes data We used the implementation of multinomial model in the R ldquonnetrdquo package (version 73-12) for analyses We also ran the negative binomial model using the ldquoMASSrdquo package (version 73-12) in R version 34 and used the glht method from the multcomp R package (14-6) to perform the Tukey comparison

Figure 6 Fire frequency aggregation for anthrome comparison (left) and Anthrome groups (right)

Figure 6 Fire frequency aggregation for anthrome comparison (left) and Anthrome groups (right)

For the data processing we used the raster (version 25-8) sp (version 12-4) and rgdal(version 12-7) packages to perform some of the preprocessing for the spatial inputs The raster packagewas also used for aggregation of the fire occurrences cropping and reclassification of anthromes

Land 2017 6 61 9 of 19

data We used the implementation of multinomial model in the R ldquonnetrdquo package (version 73-12)for analyses We also ran the negative binomial model using the ldquoMASSrdquo package (version 73-12)in R version 34 and used the glht method from the multcomp R package (14-6) to perform theTukey comparison

4 Results

41 Spatio-Temporal Patterns of Fire and Land Change

As a proxy indicator of human land use fire frequency can be interpreted as a quantitativemeasure of ldquodensityrdquo (in space and time) of land use in this case It corresponds to how actively ldquousedrdquoor ldquounder-usedrdquo a 1 km parcel of land is in relation to the types of land use that require burning(eg high for pasture and cultivation land)

Fire occurrence for the period 2000ndash2010 presents a distinct non-random spatial pattern across thestudy area (Moranrsquos I = 062) (Figure 2) The individual observations presenting the highest detectionfrequencies (gt3 per year) appear in spatial clusters and are concentrated in the northern and westernsection of the Peninsula in the states of Campeche and the Yucataacuten Quintana Roo has comparativelyfewer and less clustering fire detections Areas with less fire frequency are observed in Campeche andQuintana Roo especially in the presence of federal and state run natural protected areas (eg SianKarsquoan and Calakmul bioreserves) (Figure 1) and in locations where road and settlement density is lowThis road-settlement-fire co-location is more explicit in the Yucataacuten and northern Campeche and lessso in southern Campeche where road density decreases

Locations affected by fire (Figure 5 and Table 1) cover roughly 45 of the study area More thanhalf of the fire occurrences concentrate in NFP areas followed by 40 of FP and 2 in CH areas(1 of the total) Locations with no fire occurrence cover more than 50 of the study area No-fireoccurrences are two times more common in FP than in NFP and they are minimally present in CHareas Land changepersistence figures (total rows percentage in Table 1) indicate that roughly 23 ofthe FP shows no fire detections whereas 60 of NFP presents fire occurrence CH shows 86 of itsarea as having burned at some time (although it is hardly visible in Figure 5 because CH covers only1 of the total area)

Land 2017 6 61 10 of 19

Table 1 Cross-tabulation of fire occurrence and land changepersistence row column and total percentages per class Preliminary interpretation matrix(extendeddetailed legend for Figure 5)

Fire No Fire Row Total Total Study Area

Forest Persistence

293-Error resulting from database mismatch-Error of commission in MODIS ActiveFire product-Error induced by aggregation of landcover data

707-Core areas of mature forest that have persisted for at least 17years (1990ndash2007)-Protected areas with a predominance of mature forest-Areas of planned selective forest extraction that have not beenextracted in 17 years or longer (under rotation management)

100 54

Non Forest Persistence

608-Areas where fire is used to convert fromnon-forest vegetation land covers toother non-forest vegetation land covers(eg agriculture to urban)-Areas of active non-forest land-uses-Error resulting from databasemismatches

3918-Areas under intensive land-uses that do not require land clearingfor prolonged periods (eg citrus agriculture urban)-Secondary vegetation of at least 10 years including forest notconsidered mature by CAB 2009 This can include forest regrowth(forest transition)-Forested areas of forest communities that have been extracted inthe last 10 years and are growing back-Seasonal agricultural areas currently fallow (eg milpa)

100 43

Change (Forest toNon-Forest)

860-All land cover changes (conversion andsome modification) preceded by landclearing by fire (ie deforestation)-Core forest areas that are heavilydeforested with more intense use of landclearing by fire

137-Error of omission in MODIS Active Fire product-Error resulting from database mismatches-Land changes that do not require fire-Fringe areas that are cleared without fire after the core area hasbeen cleared with fire-Fringe areas that are cleared with low intensity fire that is notdetected by MODIS Active Fire product

100 1

Column TOTAL 45 36 100 100

Land 2017 6 61 11 of 19

42 Effect of Fire and Patch Size on Land ChangePersistence A Spatial Multinomial Logit Model

Results from the spatial multinomial logit model agree with the analysis presented above(Section 41) and indicate that past fire occurrence (pre-2007) is a useful predictor of land changepersistence categories The resulting equations and model statistics are summarized in Table 2 and inthe supplementary Appendix A The Akaike information criterion (AIC) indicates that the model withcovariates (intercept + fire and lag + control variables) performs better than alternative models (seeAppendix A) The likelihood ratio (LR) has two degrees of freedom and is significant which confirmsthat at least one of the variables in the model improves the model description

Table 2 Spatial multinomial logit model summary of trends FP = forest persistence NFP = non forestpersistence CH = change INTE = Intercept Odds = Odds ratio effects point estimates This tablecontains only FIRE and CY variables the full variable list is available in the Appendix A

CAT REF INTE CY FIRE Odds CY Odds FIRE

CH (3) FP (1) minus467 minus355 192 003 679NFP (2) minus607 minus346 020 003 122

CH Average minus537 minus350 106 003 400

FP (1) CH (3) 467 355 minus192 3466 015NFP (2) minus438 007 minus172 107 018

FP Average 015 181 minus182 1787 016

NFP (2) CH (3) 905 348 minus020 3243 082FP (1) 438 minus007 172 094 559

FP Average 671 171 076 1668 320

The maximum pseudo-likelihood and odds ratio point estimates (Table 2 and Appendix A) showthe effect and relative importance of FIRE and CY for each land changepersistence outcome in themodel At a 5 level the difference between FIRE = 1 (fire occurrence) and FIRE = 0 is statisticallydifferent for all cases (FP NFP and CH) for all three states separately and the three-state aggregatedstudy area CY is a significant covariate in the model for all of these cases Additional models wererun with control variables These full model results are presented in the Appendix A and confirm theusefulness of fire as predictor

An inspection of the pseudo-likelihood estimates for the aggregated study area (Table 2 andAppendix A) indicates that for each unit increase in FIRE (intensity) the log of the ratio of p(CH)p(FP)increases by ~192 and the log of the ratio of p(CH)p(NFP) increases by ~02 In other words for eachunit increase in FIRE (intensity) in a given pixel (in Figure 2) the odds of that same pixel belonging tocategory CH (forest to non-forest change) rather than category FP (forest persistence in Figure 3) aremultiplied by ~67 Unit increases in FIRE also increase the odds of a pixel belonging to category CHrather than NFP (no forest persistence) by 122

For every increase in one unit of Fire the odds of a pixel belonging to category NFP instead of CHare multiplied by 082 For every increase in one unit of Fire the odds of a pixel belonging to categoryNFP instead of FP are multiplied by 559 For every increase in one unit of Fire the odds of a pixelbelonging to category FP instead of CH are multiplied by 015 (almost none)

For every increase in one unit of Fire the odds of a pixel belonging to category FP instead ofNFP are multiplied by 018 (almost none) Overall FIRE estimates are negative when predicting forestpersistence (FP) and positive when predicting CH

The calculated spatial lag (CY) terms are significant for all cases CY as mentioned earlier can beinterpreted as cohesiveness of land cover patches [61] Larger CY values correspond to more similarvalues among neighboring cells (ie a larger patches of a category) Estimates of the model for theaggregated peninsula indicate that a unit increase in CY decreases the log of p(FP)p(CH) by ~minus355while the log of p(FP)p(NFP) decreases by ~minus007 This finding indicates that persistent forestareas located in large patches are very likely to remain forest (34 times more than CH) (Table 2 and

Land 2017 6 61 12 of 19

Appendix A) FP is also 107 times more likely than NFP In general CH has a negative relationship withCY This relationship can be attributed to CH occurring more often in isolated pixels corresponding tofragmented patches Conversely FP and NFP occur in larger continuous areas (Figure 3)

43 Comparison of Fire by Anthromes

Boxplots of mean fire frequency by anthromes groups suggest that fire can be used to distinguishamong anthromes groups thereby serving as an additional potential variable to examine humanimprints in the context of the Yucataacuten region (Figure 6) The croplands anthromes group has a higherfire frequency on average compared to most other anthromes categories We note that rangelandsdisplay a very large variance and thus may be difficult to distinguish from croplands and villagesFiner anthropogenic categories within the cropland groups also appear to be contrasted by the firefrequency variable (see boxplots Figure 7)

Land 2017 6 61 12 of 19

corresponding to fragmented patches Conversely FP and NFP occur in larger continuous areas (Figure 3)

43 Comparison of Fire by Anthromes

Boxplots of mean fire frequency by anthromes groups suggest that fire can be used to distinguish among anthromes groups thereby serving as an additional potential variable to examine human imprints in the context of the Yucataacuten region (Figure 6) The croplands anthromes group has a higher fire frequency on average compared to most other anthromes categories We note that rangelands display a very large variance and thus may be difficult to distinguish from croplands and villages Finer anthropogenic categories within the cropland groups also appear to be contrasted by the fire frequency variable (see boxplots Figure 7)

Tukey pairwise comparison tests between anthromes groups (applied to the negative binomial model Table 3) highlight that six and seven pairwise comparisons are significantly different at 5 and 10 level respectively Coefficients indicate relative increase or decrease of the expected log of fire frequency for categorical change in relation to the reference variable For instance there is a minus137 decrease in the log of fire frequency when an observation is found in the dense settlements rather than in croplands We find that fire frequency variable is useful to differentiate croplands with almost all categories with the exception of Villages and Rangelands Both overlap substantially on the boxplots (Figure 7)

Figure 7 Between group comparison Fire frequency by anthrome groups boxplots (left) Within group comparison Fire frequency boxplots within cropland anthrome (right)

Table 3 Between-anthromes Tukey pairwise comparison for the negative binomial models with fire count and anthromes groups Note that the reference variable is in italic

Pairwise Comparison Coefficients Standard Error t-Stat p-ValuesDense settlementsndashCroplands minus138688 043059 minus32209 00121

ForestedndashCroplands minus092198 006997 minus131762 0 RangelandsndashCroplands minus035406 026321 minus13452 07146

VillagesndashCroplands minus028199 032807 minus08595 09435 WildlandsndashCroplands minus229463 019565 minus117283 0

ForestedndashDense settlements 046491 042934 10828 08616 RangelandsndashDense settlements 103282 049872 20709 02552

VillagesndashDense settlements 110489 053579 20622 02593 WildlandsndashDense settlements minus090775 04666 minus19454 03214

RangelandsndashForested 056791 026118 21744 02076

Figure 7 Between group comparison Fire frequency by anthrome groups boxplots (left) Within groupcomparison Fire frequency boxplots within cropland anthrome (right)

Tukey pairwise comparison tests between anthromes groups (applied to the negative binomialmodel Table 3) highlight that six and seven pairwise comparisons are significantly different at 5 and10 level respectively Coefficients indicate relative increase or decrease of the expected log of firefrequency for categorical change in relation to the reference variable For instance there is a minus137decrease in the log of fire frequency when an observation is found in the dense settlements rather thanin croplands We find that fire frequency variable is useful to differentiate croplands with almost allcategories with the exception of Villages and Rangelands Both overlap substantially on the boxplots(Figure 7)

Tukey comparisons were also performed for fire frequency within the cropland anthromes groupto assess the potential of using fire frequency for finer definition of the human imprint of landscapeWe found that within croplands two out 10 and four out of 10 comparison results in significantdifferences in the log of fire frequency (Table 4) at 5 and 10 percent significance level respectivelyThis suggests that fire frequency is less useful at distinguishing within the cropland anthromes Thestrongest contrasts are found between ldquoresidential rainfed mosaicsndashremote croplands mosaicrdquo andbetween ldquoresidential irrigated croplandndashremote croplandsrdquo Both indicate decreases in the log offire frequency for locations that are found in residential rainfed and irrigated cropland compared toremote croplands

Land 2017 6 61 13 of 19

Table 3 Between-anthromes Tukey pairwise comparison for the negative binomial models with firecount and anthromes groups Note that the reference variable is in italic

Pairwise Comparison Coefficients Standard Error t-Stat p-Values

Dense settlementsndashCroplands minus138688 043059 minus32209 00121ForestedndashCroplands minus092198 006997 minus131762 0

RangelandsndashCroplands minus035406 026321 minus13452 07146VillagesndashCroplands minus028199 032807 minus08595 09435

WildlandsndashCroplands minus229463 019565 minus117283 0ForestedndashDense settlements 046491 042934 10828 08616

RangelandsndashDense settlements 103282 049872 20709 02552VillagesndashDense settlements 110489 053579 20622 02593

WildlandsndashDense settlements minus090775 04666 minus19454 03214RangelandsndashForested 056791 026118 21744 02076

VillagesndashForested 063999 032644 19605 03129WildlandsndashForested minus137266 01929 minus71159 0VillagesndashRangelands 007207 041346 01743 1

WildlandsndashRangelands minus194057 031874 minus60882 0WildlandsndashVillages minus201264 037409 minus53801 0

Table 4 Within-anthrome Tukey pairwise comparisons using the negative binomial models with firecount and anthromes croplands categories Note that the reference variable is in italic

PairwisendashComparison Coefficients Standard Error t-Stat p-Values

Populated rainfed croplandndashPopulated irrigated cropland 025239 022555 1119 07646Remote croplandsndashPopulated irrigated cropland 0572 025835 2214 01453

Residential irrigated croplandndashPopulated irrigated cropland minus061118 041094 minus14873 05244Residential rainfed mosaicndashPopulated irrigated cropland 008091 022337 03622 09955

Remote croplandsndashPopulated rainfed cropland 031961 014756 2166 01615Residential irrigated croplandndashPopulated rainfed cropland minus086357 0352 minus24533 00827

Residential rainfed mosaicndashPopulated rainfed cropland minus017148 007017 minus24437 00848Residential irrigated croplandndashRemote croplands minus118318 037387 minus31647 00105

Residential rainfed mosaicndashRemote croplands minus049109 014421 minus34054 00043Residential rainfed mosaicndashResidential irrigated cropland 069209 035061 1974 02396

5 Discussion and Conclusions

Analysis of the spatial patterns of fire in the Yucataacuten using fire data visually reproduces thegeography of human land-based activities during 2000ndash2010 including the influence of roadssettlements and natural protected areas The intra-annual temporal dimensions of fire dataapproximate key moments of seasonal agriculture and other land-based activities (Figure 4) Thesefindings are consistent with studies finding higher fire frequencies in the proximity to roads andsettlements region [40] and with research about fire and deforestation in other tropical settings(eg [2862ndash64]) and more generally about the relationship between land change road developmentand market accessibility [53546465]

The multinomial model confirms the significance of fire intensity (defined as count of fire flaggedpixels over time) and landscape configuration (represented by the spatial lag variable CY) for thepeninsula for all three types of land changepersistence outcomes Notably all change is stronglyaffected by the presence of fire The odds of a forested area becoming non-forested multiply by sixin the presence of fire This is not surprising given that the cross-tabulation analysis showed thatnearly 87 of pixels that changed from 2000 to 2007 had been flagged as fire by MODIS at some pointThe dominance of no-fire observations over fire occurrence the (pseudo) absence of fire makes for abetter predictor of forest persistence than fire occurrence per se especially for large patches (high CYvalues) Predicting non-forest persistence proved more difficult signaling the diversity of ecologicaland land use practices and transitions between them that define the NFP category as discussed in thedata section What exactly accounts for the remaining 13 is difficult to determine We can speculate

Land 2017 6 61 14 of 19

however that possible factors include data error and accuracy mismatches As some have notedMODIS products do omit fires for various reasons [40] We can also speculate on some detected firesbeing non-agricultural Finally we can also imagine some fires starting as agricultural burns butbecoming large multiday forest fires as they grow out of control [40]

Fire also proves to be a reasonable indicator to distinguish between anthromes groups (Figure 7)but less among finer anthromes categories Our analysis shows that for example with the aidof a fire frequency croplands are separable from the rest of categories and that dense settlementsare clearly distinct from villages Other categories like rangeland prove more difficult to separatesince they present larger variance Some within-variation within anthropogenic categories is alsodistinguishable For example populated irrigated is clearly separable from populated rainfed andfrom remote croplands These two former categories however are not as separable from each otherwith the aid of fire frequency alone

Perhaps some insight about differences distinguishing between- and within-anthropogeniclandscapes can be gained by looking into the distinction between quemas (legally regulated agriculturalfires) from incendios (large escape non-regulated forest fires) Both can be addressed through the use ofMODIS active fire data but cannot be thoroughly distinguished with these data alone Within-variationexists in both categories On the one hand quemas can be due to subsistence and commercial agriculturesuch as sugar cane cultivation along the border with Belize (ie either rain fed or irrigated anthromecategories) or Mennonite corn fields in Bacalar( ie the populated irrigated anthrome category) astheir spatial and temporal signatures can differ quite noticeably (Figures 2 and 4) On the other handincendios can be truly accidental or be the result of purposeful burning with nonagricultural goals(eg forcing land zoning code changes for urban development hunting practices) Future researchshould exploit these differences in order to account for a more nuanced description of the relationshipsbetween fire and human-induced land change in the region

We conclude that in subtropical forest settings in which burning is a fundamental landscape toolfire is a reasonable proxy for land change Use of fire data improves the estimation of land change andexpands our understanding of human-environment relationships that produce complex mosaics ofhighly dynamic landscapes such as those in the Mexican Yucataacuten

Acknowledgments This study was part of the SYPR (httpsyprasuedu) and EDGY (httplandchangerutgersedu) projects SYPR received support from the NASA LCLUC program (NAG-56046 511134 and 6GD98G)and the NSF BCS program (0410016) EDGY was sponsored by the Gordon and Betty Moore Foundation underGrant 1697 The authors thank Drs Birgit Schmook (El Colegio de la Frontera Sur) Laura Schneider (RutgersUniversity) and Zachary Christman (Rowan University) for their support and advice The staff of Clark Labsfacilitated the work by creating and maintaining the Idrisireg software (httpwwwclarklabsorg) with whichpreliminary analysis was performed Subsequent and final analysis was performed with R packages NNetMASS multcomp and raster

Author Contributions Marco Millones John Rogan BL Turner II conceived and designed the original researchand fieldwork Marco Millones performed the fieldwork Marco Millones performed preliminary data analysiswith Daniel A Griffith Robert Clay Harris and Benoit Parmentier executed the final data analysis John RoganBL Turner II revised earlier versions of the manuscript Marco Millones Benoit Parmentier and Robert Clay Harriswrote the paper John Rogan revised the manuscript

Conflicts of Interest The authors declare no conflicts of interest

Land 2017 6 61 3 of 19

between human intervention and the intensity of fire use across time and space (eg none in denseurban contexts high in agricultural extensive systems low or background in relatively ldquountouchedrdquoecosystems) [29] This relationship however is highly context-specific in terms of the biophysical andthe cultural characteristics of a region

The present study takes advantage of that potential by using MODIS active fire data time-series incombination with categorical land coveruse maps to examine the link between land change humanactivities and fire in the Yucataacuten Peninsula

2 Study Area

The Yucataacuten Peninsula (henceforth the Yucatan) defined in this study by the Mexican states ofCampeche Quintana Roo and Yucataacuten (Figure 1) is a region characterized by a mostly flat karsticquaternary plain The region is a highly dynamic and complex mosaic of subtropical dry forest indifferent states of ecological succession driven by human and environmental disturbance (eg firetropical storms agriculture) [32ndash35] Unless interrupted by specific disturbances such as fire-friendlyplant invasion or management practices post-fire vegetation grows back at a rapid rate after a burnIn much of the Yucataacuten Peninsula secondary vegetation can reach a height of 10 m within-five years ofclearing [36ndash38] As a consequence there is typically only a short window of time to detect land change

Land 2017 6 61 3 of 19

ecosystems) [29] This relationship however is highly context-specific in terms of the biophysical and the cultural characteristics of a region

The present study takes advantage of that potential by using MODIS active fire data time-series in combination with categorical land coveruse maps to examine the link between land change human activities and fire in the Yucataacuten Peninsula

2 Study Area

The Yucataacuten Peninsula (henceforth the Yucatan) defined in this study by the Mexican states of Campeche Quintana Roo and Yucataacuten (Figure 1) is a region characterized by a mostly flat karstic quaternary plain The region is a highly dynamic and complex mosaic of subtropical dry forest in different states of ecological succession driven by human and environmental disturbance (eg fire tropical storms agriculture) [32ndash35] Unless interrupted by specific disturbances such as fire-friendly plant invasion or management practices post-fire vegetation grows back at a rapid rate after a burn In much of the Yucataacuten Peninsula secondary vegetation can reach a height of 10 m within-five years of clearing [36ndash38] As a consequence there is typically only a short window of time to detect land change

Figure 1 Study Area Mexicorsquos Yucataacuten Peninsula Major federal roads main cities and towns state boundaries and protected areas

Fire in the Yucataacuten is not only an environmental disturbance but also the main land-clearing tool in the region It precedes most land conversion (eg urbanization clear-cut deforestation) and land modification events such as shifting cultivation pasture maintenance and secondary vegetation regrowth [3237ndash40] Persistence and maintenance of non-forest land cover types (eg pasture various crops early secondary vegetation) are also controlled by fire In the Yucataacuten two types of fire are commonly distinguished by local population and regulation quemas and incendios Quemas (~agricultural burns) are in theory legally registered and strictly regulated and scheduled for the purpose of swidden (slash-and-burn) agriculture This includes subsistence maize-based cropping (milpa) pasture maintenance and mechanized agriculture (eg sugar cane commercial corn) Incendios forestales (wildfires) are in theory accidental fires that are ignited by cigarette butts broken glass or lightning They typically occur during the dry season (MarchndashMay) can affect large areas and last for several days These fires if a consequence of human action are illegal and usually generate government agency response especially if they grow out of control and affect farming forest extraction and natural protected areas (NPA) [4041] Although the distinction can be easily

Figure 1 Study Area Mexicorsquos Yucataacuten Peninsula Major federal roads main cities and towns stateboundaries and protected areas

Fire in the Yucataacuten is not only an environmental disturbance but also the main land-clearingtool in the region It precedes most land conversion (eg urbanization clear-cut deforestation) andland modification events such as shifting cultivation pasture maintenance and secondary vegetationregrowth [3237ndash40] Persistence and maintenance of non-forest land cover types (eg pasture variouscrops early secondary vegetation) are also controlled by fire In the Yucataacuten two types of fireare commonly distinguished by local population and regulation quemas and incendios Quemas(~agricultural burns) are in theory legally registered and strictly regulated and scheduled for thepurpose of swidden (slash-and-burn) agriculture This includes subsistence maize-based cropping(milpa) pasture maintenance and mechanized agriculture (eg sugar cane commercial corn) Incendiosforestales (wildfires) are in theory accidental fires that are ignited by cigarette butts broken glassor lightning They typically occur during the dry season (MarchndashMay) can affect large areas and

Land 2017 6 61 4 of 19

last for several days These fires if a consequence of human action are illegal and usually generategovernment agency response especially if they grow out of control and affect farming forest extractionand natural protected areas (NPA) [4041] Although the distinction can be easily blurred (eg escapedburns) quemas tend to be more ubiquitous in the region are smaller in area and shorter in durationthan incendios In contrast incendios are less frequent cover large areas and temporally discrete eventsthat are often amplified in contact with hurricane blow downs [42]

Given the previously described links between various human activities and fire practices weexpect that the spatio-temporal pattern of fire can serve as a proxy for certain anthropogenic land usepractices in the Yucataacuten (eg milpa mechanized agriculture sugar cane cultivation and new urbandevelopment) Naturally occurring wild fires are less frequent in this region than fire of anthropogenicorigin This characteristic represents an opportunity to evaluate fire as a proxy for various land usesand land cover changes in the region

The primary goal of this study is to assess land cover change and persistence across theYucataacuten Peninsula by incorporating MODIS active fire occurrence data as a site-specific indicator ofhuman-induced land change The specific objectives are to (a) describe the spatio-temporal dynamicsof fire and its association with land use practices and land change (b) determine the importance offire presence to explain types of land persistence and change using a spatial multinomial logit modeland (c) explore the ability of fire frequency to discriminate between anthropogenic landscape types(anthropogenic biomes or anthromes)

Beside the specific goal stated lessons learned in this study may be of wider interest in otherregions of the world Spatial driver variables used for land-change modeling and prediction aretypically expensive to produce or not frequently updated as most countries and regions do not possesssuch information at the level of detail required Similarly land cover maps are rarely producedannually Most land cover maps are commonly produced using a census like approach with 5ndash10 yearsgaps at the country or regional levels For an increasing number of applications mapping rapidchanges within-these temporal gaps across countries boundaries may be crucial It is in this contextthat active fire data becomes useful as a predictor It has both high temporal frequency and is readilyavailable worldwide To evaluate the usefulness of fire as predictor in both data poor and rich areaswe modeled land change with and without the presence of additional spatial drivers Results reportedin this specific study should therefore be of potential interest to a wider audience of researchers andland management practitioners

3 Methodological Approach

31 Data

A comprehensive active fire dataset was constructed using NASArsquos 1 km MOD14A2 (fromTERRA) and MYD14A2 (from AQUA) 8-day composite product using various time ranges within-thetime period 2000ndash2010 [43] in order to match fire data and land cover data availability Both dataproducts provide detection confidence levels [44] of which only high and medium were used in orderto minimize potential false positive detections [2745] (Figure 2) The 1 km fire grid cell locations wereconverted to centroid points to match and extract the 30 m grid cell land cover attributes [42]

Land changepersistence information was obtained from Southern Mexico Forest Cover andClearance from c 1990 to c 2000 and to c 2007 digital maps developed by the Center for AppliedBiodiversity Science (CABS) at Conservation International [46] The original maps are based on theinterpretation of (~30 m resolution) Landsat-5 Thematic Mapper satellite imagery and are composedof five categories forest non-forest mangrove water and cloudshadow Forest cover is defined asmature forest gt3 m closed canopy [44] Thematic map accuracy was reported to have a Kappa indexof 86 with an error of commission of 1127 and an error of omission of 486 for the dominanttropical dry forest class prevalent in the study area [44] Forest and mangrove classes were mergedwhereas water clouds and shadow pixels were masked and removed from further analysis to produce

Land 2017 6 61 5 of 19

a map of land persistence and change for 2000ndash2007 with three resulting categories forest persistence(FP) non-forest persistence (NFP) and forest-to-non-forest (CH) (Figure 3) It must be noted thatin contrast with FP (ldquoold growthrdquo forest persistence) NFP by definition allows for land changesbetween sub-classes within-a broad non-forest category For example a transition from agriculture topasture or from pasture to secondary forests would be included in NFP Although lacking detailedland categories the resulting three-category map has the advantage of being more consistent thanmost multi-temporal assessments because it was produced using a consistent methodology by thesame research team explicitly for the purpose of forest change mapping [4647]

Land 2017 6 61 5 of 19

lacking detailed land categories the resulting three-category map has the advantage of being more consistent than most multi-temporal assessments because it was produced using a consistent methodology by the same research team explicitly for the purpose of forest change mapping [4647]

Figure 2 Fire frequency map 2000ndash2010 MODIS TERRA-only series Significant Getis-Ord Gi statistic (005 level) hot spots and LISA-based clusters are shown in inset (upper left) 1 = 2006 post-hurricane Wilma fires and urban development related fires 2 and 5 = Mennonite land clearing for commercial maize cultivation 3 = PEMEX oil processing plant and 4 and 6 = high yield commercial corn and bean cultivation

Figure 3 Land changepersistence classes based on the CABS (2009) land cover maps

Figure 2 Fire frequency map 2000ndash2010 MODIS TERRA-only series Significant Getis-Ord Gi statistic(005 level) hot spots and LISA-based clusters are shown in inset (upper left) 1 = 2006 post-hurricaneWilma fires and urban development related fires 2 and 5 = Mennonite land clearing for commercialmaize cultivation 3 = PEMEX oil processing plant and 4 and 6 = high yield commercial corn andbean cultivation

Anthrome map data corresponding to time interval 2001ndash2006 were obtained from the SEDACwebsite [48]) in GeoTIFF format We cropped and match the dataset to the Yucataacuten region andaggregated the original 21 anthrome categories using the six anthrome group classification Densesettlements villages croplands rangelands forested wildlands In order to match the temporal andspatial resolutions an additional fire variable was created from the MODIS time series by aggregatingyears (2001ndash2008) matching projection and coarsening the cell size This resulted in a 10 times 10 km firefrequency map used for the anthrome analysis

Additional variables commonly used in land-change modeling were included in the analysisto control for environmental and socio-economic factors Elevation and slope were derived from a90 m SRTM digital elevation model Precipitation data were derived from Tropical Rainfall MeasuringMission (TRMM) Protected Areas from CONANP (Mexican Natural Protected Area Commission)were processed to match the study area Communal property lands (ejidos) population density changeas well as the distance to road variable were derived from the Mexican Census Bureau [49] Cattledensity by municipality was obtained from the 2007 Censo Agropecuario [49]

Land 2017 6 61 6 of 19

Land 2017 6 61 5 of 19

lacking detailed land categories the resulting three-category map has the advantage of being more consistent than most multi-temporal assessments because it was produced using a consistent methodology by the same research team explicitly for the purpose of forest change mapping [4647]

Figure 2 Fire frequency map 2000ndash2010 MODIS TERRA-only series Significant Getis-Ord Gi statistic (005 level) hot spots and LISA-based clusters are shown in inset (upper left) 1 = 2006 post-hurricane Wilma fires and urban development related fires 2 and 5 = Mennonite land clearing for commercial maize cultivation 3 = PEMEX oil processing plant and 4 and 6 = high yield commercial corn and bean cultivation

Figure 3 Land changepersistence classes based on the CABS (2009) land cover maps Figure 3 Land changepersistence classes based on the CABS (2009) land cover maps

Even though MODIS fire data are constantly updated in this study we only include data to theyear 2010 We consider the 2000ndash2010 ten-year period sufficient to describe the salient points about thespatio-temporal patterns of a fire in the region More importantly the land cover data and anthromedata that we use do not go beyond 2007 and 2008 respectively For this same reason the multinomialmodeling component of this study does not use any fire data from after 2007 (see methods section)

32 Methods

The methodology has three components (a) a characterization of the spatio-temporal patternsand co-location of land changepersistence and fire (b) an assessment of the effect of fire presencelandscape patch size and other covariates land-change outcomes (FP NFP and CH) using a spatialmultinomial logit model for the period 2000ndash2007 and (c) an exploration of the ability of fire frequencyto distinguish human landscape categories defined in anthrome groups and anthrome classes

33 Characterization of Land Change and Fire Patterns

A cross-tabulation-based change analysis was performed on the simplified CABS land covermap pairs 1990ndash2000 and 2000ndash2007 resulting in one map with two persistence classes (FP and NFP)and one change class (CH) (Figure 3) Spatio-temporal dynamics of fire occurrence were derivedby manipulating the MODIS fire archive via map algebra operations (eg overlay reclassification)into map and graph summaries of annual and multi-year fire frequency After accounting for thedifferent time-spans of the TERRA and AQUA series and adjusting for double counting three separatefire occurrence sets were created a TERRA ten-year summary map (2000ndash2010) (Figure 2) and aTERRA-AQUA combined annual time-series graph (2000ndash2009) (Figure 4) Global (MoranrsquoI) and local(Getis-Ord Gi and LISA) measures of spatial autocorrelation were calculated for all sets of maps [50ndash52]Finally a second cross-tabulation analysis was performed for the land changepersistence map (FPNFP and CH) (Figure 3) and the binary fire (reclassification of Figure 2) maps in order to describe andexplore the spatial correspondence between them and the relationship between fire occurrence and thedifferent land cover categories The result of this cross-tabulation map is shown in Figure 5

Land 2017 6 61 7 of 19

Land 2017 6 61 7 of 19

Figure 4 Cumulative annual and 8-day frequency (counts) of fire occurrence (FIRE) 2000ndash2009 in the three-state Yucataacuten Peninsula blue = morning purple = afternoon Inset shows detail of intra-annual fire season for 2005

Figure 5 Cross-tabulation of land changepersistence classes (Figure 1) and fire frequency (Figure 2)

34 Effect of Fire and Patch Size on Land ChangePersistence A Spatial Multinomial Logit Model

A spatial multinomial logit model using 2003ndash2007 fire ldquodensityrdquo or ldquointensityrdquo (fire countfive years) as independent variable (FIRE) and 7 control variables was performed This model specification is used in the literature (eg [5354]) and is preferred because the dependent variable consists of three possible outcomes that are categoricalnominal in nature [55ndash57] To account for the positive spatial autocorrelation present in remotely sensed data [5859] spatial lags variables based on rook-case adjacency were calculated This was done by generating for each observation the

4000

5000

10000

15000

20000

25000

2000 2001 2002 2003 2004 2005 2006 2007 2008 2009

Terraannual

Aquaannual

Terra 8-day

r December February April June August Octoberr December February April June August October

2000

Fire Season2005

Annual

8-day

4000

5000

10000

15000

20000

25000

2000 2001 2002 2003 2004 2005 2006 2007 2008 2009

Terraannual

Aquaannual

Terra 8-day

r December February April June August Octoberr December February April June August October

2000

Fire Season2005

Annual

8-day

Figure 4 Cumulative annual and 8-day frequency (counts) of fire occurrence (FIRE) 2000ndash2009 in thethree-state Yucataacuten Peninsula blue = morning purple = afternoon Inset shows detail of intra-annualfire season for 2005

Land 2017 6 61 7 of 19

Figure 4 Cumulative annual and 8-day frequency (counts) of fire occurrence (FIRE) 2000ndash2009 in the three-state Yucataacuten Peninsula blue = morning purple = afternoon Inset shows detail of intra-annual fire season for 2005

Figure 5 Cross-tabulation of land changepersistence classes (Figure 1) and fire frequency (Figure 2)

34 Effect of Fire and Patch Size on Land ChangePersistence A Spatial Multinomial Logit Model

A spatial multinomial logit model using 2003ndash2007 fire ldquodensityrdquo or ldquointensityrdquo (fire countfive years) as independent variable (FIRE) and 7 control variables was performed This model specification is used in the literature (eg [5354]) and is preferred because the dependent variable consists of three possible outcomes that are categoricalnominal in nature [55ndash57] To account for the positive spatial autocorrelation present in remotely sensed data [5859] spatial lags variables based on rook-case adjacency were calculated This was done by generating for each observation the

4000

5000

10000

15000

20000

25000

2000 2001 2002 2003 2004 2005 2006 2007 2008 2009

Terraannual

Aquaannual

Terra 8-day

r December February April June August Octoberr December February April June August October

2000

Fire Season2005

Annual

8-day

4000

5000

10000

15000

20000

25000

2000 2001 2002 2003 2004 2005 2006 2007 2008 2009

Terraannual

Aquaannual

Terra 8-day

r December February April June August Octoberr December February April June August October

2000

Fire Season2005

Annual

8-day

Figure 5 Cross-tabulation of land changepersistence classes (Figure 1) and fire frequency (Figure 2)

34 Effect of Fire and Patch Size on Land ChangePersistence A Spatial Multinomial Logit Model

A spatial multinomial logit model using 2003ndash2007 fire ldquodensityrdquo or ldquointensityrdquo (fire countfiveyears) as independent variable (FIRE) and 7 control variables was performed This model specificationis used in the literature (eg [5354]) and is preferred because the dependent variable consists of

Land 2017 6 61 8 of 19

three possible outcomes that are categoricalnominal in nature [55ndash57] To account for the positivespatial autocorrelation present in remotely sensed data [5859] spatial lags variables based on rook-caseadjacency were calculated This was done by generating for each observation the average sum of itsneighbors of the same class (CFP CNFP and CCH) and including the lag variable in the model (seeEquation (1)) [5960] Lag values range from 0 (no like neighbors) to 1 (all four like neighbors) whileaverage Moranrsquos I values range from virtually random for CCH (00035) to weak-moderate positivefor CNFP (0392) and CFP (0391) In this particular case spatial lags also serve as an indicator oflandscape configuration and heterogeneity (ie similar to patch size and cohesion)

Pseudo-likelihood estimates were calculated for the main effects and spatial lag parameters of themultinomial model as follows (Equation (1))

Log(πhijπhir) = αj + xprimehi βj (1)

where πhij is the probability that a pixel h in the map of any class i for which fire has been detected willbecome one of land changepersistence category j (FP NFP or CH) j 6= r with land changepersistencecategory r being the reference category There are separate sets of intercept parameters αj and regressionparameters βj for each of the logit models The matrix xprimehi is the set of explanatory variables spatiallag (CY) fire (FIRE) and the commonly used control variables described Two logits equations aremodeled for each FIRE and CY population the logit comparing non-forest persistence (NFP) to forestpersistence (FP) and the logit comparing change (CH) to forest persistence (FP) [56]

35 Fire Frequency and Anthromes Characterization

Anthromes map datasets were processed to match them to the study area and temporal firecount data were aggregated to generate a fire frequency variable (Figure 6) In order to explore theassociation between fire counts and anthrome groups graphically we used boxplots of mean firefrequency by each category present in the study area dense settlements villages (in effect village andsurrounding areas) croplands rangelands forested wildlands We measured the differences in meanfire frequency across anthromes using a negative binomial model and a Tukey pairwise comparisonA binomial model was preferred over Poisson model because the overall (as well as per category) meanand variance are noticeably different (by a factor 100) which suggests over-dispersion in the Poissonparameter We also conducted Tukey comparisons for fire frequency within the cropland anthromesgroup to assess the potential of using fire count for finer definition of the human imprint of landscape

Land 2017 6 61 8 of 19

average sum of its neighbors of the same class (CFP CNFP and CCH) and including the lag variable in the model (see Equation (1)) [5960] Lag values range from 0 (no like neighbors) to 1 (all four like neighbors) while average Moranrsquos I values range from virtually random for CCH (00035) to weak-moderate positive for CNFP (0392) and CFP (0391) In this particular case spatial lags also serve as an indicator of landscape configuration and heterogeneity (ie similar to patch size and cohesion)

Pseudo-likelihood estimates were calculated for the main effects and spatial lag parameters of the multinomial model as follows (Equation (1))

Log(πhijπhir) = αj + xprimehi βj (1)

where πhij is the probability that a pixel h in the map of any class i for which fire has been detected will become one of land changepersistence category j (FP NFP or CH) j ne r with land changepersistence category r being the reference category There are separate sets of intercept parameters αj and regression parameters βj for each of the logit models The matrix xprimehi is the set of explanatory variables spatial lag (CY) fire (FIRE) and the commonly used control variables described Two logits equations are modeled for each FIRE and CY population the logit comparing non-forest persistence (NFP) to forest persistence (FP) and the logit comparing change (CH) to forest persistence (FP) [56]

35 Fire Frequency and Anthromes Characterization

Anthromes map datasets were processed to match them to the study area and temporal fire count data were aggregated to generate a fire frequency variable (Figure 6) In order to explore the association between fire counts and anthrome groups graphically we used boxplots of mean fire frequency by each category present in the study area dense settlements villages (in effect village and surrounding areas) croplands rangelands forested wildlands We measured the differences in mean fire frequency across anthromes using a negative binomial model and a Tukey pairwise comparison A binomial model was preferred over Poisson model because the overall (as well as per category) mean and variance are noticeably different (by a factor 100) which suggests over-dispersion in the Poisson parameter We also conducted Tukey comparisons for fire frequency within the cropland anthromes group to assess the potential of using fire count for finer definition of the human imprint of landscape

For the data processing we used the raster (version 25-8) sp (version 12-4) and rgdal (version 12-7) packages to perform some of the preprocessing for the spatial inputs The raster package was also used for aggregation of the fire occurrences cropping and reclassification of anthromes data We used the implementation of multinomial model in the R ldquonnetrdquo package (version 73-12) for analyses We also ran the negative binomial model using the ldquoMASSrdquo package (version 73-12) in R version 34 and used the glht method from the multcomp R package (14-6) to perform the Tukey comparison

Figure 6 Fire frequency aggregation for anthrome comparison (left) and Anthrome groups (right)

Figure 6 Fire frequency aggregation for anthrome comparison (left) and Anthrome groups (right)

For the data processing we used the raster (version 25-8) sp (version 12-4) and rgdal(version 12-7) packages to perform some of the preprocessing for the spatial inputs The raster packagewas also used for aggregation of the fire occurrences cropping and reclassification of anthromes

Land 2017 6 61 9 of 19

data We used the implementation of multinomial model in the R ldquonnetrdquo package (version 73-12)for analyses We also ran the negative binomial model using the ldquoMASSrdquo package (version 73-12)in R version 34 and used the glht method from the multcomp R package (14-6) to perform theTukey comparison

4 Results

41 Spatio-Temporal Patterns of Fire and Land Change

As a proxy indicator of human land use fire frequency can be interpreted as a quantitativemeasure of ldquodensityrdquo (in space and time) of land use in this case It corresponds to how actively ldquousedrdquoor ldquounder-usedrdquo a 1 km parcel of land is in relation to the types of land use that require burning(eg high for pasture and cultivation land)

Fire occurrence for the period 2000ndash2010 presents a distinct non-random spatial pattern across thestudy area (Moranrsquos I = 062) (Figure 2) The individual observations presenting the highest detectionfrequencies (gt3 per year) appear in spatial clusters and are concentrated in the northern and westernsection of the Peninsula in the states of Campeche and the Yucataacuten Quintana Roo has comparativelyfewer and less clustering fire detections Areas with less fire frequency are observed in Campeche andQuintana Roo especially in the presence of federal and state run natural protected areas (eg SianKarsquoan and Calakmul bioreserves) (Figure 1) and in locations where road and settlement density is lowThis road-settlement-fire co-location is more explicit in the Yucataacuten and northern Campeche and lessso in southern Campeche where road density decreases

Locations affected by fire (Figure 5 and Table 1) cover roughly 45 of the study area More thanhalf of the fire occurrences concentrate in NFP areas followed by 40 of FP and 2 in CH areas(1 of the total) Locations with no fire occurrence cover more than 50 of the study area No-fireoccurrences are two times more common in FP than in NFP and they are minimally present in CHareas Land changepersistence figures (total rows percentage in Table 1) indicate that roughly 23 ofthe FP shows no fire detections whereas 60 of NFP presents fire occurrence CH shows 86 of itsarea as having burned at some time (although it is hardly visible in Figure 5 because CH covers only1 of the total area)

Land 2017 6 61 10 of 19

Table 1 Cross-tabulation of fire occurrence and land changepersistence row column and total percentages per class Preliminary interpretation matrix(extendeddetailed legend for Figure 5)

Fire No Fire Row Total Total Study Area

Forest Persistence

293-Error resulting from database mismatch-Error of commission in MODIS ActiveFire product-Error induced by aggregation of landcover data

707-Core areas of mature forest that have persisted for at least 17years (1990ndash2007)-Protected areas with a predominance of mature forest-Areas of planned selective forest extraction that have not beenextracted in 17 years or longer (under rotation management)

100 54

Non Forest Persistence

608-Areas where fire is used to convert fromnon-forest vegetation land covers toother non-forest vegetation land covers(eg agriculture to urban)-Areas of active non-forest land-uses-Error resulting from databasemismatches

3918-Areas under intensive land-uses that do not require land clearingfor prolonged periods (eg citrus agriculture urban)-Secondary vegetation of at least 10 years including forest notconsidered mature by CAB 2009 This can include forest regrowth(forest transition)-Forested areas of forest communities that have been extracted inthe last 10 years and are growing back-Seasonal agricultural areas currently fallow (eg milpa)

100 43

Change (Forest toNon-Forest)

860-All land cover changes (conversion andsome modification) preceded by landclearing by fire (ie deforestation)-Core forest areas that are heavilydeforested with more intense use of landclearing by fire

137-Error of omission in MODIS Active Fire product-Error resulting from database mismatches-Land changes that do not require fire-Fringe areas that are cleared without fire after the core area hasbeen cleared with fire-Fringe areas that are cleared with low intensity fire that is notdetected by MODIS Active Fire product

100 1

Column TOTAL 45 36 100 100

Land 2017 6 61 11 of 19

42 Effect of Fire and Patch Size on Land ChangePersistence A Spatial Multinomial Logit Model

Results from the spatial multinomial logit model agree with the analysis presented above(Section 41) and indicate that past fire occurrence (pre-2007) is a useful predictor of land changepersistence categories The resulting equations and model statistics are summarized in Table 2 and inthe supplementary Appendix A The Akaike information criterion (AIC) indicates that the model withcovariates (intercept + fire and lag + control variables) performs better than alternative models (seeAppendix A) The likelihood ratio (LR) has two degrees of freedom and is significant which confirmsthat at least one of the variables in the model improves the model description

Table 2 Spatial multinomial logit model summary of trends FP = forest persistence NFP = non forestpersistence CH = change INTE = Intercept Odds = Odds ratio effects point estimates This tablecontains only FIRE and CY variables the full variable list is available in the Appendix A

CAT REF INTE CY FIRE Odds CY Odds FIRE

CH (3) FP (1) minus467 minus355 192 003 679NFP (2) minus607 minus346 020 003 122

CH Average minus537 minus350 106 003 400

FP (1) CH (3) 467 355 minus192 3466 015NFP (2) minus438 007 minus172 107 018

FP Average 015 181 minus182 1787 016

NFP (2) CH (3) 905 348 minus020 3243 082FP (1) 438 minus007 172 094 559

FP Average 671 171 076 1668 320

The maximum pseudo-likelihood and odds ratio point estimates (Table 2 and Appendix A) showthe effect and relative importance of FIRE and CY for each land changepersistence outcome in themodel At a 5 level the difference between FIRE = 1 (fire occurrence) and FIRE = 0 is statisticallydifferent for all cases (FP NFP and CH) for all three states separately and the three-state aggregatedstudy area CY is a significant covariate in the model for all of these cases Additional models wererun with control variables These full model results are presented in the Appendix A and confirm theusefulness of fire as predictor

An inspection of the pseudo-likelihood estimates for the aggregated study area (Table 2 andAppendix A) indicates that for each unit increase in FIRE (intensity) the log of the ratio of p(CH)p(FP)increases by ~192 and the log of the ratio of p(CH)p(NFP) increases by ~02 In other words for eachunit increase in FIRE (intensity) in a given pixel (in Figure 2) the odds of that same pixel belonging tocategory CH (forest to non-forest change) rather than category FP (forest persistence in Figure 3) aremultiplied by ~67 Unit increases in FIRE also increase the odds of a pixel belonging to category CHrather than NFP (no forest persistence) by 122

For every increase in one unit of Fire the odds of a pixel belonging to category NFP instead of CHare multiplied by 082 For every increase in one unit of Fire the odds of a pixel belonging to categoryNFP instead of FP are multiplied by 559 For every increase in one unit of Fire the odds of a pixelbelonging to category FP instead of CH are multiplied by 015 (almost none)

For every increase in one unit of Fire the odds of a pixel belonging to category FP instead ofNFP are multiplied by 018 (almost none) Overall FIRE estimates are negative when predicting forestpersistence (FP) and positive when predicting CH

The calculated spatial lag (CY) terms are significant for all cases CY as mentioned earlier can beinterpreted as cohesiveness of land cover patches [61] Larger CY values correspond to more similarvalues among neighboring cells (ie a larger patches of a category) Estimates of the model for theaggregated peninsula indicate that a unit increase in CY decreases the log of p(FP)p(CH) by ~minus355while the log of p(FP)p(NFP) decreases by ~minus007 This finding indicates that persistent forestareas located in large patches are very likely to remain forest (34 times more than CH) (Table 2 and

Land 2017 6 61 12 of 19

Appendix A) FP is also 107 times more likely than NFP In general CH has a negative relationship withCY This relationship can be attributed to CH occurring more often in isolated pixels corresponding tofragmented patches Conversely FP and NFP occur in larger continuous areas (Figure 3)

43 Comparison of Fire by Anthromes

Boxplots of mean fire frequency by anthromes groups suggest that fire can be used to distinguishamong anthromes groups thereby serving as an additional potential variable to examine humanimprints in the context of the Yucataacuten region (Figure 6) The croplands anthromes group has a higherfire frequency on average compared to most other anthromes categories We note that rangelandsdisplay a very large variance and thus may be difficult to distinguish from croplands and villagesFiner anthropogenic categories within the cropland groups also appear to be contrasted by the firefrequency variable (see boxplots Figure 7)

Land 2017 6 61 12 of 19

corresponding to fragmented patches Conversely FP and NFP occur in larger continuous areas (Figure 3)

43 Comparison of Fire by Anthromes

Boxplots of mean fire frequency by anthromes groups suggest that fire can be used to distinguish among anthromes groups thereby serving as an additional potential variable to examine human imprints in the context of the Yucataacuten region (Figure 6) The croplands anthromes group has a higher fire frequency on average compared to most other anthromes categories We note that rangelands display a very large variance and thus may be difficult to distinguish from croplands and villages Finer anthropogenic categories within the cropland groups also appear to be contrasted by the fire frequency variable (see boxplots Figure 7)

Tukey pairwise comparison tests between anthromes groups (applied to the negative binomial model Table 3) highlight that six and seven pairwise comparisons are significantly different at 5 and 10 level respectively Coefficients indicate relative increase or decrease of the expected log of fire frequency for categorical change in relation to the reference variable For instance there is a minus137 decrease in the log of fire frequency when an observation is found in the dense settlements rather than in croplands We find that fire frequency variable is useful to differentiate croplands with almost all categories with the exception of Villages and Rangelands Both overlap substantially on the boxplots (Figure 7)

Figure 7 Between group comparison Fire frequency by anthrome groups boxplots (left) Within group comparison Fire frequency boxplots within cropland anthrome (right)

Table 3 Between-anthromes Tukey pairwise comparison for the negative binomial models with fire count and anthromes groups Note that the reference variable is in italic

Pairwise Comparison Coefficients Standard Error t-Stat p-ValuesDense settlementsndashCroplands minus138688 043059 minus32209 00121

ForestedndashCroplands minus092198 006997 minus131762 0 RangelandsndashCroplands minus035406 026321 minus13452 07146

VillagesndashCroplands minus028199 032807 minus08595 09435 WildlandsndashCroplands minus229463 019565 minus117283 0

ForestedndashDense settlements 046491 042934 10828 08616 RangelandsndashDense settlements 103282 049872 20709 02552

VillagesndashDense settlements 110489 053579 20622 02593 WildlandsndashDense settlements minus090775 04666 minus19454 03214

RangelandsndashForested 056791 026118 21744 02076

Figure 7 Between group comparison Fire frequency by anthrome groups boxplots (left) Within groupcomparison Fire frequency boxplots within cropland anthrome (right)

Tukey pairwise comparison tests between anthromes groups (applied to the negative binomialmodel Table 3) highlight that six and seven pairwise comparisons are significantly different at 5 and10 level respectively Coefficients indicate relative increase or decrease of the expected log of firefrequency for categorical change in relation to the reference variable For instance there is a minus137decrease in the log of fire frequency when an observation is found in the dense settlements rather thanin croplands We find that fire frequency variable is useful to differentiate croplands with almost allcategories with the exception of Villages and Rangelands Both overlap substantially on the boxplots(Figure 7)

Tukey comparisons were also performed for fire frequency within the cropland anthromes groupto assess the potential of using fire frequency for finer definition of the human imprint of landscapeWe found that within croplands two out 10 and four out of 10 comparison results in significantdifferences in the log of fire frequency (Table 4) at 5 and 10 percent significance level respectivelyThis suggests that fire frequency is less useful at distinguishing within the cropland anthromes Thestrongest contrasts are found between ldquoresidential rainfed mosaicsndashremote croplands mosaicrdquo andbetween ldquoresidential irrigated croplandndashremote croplandsrdquo Both indicate decreases in the log offire frequency for locations that are found in residential rainfed and irrigated cropland compared toremote croplands

Land 2017 6 61 13 of 19

Table 3 Between-anthromes Tukey pairwise comparison for the negative binomial models with firecount and anthromes groups Note that the reference variable is in italic

Pairwise Comparison Coefficients Standard Error t-Stat p-Values

Dense settlementsndashCroplands minus138688 043059 minus32209 00121ForestedndashCroplands minus092198 006997 minus131762 0

RangelandsndashCroplands minus035406 026321 minus13452 07146VillagesndashCroplands minus028199 032807 minus08595 09435

WildlandsndashCroplands minus229463 019565 minus117283 0ForestedndashDense settlements 046491 042934 10828 08616

RangelandsndashDense settlements 103282 049872 20709 02552VillagesndashDense settlements 110489 053579 20622 02593

WildlandsndashDense settlements minus090775 04666 minus19454 03214RangelandsndashForested 056791 026118 21744 02076

VillagesndashForested 063999 032644 19605 03129WildlandsndashForested minus137266 01929 minus71159 0VillagesndashRangelands 007207 041346 01743 1

WildlandsndashRangelands minus194057 031874 minus60882 0WildlandsndashVillages minus201264 037409 minus53801 0

Table 4 Within-anthrome Tukey pairwise comparisons using the negative binomial models with firecount and anthromes croplands categories Note that the reference variable is in italic

PairwisendashComparison Coefficients Standard Error t-Stat p-Values

Populated rainfed croplandndashPopulated irrigated cropland 025239 022555 1119 07646Remote croplandsndashPopulated irrigated cropland 0572 025835 2214 01453

Residential irrigated croplandndashPopulated irrigated cropland minus061118 041094 minus14873 05244Residential rainfed mosaicndashPopulated irrigated cropland 008091 022337 03622 09955

Remote croplandsndashPopulated rainfed cropland 031961 014756 2166 01615Residential irrigated croplandndashPopulated rainfed cropland minus086357 0352 minus24533 00827

Residential rainfed mosaicndashPopulated rainfed cropland minus017148 007017 minus24437 00848Residential irrigated croplandndashRemote croplands minus118318 037387 minus31647 00105

Residential rainfed mosaicndashRemote croplands minus049109 014421 minus34054 00043Residential rainfed mosaicndashResidential irrigated cropland 069209 035061 1974 02396

5 Discussion and Conclusions

Analysis of the spatial patterns of fire in the Yucataacuten using fire data visually reproduces thegeography of human land-based activities during 2000ndash2010 including the influence of roadssettlements and natural protected areas The intra-annual temporal dimensions of fire dataapproximate key moments of seasonal agriculture and other land-based activities (Figure 4) Thesefindings are consistent with studies finding higher fire frequencies in the proximity to roads andsettlements region [40] and with research about fire and deforestation in other tropical settings(eg [2862ndash64]) and more generally about the relationship between land change road developmentand market accessibility [53546465]

The multinomial model confirms the significance of fire intensity (defined as count of fire flaggedpixels over time) and landscape configuration (represented by the spatial lag variable CY) for thepeninsula for all three types of land changepersistence outcomes Notably all change is stronglyaffected by the presence of fire The odds of a forested area becoming non-forested multiply by sixin the presence of fire This is not surprising given that the cross-tabulation analysis showed thatnearly 87 of pixels that changed from 2000 to 2007 had been flagged as fire by MODIS at some pointThe dominance of no-fire observations over fire occurrence the (pseudo) absence of fire makes for abetter predictor of forest persistence than fire occurrence per se especially for large patches (high CYvalues) Predicting non-forest persistence proved more difficult signaling the diversity of ecologicaland land use practices and transitions between them that define the NFP category as discussed in thedata section What exactly accounts for the remaining 13 is difficult to determine We can speculate

Land 2017 6 61 14 of 19

however that possible factors include data error and accuracy mismatches As some have notedMODIS products do omit fires for various reasons [40] We can also speculate on some detected firesbeing non-agricultural Finally we can also imagine some fires starting as agricultural burns butbecoming large multiday forest fires as they grow out of control [40]

Fire also proves to be a reasonable indicator to distinguish between anthromes groups (Figure 7)but less among finer anthromes categories Our analysis shows that for example with the aidof a fire frequency croplands are separable from the rest of categories and that dense settlementsare clearly distinct from villages Other categories like rangeland prove more difficult to separatesince they present larger variance Some within-variation within anthropogenic categories is alsodistinguishable For example populated irrigated is clearly separable from populated rainfed andfrom remote croplands These two former categories however are not as separable from each otherwith the aid of fire frequency alone

Perhaps some insight about differences distinguishing between- and within-anthropogeniclandscapes can be gained by looking into the distinction between quemas (legally regulated agriculturalfires) from incendios (large escape non-regulated forest fires) Both can be addressed through the use ofMODIS active fire data but cannot be thoroughly distinguished with these data alone Within-variationexists in both categories On the one hand quemas can be due to subsistence and commercial agriculturesuch as sugar cane cultivation along the border with Belize (ie either rain fed or irrigated anthromecategories) or Mennonite corn fields in Bacalar( ie the populated irrigated anthrome category) astheir spatial and temporal signatures can differ quite noticeably (Figures 2 and 4) On the other handincendios can be truly accidental or be the result of purposeful burning with nonagricultural goals(eg forcing land zoning code changes for urban development hunting practices) Future researchshould exploit these differences in order to account for a more nuanced description of the relationshipsbetween fire and human-induced land change in the region

We conclude that in subtropical forest settings in which burning is a fundamental landscape toolfire is a reasonable proxy for land change Use of fire data improves the estimation of land change andexpands our understanding of human-environment relationships that produce complex mosaics ofhighly dynamic landscapes such as those in the Mexican Yucataacuten

Acknowledgments This study was part of the SYPR (httpsyprasuedu) and EDGY (httplandchangerutgersedu) projects SYPR received support from the NASA LCLUC program (NAG-56046 511134 and 6GD98G)and the NSF BCS program (0410016) EDGY was sponsored by the Gordon and Betty Moore Foundation underGrant 1697 The authors thank Drs Birgit Schmook (El Colegio de la Frontera Sur) Laura Schneider (RutgersUniversity) and Zachary Christman (Rowan University) for their support and advice The staff of Clark Labsfacilitated the work by creating and maintaining the Idrisireg software (httpwwwclarklabsorg) with whichpreliminary analysis was performed Subsequent and final analysis was performed with R packages NNetMASS multcomp and raster

Author Contributions Marco Millones John Rogan BL Turner II conceived and designed the original researchand fieldwork Marco Millones performed the fieldwork Marco Millones performed preliminary data analysiswith Daniel A Griffith Robert Clay Harris and Benoit Parmentier executed the final data analysis John RoganBL Turner II revised earlier versions of the manuscript Marco Millones Benoit Parmentier and Robert Clay Harriswrote the paper John Rogan revised the manuscript

Conflicts of Interest The authors declare no conflicts of interest

Land 2017 6 61 4 of 19

last for several days These fires if a consequence of human action are illegal and usually generategovernment agency response especially if they grow out of control and affect farming forest extractionand natural protected areas (NPA) [4041] Although the distinction can be easily blurred (eg escapedburns) quemas tend to be more ubiquitous in the region are smaller in area and shorter in durationthan incendios In contrast incendios are less frequent cover large areas and temporally discrete eventsthat are often amplified in contact with hurricane blow downs [42]

Given the previously described links between various human activities and fire practices weexpect that the spatio-temporal pattern of fire can serve as a proxy for certain anthropogenic land usepractices in the Yucataacuten (eg milpa mechanized agriculture sugar cane cultivation and new urbandevelopment) Naturally occurring wild fires are less frequent in this region than fire of anthropogenicorigin This characteristic represents an opportunity to evaluate fire as a proxy for various land usesand land cover changes in the region

The primary goal of this study is to assess land cover change and persistence across theYucataacuten Peninsula by incorporating MODIS active fire occurrence data as a site-specific indicator ofhuman-induced land change The specific objectives are to (a) describe the spatio-temporal dynamicsof fire and its association with land use practices and land change (b) determine the importance offire presence to explain types of land persistence and change using a spatial multinomial logit modeland (c) explore the ability of fire frequency to discriminate between anthropogenic landscape types(anthropogenic biomes or anthromes)

Beside the specific goal stated lessons learned in this study may be of wider interest in otherregions of the world Spatial driver variables used for land-change modeling and prediction aretypically expensive to produce or not frequently updated as most countries and regions do not possesssuch information at the level of detail required Similarly land cover maps are rarely producedannually Most land cover maps are commonly produced using a census like approach with 5ndash10 yearsgaps at the country or regional levels For an increasing number of applications mapping rapidchanges within-these temporal gaps across countries boundaries may be crucial It is in this contextthat active fire data becomes useful as a predictor It has both high temporal frequency and is readilyavailable worldwide To evaluate the usefulness of fire as predictor in both data poor and rich areaswe modeled land change with and without the presence of additional spatial drivers Results reportedin this specific study should therefore be of potential interest to a wider audience of researchers andland management practitioners

3 Methodological Approach

31 Data

A comprehensive active fire dataset was constructed using NASArsquos 1 km MOD14A2 (fromTERRA) and MYD14A2 (from AQUA) 8-day composite product using various time ranges within-thetime period 2000ndash2010 [43] in order to match fire data and land cover data availability Both dataproducts provide detection confidence levels [44] of which only high and medium were used in orderto minimize potential false positive detections [2745] (Figure 2) The 1 km fire grid cell locations wereconverted to centroid points to match and extract the 30 m grid cell land cover attributes [42]

Land changepersistence information was obtained from Southern Mexico Forest Cover andClearance from c 1990 to c 2000 and to c 2007 digital maps developed by the Center for AppliedBiodiversity Science (CABS) at Conservation International [46] The original maps are based on theinterpretation of (~30 m resolution) Landsat-5 Thematic Mapper satellite imagery and are composedof five categories forest non-forest mangrove water and cloudshadow Forest cover is defined asmature forest gt3 m closed canopy [44] Thematic map accuracy was reported to have a Kappa indexof 86 with an error of commission of 1127 and an error of omission of 486 for the dominanttropical dry forest class prevalent in the study area [44] Forest and mangrove classes were mergedwhereas water clouds and shadow pixels were masked and removed from further analysis to produce

Land 2017 6 61 5 of 19

a map of land persistence and change for 2000ndash2007 with three resulting categories forest persistence(FP) non-forest persistence (NFP) and forest-to-non-forest (CH) (Figure 3) It must be noted thatin contrast with FP (ldquoold growthrdquo forest persistence) NFP by definition allows for land changesbetween sub-classes within-a broad non-forest category For example a transition from agriculture topasture or from pasture to secondary forests would be included in NFP Although lacking detailedland categories the resulting three-category map has the advantage of being more consistent thanmost multi-temporal assessments because it was produced using a consistent methodology by thesame research team explicitly for the purpose of forest change mapping [4647]

Land 2017 6 61 5 of 19

lacking detailed land categories the resulting three-category map has the advantage of being more consistent than most multi-temporal assessments because it was produced using a consistent methodology by the same research team explicitly for the purpose of forest change mapping [4647]

Figure 2 Fire frequency map 2000ndash2010 MODIS TERRA-only series Significant Getis-Ord Gi statistic (005 level) hot spots and LISA-based clusters are shown in inset (upper left) 1 = 2006 post-hurricane Wilma fires and urban development related fires 2 and 5 = Mennonite land clearing for commercial maize cultivation 3 = PEMEX oil processing plant and 4 and 6 = high yield commercial corn and bean cultivation

Figure 3 Land changepersistence classes based on the CABS (2009) land cover maps

Figure 2 Fire frequency map 2000ndash2010 MODIS TERRA-only series Significant Getis-Ord Gi statistic(005 level) hot spots and LISA-based clusters are shown in inset (upper left) 1 = 2006 post-hurricaneWilma fires and urban development related fires 2 and 5 = Mennonite land clearing for commercialmaize cultivation 3 = PEMEX oil processing plant and 4 and 6 = high yield commercial corn andbean cultivation

Anthrome map data corresponding to time interval 2001ndash2006 were obtained from the SEDACwebsite [48]) in GeoTIFF format We cropped and match the dataset to the Yucataacuten region andaggregated the original 21 anthrome categories using the six anthrome group classification Densesettlements villages croplands rangelands forested wildlands In order to match the temporal andspatial resolutions an additional fire variable was created from the MODIS time series by aggregatingyears (2001ndash2008) matching projection and coarsening the cell size This resulted in a 10 times 10 km firefrequency map used for the anthrome analysis

Additional variables commonly used in land-change modeling were included in the analysisto control for environmental and socio-economic factors Elevation and slope were derived from a90 m SRTM digital elevation model Precipitation data were derived from Tropical Rainfall MeasuringMission (TRMM) Protected Areas from CONANP (Mexican Natural Protected Area Commission)were processed to match the study area Communal property lands (ejidos) population density changeas well as the distance to road variable were derived from the Mexican Census Bureau [49] Cattledensity by municipality was obtained from the 2007 Censo Agropecuario [49]

Land 2017 6 61 6 of 19

Land 2017 6 61 5 of 19

lacking detailed land categories the resulting three-category map has the advantage of being more consistent than most multi-temporal assessments because it was produced using a consistent methodology by the same research team explicitly for the purpose of forest change mapping [4647]

Figure 2 Fire frequency map 2000ndash2010 MODIS TERRA-only series Significant Getis-Ord Gi statistic (005 level) hot spots and LISA-based clusters are shown in inset (upper left) 1 = 2006 post-hurricane Wilma fires and urban development related fires 2 and 5 = Mennonite land clearing for commercial maize cultivation 3 = PEMEX oil processing plant and 4 and 6 = high yield commercial corn and bean cultivation

Figure 3 Land changepersistence classes based on the CABS (2009) land cover maps Figure 3 Land changepersistence classes based on the CABS (2009) land cover maps

Even though MODIS fire data are constantly updated in this study we only include data to theyear 2010 We consider the 2000ndash2010 ten-year period sufficient to describe the salient points about thespatio-temporal patterns of a fire in the region More importantly the land cover data and anthromedata that we use do not go beyond 2007 and 2008 respectively For this same reason the multinomialmodeling component of this study does not use any fire data from after 2007 (see methods section)

32 Methods

The methodology has three components (a) a characterization of the spatio-temporal patternsand co-location of land changepersistence and fire (b) an assessment of the effect of fire presencelandscape patch size and other covariates land-change outcomes (FP NFP and CH) using a spatialmultinomial logit model for the period 2000ndash2007 and (c) an exploration of the ability of fire frequencyto distinguish human landscape categories defined in anthrome groups and anthrome classes

33 Characterization of Land Change and Fire Patterns

A cross-tabulation-based change analysis was performed on the simplified CABS land covermap pairs 1990ndash2000 and 2000ndash2007 resulting in one map with two persistence classes (FP and NFP)and one change class (CH) (Figure 3) Spatio-temporal dynamics of fire occurrence were derivedby manipulating the MODIS fire archive via map algebra operations (eg overlay reclassification)into map and graph summaries of annual and multi-year fire frequency After accounting for thedifferent time-spans of the TERRA and AQUA series and adjusting for double counting three separatefire occurrence sets were created a TERRA ten-year summary map (2000ndash2010) (Figure 2) and aTERRA-AQUA combined annual time-series graph (2000ndash2009) (Figure 4) Global (MoranrsquoI) and local(Getis-Ord Gi and LISA) measures of spatial autocorrelation were calculated for all sets of maps [50ndash52]Finally a second cross-tabulation analysis was performed for the land changepersistence map (FPNFP and CH) (Figure 3) and the binary fire (reclassification of Figure 2) maps in order to describe andexplore the spatial correspondence between them and the relationship between fire occurrence and thedifferent land cover categories The result of this cross-tabulation map is shown in Figure 5

Land 2017 6 61 7 of 19

Land 2017 6 61 7 of 19

Figure 4 Cumulative annual and 8-day frequency (counts) of fire occurrence (FIRE) 2000ndash2009 in the three-state Yucataacuten Peninsula blue = morning purple = afternoon Inset shows detail of intra-annual fire season for 2005

Figure 5 Cross-tabulation of land changepersistence classes (Figure 1) and fire frequency (Figure 2)

34 Effect of Fire and Patch Size on Land ChangePersistence A Spatial Multinomial Logit Model

A spatial multinomial logit model using 2003ndash2007 fire ldquodensityrdquo or ldquointensityrdquo (fire countfive years) as independent variable (FIRE) and 7 control variables was performed This model specification is used in the literature (eg [5354]) and is preferred because the dependent variable consists of three possible outcomes that are categoricalnominal in nature [55ndash57] To account for the positive spatial autocorrelation present in remotely sensed data [5859] spatial lags variables based on rook-case adjacency were calculated This was done by generating for each observation the

4000

5000

10000

15000

20000

25000

2000 2001 2002 2003 2004 2005 2006 2007 2008 2009

Terraannual

Aquaannual

Terra 8-day

r December February April June August Octoberr December February April June August October

2000

Fire Season2005

Annual

8-day

4000

5000

10000

15000

20000

25000

2000 2001 2002 2003 2004 2005 2006 2007 2008 2009

Terraannual

Aquaannual

Terra 8-day

r December February April June August Octoberr December February April June August October

2000

Fire Season2005

Annual

8-day

Figure 4 Cumulative annual and 8-day frequency (counts) of fire occurrence (FIRE) 2000ndash2009 in thethree-state Yucataacuten Peninsula blue = morning purple = afternoon Inset shows detail of intra-annualfire season for 2005

Land 2017 6 61 7 of 19

Figure 4 Cumulative annual and 8-day frequency (counts) of fire occurrence (FIRE) 2000ndash2009 in the three-state Yucataacuten Peninsula blue = morning purple = afternoon Inset shows detail of intra-annual fire season for 2005

Figure 5 Cross-tabulation of land changepersistence classes (Figure 1) and fire frequency (Figure 2)

34 Effect of Fire and Patch Size on Land ChangePersistence A Spatial Multinomial Logit Model

A spatial multinomial logit model using 2003ndash2007 fire ldquodensityrdquo or ldquointensityrdquo (fire countfive years) as independent variable (FIRE) and 7 control variables was performed This model specification is used in the literature (eg [5354]) and is preferred because the dependent variable consists of three possible outcomes that are categoricalnominal in nature [55ndash57] To account for the positive spatial autocorrelation present in remotely sensed data [5859] spatial lags variables based on rook-case adjacency were calculated This was done by generating for each observation the

4000

5000

10000

15000

20000

25000

2000 2001 2002 2003 2004 2005 2006 2007 2008 2009

Terraannual

Aquaannual

Terra 8-day

r December February April June August Octoberr December February April June August October

2000

Fire Season2005

Annual

8-day

4000

5000

10000

15000

20000

25000

2000 2001 2002 2003 2004 2005 2006 2007 2008 2009

Terraannual

Aquaannual

Terra 8-day

r December February April June August Octoberr December February April June August October

2000

Fire Season2005

Annual

8-day

Figure 5 Cross-tabulation of land changepersistence classes (Figure 1) and fire frequency (Figure 2)

34 Effect of Fire and Patch Size on Land ChangePersistence A Spatial Multinomial Logit Model

A spatial multinomial logit model using 2003ndash2007 fire ldquodensityrdquo or ldquointensityrdquo (fire countfiveyears) as independent variable (FIRE) and 7 control variables was performed This model specificationis used in the literature (eg [5354]) and is preferred because the dependent variable consists of

Land 2017 6 61 8 of 19

three possible outcomes that are categoricalnominal in nature [55ndash57] To account for the positivespatial autocorrelation present in remotely sensed data [5859] spatial lags variables based on rook-caseadjacency were calculated This was done by generating for each observation the average sum of itsneighbors of the same class (CFP CNFP and CCH) and including the lag variable in the model (seeEquation (1)) [5960] Lag values range from 0 (no like neighbors) to 1 (all four like neighbors) whileaverage Moranrsquos I values range from virtually random for CCH (00035) to weak-moderate positivefor CNFP (0392) and CFP (0391) In this particular case spatial lags also serve as an indicator oflandscape configuration and heterogeneity (ie similar to patch size and cohesion)

Pseudo-likelihood estimates were calculated for the main effects and spatial lag parameters of themultinomial model as follows (Equation (1))

Log(πhijπhir) = αj + xprimehi βj (1)

where πhij is the probability that a pixel h in the map of any class i for which fire has been detected willbecome one of land changepersistence category j (FP NFP or CH) j 6= r with land changepersistencecategory r being the reference category There are separate sets of intercept parameters αj and regressionparameters βj for each of the logit models The matrix xprimehi is the set of explanatory variables spatiallag (CY) fire (FIRE) and the commonly used control variables described Two logits equations aremodeled for each FIRE and CY population the logit comparing non-forest persistence (NFP) to forestpersistence (FP) and the logit comparing change (CH) to forest persistence (FP) [56]

35 Fire Frequency and Anthromes Characterization

Anthromes map datasets were processed to match them to the study area and temporal firecount data were aggregated to generate a fire frequency variable (Figure 6) In order to explore theassociation between fire counts and anthrome groups graphically we used boxplots of mean firefrequency by each category present in the study area dense settlements villages (in effect village andsurrounding areas) croplands rangelands forested wildlands We measured the differences in meanfire frequency across anthromes using a negative binomial model and a Tukey pairwise comparisonA binomial model was preferred over Poisson model because the overall (as well as per category) meanand variance are noticeably different (by a factor 100) which suggests over-dispersion in the Poissonparameter We also conducted Tukey comparisons for fire frequency within the cropland anthromesgroup to assess the potential of using fire count for finer definition of the human imprint of landscape

Land 2017 6 61 8 of 19

average sum of its neighbors of the same class (CFP CNFP and CCH) and including the lag variable in the model (see Equation (1)) [5960] Lag values range from 0 (no like neighbors) to 1 (all four like neighbors) while average Moranrsquos I values range from virtually random for CCH (00035) to weak-moderate positive for CNFP (0392) and CFP (0391) In this particular case spatial lags also serve as an indicator of landscape configuration and heterogeneity (ie similar to patch size and cohesion)

Pseudo-likelihood estimates were calculated for the main effects and spatial lag parameters of the multinomial model as follows (Equation (1))

Log(πhijπhir) = αj + xprimehi βj (1)

where πhij is the probability that a pixel h in the map of any class i for which fire has been detected will become one of land changepersistence category j (FP NFP or CH) j ne r with land changepersistence category r being the reference category There are separate sets of intercept parameters αj and regression parameters βj for each of the logit models The matrix xprimehi is the set of explanatory variables spatial lag (CY) fire (FIRE) and the commonly used control variables described Two logits equations are modeled for each FIRE and CY population the logit comparing non-forest persistence (NFP) to forest persistence (FP) and the logit comparing change (CH) to forest persistence (FP) [56]

35 Fire Frequency and Anthromes Characterization

Anthromes map datasets were processed to match them to the study area and temporal fire count data were aggregated to generate a fire frequency variable (Figure 6) In order to explore the association between fire counts and anthrome groups graphically we used boxplots of mean fire frequency by each category present in the study area dense settlements villages (in effect village and surrounding areas) croplands rangelands forested wildlands We measured the differences in mean fire frequency across anthromes using a negative binomial model and a Tukey pairwise comparison A binomial model was preferred over Poisson model because the overall (as well as per category) mean and variance are noticeably different (by a factor 100) which suggests over-dispersion in the Poisson parameter We also conducted Tukey comparisons for fire frequency within the cropland anthromes group to assess the potential of using fire count for finer definition of the human imprint of landscape

For the data processing we used the raster (version 25-8) sp (version 12-4) and rgdal (version 12-7) packages to perform some of the preprocessing for the spatial inputs The raster package was also used for aggregation of the fire occurrences cropping and reclassification of anthromes data We used the implementation of multinomial model in the R ldquonnetrdquo package (version 73-12) for analyses We also ran the negative binomial model using the ldquoMASSrdquo package (version 73-12) in R version 34 and used the glht method from the multcomp R package (14-6) to perform the Tukey comparison

Figure 6 Fire frequency aggregation for anthrome comparison (left) and Anthrome groups (right)

Figure 6 Fire frequency aggregation for anthrome comparison (left) and Anthrome groups (right)

For the data processing we used the raster (version 25-8) sp (version 12-4) and rgdal(version 12-7) packages to perform some of the preprocessing for the spatial inputs The raster packagewas also used for aggregation of the fire occurrences cropping and reclassification of anthromes

Land 2017 6 61 9 of 19

data We used the implementation of multinomial model in the R ldquonnetrdquo package (version 73-12)for analyses We also ran the negative binomial model using the ldquoMASSrdquo package (version 73-12)in R version 34 and used the glht method from the multcomp R package (14-6) to perform theTukey comparison

4 Results

41 Spatio-Temporal Patterns of Fire and Land Change

As a proxy indicator of human land use fire frequency can be interpreted as a quantitativemeasure of ldquodensityrdquo (in space and time) of land use in this case It corresponds to how actively ldquousedrdquoor ldquounder-usedrdquo a 1 km parcel of land is in relation to the types of land use that require burning(eg high for pasture and cultivation land)

Fire occurrence for the period 2000ndash2010 presents a distinct non-random spatial pattern across thestudy area (Moranrsquos I = 062) (Figure 2) The individual observations presenting the highest detectionfrequencies (gt3 per year) appear in spatial clusters and are concentrated in the northern and westernsection of the Peninsula in the states of Campeche and the Yucataacuten Quintana Roo has comparativelyfewer and less clustering fire detections Areas with less fire frequency are observed in Campeche andQuintana Roo especially in the presence of federal and state run natural protected areas (eg SianKarsquoan and Calakmul bioreserves) (Figure 1) and in locations where road and settlement density is lowThis road-settlement-fire co-location is more explicit in the Yucataacuten and northern Campeche and lessso in southern Campeche where road density decreases

Locations affected by fire (Figure 5 and Table 1) cover roughly 45 of the study area More thanhalf of the fire occurrences concentrate in NFP areas followed by 40 of FP and 2 in CH areas(1 of the total) Locations with no fire occurrence cover more than 50 of the study area No-fireoccurrences are two times more common in FP than in NFP and they are minimally present in CHareas Land changepersistence figures (total rows percentage in Table 1) indicate that roughly 23 ofthe FP shows no fire detections whereas 60 of NFP presents fire occurrence CH shows 86 of itsarea as having burned at some time (although it is hardly visible in Figure 5 because CH covers only1 of the total area)

Land 2017 6 61 10 of 19

Table 1 Cross-tabulation of fire occurrence and land changepersistence row column and total percentages per class Preliminary interpretation matrix(extendeddetailed legend for Figure 5)

Fire No Fire Row Total Total Study Area

Forest Persistence

293-Error resulting from database mismatch-Error of commission in MODIS ActiveFire product-Error induced by aggregation of landcover data

707-Core areas of mature forest that have persisted for at least 17years (1990ndash2007)-Protected areas with a predominance of mature forest-Areas of planned selective forest extraction that have not beenextracted in 17 years or longer (under rotation management)

100 54

Non Forest Persistence

608-Areas where fire is used to convert fromnon-forest vegetation land covers toother non-forest vegetation land covers(eg agriculture to urban)-Areas of active non-forest land-uses-Error resulting from databasemismatches

3918-Areas under intensive land-uses that do not require land clearingfor prolonged periods (eg citrus agriculture urban)-Secondary vegetation of at least 10 years including forest notconsidered mature by CAB 2009 This can include forest regrowth(forest transition)-Forested areas of forest communities that have been extracted inthe last 10 years and are growing back-Seasonal agricultural areas currently fallow (eg milpa)

100 43

Change (Forest toNon-Forest)

860-All land cover changes (conversion andsome modification) preceded by landclearing by fire (ie deforestation)-Core forest areas that are heavilydeforested with more intense use of landclearing by fire

137-Error of omission in MODIS Active Fire product-Error resulting from database mismatches-Land changes that do not require fire-Fringe areas that are cleared without fire after the core area hasbeen cleared with fire-Fringe areas that are cleared with low intensity fire that is notdetected by MODIS Active Fire product

100 1

Column TOTAL 45 36 100 100

Land 2017 6 61 11 of 19

42 Effect of Fire and Patch Size on Land ChangePersistence A Spatial Multinomial Logit Model

Results from the spatial multinomial logit model agree with the analysis presented above(Section 41) and indicate that past fire occurrence (pre-2007) is a useful predictor of land changepersistence categories The resulting equations and model statistics are summarized in Table 2 and inthe supplementary Appendix A The Akaike information criterion (AIC) indicates that the model withcovariates (intercept + fire and lag + control variables) performs better than alternative models (seeAppendix A) The likelihood ratio (LR) has two degrees of freedom and is significant which confirmsthat at least one of the variables in the model improves the model description

Table 2 Spatial multinomial logit model summary of trends FP = forest persistence NFP = non forestpersistence CH = change INTE = Intercept Odds = Odds ratio effects point estimates This tablecontains only FIRE and CY variables the full variable list is available in the Appendix A

CAT REF INTE CY FIRE Odds CY Odds FIRE

CH (3) FP (1) minus467 minus355 192 003 679NFP (2) minus607 minus346 020 003 122

CH Average minus537 minus350 106 003 400

FP (1) CH (3) 467 355 minus192 3466 015NFP (2) minus438 007 minus172 107 018

FP Average 015 181 minus182 1787 016

NFP (2) CH (3) 905 348 minus020 3243 082FP (1) 438 minus007 172 094 559

FP Average 671 171 076 1668 320

The maximum pseudo-likelihood and odds ratio point estimates (Table 2 and Appendix A) showthe effect and relative importance of FIRE and CY for each land changepersistence outcome in themodel At a 5 level the difference between FIRE = 1 (fire occurrence) and FIRE = 0 is statisticallydifferent for all cases (FP NFP and CH) for all three states separately and the three-state aggregatedstudy area CY is a significant covariate in the model for all of these cases Additional models wererun with control variables These full model results are presented in the Appendix A and confirm theusefulness of fire as predictor

An inspection of the pseudo-likelihood estimates for the aggregated study area (Table 2 andAppendix A) indicates that for each unit increase in FIRE (intensity) the log of the ratio of p(CH)p(FP)increases by ~192 and the log of the ratio of p(CH)p(NFP) increases by ~02 In other words for eachunit increase in FIRE (intensity) in a given pixel (in Figure 2) the odds of that same pixel belonging tocategory CH (forest to non-forest change) rather than category FP (forest persistence in Figure 3) aremultiplied by ~67 Unit increases in FIRE also increase the odds of a pixel belonging to category CHrather than NFP (no forest persistence) by 122

For every increase in one unit of Fire the odds of a pixel belonging to category NFP instead of CHare multiplied by 082 For every increase in one unit of Fire the odds of a pixel belonging to categoryNFP instead of FP are multiplied by 559 For every increase in one unit of Fire the odds of a pixelbelonging to category FP instead of CH are multiplied by 015 (almost none)

For every increase in one unit of Fire the odds of a pixel belonging to category FP instead ofNFP are multiplied by 018 (almost none) Overall FIRE estimates are negative when predicting forestpersistence (FP) and positive when predicting CH

The calculated spatial lag (CY) terms are significant for all cases CY as mentioned earlier can beinterpreted as cohesiveness of land cover patches [61] Larger CY values correspond to more similarvalues among neighboring cells (ie a larger patches of a category) Estimates of the model for theaggregated peninsula indicate that a unit increase in CY decreases the log of p(FP)p(CH) by ~minus355while the log of p(FP)p(NFP) decreases by ~minus007 This finding indicates that persistent forestareas located in large patches are very likely to remain forest (34 times more than CH) (Table 2 and

Land 2017 6 61 12 of 19

Appendix A) FP is also 107 times more likely than NFP In general CH has a negative relationship withCY This relationship can be attributed to CH occurring more often in isolated pixels corresponding tofragmented patches Conversely FP and NFP occur in larger continuous areas (Figure 3)

43 Comparison of Fire by Anthromes

Boxplots of mean fire frequency by anthromes groups suggest that fire can be used to distinguishamong anthromes groups thereby serving as an additional potential variable to examine humanimprints in the context of the Yucataacuten region (Figure 6) The croplands anthromes group has a higherfire frequency on average compared to most other anthromes categories We note that rangelandsdisplay a very large variance and thus may be difficult to distinguish from croplands and villagesFiner anthropogenic categories within the cropland groups also appear to be contrasted by the firefrequency variable (see boxplots Figure 7)

Land 2017 6 61 12 of 19

corresponding to fragmented patches Conversely FP and NFP occur in larger continuous areas (Figure 3)

43 Comparison of Fire by Anthromes

Boxplots of mean fire frequency by anthromes groups suggest that fire can be used to distinguish among anthromes groups thereby serving as an additional potential variable to examine human imprints in the context of the Yucataacuten region (Figure 6) The croplands anthromes group has a higher fire frequency on average compared to most other anthromes categories We note that rangelands display a very large variance and thus may be difficult to distinguish from croplands and villages Finer anthropogenic categories within the cropland groups also appear to be contrasted by the fire frequency variable (see boxplots Figure 7)

Tukey pairwise comparison tests between anthromes groups (applied to the negative binomial model Table 3) highlight that six and seven pairwise comparisons are significantly different at 5 and 10 level respectively Coefficients indicate relative increase or decrease of the expected log of fire frequency for categorical change in relation to the reference variable For instance there is a minus137 decrease in the log of fire frequency when an observation is found in the dense settlements rather than in croplands We find that fire frequency variable is useful to differentiate croplands with almost all categories with the exception of Villages and Rangelands Both overlap substantially on the boxplots (Figure 7)

Figure 7 Between group comparison Fire frequency by anthrome groups boxplots (left) Within group comparison Fire frequency boxplots within cropland anthrome (right)

Table 3 Between-anthromes Tukey pairwise comparison for the negative binomial models with fire count and anthromes groups Note that the reference variable is in italic

Pairwise Comparison Coefficients Standard Error t-Stat p-ValuesDense settlementsndashCroplands minus138688 043059 minus32209 00121

ForestedndashCroplands minus092198 006997 minus131762 0 RangelandsndashCroplands minus035406 026321 minus13452 07146

VillagesndashCroplands minus028199 032807 minus08595 09435 WildlandsndashCroplands minus229463 019565 minus117283 0

ForestedndashDense settlements 046491 042934 10828 08616 RangelandsndashDense settlements 103282 049872 20709 02552

VillagesndashDense settlements 110489 053579 20622 02593 WildlandsndashDense settlements minus090775 04666 minus19454 03214

RangelandsndashForested 056791 026118 21744 02076

Figure 7 Between group comparison Fire frequency by anthrome groups boxplots (left) Within groupcomparison Fire frequency boxplots within cropland anthrome (right)

Tukey pairwise comparison tests between anthromes groups (applied to the negative binomialmodel Table 3) highlight that six and seven pairwise comparisons are significantly different at 5 and10 level respectively Coefficients indicate relative increase or decrease of the expected log of firefrequency for categorical change in relation to the reference variable For instance there is a minus137decrease in the log of fire frequency when an observation is found in the dense settlements rather thanin croplands We find that fire frequency variable is useful to differentiate croplands with almost allcategories with the exception of Villages and Rangelands Both overlap substantially on the boxplots(Figure 7)

Tukey comparisons were also performed for fire frequency within the cropland anthromes groupto assess the potential of using fire frequency for finer definition of the human imprint of landscapeWe found that within croplands two out 10 and four out of 10 comparison results in significantdifferences in the log of fire frequency (Table 4) at 5 and 10 percent significance level respectivelyThis suggests that fire frequency is less useful at distinguishing within the cropland anthromes Thestrongest contrasts are found between ldquoresidential rainfed mosaicsndashremote croplands mosaicrdquo andbetween ldquoresidential irrigated croplandndashremote croplandsrdquo Both indicate decreases in the log offire frequency for locations that are found in residential rainfed and irrigated cropland compared toremote croplands

Land 2017 6 61 13 of 19

Table 3 Between-anthromes Tukey pairwise comparison for the negative binomial models with firecount and anthromes groups Note that the reference variable is in italic

Pairwise Comparison Coefficients Standard Error t-Stat p-Values

Dense settlementsndashCroplands minus138688 043059 minus32209 00121ForestedndashCroplands minus092198 006997 minus131762 0

RangelandsndashCroplands minus035406 026321 minus13452 07146VillagesndashCroplands minus028199 032807 minus08595 09435

WildlandsndashCroplands minus229463 019565 minus117283 0ForestedndashDense settlements 046491 042934 10828 08616

RangelandsndashDense settlements 103282 049872 20709 02552VillagesndashDense settlements 110489 053579 20622 02593

WildlandsndashDense settlements minus090775 04666 minus19454 03214RangelandsndashForested 056791 026118 21744 02076

VillagesndashForested 063999 032644 19605 03129WildlandsndashForested minus137266 01929 minus71159 0VillagesndashRangelands 007207 041346 01743 1

WildlandsndashRangelands minus194057 031874 minus60882 0WildlandsndashVillages minus201264 037409 minus53801 0

Table 4 Within-anthrome Tukey pairwise comparisons using the negative binomial models with firecount and anthromes croplands categories Note that the reference variable is in italic

PairwisendashComparison Coefficients Standard Error t-Stat p-Values

Populated rainfed croplandndashPopulated irrigated cropland 025239 022555 1119 07646Remote croplandsndashPopulated irrigated cropland 0572 025835 2214 01453

Residential irrigated croplandndashPopulated irrigated cropland minus061118 041094 minus14873 05244Residential rainfed mosaicndashPopulated irrigated cropland 008091 022337 03622 09955

Remote croplandsndashPopulated rainfed cropland 031961 014756 2166 01615Residential irrigated croplandndashPopulated rainfed cropland minus086357 0352 minus24533 00827

Residential rainfed mosaicndashPopulated rainfed cropland minus017148 007017 minus24437 00848Residential irrigated croplandndashRemote croplands minus118318 037387 minus31647 00105

Residential rainfed mosaicndashRemote croplands minus049109 014421 minus34054 00043Residential rainfed mosaicndashResidential irrigated cropland 069209 035061 1974 02396

5 Discussion and Conclusions

Analysis of the spatial patterns of fire in the Yucataacuten using fire data visually reproduces thegeography of human land-based activities during 2000ndash2010 including the influence of roadssettlements and natural protected areas The intra-annual temporal dimensions of fire dataapproximate key moments of seasonal agriculture and other land-based activities (Figure 4) Thesefindings are consistent with studies finding higher fire frequencies in the proximity to roads andsettlements region [40] and with research about fire and deforestation in other tropical settings(eg [2862ndash64]) and more generally about the relationship between land change road developmentand market accessibility [53546465]

The multinomial model confirms the significance of fire intensity (defined as count of fire flaggedpixels over time) and landscape configuration (represented by the spatial lag variable CY) for thepeninsula for all three types of land changepersistence outcomes Notably all change is stronglyaffected by the presence of fire The odds of a forested area becoming non-forested multiply by sixin the presence of fire This is not surprising given that the cross-tabulation analysis showed thatnearly 87 of pixels that changed from 2000 to 2007 had been flagged as fire by MODIS at some pointThe dominance of no-fire observations over fire occurrence the (pseudo) absence of fire makes for abetter predictor of forest persistence than fire occurrence per se especially for large patches (high CYvalues) Predicting non-forest persistence proved more difficult signaling the diversity of ecologicaland land use practices and transitions between them that define the NFP category as discussed in thedata section What exactly accounts for the remaining 13 is difficult to determine We can speculate

Land 2017 6 61 14 of 19

however that possible factors include data error and accuracy mismatches As some have notedMODIS products do omit fires for various reasons [40] We can also speculate on some detected firesbeing non-agricultural Finally we can also imagine some fires starting as agricultural burns butbecoming large multiday forest fires as they grow out of control [40]

Fire also proves to be a reasonable indicator to distinguish between anthromes groups (Figure 7)but less among finer anthromes categories Our analysis shows that for example with the aidof a fire frequency croplands are separable from the rest of categories and that dense settlementsare clearly distinct from villages Other categories like rangeland prove more difficult to separatesince they present larger variance Some within-variation within anthropogenic categories is alsodistinguishable For example populated irrigated is clearly separable from populated rainfed andfrom remote croplands These two former categories however are not as separable from each otherwith the aid of fire frequency alone

Perhaps some insight about differences distinguishing between- and within-anthropogeniclandscapes can be gained by looking into the distinction between quemas (legally regulated agriculturalfires) from incendios (large escape non-regulated forest fires) Both can be addressed through the use ofMODIS active fire data but cannot be thoroughly distinguished with these data alone Within-variationexists in both categories On the one hand quemas can be due to subsistence and commercial agriculturesuch as sugar cane cultivation along the border with Belize (ie either rain fed or irrigated anthromecategories) or Mennonite corn fields in Bacalar( ie the populated irrigated anthrome category) astheir spatial and temporal signatures can differ quite noticeably (Figures 2 and 4) On the other handincendios can be truly accidental or be the result of purposeful burning with nonagricultural goals(eg forcing land zoning code changes for urban development hunting practices) Future researchshould exploit these differences in order to account for a more nuanced description of the relationshipsbetween fire and human-induced land change in the region

We conclude that in subtropical forest settings in which burning is a fundamental landscape toolfire is a reasonable proxy for land change Use of fire data improves the estimation of land change andexpands our understanding of human-environment relationships that produce complex mosaics ofhighly dynamic landscapes such as those in the Mexican Yucataacuten

Acknowledgments This study was part of the SYPR (httpsyprasuedu) and EDGY (httplandchangerutgersedu) projects SYPR received support from the NASA LCLUC program (NAG-56046 511134 and 6GD98G)and the NSF BCS program (0410016) EDGY was sponsored by the Gordon and Betty Moore Foundation underGrant 1697 The authors thank Drs Birgit Schmook (El Colegio de la Frontera Sur) Laura Schneider (RutgersUniversity) and Zachary Christman (Rowan University) for their support and advice The staff of Clark Labsfacilitated the work by creating and maintaining the Idrisireg software (httpwwwclarklabsorg) with whichpreliminary analysis was performed Subsequent and final analysis was performed with R packages NNetMASS multcomp and raster

Author Contributions Marco Millones John Rogan BL Turner II conceived and designed the original researchand fieldwork Marco Millones performed the fieldwork Marco Millones performed preliminary data analysiswith Daniel A Griffith Robert Clay Harris and Benoit Parmentier executed the final data analysis John RoganBL Turner II revised earlier versions of the manuscript Marco Millones Benoit Parmentier and Robert Clay Harriswrote the paper John Rogan revised the manuscript

Conflicts of Interest The authors declare no conflicts of interest

Land 2017 6 61 5 of 19

a map of land persistence and change for 2000ndash2007 with three resulting categories forest persistence(FP) non-forest persistence (NFP) and forest-to-non-forest (CH) (Figure 3) It must be noted thatin contrast with FP (ldquoold growthrdquo forest persistence) NFP by definition allows for land changesbetween sub-classes within-a broad non-forest category For example a transition from agriculture topasture or from pasture to secondary forests would be included in NFP Although lacking detailedland categories the resulting three-category map has the advantage of being more consistent thanmost multi-temporal assessments because it was produced using a consistent methodology by thesame research team explicitly for the purpose of forest change mapping [4647]

Land 2017 6 61 5 of 19

lacking detailed land categories the resulting three-category map has the advantage of being more consistent than most multi-temporal assessments because it was produced using a consistent methodology by the same research team explicitly for the purpose of forest change mapping [4647]

Figure 2 Fire frequency map 2000ndash2010 MODIS TERRA-only series Significant Getis-Ord Gi statistic (005 level) hot spots and LISA-based clusters are shown in inset (upper left) 1 = 2006 post-hurricane Wilma fires and urban development related fires 2 and 5 = Mennonite land clearing for commercial maize cultivation 3 = PEMEX oil processing plant and 4 and 6 = high yield commercial corn and bean cultivation

Figure 3 Land changepersistence classes based on the CABS (2009) land cover maps

Figure 2 Fire frequency map 2000ndash2010 MODIS TERRA-only series Significant Getis-Ord Gi statistic(005 level) hot spots and LISA-based clusters are shown in inset (upper left) 1 = 2006 post-hurricaneWilma fires and urban development related fires 2 and 5 = Mennonite land clearing for commercialmaize cultivation 3 = PEMEX oil processing plant and 4 and 6 = high yield commercial corn andbean cultivation

Anthrome map data corresponding to time interval 2001ndash2006 were obtained from the SEDACwebsite [48]) in GeoTIFF format We cropped and match the dataset to the Yucataacuten region andaggregated the original 21 anthrome categories using the six anthrome group classification Densesettlements villages croplands rangelands forested wildlands In order to match the temporal andspatial resolutions an additional fire variable was created from the MODIS time series by aggregatingyears (2001ndash2008) matching projection and coarsening the cell size This resulted in a 10 times 10 km firefrequency map used for the anthrome analysis

Additional variables commonly used in land-change modeling were included in the analysisto control for environmental and socio-economic factors Elevation and slope were derived from a90 m SRTM digital elevation model Precipitation data were derived from Tropical Rainfall MeasuringMission (TRMM) Protected Areas from CONANP (Mexican Natural Protected Area Commission)were processed to match the study area Communal property lands (ejidos) population density changeas well as the distance to road variable were derived from the Mexican Census Bureau [49] Cattledensity by municipality was obtained from the 2007 Censo Agropecuario [49]

Land 2017 6 61 6 of 19

Land 2017 6 61 5 of 19

lacking detailed land categories the resulting three-category map has the advantage of being more consistent than most multi-temporal assessments because it was produced using a consistent methodology by the same research team explicitly for the purpose of forest change mapping [4647]

Figure 2 Fire frequency map 2000ndash2010 MODIS TERRA-only series Significant Getis-Ord Gi statistic (005 level) hot spots and LISA-based clusters are shown in inset (upper left) 1 = 2006 post-hurricane Wilma fires and urban development related fires 2 and 5 = Mennonite land clearing for commercial maize cultivation 3 = PEMEX oil processing plant and 4 and 6 = high yield commercial corn and bean cultivation

Figure 3 Land changepersistence classes based on the CABS (2009) land cover maps Figure 3 Land changepersistence classes based on the CABS (2009) land cover maps

Even though MODIS fire data are constantly updated in this study we only include data to theyear 2010 We consider the 2000ndash2010 ten-year period sufficient to describe the salient points about thespatio-temporal patterns of a fire in the region More importantly the land cover data and anthromedata that we use do not go beyond 2007 and 2008 respectively For this same reason the multinomialmodeling component of this study does not use any fire data from after 2007 (see methods section)

32 Methods

The methodology has three components (a) a characterization of the spatio-temporal patternsand co-location of land changepersistence and fire (b) an assessment of the effect of fire presencelandscape patch size and other covariates land-change outcomes (FP NFP and CH) using a spatialmultinomial logit model for the period 2000ndash2007 and (c) an exploration of the ability of fire frequencyto distinguish human landscape categories defined in anthrome groups and anthrome classes

33 Characterization of Land Change and Fire Patterns

A cross-tabulation-based change analysis was performed on the simplified CABS land covermap pairs 1990ndash2000 and 2000ndash2007 resulting in one map with two persistence classes (FP and NFP)and one change class (CH) (Figure 3) Spatio-temporal dynamics of fire occurrence were derivedby manipulating the MODIS fire archive via map algebra operations (eg overlay reclassification)into map and graph summaries of annual and multi-year fire frequency After accounting for thedifferent time-spans of the TERRA and AQUA series and adjusting for double counting three separatefire occurrence sets were created a TERRA ten-year summary map (2000ndash2010) (Figure 2) and aTERRA-AQUA combined annual time-series graph (2000ndash2009) (Figure 4) Global (MoranrsquoI) and local(Getis-Ord Gi and LISA) measures of spatial autocorrelation were calculated for all sets of maps [50ndash52]Finally a second cross-tabulation analysis was performed for the land changepersistence map (FPNFP and CH) (Figure 3) and the binary fire (reclassification of Figure 2) maps in order to describe andexplore the spatial correspondence between them and the relationship between fire occurrence and thedifferent land cover categories The result of this cross-tabulation map is shown in Figure 5

Land 2017 6 61 7 of 19

Land 2017 6 61 7 of 19

Figure 4 Cumulative annual and 8-day frequency (counts) of fire occurrence (FIRE) 2000ndash2009 in the three-state Yucataacuten Peninsula blue = morning purple = afternoon Inset shows detail of intra-annual fire season for 2005

Figure 5 Cross-tabulation of land changepersistence classes (Figure 1) and fire frequency (Figure 2)

34 Effect of Fire and Patch Size on Land ChangePersistence A Spatial Multinomial Logit Model

A spatial multinomial logit model using 2003ndash2007 fire ldquodensityrdquo or ldquointensityrdquo (fire countfive years) as independent variable (FIRE) and 7 control variables was performed This model specification is used in the literature (eg [5354]) and is preferred because the dependent variable consists of three possible outcomes that are categoricalnominal in nature [55ndash57] To account for the positive spatial autocorrelation present in remotely sensed data [5859] spatial lags variables based on rook-case adjacency were calculated This was done by generating for each observation the

4000

5000

10000

15000

20000

25000

2000 2001 2002 2003 2004 2005 2006 2007 2008 2009

Terraannual

Aquaannual

Terra 8-day

r December February April June August Octoberr December February April June August October

2000

Fire Season2005

Annual

8-day

4000

5000

10000

15000

20000

25000

2000 2001 2002 2003 2004 2005 2006 2007 2008 2009

Terraannual

Aquaannual

Terra 8-day

r December February April June August Octoberr December February April June August October

2000

Fire Season2005

Annual

8-day

Figure 4 Cumulative annual and 8-day frequency (counts) of fire occurrence (FIRE) 2000ndash2009 in thethree-state Yucataacuten Peninsula blue = morning purple = afternoon Inset shows detail of intra-annualfire season for 2005

Land 2017 6 61 7 of 19

Figure 4 Cumulative annual and 8-day frequency (counts) of fire occurrence (FIRE) 2000ndash2009 in the three-state Yucataacuten Peninsula blue = morning purple = afternoon Inset shows detail of intra-annual fire season for 2005

Figure 5 Cross-tabulation of land changepersistence classes (Figure 1) and fire frequency (Figure 2)

34 Effect of Fire and Patch Size on Land ChangePersistence A Spatial Multinomial Logit Model

A spatial multinomial logit model using 2003ndash2007 fire ldquodensityrdquo or ldquointensityrdquo (fire countfive years) as independent variable (FIRE) and 7 control variables was performed This model specification is used in the literature (eg [5354]) and is preferred because the dependent variable consists of three possible outcomes that are categoricalnominal in nature [55ndash57] To account for the positive spatial autocorrelation present in remotely sensed data [5859] spatial lags variables based on rook-case adjacency were calculated This was done by generating for each observation the

4000

5000

10000

15000

20000

25000

2000 2001 2002 2003 2004 2005 2006 2007 2008 2009

Terraannual

Aquaannual

Terra 8-day

r December February April June August Octoberr December February April June August October

2000

Fire Season2005

Annual

8-day

4000

5000

10000

15000

20000

25000

2000 2001 2002 2003 2004 2005 2006 2007 2008 2009

Terraannual

Aquaannual

Terra 8-day

r December February April June August Octoberr December February April June August October

2000

Fire Season2005

Annual

8-day

Figure 5 Cross-tabulation of land changepersistence classes (Figure 1) and fire frequency (Figure 2)

34 Effect of Fire and Patch Size on Land ChangePersistence A Spatial Multinomial Logit Model

A spatial multinomial logit model using 2003ndash2007 fire ldquodensityrdquo or ldquointensityrdquo (fire countfiveyears) as independent variable (FIRE) and 7 control variables was performed This model specificationis used in the literature (eg [5354]) and is preferred because the dependent variable consists of

Land 2017 6 61 8 of 19

three possible outcomes that are categoricalnominal in nature [55ndash57] To account for the positivespatial autocorrelation present in remotely sensed data [5859] spatial lags variables based on rook-caseadjacency were calculated This was done by generating for each observation the average sum of itsneighbors of the same class (CFP CNFP and CCH) and including the lag variable in the model (seeEquation (1)) [5960] Lag values range from 0 (no like neighbors) to 1 (all four like neighbors) whileaverage Moranrsquos I values range from virtually random for CCH (00035) to weak-moderate positivefor CNFP (0392) and CFP (0391) In this particular case spatial lags also serve as an indicator oflandscape configuration and heterogeneity (ie similar to patch size and cohesion)

Pseudo-likelihood estimates were calculated for the main effects and spatial lag parameters of themultinomial model as follows (Equation (1))

Log(πhijπhir) = αj + xprimehi βj (1)

where πhij is the probability that a pixel h in the map of any class i for which fire has been detected willbecome one of land changepersistence category j (FP NFP or CH) j 6= r with land changepersistencecategory r being the reference category There are separate sets of intercept parameters αj and regressionparameters βj for each of the logit models The matrix xprimehi is the set of explanatory variables spatiallag (CY) fire (FIRE) and the commonly used control variables described Two logits equations aremodeled for each FIRE and CY population the logit comparing non-forest persistence (NFP) to forestpersistence (FP) and the logit comparing change (CH) to forest persistence (FP) [56]

35 Fire Frequency and Anthromes Characterization

Anthromes map datasets were processed to match them to the study area and temporal firecount data were aggregated to generate a fire frequency variable (Figure 6) In order to explore theassociation between fire counts and anthrome groups graphically we used boxplots of mean firefrequency by each category present in the study area dense settlements villages (in effect village andsurrounding areas) croplands rangelands forested wildlands We measured the differences in meanfire frequency across anthromes using a negative binomial model and a Tukey pairwise comparisonA binomial model was preferred over Poisson model because the overall (as well as per category) meanand variance are noticeably different (by a factor 100) which suggests over-dispersion in the Poissonparameter We also conducted Tukey comparisons for fire frequency within the cropland anthromesgroup to assess the potential of using fire count for finer definition of the human imprint of landscape

Land 2017 6 61 8 of 19

average sum of its neighbors of the same class (CFP CNFP and CCH) and including the lag variable in the model (see Equation (1)) [5960] Lag values range from 0 (no like neighbors) to 1 (all four like neighbors) while average Moranrsquos I values range from virtually random for CCH (00035) to weak-moderate positive for CNFP (0392) and CFP (0391) In this particular case spatial lags also serve as an indicator of landscape configuration and heterogeneity (ie similar to patch size and cohesion)

Pseudo-likelihood estimates were calculated for the main effects and spatial lag parameters of the multinomial model as follows (Equation (1))

Log(πhijπhir) = αj + xprimehi βj (1)

where πhij is the probability that a pixel h in the map of any class i for which fire has been detected will become one of land changepersistence category j (FP NFP or CH) j ne r with land changepersistence category r being the reference category There are separate sets of intercept parameters αj and regression parameters βj for each of the logit models The matrix xprimehi is the set of explanatory variables spatial lag (CY) fire (FIRE) and the commonly used control variables described Two logits equations are modeled for each FIRE and CY population the logit comparing non-forest persistence (NFP) to forest persistence (FP) and the logit comparing change (CH) to forest persistence (FP) [56]

35 Fire Frequency and Anthromes Characterization

Anthromes map datasets were processed to match them to the study area and temporal fire count data were aggregated to generate a fire frequency variable (Figure 6) In order to explore the association between fire counts and anthrome groups graphically we used boxplots of mean fire frequency by each category present in the study area dense settlements villages (in effect village and surrounding areas) croplands rangelands forested wildlands We measured the differences in mean fire frequency across anthromes using a negative binomial model and a Tukey pairwise comparison A binomial model was preferred over Poisson model because the overall (as well as per category) mean and variance are noticeably different (by a factor 100) which suggests over-dispersion in the Poisson parameter We also conducted Tukey comparisons for fire frequency within the cropland anthromes group to assess the potential of using fire count for finer definition of the human imprint of landscape

For the data processing we used the raster (version 25-8) sp (version 12-4) and rgdal (version 12-7) packages to perform some of the preprocessing for the spatial inputs The raster package was also used for aggregation of the fire occurrences cropping and reclassification of anthromes data We used the implementation of multinomial model in the R ldquonnetrdquo package (version 73-12) for analyses We also ran the negative binomial model using the ldquoMASSrdquo package (version 73-12) in R version 34 and used the glht method from the multcomp R package (14-6) to perform the Tukey comparison

Figure 6 Fire frequency aggregation for anthrome comparison (left) and Anthrome groups (right)

Figure 6 Fire frequency aggregation for anthrome comparison (left) and Anthrome groups (right)

For the data processing we used the raster (version 25-8) sp (version 12-4) and rgdal(version 12-7) packages to perform some of the preprocessing for the spatial inputs The raster packagewas also used for aggregation of the fire occurrences cropping and reclassification of anthromes

Land 2017 6 61 9 of 19

data We used the implementation of multinomial model in the R ldquonnetrdquo package (version 73-12)for analyses We also ran the negative binomial model using the ldquoMASSrdquo package (version 73-12)in R version 34 and used the glht method from the multcomp R package (14-6) to perform theTukey comparison

4 Results

41 Spatio-Temporal Patterns of Fire and Land Change

As a proxy indicator of human land use fire frequency can be interpreted as a quantitativemeasure of ldquodensityrdquo (in space and time) of land use in this case It corresponds to how actively ldquousedrdquoor ldquounder-usedrdquo a 1 km parcel of land is in relation to the types of land use that require burning(eg high for pasture and cultivation land)

Fire occurrence for the period 2000ndash2010 presents a distinct non-random spatial pattern across thestudy area (Moranrsquos I = 062) (Figure 2) The individual observations presenting the highest detectionfrequencies (gt3 per year) appear in spatial clusters and are concentrated in the northern and westernsection of the Peninsula in the states of Campeche and the Yucataacuten Quintana Roo has comparativelyfewer and less clustering fire detections Areas with less fire frequency are observed in Campeche andQuintana Roo especially in the presence of federal and state run natural protected areas (eg SianKarsquoan and Calakmul bioreserves) (Figure 1) and in locations where road and settlement density is lowThis road-settlement-fire co-location is more explicit in the Yucataacuten and northern Campeche and lessso in southern Campeche where road density decreases

Locations affected by fire (Figure 5 and Table 1) cover roughly 45 of the study area More thanhalf of the fire occurrences concentrate in NFP areas followed by 40 of FP and 2 in CH areas(1 of the total) Locations with no fire occurrence cover more than 50 of the study area No-fireoccurrences are two times more common in FP than in NFP and they are minimally present in CHareas Land changepersistence figures (total rows percentage in Table 1) indicate that roughly 23 ofthe FP shows no fire detections whereas 60 of NFP presents fire occurrence CH shows 86 of itsarea as having burned at some time (although it is hardly visible in Figure 5 because CH covers only1 of the total area)

Land 2017 6 61 10 of 19

Table 1 Cross-tabulation of fire occurrence and land changepersistence row column and total percentages per class Preliminary interpretation matrix(extendeddetailed legend for Figure 5)

Fire No Fire Row Total Total Study Area

Forest Persistence

293-Error resulting from database mismatch-Error of commission in MODIS ActiveFire product-Error induced by aggregation of landcover data

707-Core areas of mature forest that have persisted for at least 17years (1990ndash2007)-Protected areas with a predominance of mature forest-Areas of planned selective forest extraction that have not beenextracted in 17 years or longer (under rotation management)

100 54

Non Forest Persistence

608-Areas where fire is used to convert fromnon-forest vegetation land covers toother non-forest vegetation land covers(eg agriculture to urban)-Areas of active non-forest land-uses-Error resulting from databasemismatches

3918-Areas under intensive land-uses that do not require land clearingfor prolonged periods (eg citrus agriculture urban)-Secondary vegetation of at least 10 years including forest notconsidered mature by CAB 2009 This can include forest regrowth(forest transition)-Forested areas of forest communities that have been extracted inthe last 10 years and are growing back-Seasonal agricultural areas currently fallow (eg milpa)

100 43

Change (Forest toNon-Forest)

860-All land cover changes (conversion andsome modification) preceded by landclearing by fire (ie deforestation)-Core forest areas that are heavilydeforested with more intense use of landclearing by fire

137-Error of omission in MODIS Active Fire product-Error resulting from database mismatches-Land changes that do not require fire-Fringe areas that are cleared without fire after the core area hasbeen cleared with fire-Fringe areas that are cleared with low intensity fire that is notdetected by MODIS Active Fire product

100 1

Column TOTAL 45 36 100 100

Land 2017 6 61 11 of 19

42 Effect of Fire and Patch Size on Land ChangePersistence A Spatial Multinomial Logit Model

Results from the spatial multinomial logit model agree with the analysis presented above(Section 41) and indicate that past fire occurrence (pre-2007) is a useful predictor of land changepersistence categories The resulting equations and model statistics are summarized in Table 2 and inthe supplementary Appendix A The Akaike information criterion (AIC) indicates that the model withcovariates (intercept + fire and lag + control variables) performs better than alternative models (seeAppendix A) The likelihood ratio (LR) has two degrees of freedom and is significant which confirmsthat at least one of the variables in the model improves the model description

Table 2 Spatial multinomial logit model summary of trends FP = forest persistence NFP = non forestpersistence CH = change INTE = Intercept Odds = Odds ratio effects point estimates This tablecontains only FIRE and CY variables the full variable list is available in the Appendix A

CAT REF INTE CY FIRE Odds CY Odds FIRE

CH (3) FP (1) minus467 minus355 192 003 679NFP (2) minus607 minus346 020 003 122

CH Average minus537 minus350 106 003 400

FP (1) CH (3) 467 355 minus192 3466 015NFP (2) minus438 007 minus172 107 018

FP Average 015 181 minus182 1787 016

NFP (2) CH (3) 905 348 minus020 3243 082FP (1) 438 minus007 172 094 559

FP Average 671 171 076 1668 320

The maximum pseudo-likelihood and odds ratio point estimates (Table 2 and Appendix A) showthe effect and relative importance of FIRE and CY for each land changepersistence outcome in themodel At a 5 level the difference between FIRE = 1 (fire occurrence) and FIRE = 0 is statisticallydifferent for all cases (FP NFP and CH) for all three states separately and the three-state aggregatedstudy area CY is a significant covariate in the model for all of these cases Additional models wererun with control variables These full model results are presented in the Appendix A and confirm theusefulness of fire as predictor

An inspection of the pseudo-likelihood estimates for the aggregated study area (Table 2 andAppendix A) indicates that for each unit increase in FIRE (intensity) the log of the ratio of p(CH)p(FP)increases by ~192 and the log of the ratio of p(CH)p(NFP) increases by ~02 In other words for eachunit increase in FIRE (intensity) in a given pixel (in Figure 2) the odds of that same pixel belonging tocategory CH (forest to non-forest change) rather than category FP (forest persistence in Figure 3) aremultiplied by ~67 Unit increases in FIRE also increase the odds of a pixel belonging to category CHrather than NFP (no forest persistence) by 122

For every increase in one unit of Fire the odds of a pixel belonging to category NFP instead of CHare multiplied by 082 For every increase in one unit of Fire the odds of a pixel belonging to categoryNFP instead of FP are multiplied by 559 For every increase in one unit of Fire the odds of a pixelbelonging to category FP instead of CH are multiplied by 015 (almost none)

For every increase in one unit of Fire the odds of a pixel belonging to category FP instead ofNFP are multiplied by 018 (almost none) Overall FIRE estimates are negative when predicting forestpersistence (FP) and positive when predicting CH

The calculated spatial lag (CY) terms are significant for all cases CY as mentioned earlier can beinterpreted as cohesiveness of land cover patches [61] Larger CY values correspond to more similarvalues among neighboring cells (ie a larger patches of a category) Estimates of the model for theaggregated peninsula indicate that a unit increase in CY decreases the log of p(FP)p(CH) by ~minus355while the log of p(FP)p(NFP) decreases by ~minus007 This finding indicates that persistent forestareas located in large patches are very likely to remain forest (34 times more than CH) (Table 2 and

Land 2017 6 61 12 of 19

Appendix A) FP is also 107 times more likely than NFP In general CH has a negative relationship withCY This relationship can be attributed to CH occurring more often in isolated pixels corresponding tofragmented patches Conversely FP and NFP occur in larger continuous areas (Figure 3)

43 Comparison of Fire by Anthromes

Boxplots of mean fire frequency by anthromes groups suggest that fire can be used to distinguishamong anthromes groups thereby serving as an additional potential variable to examine humanimprints in the context of the Yucataacuten region (Figure 6) The croplands anthromes group has a higherfire frequency on average compared to most other anthromes categories We note that rangelandsdisplay a very large variance and thus may be difficult to distinguish from croplands and villagesFiner anthropogenic categories within the cropland groups also appear to be contrasted by the firefrequency variable (see boxplots Figure 7)

Land 2017 6 61 12 of 19

corresponding to fragmented patches Conversely FP and NFP occur in larger continuous areas (Figure 3)

43 Comparison of Fire by Anthromes

Boxplots of mean fire frequency by anthromes groups suggest that fire can be used to distinguish among anthromes groups thereby serving as an additional potential variable to examine human imprints in the context of the Yucataacuten region (Figure 6) The croplands anthromes group has a higher fire frequency on average compared to most other anthromes categories We note that rangelands display a very large variance and thus may be difficult to distinguish from croplands and villages Finer anthropogenic categories within the cropland groups also appear to be contrasted by the fire frequency variable (see boxplots Figure 7)

Tukey pairwise comparison tests between anthromes groups (applied to the negative binomial model Table 3) highlight that six and seven pairwise comparisons are significantly different at 5 and 10 level respectively Coefficients indicate relative increase or decrease of the expected log of fire frequency for categorical change in relation to the reference variable For instance there is a minus137 decrease in the log of fire frequency when an observation is found in the dense settlements rather than in croplands We find that fire frequency variable is useful to differentiate croplands with almost all categories with the exception of Villages and Rangelands Both overlap substantially on the boxplots (Figure 7)

Figure 7 Between group comparison Fire frequency by anthrome groups boxplots (left) Within group comparison Fire frequency boxplots within cropland anthrome (right)

Table 3 Between-anthromes Tukey pairwise comparison for the negative binomial models with fire count and anthromes groups Note that the reference variable is in italic

Pairwise Comparison Coefficients Standard Error t-Stat p-ValuesDense settlementsndashCroplands minus138688 043059 minus32209 00121

ForestedndashCroplands minus092198 006997 minus131762 0 RangelandsndashCroplands minus035406 026321 minus13452 07146

VillagesndashCroplands minus028199 032807 minus08595 09435 WildlandsndashCroplands minus229463 019565 minus117283 0

ForestedndashDense settlements 046491 042934 10828 08616 RangelandsndashDense settlements 103282 049872 20709 02552

VillagesndashDense settlements 110489 053579 20622 02593 WildlandsndashDense settlements minus090775 04666 minus19454 03214

RangelandsndashForested 056791 026118 21744 02076

Figure 7 Between group comparison Fire frequency by anthrome groups boxplots (left) Within groupcomparison Fire frequency boxplots within cropland anthrome (right)

Tukey pairwise comparison tests between anthromes groups (applied to the negative binomialmodel Table 3) highlight that six and seven pairwise comparisons are significantly different at 5 and10 level respectively Coefficients indicate relative increase or decrease of the expected log of firefrequency for categorical change in relation to the reference variable For instance there is a minus137decrease in the log of fire frequency when an observation is found in the dense settlements rather thanin croplands We find that fire frequency variable is useful to differentiate croplands with almost allcategories with the exception of Villages and Rangelands Both overlap substantially on the boxplots(Figure 7)

Tukey comparisons were also performed for fire frequency within the cropland anthromes groupto assess the potential of using fire frequency for finer definition of the human imprint of landscapeWe found that within croplands two out 10 and four out of 10 comparison results in significantdifferences in the log of fire frequency (Table 4) at 5 and 10 percent significance level respectivelyThis suggests that fire frequency is less useful at distinguishing within the cropland anthromes Thestrongest contrasts are found between ldquoresidential rainfed mosaicsndashremote croplands mosaicrdquo andbetween ldquoresidential irrigated croplandndashremote croplandsrdquo Both indicate decreases in the log offire frequency for locations that are found in residential rainfed and irrigated cropland compared toremote croplands

Land 2017 6 61 13 of 19

Table 3 Between-anthromes Tukey pairwise comparison for the negative binomial models with firecount and anthromes groups Note that the reference variable is in italic

Pairwise Comparison Coefficients Standard Error t-Stat p-Values

Dense settlementsndashCroplands minus138688 043059 minus32209 00121ForestedndashCroplands minus092198 006997 minus131762 0

RangelandsndashCroplands minus035406 026321 minus13452 07146VillagesndashCroplands minus028199 032807 minus08595 09435

WildlandsndashCroplands minus229463 019565 minus117283 0ForestedndashDense settlements 046491 042934 10828 08616

RangelandsndashDense settlements 103282 049872 20709 02552VillagesndashDense settlements 110489 053579 20622 02593

WildlandsndashDense settlements minus090775 04666 minus19454 03214RangelandsndashForested 056791 026118 21744 02076

VillagesndashForested 063999 032644 19605 03129WildlandsndashForested minus137266 01929 minus71159 0VillagesndashRangelands 007207 041346 01743 1

WildlandsndashRangelands minus194057 031874 minus60882 0WildlandsndashVillages minus201264 037409 minus53801 0

Table 4 Within-anthrome Tukey pairwise comparisons using the negative binomial models with firecount and anthromes croplands categories Note that the reference variable is in italic

PairwisendashComparison Coefficients Standard Error t-Stat p-Values

Populated rainfed croplandndashPopulated irrigated cropland 025239 022555 1119 07646Remote croplandsndashPopulated irrigated cropland 0572 025835 2214 01453

Residential irrigated croplandndashPopulated irrigated cropland minus061118 041094 minus14873 05244Residential rainfed mosaicndashPopulated irrigated cropland 008091 022337 03622 09955

Remote croplandsndashPopulated rainfed cropland 031961 014756 2166 01615Residential irrigated croplandndashPopulated rainfed cropland minus086357 0352 minus24533 00827

Residential rainfed mosaicndashPopulated rainfed cropland minus017148 007017 minus24437 00848Residential irrigated croplandndashRemote croplands minus118318 037387 minus31647 00105

Residential rainfed mosaicndashRemote croplands minus049109 014421 minus34054 00043Residential rainfed mosaicndashResidential irrigated cropland 069209 035061 1974 02396

5 Discussion and Conclusions

Analysis of the spatial patterns of fire in the Yucataacuten using fire data visually reproduces thegeography of human land-based activities during 2000ndash2010 including the influence of roadssettlements and natural protected areas The intra-annual temporal dimensions of fire dataapproximate key moments of seasonal agriculture and other land-based activities (Figure 4) Thesefindings are consistent with studies finding higher fire frequencies in the proximity to roads andsettlements region [40] and with research about fire and deforestation in other tropical settings(eg [2862ndash64]) and more generally about the relationship between land change road developmentand market accessibility [53546465]

The multinomial model confirms the significance of fire intensity (defined as count of fire flaggedpixels over time) and landscape configuration (represented by the spatial lag variable CY) for thepeninsula for all three types of land changepersistence outcomes Notably all change is stronglyaffected by the presence of fire The odds of a forested area becoming non-forested multiply by sixin the presence of fire This is not surprising given that the cross-tabulation analysis showed thatnearly 87 of pixels that changed from 2000 to 2007 had been flagged as fire by MODIS at some pointThe dominance of no-fire observations over fire occurrence the (pseudo) absence of fire makes for abetter predictor of forest persistence than fire occurrence per se especially for large patches (high CYvalues) Predicting non-forest persistence proved more difficult signaling the diversity of ecologicaland land use practices and transitions between them that define the NFP category as discussed in thedata section What exactly accounts for the remaining 13 is difficult to determine We can speculate

Land 2017 6 61 14 of 19

however that possible factors include data error and accuracy mismatches As some have notedMODIS products do omit fires for various reasons [40] We can also speculate on some detected firesbeing non-agricultural Finally we can also imagine some fires starting as agricultural burns butbecoming large multiday forest fires as they grow out of control [40]

Fire also proves to be a reasonable indicator to distinguish between anthromes groups (Figure 7)but less among finer anthromes categories Our analysis shows that for example with the aidof a fire frequency croplands are separable from the rest of categories and that dense settlementsare clearly distinct from villages Other categories like rangeland prove more difficult to separatesince they present larger variance Some within-variation within anthropogenic categories is alsodistinguishable For example populated irrigated is clearly separable from populated rainfed andfrom remote croplands These two former categories however are not as separable from each otherwith the aid of fire frequency alone

Perhaps some insight about differences distinguishing between- and within-anthropogeniclandscapes can be gained by looking into the distinction between quemas (legally regulated agriculturalfires) from incendios (large escape non-regulated forest fires) Both can be addressed through the use ofMODIS active fire data but cannot be thoroughly distinguished with these data alone Within-variationexists in both categories On the one hand quemas can be due to subsistence and commercial agriculturesuch as sugar cane cultivation along the border with Belize (ie either rain fed or irrigated anthromecategories) or Mennonite corn fields in Bacalar( ie the populated irrigated anthrome category) astheir spatial and temporal signatures can differ quite noticeably (Figures 2 and 4) On the other handincendios can be truly accidental or be the result of purposeful burning with nonagricultural goals(eg forcing land zoning code changes for urban development hunting practices) Future researchshould exploit these differences in order to account for a more nuanced description of the relationshipsbetween fire and human-induced land change in the region

We conclude that in subtropical forest settings in which burning is a fundamental landscape toolfire is a reasonable proxy for land change Use of fire data improves the estimation of land change andexpands our understanding of human-environment relationships that produce complex mosaics ofhighly dynamic landscapes such as those in the Mexican Yucataacuten

Acknowledgments This study was part of the SYPR (httpsyprasuedu) and EDGY (httplandchangerutgersedu) projects SYPR received support from the NASA LCLUC program (NAG-56046 511134 and 6GD98G)and the NSF BCS program (0410016) EDGY was sponsored by the Gordon and Betty Moore Foundation underGrant 1697 The authors thank Drs Birgit Schmook (El Colegio de la Frontera Sur) Laura Schneider (RutgersUniversity) and Zachary Christman (Rowan University) for their support and advice The staff of Clark Labsfacilitated the work by creating and maintaining the Idrisireg software (httpwwwclarklabsorg) with whichpreliminary analysis was performed Subsequent and final analysis was performed with R packages NNetMASS multcomp and raster

Author Contributions Marco Millones John Rogan BL Turner II conceived and designed the original researchand fieldwork Marco Millones performed the fieldwork Marco Millones performed preliminary data analysiswith Daniel A Griffith Robert Clay Harris and Benoit Parmentier executed the final data analysis John RoganBL Turner II revised earlier versions of the manuscript Marco Millones Benoit Parmentier and Robert Clay Harriswrote the paper John Rogan revised the manuscript

Conflicts of Interest The authors declare no conflicts of interest

Land 2017 6 61 6 of 19

Land 2017 6 61 5 of 19

lacking detailed land categories the resulting three-category map has the advantage of being more consistent than most multi-temporal assessments because it was produced using a consistent methodology by the same research team explicitly for the purpose of forest change mapping [4647]

Figure 2 Fire frequency map 2000ndash2010 MODIS TERRA-only series Significant Getis-Ord Gi statistic (005 level) hot spots and LISA-based clusters are shown in inset (upper left) 1 = 2006 post-hurricane Wilma fires and urban development related fires 2 and 5 = Mennonite land clearing for commercial maize cultivation 3 = PEMEX oil processing plant and 4 and 6 = high yield commercial corn and bean cultivation

Figure 3 Land changepersistence classes based on the CABS (2009) land cover maps Figure 3 Land changepersistence classes based on the CABS (2009) land cover maps

Even though MODIS fire data are constantly updated in this study we only include data to theyear 2010 We consider the 2000ndash2010 ten-year period sufficient to describe the salient points about thespatio-temporal patterns of a fire in the region More importantly the land cover data and anthromedata that we use do not go beyond 2007 and 2008 respectively For this same reason the multinomialmodeling component of this study does not use any fire data from after 2007 (see methods section)

32 Methods

The methodology has three components (a) a characterization of the spatio-temporal patternsand co-location of land changepersistence and fire (b) an assessment of the effect of fire presencelandscape patch size and other covariates land-change outcomes (FP NFP and CH) using a spatialmultinomial logit model for the period 2000ndash2007 and (c) an exploration of the ability of fire frequencyto distinguish human landscape categories defined in anthrome groups and anthrome classes

33 Characterization of Land Change and Fire Patterns

A cross-tabulation-based change analysis was performed on the simplified CABS land covermap pairs 1990ndash2000 and 2000ndash2007 resulting in one map with two persistence classes (FP and NFP)and one change class (CH) (Figure 3) Spatio-temporal dynamics of fire occurrence were derivedby manipulating the MODIS fire archive via map algebra operations (eg overlay reclassification)into map and graph summaries of annual and multi-year fire frequency After accounting for thedifferent time-spans of the TERRA and AQUA series and adjusting for double counting three separatefire occurrence sets were created a TERRA ten-year summary map (2000ndash2010) (Figure 2) and aTERRA-AQUA combined annual time-series graph (2000ndash2009) (Figure 4) Global (MoranrsquoI) and local(Getis-Ord Gi and LISA) measures of spatial autocorrelation were calculated for all sets of maps [50ndash52]Finally a second cross-tabulation analysis was performed for the land changepersistence map (FPNFP and CH) (Figure 3) and the binary fire (reclassification of Figure 2) maps in order to describe andexplore the spatial correspondence between them and the relationship between fire occurrence and thedifferent land cover categories The result of this cross-tabulation map is shown in Figure 5

Land 2017 6 61 7 of 19

Land 2017 6 61 7 of 19

Figure 4 Cumulative annual and 8-day frequency (counts) of fire occurrence (FIRE) 2000ndash2009 in the three-state Yucataacuten Peninsula blue = morning purple = afternoon Inset shows detail of intra-annual fire season for 2005

Figure 5 Cross-tabulation of land changepersistence classes (Figure 1) and fire frequency (Figure 2)

34 Effect of Fire and Patch Size on Land ChangePersistence A Spatial Multinomial Logit Model

A spatial multinomial logit model using 2003ndash2007 fire ldquodensityrdquo or ldquointensityrdquo (fire countfive years) as independent variable (FIRE) and 7 control variables was performed This model specification is used in the literature (eg [5354]) and is preferred because the dependent variable consists of three possible outcomes that are categoricalnominal in nature [55ndash57] To account for the positive spatial autocorrelation present in remotely sensed data [5859] spatial lags variables based on rook-case adjacency were calculated This was done by generating for each observation the

4000

5000

10000

15000

20000

25000

2000 2001 2002 2003 2004 2005 2006 2007 2008 2009

Terraannual

Aquaannual

Terra 8-day

r December February April June August Octoberr December February April June August October

2000

Fire Season2005

Annual

8-day

4000

5000

10000

15000

20000

25000

2000 2001 2002 2003 2004 2005 2006 2007 2008 2009

Terraannual

Aquaannual

Terra 8-day

r December February April June August Octoberr December February April June August October

2000

Fire Season2005

Annual

8-day

Figure 4 Cumulative annual and 8-day frequency (counts) of fire occurrence (FIRE) 2000ndash2009 in thethree-state Yucataacuten Peninsula blue = morning purple = afternoon Inset shows detail of intra-annualfire season for 2005

Land 2017 6 61 7 of 19

Figure 4 Cumulative annual and 8-day frequency (counts) of fire occurrence (FIRE) 2000ndash2009 in the three-state Yucataacuten Peninsula blue = morning purple = afternoon Inset shows detail of intra-annual fire season for 2005

Figure 5 Cross-tabulation of land changepersistence classes (Figure 1) and fire frequency (Figure 2)

34 Effect of Fire and Patch Size on Land ChangePersistence A Spatial Multinomial Logit Model

A spatial multinomial logit model using 2003ndash2007 fire ldquodensityrdquo or ldquointensityrdquo (fire countfive years) as independent variable (FIRE) and 7 control variables was performed This model specification is used in the literature (eg [5354]) and is preferred because the dependent variable consists of three possible outcomes that are categoricalnominal in nature [55ndash57] To account for the positive spatial autocorrelation present in remotely sensed data [5859] spatial lags variables based on rook-case adjacency were calculated This was done by generating for each observation the

4000

5000

10000

15000

20000

25000

2000 2001 2002 2003 2004 2005 2006 2007 2008 2009

Terraannual

Aquaannual

Terra 8-day

r December February April June August Octoberr December February April June August October

2000

Fire Season2005

Annual

8-day

4000

5000

10000

15000

20000

25000

2000 2001 2002 2003 2004 2005 2006 2007 2008 2009

Terraannual

Aquaannual

Terra 8-day

r December February April June August Octoberr December February April June August October

2000

Fire Season2005

Annual

8-day

Figure 5 Cross-tabulation of land changepersistence classes (Figure 1) and fire frequency (Figure 2)

34 Effect of Fire and Patch Size on Land ChangePersistence A Spatial Multinomial Logit Model

A spatial multinomial logit model using 2003ndash2007 fire ldquodensityrdquo or ldquointensityrdquo (fire countfiveyears) as independent variable (FIRE) and 7 control variables was performed This model specificationis used in the literature (eg [5354]) and is preferred because the dependent variable consists of

Land 2017 6 61 8 of 19

three possible outcomes that are categoricalnominal in nature [55ndash57] To account for the positivespatial autocorrelation present in remotely sensed data [5859] spatial lags variables based on rook-caseadjacency were calculated This was done by generating for each observation the average sum of itsneighbors of the same class (CFP CNFP and CCH) and including the lag variable in the model (seeEquation (1)) [5960] Lag values range from 0 (no like neighbors) to 1 (all four like neighbors) whileaverage Moranrsquos I values range from virtually random for CCH (00035) to weak-moderate positivefor CNFP (0392) and CFP (0391) In this particular case spatial lags also serve as an indicator oflandscape configuration and heterogeneity (ie similar to patch size and cohesion)

Pseudo-likelihood estimates were calculated for the main effects and spatial lag parameters of themultinomial model as follows (Equation (1))

Log(πhijπhir) = αj + xprimehi βj (1)

where πhij is the probability that a pixel h in the map of any class i for which fire has been detected willbecome one of land changepersistence category j (FP NFP or CH) j 6= r with land changepersistencecategory r being the reference category There are separate sets of intercept parameters αj and regressionparameters βj for each of the logit models The matrix xprimehi is the set of explanatory variables spatiallag (CY) fire (FIRE) and the commonly used control variables described Two logits equations aremodeled for each FIRE and CY population the logit comparing non-forest persistence (NFP) to forestpersistence (FP) and the logit comparing change (CH) to forest persistence (FP) [56]

35 Fire Frequency and Anthromes Characterization

Anthromes map datasets were processed to match them to the study area and temporal firecount data were aggregated to generate a fire frequency variable (Figure 6) In order to explore theassociation between fire counts and anthrome groups graphically we used boxplots of mean firefrequency by each category present in the study area dense settlements villages (in effect village andsurrounding areas) croplands rangelands forested wildlands We measured the differences in meanfire frequency across anthromes using a negative binomial model and a Tukey pairwise comparisonA binomial model was preferred over Poisson model because the overall (as well as per category) meanand variance are noticeably different (by a factor 100) which suggests over-dispersion in the Poissonparameter We also conducted Tukey comparisons for fire frequency within the cropland anthromesgroup to assess the potential of using fire count for finer definition of the human imprint of landscape

Land 2017 6 61 8 of 19

average sum of its neighbors of the same class (CFP CNFP and CCH) and including the lag variable in the model (see Equation (1)) [5960] Lag values range from 0 (no like neighbors) to 1 (all four like neighbors) while average Moranrsquos I values range from virtually random for CCH (00035) to weak-moderate positive for CNFP (0392) and CFP (0391) In this particular case spatial lags also serve as an indicator of landscape configuration and heterogeneity (ie similar to patch size and cohesion)

Pseudo-likelihood estimates were calculated for the main effects and spatial lag parameters of the multinomial model as follows (Equation (1))

Log(πhijπhir) = αj + xprimehi βj (1)

where πhij is the probability that a pixel h in the map of any class i for which fire has been detected will become one of land changepersistence category j (FP NFP or CH) j ne r with land changepersistence category r being the reference category There are separate sets of intercept parameters αj and regression parameters βj for each of the logit models The matrix xprimehi is the set of explanatory variables spatial lag (CY) fire (FIRE) and the commonly used control variables described Two logits equations are modeled for each FIRE and CY population the logit comparing non-forest persistence (NFP) to forest persistence (FP) and the logit comparing change (CH) to forest persistence (FP) [56]

35 Fire Frequency and Anthromes Characterization

Anthromes map datasets were processed to match them to the study area and temporal fire count data were aggregated to generate a fire frequency variable (Figure 6) In order to explore the association between fire counts and anthrome groups graphically we used boxplots of mean fire frequency by each category present in the study area dense settlements villages (in effect village and surrounding areas) croplands rangelands forested wildlands We measured the differences in mean fire frequency across anthromes using a negative binomial model and a Tukey pairwise comparison A binomial model was preferred over Poisson model because the overall (as well as per category) mean and variance are noticeably different (by a factor 100) which suggests over-dispersion in the Poisson parameter We also conducted Tukey comparisons for fire frequency within the cropland anthromes group to assess the potential of using fire count for finer definition of the human imprint of landscape

For the data processing we used the raster (version 25-8) sp (version 12-4) and rgdal (version 12-7) packages to perform some of the preprocessing for the spatial inputs The raster package was also used for aggregation of the fire occurrences cropping and reclassification of anthromes data We used the implementation of multinomial model in the R ldquonnetrdquo package (version 73-12) for analyses We also ran the negative binomial model using the ldquoMASSrdquo package (version 73-12) in R version 34 and used the glht method from the multcomp R package (14-6) to perform the Tukey comparison

Figure 6 Fire frequency aggregation for anthrome comparison (left) and Anthrome groups (right)

Figure 6 Fire frequency aggregation for anthrome comparison (left) and Anthrome groups (right)

For the data processing we used the raster (version 25-8) sp (version 12-4) and rgdal(version 12-7) packages to perform some of the preprocessing for the spatial inputs The raster packagewas also used for aggregation of the fire occurrences cropping and reclassification of anthromes

Land 2017 6 61 9 of 19

data We used the implementation of multinomial model in the R ldquonnetrdquo package (version 73-12)for analyses We also ran the negative binomial model using the ldquoMASSrdquo package (version 73-12)in R version 34 and used the glht method from the multcomp R package (14-6) to perform theTukey comparison

4 Results

41 Spatio-Temporal Patterns of Fire and Land Change

As a proxy indicator of human land use fire frequency can be interpreted as a quantitativemeasure of ldquodensityrdquo (in space and time) of land use in this case It corresponds to how actively ldquousedrdquoor ldquounder-usedrdquo a 1 km parcel of land is in relation to the types of land use that require burning(eg high for pasture and cultivation land)

Fire occurrence for the period 2000ndash2010 presents a distinct non-random spatial pattern across thestudy area (Moranrsquos I = 062) (Figure 2) The individual observations presenting the highest detectionfrequencies (gt3 per year) appear in spatial clusters and are concentrated in the northern and westernsection of the Peninsula in the states of Campeche and the Yucataacuten Quintana Roo has comparativelyfewer and less clustering fire detections Areas with less fire frequency are observed in Campeche andQuintana Roo especially in the presence of federal and state run natural protected areas (eg SianKarsquoan and Calakmul bioreserves) (Figure 1) and in locations where road and settlement density is lowThis road-settlement-fire co-location is more explicit in the Yucataacuten and northern Campeche and lessso in southern Campeche where road density decreases

Locations affected by fire (Figure 5 and Table 1) cover roughly 45 of the study area More thanhalf of the fire occurrences concentrate in NFP areas followed by 40 of FP and 2 in CH areas(1 of the total) Locations with no fire occurrence cover more than 50 of the study area No-fireoccurrences are two times more common in FP than in NFP and they are minimally present in CHareas Land changepersistence figures (total rows percentage in Table 1) indicate that roughly 23 ofthe FP shows no fire detections whereas 60 of NFP presents fire occurrence CH shows 86 of itsarea as having burned at some time (although it is hardly visible in Figure 5 because CH covers only1 of the total area)

Land 2017 6 61 10 of 19

Table 1 Cross-tabulation of fire occurrence and land changepersistence row column and total percentages per class Preliminary interpretation matrix(extendeddetailed legend for Figure 5)

Fire No Fire Row Total Total Study Area

Forest Persistence

293-Error resulting from database mismatch-Error of commission in MODIS ActiveFire product-Error induced by aggregation of landcover data

707-Core areas of mature forest that have persisted for at least 17years (1990ndash2007)-Protected areas with a predominance of mature forest-Areas of planned selective forest extraction that have not beenextracted in 17 years or longer (under rotation management)

100 54

Non Forest Persistence

608-Areas where fire is used to convert fromnon-forest vegetation land covers toother non-forest vegetation land covers(eg agriculture to urban)-Areas of active non-forest land-uses-Error resulting from databasemismatches

3918-Areas under intensive land-uses that do not require land clearingfor prolonged periods (eg citrus agriculture urban)-Secondary vegetation of at least 10 years including forest notconsidered mature by CAB 2009 This can include forest regrowth(forest transition)-Forested areas of forest communities that have been extracted inthe last 10 years and are growing back-Seasonal agricultural areas currently fallow (eg milpa)

100 43

Change (Forest toNon-Forest)

860-All land cover changes (conversion andsome modification) preceded by landclearing by fire (ie deforestation)-Core forest areas that are heavilydeforested with more intense use of landclearing by fire

137-Error of omission in MODIS Active Fire product-Error resulting from database mismatches-Land changes that do not require fire-Fringe areas that are cleared without fire after the core area hasbeen cleared with fire-Fringe areas that are cleared with low intensity fire that is notdetected by MODIS Active Fire product

100 1

Column TOTAL 45 36 100 100

Land 2017 6 61 11 of 19

42 Effect of Fire and Patch Size on Land ChangePersistence A Spatial Multinomial Logit Model

Results from the spatial multinomial logit model agree with the analysis presented above(Section 41) and indicate that past fire occurrence (pre-2007) is a useful predictor of land changepersistence categories The resulting equations and model statistics are summarized in Table 2 and inthe supplementary Appendix A The Akaike information criterion (AIC) indicates that the model withcovariates (intercept + fire and lag + control variables) performs better than alternative models (seeAppendix A) The likelihood ratio (LR) has two degrees of freedom and is significant which confirmsthat at least one of the variables in the model improves the model description

Table 2 Spatial multinomial logit model summary of trends FP = forest persistence NFP = non forestpersistence CH = change INTE = Intercept Odds = Odds ratio effects point estimates This tablecontains only FIRE and CY variables the full variable list is available in the Appendix A

CAT REF INTE CY FIRE Odds CY Odds FIRE

CH (3) FP (1) minus467 minus355 192 003 679NFP (2) minus607 minus346 020 003 122

CH Average minus537 minus350 106 003 400

FP (1) CH (3) 467 355 minus192 3466 015NFP (2) minus438 007 minus172 107 018

FP Average 015 181 minus182 1787 016

NFP (2) CH (3) 905 348 minus020 3243 082FP (1) 438 minus007 172 094 559

FP Average 671 171 076 1668 320

The maximum pseudo-likelihood and odds ratio point estimates (Table 2 and Appendix A) showthe effect and relative importance of FIRE and CY for each land changepersistence outcome in themodel At a 5 level the difference between FIRE = 1 (fire occurrence) and FIRE = 0 is statisticallydifferent for all cases (FP NFP and CH) for all three states separately and the three-state aggregatedstudy area CY is a significant covariate in the model for all of these cases Additional models wererun with control variables These full model results are presented in the Appendix A and confirm theusefulness of fire as predictor

An inspection of the pseudo-likelihood estimates for the aggregated study area (Table 2 andAppendix A) indicates that for each unit increase in FIRE (intensity) the log of the ratio of p(CH)p(FP)increases by ~192 and the log of the ratio of p(CH)p(NFP) increases by ~02 In other words for eachunit increase in FIRE (intensity) in a given pixel (in Figure 2) the odds of that same pixel belonging tocategory CH (forest to non-forest change) rather than category FP (forest persistence in Figure 3) aremultiplied by ~67 Unit increases in FIRE also increase the odds of a pixel belonging to category CHrather than NFP (no forest persistence) by 122

For every increase in one unit of Fire the odds of a pixel belonging to category NFP instead of CHare multiplied by 082 For every increase in one unit of Fire the odds of a pixel belonging to categoryNFP instead of FP are multiplied by 559 For every increase in one unit of Fire the odds of a pixelbelonging to category FP instead of CH are multiplied by 015 (almost none)

For every increase in one unit of Fire the odds of a pixel belonging to category FP instead ofNFP are multiplied by 018 (almost none) Overall FIRE estimates are negative when predicting forestpersistence (FP) and positive when predicting CH

The calculated spatial lag (CY) terms are significant for all cases CY as mentioned earlier can beinterpreted as cohesiveness of land cover patches [61] Larger CY values correspond to more similarvalues among neighboring cells (ie a larger patches of a category) Estimates of the model for theaggregated peninsula indicate that a unit increase in CY decreases the log of p(FP)p(CH) by ~minus355while the log of p(FP)p(NFP) decreases by ~minus007 This finding indicates that persistent forestareas located in large patches are very likely to remain forest (34 times more than CH) (Table 2 and

Land 2017 6 61 12 of 19

Appendix A) FP is also 107 times more likely than NFP In general CH has a negative relationship withCY This relationship can be attributed to CH occurring more often in isolated pixels corresponding tofragmented patches Conversely FP and NFP occur in larger continuous areas (Figure 3)

43 Comparison of Fire by Anthromes

Boxplots of mean fire frequency by anthromes groups suggest that fire can be used to distinguishamong anthromes groups thereby serving as an additional potential variable to examine humanimprints in the context of the Yucataacuten region (Figure 6) The croplands anthromes group has a higherfire frequency on average compared to most other anthromes categories We note that rangelandsdisplay a very large variance and thus may be difficult to distinguish from croplands and villagesFiner anthropogenic categories within the cropland groups also appear to be contrasted by the firefrequency variable (see boxplots Figure 7)

Land 2017 6 61 12 of 19

corresponding to fragmented patches Conversely FP and NFP occur in larger continuous areas (Figure 3)

43 Comparison of Fire by Anthromes

Boxplots of mean fire frequency by anthromes groups suggest that fire can be used to distinguish among anthromes groups thereby serving as an additional potential variable to examine human imprints in the context of the Yucataacuten region (Figure 6) The croplands anthromes group has a higher fire frequency on average compared to most other anthromes categories We note that rangelands display a very large variance and thus may be difficult to distinguish from croplands and villages Finer anthropogenic categories within the cropland groups also appear to be contrasted by the fire frequency variable (see boxplots Figure 7)

Tukey pairwise comparison tests between anthromes groups (applied to the negative binomial model Table 3) highlight that six and seven pairwise comparisons are significantly different at 5 and 10 level respectively Coefficients indicate relative increase or decrease of the expected log of fire frequency for categorical change in relation to the reference variable For instance there is a minus137 decrease in the log of fire frequency when an observation is found in the dense settlements rather than in croplands We find that fire frequency variable is useful to differentiate croplands with almost all categories with the exception of Villages and Rangelands Both overlap substantially on the boxplots (Figure 7)

Figure 7 Between group comparison Fire frequency by anthrome groups boxplots (left) Within group comparison Fire frequency boxplots within cropland anthrome (right)

Table 3 Between-anthromes Tukey pairwise comparison for the negative binomial models with fire count and anthromes groups Note that the reference variable is in italic

Pairwise Comparison Coefficients Standard Error t-Stat p-ValuesDense settlementsndashCroplands minus138688 043059 minus32209 00121

ForestedndashCroplands minus092198 006997 minus131762 0 RangelandsndashCroplands minus035406 026321 minus13452 07146

VillagesndashCroplands minus028199 032807 minus08595 09435 WildlandsndashCroplands minus229463 019565 minus117283 0

ForestedndashDense settlements 046491 042934 10828 08616 RangelandsndashDense settlements 103282 049872 20709 02552

VillagesndashDense settlements 110489 053579 20622 02593 WildlandsndashDense settlements minus090775 04666 minus19454 03214

RangelandsndashForested 056791 026118 21744 02076

Figure 7 Between group comparison Fire frequency by anthrome groups boxplots (left) Within groupcomparison Fire frequency boxplots within cropland anthrome (right)

Tukey pairwise comparison tests between anthromes groups (applied to the negative binomialmodel Table 3) highlight that six and seven pairwise comparisons are significantly different at 5 and10 level respectively Coefficients indicate relative increase or decrease of the expected log of firefrequency for categorical change in relation to the reference variable For instance there is a minus137decrease in the log of fire frequency when an observation is found in the dense settlements rather thanin croplands We find that fire frequency variable is useful to differentiate croplands with almost allcategories with the exception of Villages and Rangelands Both overlap substantially on the boxplots(Figure 7)

Tukey comparisons were also performed for fire frequency within the cropland anthromes groupto assess the potential of using fire frequency for finer definition of the human imprint of landscapeWe found that within croplands two out 10 and four out of 10 comparison results in significantdifferences in the log of fire frequency (Table 4) at 5 and 10 percent significance level respectivelyThis suggests that fire frequency is less useful at distinguishing within the cropland anthromes Thestrongest contrasts are found between ldquoresidential rainfed mosaicsndashremote croplands mosaicrdquo andbetween ldquoresidential irrigated croplandndashremote croplandsrdquo Both indicate decreases in the log offire frequency for locations that are found in residential rainfed and irrigated cropland compared toremote croplands

Land 2017 6 61 13 of 19

Table 3 Between-anthromes Tukey pairwise comparison for the negative binomial models with firecount and anthromes groups Note that the reference variable is in italic

Pairwise Comparison Coefficients Standard Error t-Stat p-Values

Dense settlementsndashCroplands minus138688 043059 minus32209 00121ForestedndashCroplands minus092198 006997 minus131762 0

RangelandsndashCroplands minus035406 026321 minus13452 07146VillagesndashCroplands minus028199 032807 minus08595 09435

WildlandsndashCroplands minus229463 019565 minus117283 0ForestedndashDense settlements 046491 042934 10828 08616

RangelandsndashDense settlements 103282 049872 20709 02552VillagesndashDense settlements 110489 053579 20622 02593

WildlandsndashDense settlements minus090775 04666 minus19454 03214RangelandsndashForested 056791 026118 21744 02076

VillagesndashForested 063999 032644 19605 03129WildlandsndashForested minus137266 01929 minus71159 0VillagesndashRangelands 007207 041346 01743 1

WildlandsndashRangelands minus194057 031874 minus60882 0WildlandsndashVillages minus201264 037409 minus53801 0

Table 4 Within-anthrome Tukey pairwise comparisons using the negative binomial models with firecount and anthromes croplands categories Note that the reference variable is in italic

PairwisendashComparison Coefficients Standard Error t-Stat p-Values

Populated rainfed croplandndashPopulated irrigated cropland 025239 022555 1119 07646Remote croplandsndashPopulated irrigated cropland 0572 025835 2214 01453

Residential irrigated croplandndashPopulated irrigated cropland minus061118 041094 minus14873 05244Residential rainfed mosaicndashPopulated irrigated cropland 008091 022337 03622 09955

Remote croplandsndashPopulated rainfed cropland 031961 014756 2166 01615Residential irrigated croplandndashPopulated rainfed cropland minus086357 0352 minus24533 00827

Residential rainfed mosaicndashPopulated rainfed cropland minus017148 007017 minus24437 00848Residential irrigated croplandndashRemote croplands minus118318 037387 minus31647 00105

Residential rainfed mosaicndashRemote croplands minus049109 014421 minus34054 00043Residential rainfed mosaicndashResidential irrigated cropland 069209 035061 1974 02396

5 Discussion and Conclusions

Analysis of the spatial patterns of fire in the Yucataacuten using fire data visually reproduces thegeography of human land-based activities during 2000ndash2010 including the influence of roadssettlements and natural protected areas The intra-annual temporal dimensions of fire dataapproximate key moments of seasonal agriculture and other land-based activities (Figure 4) Thesefindings are consistent with studies finding higher fire frequencies in the proximity to roads andsettlements region [40] and with research about fire and deforestation in other tropical settings(eg [2862ndash64]) and more generally about the relationship between land change road developmentand market accessibility [53546465]

The multinomial model confirms the significance of fire intensity (defined as count of fire flaggedpixels over time) and landscape configuration (represented by the spatial lag variable CY) for thepeninsula for all three types of land changepersistence outcomes Notably all change is stronglyaffected by the presence of fire The odds of a forested area becoming non-forested multiply by sixin the presence of fire This is not surprising given that the cross-tabulation analysis showed thatnearly 87 of pixels that changed from 2000 to 2007 had been flagged as fire by MODIS at some pointThe dominance of no-fire observations over fire occurrence the (pseudo) absence of fire makes for abetter predictor of forest persistence than fire occurrence per se especially for large patches (high CYvalues) Predicting non-forest persistence proved more difficult signaling the diversity of ecologicaland land use practices and transitions between them that define the NFP category as discussed in thedata section What exactly accounts for the remaining 13 is difficult to determine We can speculate

Land 2017 6 61 14 of 19

however that possible factors include data error and accuracy mismatches As some have notedMODIS products do omit fires for various reasons [40] We can also speculate on some detected firesbeing non-agricultural Finally we can also imagine some fires starting as agricultural burns butbecoming large multiday forest fires as they grow out of control [40]

Fire also proves to be a reasonable indicator to distinguish between anthromes groups (Figure 7)but less among finer anthromes categories Our analysis shows that for example with the aidof a fire frequency croplands are separable from the rest of categories and that dense settlementsare clearly distinct from villages Other categories like rangeland prove more difficult to separatesince they present larger variance Some within-variation within anthropogenic categories is alsodistinguishable For example populated irrigated is clearly separable from populated rainfed andfrom remote croplands These two former categories however are not as separable from each otherwith the aid of fire frequency alone

Perhaps some insight about differences distinguishing between- and within-anthropogeniclandscapes can be gained by looking into the distinction between quemas (legally regulated agriculturalfires) from incendios (large escape non-regulated forest fires) Both can be addressed through the use ofMODIS active fire data but cannot be thoroughly distinguished with these data alone Within-variationexists in both categories On the one hand quemas can be due to subsistence and commercial agriculturesuch as sugar cane cultivation along the border with Belize (ie either rain fed or irrigated anthromecategories) or Mennonite corn fields in Bacalar( ie the populated irrigated anthrome category) astheir spatial and temporal signatures can differ quite noticeably (Figures 2 and 4) On the other handincendios can be truly accidental or be the result of purposeful burning with nonagricultural goals(eg forcing land zoning code changes for urban development hunting practices) Future researchshould exploit these differences in order to account for a more nuanced description of the relationshipsbetween fire and human-induced land change in the region

We conclude that in subtropical forest settings in which burning is a fundamental landscape toolfire is a reasonable proxy for land change Use of fire data improves the estimation of land change andexpands our understanding of human-environment relationships that produce complex mosaics ofhighly dynamic landscapes such as those in the Mexican Yucataacuten

Acknowledgments This study was part of the SYPR (httpsyprasuedu) and EDGY (httplandchangerutgersedu) projects SYPR received support from the NASA LCLUC program (NAG-56046 511134 and 6GD98G)and the NSF BCS program (0410016) EDGY was sponsored by the Gordon and Betty Moore Foundation underGrant 1697 The authors thank Drs Birgit Schmook (El Colegio de la Frontera Sur) Laura Schneider (RutgersUniversity) and Zachary Christman (Rowan University) for their support and advice The staff of Clark Labsfacilitated the work by creating and maintaining the Idrisireg software (httpwwwclarklabsorg) with whichpreliminary analysis was performed Subsequent and final analysis was performed with R packages NNetMASS multcomp and raster

Author Contributions Marco Millones John Rogan BL Turner II conceived and designed the original researchand fieldwork Marco Millones performed the fieldwork Marco Millones performed preliminary data analysiswith Daniel A Griffith Robert Clay Harris and Benoit Parmentier executed the final data analysis John RoganBL Turner II revised earlier versions of the manuscript Marco Millones Benoit Parmentier and Robert Clay Harriswrote the paper John Rogan revised the manuscript

Conflicts of Interest The authors declare no conflicts of interest

Land 2017 6 61 7 of 19

Land 2017 6 61 7 of 19

Figure 4 Cumulative annual and 8-day frequency (counts) of fire occurrence (FIRE) 2000ndash2009 in the three-state Yucataacuten Peninsula blue = morning purple = afternoon Inset shows detail of intra-annual fire season for 2005

Figure 5 Cross-tabulation of land changepersistence classes (Figure 1) and fire frequency (Figure 2)

34 Effect of Fire and Patch Size on Land ChangePersistence A Spatial Multinomial Logit Model

A spatial multinomial logit model using 2003ndash2007 fire ldquodensityrdquo or ldquointensityrdquo (fire countfive years) as independent variable (FIRE) and 7 control variables was performed This model specification is used in the literature (eg [5354]) and is preferred because the dependent variable consists of three possible outcomes that are categoricalnominal in nature [55ndash57] To account for the positive spatial autocorrelation present in remotely sensed data [5859] spatial lags variables based on rook-case adjacency were calculated This was done by generating for each observation the

4000

5000

10000

15000

20000

25000

2000 2001 2002 2003 2004 2005 2006 2007 2008 2009

Terraannual

Aquaannual

Terra 8-day

r December February April June August Octoberr December February April June August October

2000

Fire Season2005

Annual

8-day

4000

5000

10000

15000

20000

25000

2000 2001 2002 2003 2004 2005 2006 2007 2008 2009

Terraannual

Aquaannual

Terra 8-day

r December February April June August Octoberr December February April June August October

2000

Fire Season2005

Annual

8-day

Figure 4 Cumulative annual and 8-day frequency (counts) of fire occurrence (FIRE) 2000ndash2009 in thethree-state Yucataacuten Peninsula blue = morning purple = afternoon Inset shows detail of intra-annualfire season for 2005

Land 2017 6 61 7 of 19

Figure 4 Cumulative annual and 8-day frequency (counts) of fire occurrence (FIRE) 2000ndash2009 in the three-state Yucataacuten Peninsula blue = morning purple = afternoon Inset shows detail of intra-annual fire season for 2005

Figure 5 Cross-tabulation of land changepersistence classes (Figure 1) and fire frequency (Figure 2)

34 Effect of Fire and Patch Size on Land ChangePersistence A Spatial Multinomial Logit Model

A spatial multinomial logit model using 2003ndash2007 fire ldquodensityrdquo or ldquointensityrdquo (fire countfive years) as independent variable (FIRE) and 7 control variables was performed This model specification is used in the literature (eg [5354]) and is preferred because the dependent variable consists of three possible outcomes that are categoricalnominal in nature [55ndash57] To account for the positive spatial autocorrelation present in remotely sensed data [5859] spatial lags variables based on rook-case adjacency were calculated This was done by generating for each observation the

4000

5000

10000

15000

20000

25000

2000 2001 2002 2003 2004 2005 2006 2007 2008 2009

Terraannual

Aquaannual

Terra 8-day

r December February April June August Octoberr December February April June August October

2000

Fire Season2005

Annual

8-day

4000

5000

10000

15000

20000

25000

2000 2001 2002 2003 2004 2005 2006 2007 2008 2009

Terraannual

Aquaannual

Terra 8-day

r December February April June August Octoberr December February April June August October

2000

Fire Season2005

Annual

8-day

Figure 5 Cross-tabulation of land changepersistence classes (Figure 1) and fire frequency (Figure 2)

34 Effect of Fire and Patch Size on Land ChangePersistence A Spatial Multinomial Logit Model

A spatial multinomial logit model using 2003ndash2007 fire ldquodensityrdquo or ldquointensityrdquo (fire countfiveyears) as independent variable (FIRE) and 7 control variables was performed This model specificationis used in the literature (eg [5354]) and is preferred because the dependent variable consists of

Land 2017 6 61 8 of 19

three possible outcomes that are categoricalnominal in nature [55ndash57] To account for the positivespatial autocorrelation present in remotely sensed data [5859] spatial lags variables based on rook-caseadjacency were calculated This was done by generating for each observation the average sum of itsneighbors of the same class (CFP CNFP and CCH) and including the lag variable in the model (seeEquation (1)) [5960] Lag values range from 0 (no like neighbors) to 1 (all four like neighbors) whileaverage Moranrsquos I values range from virtually random for CCH (00035) to weak-moderate positivefor CNFP (0392) and CFP (0391) In this particular case spatial lags also serve as an indicator oflandscape configuration and heterogeneity (ie similar to patch size and cohesion)

Pseudo-likelihood estimates were calculated for the main effects and spatial lag parameters of themultinomial model as follows (Equation (1))

Log(πhijπhir) = αj + xprimehi βj (1)

where πhij is the probability that a pixel h in the map of any class i for which fire has been detected willbecome one of land changepersistence category j (FP NFP or CH) j 6= r with land changepersistencecategory r being the reference category There are separate sets of intercept parameters αj and regressionparameters βj for each of the logit models The matrix xprimehi is the set of explanatory variables spatiallag (CY) fire (FIRE) and the commonly used control variables described Two logits equations aremodeled for each FIRE and CY population the logit comparing non-forest persistence (NFP) to forestpersistence (FP) and the logit comparing change (CH) to forest persistence (FP) [56]

35 Fire Frequency and Anthromes Characterization

Anthromes map datasets were processed to match them to the study area and temporal firecount data were aggregated to generate a fire frequency variable (Figure 6) In order to explore theassociation between fire counts and anthrome groups graphically we used boxplots of mean firefrequency by each category present in the study area dense settlements villages (in effect village andsurrounding areas) croplands rangelands forested wildlands We measured the differences in meanfire frequency across anthromes using a negative binomial model and a Tukey pairwise comparisonA binomial model was preferred over Poisson model because the overall (as well as per category) meanand variance are noticeably different (by a factor 100) which suggests over-dispersion in the Poissonparameter We also conducted Tukey comparisons for fire frequency within the cropland anthromesgroup to assess the potential of using fire count for finer definition of the human imprint of landscape

Land 2017 6 61 8 of 19

average sum of its neighbors of the same class (CFP CNFP and CCH) and including the lag variable in the model (see Equation (1)) [5960] Lag values range from 0 (no like neighbors) to 1 (all four like neighbors) while average Moranrsquos I values range from virtually random for CCH (00035) to weak-moderate positive for CNFP (0392) and CFP (0391) In this particular case spatial lags also serve as an indicator of landscape configuration and heterogeneity (ie similar to patch size and cohesion)

Pseudo-likelihood estimates were calculated for the main effects and spatial lag parameters of the multinomial model as follows (Equation (1))

Log(πhijπhir) = αj + xprimehi βj (1)

where πhij is the probability that a pixel h in the map of any class i for which fire has been detected will become one of land changepersistence category j (FP NFP or CH) j ne r with land changepersistence category r being the reference category There are separate sets of intercept parameters αj and regression parameters βj for each of the logit models The matrix xprimehi is the set of explanatory variables spatial lag (CY) fire (FIRE) and the commonly used control variables described Two logits equations are modeled for each FIRE and CY population the logit comparing non-forest persistence (NFP) to forest persistence (FP) and the logit comparing change (CH) to forest persistence (FP) [56]

35 Fire Frequency and Anthromes Characterization

Anthromes map datasets were processed to match them to the study area and temporal fire count data were aggregated to generate a fire frequency variable (Figure 6) In order to explore the association between fire counts and anthrome groups graphically we used boxplots of mean fire frequency by each category present in the study area dense settlements villages (in effect village and surrounding areas) croplands rangelands forested wildlands We measured the differences in mean fire frequency across anthromes using a negative binomial model and a Tukey pairwise comparison A binomial model was preferred over Poisson model because the overall (as well as per category) mean and variance are noticeably different (by a factor 100) which suggests over-dispersion in the Poisson parameter We also conducted Tukey comparisons for fire frequency within the cropland anthromes group to assess the potential of using fire count for finer definition of the human imprint of landscape

For the data processing we used the raster (version 25-8) sp (version 12-4) and rgdal (version 12-7) packages to perform some of the preprocessing for the spatial inputs The raster package was also used for aggregation of the fire occurrences cropping and reclassification of anthromes data We used the implementation of multinomial model in the R ldquonnetrdquo package (version 73-12) for analyses We also ran the negative binomial model using the ldquoMASSrdquo package (version 73-12) in R version 34 and used the glht method from the multcomp R package (14-6) to perform the Tukey comparison

Figure 6 Fire frequency aggregation for anthrome comparison (left) and Anthrome groups (right)

Figure 6 Fire frequency aggregation for anthrome comparison (left) and Anthrome groups (right)

For the data processing we used the raster (version 25-8) sp (version 12-4) and rgdal(version 12-7) packages to perform some of the preprocessing for the spatial inputs The raster packagewas also used for aggregation of the fire occurrences cropping and reclassification of anthromes

Land 2017 6 61 9 of 19

data We used the implementation of multinomial model in the R ldquonnetrdquo package (version 73-12)for analyses We also ran the negative binomial model using the ldquoMASSrdquo package (version 73-12)in R version 34 and used the glht method from the multcomp R package (14-6) to perform theTukey comparison

4 Results

41 Spatio-Temporal Patterns of Fire and Land Change

As a proxy indicator of human land use fire frequency can be interpreted as a quantitativemeasure of ldquodensityrdquo (in space and time) of land use in this case It corresponds to how actively ldquousedrdquoor ldquounder-usedrdquo a 1 km parcel of land is in relation to the types of land use that require burning(eg high for pasture and cultivation land)

Fire occurrence for the period 2000ndash2010 presents a distinct non-random spatial pattern across thestudy area (Moranrsquos I = 062) (Figure 2) The individual observations presenting the highest detectionfrequencies (gt3 per year) appear in spatial clusters and are concentrated in the northern and westernsection of the Peninsula in the states of Campeche and the Yucataacuten Quintana Roo has comparativelyfewer and less clustering fire detections Areas with less fire frequency are observed in Campeche andQuintana Roo especially in the presence of federal and state run natural protected areas (eg SianKarsquoan and Calakmul bioreserves) (Figure 1) and in locations where road and settlement density is lowThis road-settlement-fire co-location is more explicit in the Yucataacuten and northern Campeche and lessso in southern Campeche where road density decreases

Locations affected by fire (Figure 5 and Table 1) cover roughly 45 of the study area More thanhalf of the fire occurrences concentrate in NFP areas followed by 40 of FP and 2 in CH areas(1 of the total) Locations with no fire occurrence cover more than 50 of the study area No-fireoccurrences are two times more common in FP than in NFP and they are minimally present in CHareas Land changepersistence figures (total rows percentage in Table 1) indicate that roughly 23 ofthe FP shows no fire detections whereas 60 of NFP presents fire occurrence CH shows 86 of itsarea as having burned at some time (although it is hardly visible in Figure 5 because CH covers only1 of the total area)

Land 2017 6 61 10 of 19

Table 1 Cross-tabulation of fire occurrence and land changepersistence row column and total percentages per class Preliminary interpretation matrix(extendeddetailed legend for Figure 5)

Fire No Fire Row Total Total Study Area

Forest Persistence

293-Error resulting from database mismatch-Error of commission in MODIS ActiveFire product-Error induced by aggregation of landcover data

707-Core areas of mature forest that have persisted for at least 17years (1990ndash2007)-Protected areas with a predominance of mature forest-Areas of planned selective forest extraction that have not beenextracted in 17 years or longer (under rotation management)

100 54

Non Forest Persistence

608-Areas where fire is used to convert fromnon-forest vegetation land covers toother non-forest vegetation land covers(eg agriculture to urban)-Areas of active non-forest land-uses-Error resulting from databasemismatches

3918-Areas under intensive land-uses that do not require land clearingfor prolonged periods (eg citrus agriculture urban)-Secondary vegetation of at least 10 years including forest notconsidered mature by CAB 2009 This can include forest regrowth(forest transition)-Forested areas of forest communities that have been extracted inthe last 10 years and are growing back-Seasonal agricultural areas currently fallow (eg milpa)

100 43

Change (Forest toNon-Forest)

860-All land cover changes (conversion andsome modification) preceded by landclearing by fire (ie deforestation)-Core forest areas that are heavilydeforested with more intense use of landclearing by fire

137-Error of omission in MODIS Active Fire product-Error resulting from database mismatches-Land changes that do not require fire-Fringe areas that are cleared without fire after the core area hasbeen cleared with fire-Fringe areas that are cleared with low intensity fire that is notdetected by MODIS Active Fire product

100 1

Column TOTAL 45 36 100 100

Land 2017 6 61 11 of 19

42 Effect of Fire and Patch Size on Land ChangePersistence A Spatial Multinomial Logit Model

Results from the spatial multinomial logit model agree with the analysis presented above(Section 41) and indicate that past fire occurrence (pre-2007) is a useful predictor of land changepersistence categories The resulting equations and model statistics are summarized in Table 2 and inthe supplementary Appendix A The Akaike information criterion (AIC) indicates that the model withcovariates (intercept + fire and lag + control variables) performs better than alternative models (seeAppendix A) The likelihood ratio (LR) has two degrees of freedom and is significant which confirmsthat at least one of the variables in the model improves the model description

Table 2 Spatial multinomial logit model summary of trends FP = forest persistence NFP = non forestpersistence CH = change INTE = Intercept Odds = Odds ratio effects point estimates This tablecontains only FIRE and CY variables the full variable list is available in the Appendix A

CAT REF INTE CY FIRE Odds CY Odds FIRE

CH (3) FP (1) minus467 minus355 192 003 679NFP (2) minus607 minus346 020 003 122

CH Average minus537 minus350 106 003 400

FP (1) CH (3) 467 355 minus192 3466 015NFP (2) minus438 007 minus172 107 018

FP Average 015 181 minus182 1787 016

NFP (2) CH (3) 905 348 minus020 3243 082FP (1) 438 minus007 172 094 559

FP Average 671 171 076 1668 320

The maximum pseudo-likelihood and odds ratio point estimates (Table 2 and Appendix A) showthe effect and relative importance of FIRE and CY for each land changepersistence outcome in themodel At a 5 level the difference between FIRE = 1 (fire occurrence) and FIRE = 0 is statisticallydifferent for all cases (FP NFP and CH) for all three states separately and the three-state aggregatedstudy area CY is a significant covariate in the model for all of these cases Additional models wererun with control variables These full model results are presented in the Appendix A and confirm theusefulness of fire as predictor

An inspection of the pseudo-likelihood estimates for the aggregated study area (Table 2 andAppendix A) indicates that for each unit increase in FIRE (intensity) the log of the ratio of p(CH)p(FP)increases by ~192 and the log of the ratio of p(CH)p(NFP) increases by ~02 In other words for eachunit increase in FIRE (intensity) in a given pixel (in Figure 2) the odds of that same pixel belonging tocategory CH (forest to non-forest change) rather than category FP (forest persistence in Figure 3) aremultiplied by ~67 Unit increases in FIRE also increase the odds of a pixel belonging to category CHrather than NFP (no forest persistence) by 122

For every increase in one unit of Fire the odds of a pixel belonging to category NFP instead of CHare multiplied by 082 For every increase in one unit of Fire the odds of a pixel belonging to categoryNFP instead of FP are multiplied by 559 For every increase in one unit of Fire the odds of a pixelbelonging to category FP instead of CH are multiplied by 015 (almost none)

For every increase in one unit of Fire the odds of a pixel belonging to category FP instead ofNFP are multiplied by 018 (almost none) Overall FIRE estimates are negative when predicting forestpersistence (FP) and positive when predicting CH

The calculated spatial lag (CY) terms are significant for all cases CY as mentioned earlier can beinterpreted as cohesiveness of land cover patches [61] Larger CY values correspond to more similarvalues among neighboring cells (ie a larger patches of a category) Estimates of the model for theaggregated peninsula indicate that a unit increase in CY decreases the log of p(FP)p(CH) by ~minus355while the log of p(FP)p(NFP) decreases by ~minus007 This finding indicates that persistent forestareas located in large patches are very likely to remain forest (34 times more than CH) (Table 2 and

Land 2017 6 61 12 of 19

Appendix A) FP is also 107 times more likely than NFP In general CH has a negative relationship withCY This relationship can be attributed to CH occurring more often in isolated pixels corresponding tofragmented patches Conversely FP and NFP occur in larger continuous areas (Figure 3)

43 Comparison of Fire by Anthromes

Boxplots of mean fire frequency by anthromes groups suggest that fire can be used to distinguishamong anthromes groups thereby serving as an additional potential variable to examine humanimprints in the context of the Yucataacuten region (Figure 6) The croplands anthromes group has a higherfire frequency on average compared to most other anthromes categories We note that rangelandsdisplay a very large variance and thus may be difficult to distinguish from croplands and villagesFiner anthropogenic categories within the cropland groups also appear to be contrasted by the firefrequency variable (see boxplots Figure 7)

Land 2017 6 61 12 of 19

corresponding to fragmented patches Conversely FP and NFP occur in larger continuous areas (Figure 3)

43 Comparison of Fire by Anthromes

Boxplots of mean fire frequency by anthromes groups suggest that fire can be used to distinguish among anthromes groups thereby serving as an additional potential variable to examine human imprints in the context of the Yucataacuten region (Figure 6) The croplands anthromes group has a higher fire frequency on average compared to most other anthromes categories We note that rangelands display a very large variance and thus may be difficult to distinguish from croplands and villages Finer anthropogenic categories within the cropland groups also appear to be contrasted by the fire frequency variable (see boxplots Figure 7)

Tukey pairwise comparison tests between anthromes groups (applied to the negative binomial model Table 3) highlight that six and seven pairwise comparisons are significantly different at 5 and 10 level respectively Coefficients indicate relative increase or decrease of the expected log of fire frequency for categorical change in relation to the reference variable For instance there is a minus137 decrease in the log of fire frequency when an observation is found in the dense settlements rather than in croplands We find that fire frequency variable is useful to differentiate croplands with almost all categories with the exception of Villages and Rangelands Both overlap substantially on the boxplots (Figure 7)

Figure 7 Between group comparison Fire frequency by anthrome groups boxplots (left) Within group comparison Fire frequency boxplots within cropland anthrome (right)

Table 3 Between-anthromes Tukey pairwise comparison for the negative binomial models with fire count and anthromes groups Note that the reference variable is in italic

Pairwise Comparison Coefficients Standard Error t-Stat p-ValuesDense settlementsndashCroplands minus138688 043059 minus32209 00121

ForestedndashCroplands minus092198 006997 minus131762 0 RangelandsndashCroplands minus035406 026321 minus13452 07146

VillagesndashCroplands minus028199 032807 minus08595 09435 WildlandsndashCroplands minus229463 019565 minus117283 0

ForestedndashDense settlements 046491 042934 10828 08616 RangelandsndashDense settlements 103282 049872 20709 02552

VillagesndashDense settlements 110489 053579 20622 02593 WildlandsndashDense settlements minus090775 04666 minus19454 03214

RangelandsndashForested 056791 026118 21744 02076

Figure 7 Between group comparison Fire frequency by anthrome groups boxplots (left) Within groupcomparison Fire frequency boxplots within cropland anthrome (right)

Tukey pairwise comparison tests between anthromes groups (applied to the negative binomialmodel Table 3) highlight that six and seven pairwise comparisons are significantly different at 5 and10 level respectively Coefficients indicate relative increase or decrease of the expected log of firefrequency for categorical change in relation to the reference variable For instance there is a minus137decrease in the log of fire frequency when an observation is found in the dense settlements rather thanin croplands We find that fire frequency variable is useful to differentiate croplands with almost allcategories with the exception of Villages and Rangelands Both overlap substantially on the boxplots(Figure 7)

Tukey comparisons were also performed for fire frequency within the cropland anthromes groupto assess the potential of using fire frequency for finer definition of the human imprint of landscapeWe found that within croplands two out 10 and four out of 10 comparison results in significantdifferences in the log of fire frequency (Table 4) at 5 and 10 percent significance level respectivelyThis suggests that fire frequency is less useful at distinguishing within the cropland anthromes Thestrongest contrasts are found between ldquoresidential rainfed mosaicsndashremote croplands mosaicrdquo andbetween ldquoresidential irrigated croplandndashremote croplandsrdquo Both indicate decreases in the log offire frequency for locations that are found in residential rainfed and irrigated cropland compared toremote croplands

Land 2017 6 61 13 of 19

Table 3 Between-anthromes Tukey pairwise comparison for the negative binomial models with firecount and anthromes groups Note that the reference variable is in italic

Pairwise Comparison Coefficients Standard Error t-Stat p-Values

Dense settlementsndashCroplands minus138688 043059 minus32209 00121ForestedndashCroplands minus092198 006997 minus131762 0

RangelandsndashCroplands minus035406 026321 minus13452 07146VillagesndashCroplands minus028199 032807 minus08595 09435

WildlandsndashCroplands minus229463 019565 minus117283 0ForestedndashDense settlements 046491 042934 10828 08616

RangelandsndashDense settlements 103282 049872 20709 02552VillagesndashDense settlements 110489 053579 20622 02593

WildlandsndashDense settlements minus090775 04666 minus19454 03214RangelandsndashForested 056791 026118 21744 02076

VillagesndashForested 063999 032644 19605 03129WildlandsndashForested minus137266 01929 minus71159 0VillagesndashRangelands 007207 041346 01743 1

WildlandsndashRangelands minus194057 031874 minus60882 0WildlandsndashVillages minus201264 037409 minus53801 0

Table 4 Within-anthrome Tukey pairwise comparisons using the negative binomial models with firecount and anthromes croplands categories Note that the reference variable is in italic

PairwisendashComparison Coefficients Standard Error t-Stat p-Values

Populated rainfed croplandndashPopulated irrigated cropland 025239 022555 1119 07646Remote croplandsndashPopulated irrigated cropland 0572 025835 2214 01453

Residential irrigated croplandndashPopulated irrigated cropland minus061118 041094 minus14873 05244Residential rainfed mosaicndashPopulated irrigated cropland 008091 022337 03622 09955

Remote croplandsndashPopulated rainfed cropland 031961 014756 2166 01615Residential irrigated croplandndashPopulated rainfed cropland minus086357 0352 minus24533 00827

Residential rainfed mosaicndashPopulated rainfed cropland minus017148 007017 minus24437 00848Residential irrigated croplandndashRemote croplands minus118318 037387 minus31647 00105

Residential rainfed mosaicndashRemote croplands minus049109 014421 minus34054 00043Residential rainfed mosaicndashResidential irrigated cropland 069209 035061 1974 02396

5 Discussion and Conclusions

Analysis of the spatial patterns of fire in the Yucataacuten using fire data visually reproduces thegeography of human land-based activities during 2000ndash2010 including the influence of roadssettlements and natural protected areas The intra-annual temporal dimensions of fire dataapproximate key moments of seasonal agriculture and other land-based activities (Figure 4) Thesefindings are consistent with studies finding higher fire frequencies in the proximity to roads andsettlements region [40] and with research about fire and deforestation in other tropical settings(eg [2862ndash64]) and more generally about the relationship between land change road developmentand market accessibility [53546465]

The multinomial model confirms the significance of fire intensity (defined as count of fire flaggedpixels over time) and landscape configuration (represented by the spatial lag variable CY) for thepeninsula for all three types of land changepersistence outcomes Notably all change is stronglyaffected by the presence of fire The odds of a forested area becoming non-forested multiply by sixin the presence of fire This is not surprising given that the cross-tabulation analysis showed thatnearly 87 of pixels that changed from 2000 to 2007 had been flagged as fire by MODIS at some pointThe dominance of no-fire observations over fire occurrence the (pseudo) absence of fire makes for abetter predictor of forest persistence than fire occurrence per se especially for large patches (high CYvalues) Predicting non-forest persistence proved more difficult signaling the diversity of ecologicaland land use practices and transitions between them that define the NFP category as discussed in thedata section What exactly accounts for the remaining 13 is difficult to determine We can speculate

Land 2017 6 61 14 of 19

however that possible factors include data error and accuracy mismatches As some have notedMODIS products do omit fires for various reasons [40] We can also speculate on some detected firesbeing non-agricultural Finally we can also imagine some fires starting as agricultural burns butbecoming large multiday forest fires as they grow out of control [40]

Fire also proves to be a reasonable indicator to distinguish between anthromes groups (Figure 7)but less among finer anthromes categories Our analysis shows that for example with the aidof a fire frequency croplands are separable from the rest of categories and that dense settlementsare clearly distinct from villages Other categories like rangeland prove more difficult to separatesince they present larger variance Some within-variation within anthropogenic categories is alsodistinguishable For example populated irrigated is clearly separable from populated rainfed andfrom remote croplands These two former categories however are not as separable from each otherwith the aid of fire frequency alone

Perhaps some insight about differences distinguishing between- and within-anthropogeniclandscapes can be gained by looking into the distinction between quemas (legally regulated agriculturalfires) from incendios (large escape non-regulated forest fires) Both can be addressed through the use ofMODIS active fire data but cannot be thoroughly distinguished with these data alone Within-variationexists in both categories On the one hand quemas can be due to subsistence and commercial agriculturesuch as sugar cane cultivation along the border with Belize (ie either rain fed or irrigated anthromecategories) or Mennonite corn fields in Bacalar( ie the populated irrigated anthrome category) astheir spatial and temporal signatures can differ quite noticeably (Figures 2 and 4) On the other handincendios can be truly accidental or be the result of purposeful burning with nonagricultural goals(eg forcing land zoning code changes for urban development hunting practices) Future researchshould exploit these differences in order to account for a more nuanced description of the relationshipsbetween fire and human-induced land change in the region

We conclude that in subtropical forest settings in which burning is a fundamental landscape toolfire is a reasonable proxy for land change Use of fire data improves the estimation of land change andexpands our understanding of human-environment relationships that produce complex mosaics ofhighly dynamic landscapes such as those in the Mexican Yucataacuten

Acknowledgments This study was part of the SYPR (httpsyprasuedu) and EDGY (httplandchangerutgersedu) projects SYPR received support from the NASA LCLUC program (NAG-56046 511134 and 6GD98G)and the NSF BCS program (0410016) EDGY was sponsored by the Gordon and Betty Moore Foundation underGrant 1697 The authors thank Drs Birgit Schmook (El Colegio de la Frontera Sur) Laura Schneider (RutgersUniversity) and Zachary Christman (Rowan University) for their support and advice The staff of Clark Labsfacilitated the work by creating and maintaining the Idrisireg software (httpwwwclarklabsorg) with whichpreliminary analysis was performed Subsequent and final analysis was performed with R packages NNetMASS multcomp and raster

Author Contributions Marco Millones John Rogan BL Turner II conceived and designed the original researchand fieldwork Marco Millones performed the fieldwork Marco Millones performed preliminary data analysiswith Daniel A Griffith Robert Clay Harris and Benoit Parmentier executed the final data analysis John RoganBL Turner II revised earlier versions of the manuscript Marco Millones Benoit Parmentier and Robert Clay Harriswrote the paper John Rogan revised the manuscript

Conflicts of Interest The authors declare no conflicts of interest

Land 2017 6 61 8 of 19

three possible outcomes that are categoricalnominal in nature [55ndash57] To account for the positivespatial autocorrelation present in remotely sensed data [5859] spatial lags variables based on rook-caseadjacency were calculated This was done by generating for each observation the average sum of itsneighbors of the same class (CFP CNFP and CCH) and including the lag variable in the model (seeEquation (1)) [5960] Lag values range from 0 (no like neighbors) to 1 (all four like neighbors) whileaverage Moranrsquos I values range from virtually random for CCH (00035) to weak-moderate positivefor CNFP (0392) and CFP (0391) In this particular case spatial lags also serve as an indicator oflandscape configuration and heterogeneity (ie similar to patch size and cohesion)

Pseudo-likelihood estimates were calculated for the main effects and spatial lag parameters of themultinomial model as follows (Equation (1))

Log(πhijπhir) = αj + xprimehi βj (1)

where πhij is the probability that a pixel h in the map of any class i for which fire has been detected willbecome one of land changepersistence category j (FP NFP or CH) j 6= r with land changepersistencecategory r being the reference category There are separate sets of intercept parameters αj and regressionparameters βj for each of the logit models The matrix xprimehi is the set of explanatory variables spatiallag (CY) fire (FIRE) and the commonly used control variables described Two logits equations aremodeled for each FIRE and CY population the logit comparing non-forest persistence (NFP) to forestpersistence (FP) and the logit comparing change (CH) to forest persistence (FP) [56]

35 Fire Frequency and Anthromes Characterization

Anthromes map datasets were processed to match them to the study area and temporal firecount data were aggregated to generate a fire frequency variable (Figure 6) In order to explore theassociation between fire counts and anthrome groups graphically we used boxplots of mean firefrequency by each category present in the study area dense settlements villages (in effect village andsurrounding areas) croplands rangelands forested wildlands We measured the differences in meanfire frequency across anthromes using a negative binomial model and a Tukey pairwise comparisonA binomial model was preferred over Poisson model because the overall (as well as per category) meanand variance are noticeably different (by a factor 100) which suggests over-dispersion in the Poissonparameter We also conducted Tukey comparisons for fire frequency within the cropland anthromesgroup to assess the potential of using fire count for finer definition of the human imprint of landscape

Land 2017 6 61 8 of 19

average sum of its neighbors of the same class (CFP CNFP and CCH) and including the lag variable in the model (see Equation (1)) [5960] Lag values range from 0 (no like neighbors) to 1 (all four like neighbors) while average Moranrsquos I values range from virtually random for CCH (00035) to weak-moderate positive for CNFP (0392) and CFP (0391) In this particular case spatial lags also serve as an indicator of landscape configuration and heterogeneity (ie similar to patch size and cohesion)

Pseudo-likelihood estimates were calculated for the main effects and spatial lag parameters of the multinomial model as follows (Equation (1))

Log(πhijπhir) = αj + xprimehi βj (1)

where πhij is the probability that a pixel h in the map of any class i for which fire has been detected will become one of land changepersistence category j (FP NFP or CH) j ne r with land changepersistence category r being the reference category There are separate sets of intercept parameters αj and regression parameters βj for each of the logit models The matrix xprimehi is the set of explanatory variables spatial lag (CY) fire (FIRE) and the commonly used control variables described Two logits equations are modeled for each FIRE and CY population the logit comparing non-forest persistence (NFP) to forest persistence (FP) and the logit comparing change (CH) to forest persistence (FP) [56]

35 Fire Frequency and Anthromes Characterization

Anthromes map datasets were processed to match them to the study area and temporal fire count data were aggregated to generate a fire frequency variable (Figure 6) In order to explore the association between fire counts and anthrome groups graphically we used boxplots of mean fire frequency by each category present in the study area dense settlements villages (in effect village and surrounding areas) croplands rangelands forested wildlands We measured the differences in mean fire frequency across anthromes using a negative binomial model and a Tukey pairwise comparison A binomial model was preferred over Poisson model because the overall (as well as per category) mean and variance are noticeably different (by a factor 100) which suggests over-dispersion in the Poisson parameter We also conducted Tukey comparisons for fire frequency within the cropland anthromes group to assess the potential of using fire count for finer definition of the human imprint of landscape

For the data processing we used the raster (version 25-8) sp (version 12-4) and rgdal (version 12-7) packages to perform some of the preprocessing for the spatial inputs The raster package was also used for aggregation of the fire occurrences cropping and reclassification of anthromes data We used the implementation of multinomial model in the R ldquonnetrdquo package (version 73-12) for analyses We also ran the negative binomial model using the ldquoMASSrdquo package (version 73-12) in R version 34 and used the glht method from the multcomp R package (14-6) to perform the Tukey comparison

Figure 6 Fire frequency aggregation for anthrome comparison (left) and Anthrome groups (right)

Figure 6 Fire frequency aggregation for anthrome comparison (left) and Anthrome groups (right)

For the data processing we used the raster (version 25-8) sp (version 12-4) and rgdal(version 12-7) packages to perform some of the preprocessing for the spatial inputs The raster packagewas also used for aggregation of the fire occurrences cropping and reclassification of anthromes

Land 2017 6 61 9 of 19

data We used the implementation of multinomial model in the R ldquonnetrdquo package (version 73-12)for analyses We also ran the negative binomial model using the ldquoMASSrdquo package (version 73-12)in R version 34 and used the glht method from the multcomp R package (14-6) to perform theTukey comparison

4 Results

41 Spatio-Temporal Patterns of Fire and Land Change

As a proxy indicator of human land use fire frequency can be interpreted as a quantitativemeasure of ldquodensityrdquo (in space and time) of land use in this case It corresponds to how actively ldquousedrdquoor ldquounder-usedrdquo a 1 km parcel of land is in relation to the types of land use that require burning(eg high for pasture and cultivation land)

Fire occurrence for the period 2000ndash2010 presents a distinct non-random spatial pattern across thestudy area (Moranrsquos I = 062) (Figure 2) The individual observations presenting the highest detectionfrequencies (gt3 per year) appear in spatial clusters and are concentrated in the northern and westernsection of the Peninsula in the states of Campeche and the Yucataacuten Quintana Roo has comparativelyfewer and less clustering fire detections Areas with less fire frequency are observed in Campeche andQuintana Roo especially in the presence of federal and state run natural protected areas (eg SianKarsquoan and Calakmul bioreserves) (Figure 1) and in locations where road and settlement density is lowThis road-settlement-fire co-location is more explicit in the Yucataacuten and northern Campeche and lessso in southern Campeche where road density decreases

Locations affected by fire (Figure 5 and Table 1) cover roughly 45 of the study area More thanhalf of the fire occurrences concentrate in NFP areas followed by 40 of FP and 2 in CH areas(1 of the total) Locations with no fire occurrence cover more than 50 of the study area No-fireoccurrences are two times more common in FP than in NFP and they are minimally present in CHareas Land changepersistence figures (total rows percentage in Table 1) indicate that roughly 23 ofthe FP shows no fire detections whereas 60 of NFP presents fire occurrence CH shows 86 of itsarea as having burned at some time (although it is hardly visible in Figure 5 because CH covers only1 of the total area)

Land 2017 6 61 10 of 19

Table 1 Cross-tabulation of fire occurrence and land changepersistence row column and total percentages per class Preliminary interpretation matrix(extendeddetailed legend for Figure 5)

Fire No Fire Row Total Total Study Area

Forest Persistence

293-Error resulting from database mismatch-Error of commission in MODIS ActiveFire product-Error induced by aggregation of landcover data

707-Core areas of mature forest that have persisted for at least 17years (1990ndash2007)-Protected areas with a predominance of mature forest-Areas of planned selective forest extraction that have not beenextracted in 17 years or longer (under rotation management)

100 54

Non Forest Persistence

608-Areas where fire is used to convert fromnon-forest vegetation land covers toother non-forest vegetation land covers(eg agriculture to urban)-Areas of active non-forest land-uses-Error resulting from databasemismatches

3918-Areas under intensive land-uses that do not require land clearingfor prolonged periods (eg citrus agriculture urban)-Secondary vegetation of at least 10 years including forest notconsidered mature by CAB 2009 This can include forest regrowth(forest transition)-Forested areas of forest communities that have been extracted inthe last 10 years and are growing back-Seasonal agricultural areas currently fallow (eg milpa)

100 43

Change (Forest toNon-Forest)

860-All land cover changes (conversion andsome modification) preceded by landclearing by fire (ie deforestation)-Core forest areas that are heavilydeforested with more intense use of landclearing by fire

137-Error of omission in MODIS Active Fire product-Error resulting from database mismatches-Land changes that do not require fire-Fringe areas that are cleared without fire after the core area hasbeen cleared with fire-Fringe areas that are cleared with low intensity fire that is notdetected by MODIS Active Fire product

100 1

Column TOTAL 45 36 100 100

Land 2017 6 61 11 of 19

42 Effect of Fire and Patch Size on Land ChangePersistence A Spatial Multinomial Logit Model

Results from the spatial multinomial logit model agree with the analysis presented above(Section 41) and indicate that past fire occurrence (pre-2007) is a useful predictor of land changepersistence categories The resulting equations and model statistics are summarized in Table 2 and inthe supplementary Appendix A The Akaike information criterion (AIC) indicates that the model withcovariates (intercept + fire and lag + control variables) performs better than alternative models (seeAppendix A) The likelihood ratio (LR) has two degrees of freedom and is significant which confirmsthat at least one of the variables in the model improves the model description

Table 2 Spatial multinomial logit model summary of trends FP = forest persistence NFP = non forestpersistence CH = change INTE = Intercept Odds = Odds ratio effects point estimates This tablecontains only FIRE and CY variables the full variable list is available in the Appendix A

CAT REF INTE CY FIRE Odds CY Odds FIRE

CH (3) FP (1) minus467 minus355 192 003 679NFP (2) minus607 minus346 020 003 122

CH Average minus537 minus350 106 003 400

FP (1) CH (3) 467 355 minus192 3466 015NFP (2) minus438 007 minus172 107 018

FP Average 015 181 minus182 1787 016

NFP (2) CH (3) 905 348 minus020 3243 082FP (1) 438 minus007 172 094 559

FP Average 671 171 076 1668 320

The maximum pseudo-likelihood and odds ratio point estimates (Table 2 and Appendix A) showthe effect and relative importance of FIRE and CY for each land changepersistence outcome in themodel At a 5 level the difference between FIRE = 1 (fire occurrence) and FIRE = 0 is statisticallydifferent for all cases (FP NFP and CH) for all three states separately and the three-state aggregatedstudy area CY is a significant covariate in the model for all of these cases Additional models wererun with control variables These full model results are presented in the Appendix A and confirm theusefulness of fire as predictor

An inspection of the pseudo-likelihood estimates for the aggregated study area (Table 2 andAppendix A) indicates that for each unit increase in FIRE (intensity) the log of the ratio of p(CH)p(FP)increases by ~192 and the log of the ratio of p(CH)p(NFP) increases by ~02 In other words for eachunit increase in FIRE (intensity) in a given pixel (in Figure 2) the odds of that same pixel belonging tocategory CH (forest to non-forest change) rather than category FP (forest persistence in Figure 3) aremultiplied by ~67 Unit increases in FIRE also increase the odds of a pixel belonging to category CHrather than NFP (no forest persistence) by 122

For every increase in one unit of Fire the odds of a pixel belonging to category NFP instead of CHare multiplied by 082 For every increase in one unit of Fire the odds of a pixel belonging to categoryNFP instead of FP are multiplied by 559 For every increase in one unit of Fire the odds of a pixelbelonging to category FP instead of CH are multiplied by 015 (almost none)

For every increase in one unit of Fire the odds of a pixel belonging to category FP instead ofNFP are multiplied by 018 (almost none) Overall FIRE estimates are negative when predicting forestpersistence (FP) and positive when predicting CH

The calculated spatial lag (CY) terms are significant for all cases CY as mentioned earlier can beinterpreted as cohesiveness of land cover patches [61] Larger CY values correspond to more similarvalues among neighboring cells (ie a larger patches of a category) Estimates of the model for theaggregated peninsula indicate that a unit increase in CY decreases the log of p(FP)p(CH) by ~minus355while the log of p(FP)p(NFP) decreases by ~minus007 This finding indicates that persistent forestareas located in large patches are very likely to remain forest (34 times more than CH) (Table 2 and

Land 2017 6 61 12 of 19

Appendix A) FP is also 107 times more likely than NFP In general CH has a negative relationship withCY This relationship can be attributed to CH occurring more often in isolated pixels corresponding tofragmented patches Conversely FP and NFP occur in larger continuous areas (Figure 3)

43 Comparison of Fire by Anthromes

Boxplots of mean fire frequency by anthromes groups suggest that fire can be used to distinguishamong anthromes groups thereby serving as an additional potential variable to examine humanimprints in the context of the Yucataacuten region (Figure 6) The croplands anthromes group has a higherfire frequency on average compared to most other anthromes categories We note that rangelandsdisplay a very large variance and thus may be difficult to distinguish from croplands and villagesFiner anthropogenic categories within the cropland groups also appear to be contrasted by the firefrequency variable (see boxplots Figure 7)

Land 2017 6 61 12 of 19

corresponding to fragmented patches Conversely FP and NFP occur in larger continuous areas (Figure 3)

43 Comparison of Fire by Anthromes

Boxplots of mean fire frequency by anthromes groups suggest that fire can be used to distinguish among anthromes groups thereby serving as an additional potential variable to examine human imprints in the context of the Yucataacuten region (Figure 6) The croplands anthromes group has a higher fire frequency on average compared to most other anthromes categories We note that rangelands display a very large variance and thus may be difficult to distinguish from croplands and villages Finer anthropogenic categories within the cropland groups also appear to be contrasted by the fire frequency variable (see boxplots Figure 7)

Tukey pairwise comparison tests between anthromes groups (applied to the negative binomial model Table 3) highlight that six and seven pairwise comparisons are significantly different at 5 and 10 level respectively Coefficients indicate relative increase or decrease of the expected log of fire frequency for categorical change in relation to the reference variable For instance there is a minus137 decrease in the log of fire frequency when an observation is found in the dense settlements rather than in croplands We find that fire frequency variable is useful to differentiate croplands with almost all categories with the exception of Villages and Rangelands Both overlap substantially on the boxplots (Figure 7)

Figure 7 Between group comparison Fire frequency by anthrome groups boxplots (left) Within group comparison Fire frequency boxplots within cropland anthrome (right)

Table 3 Between-anthromes Tukey pairwise comparison for the negative binomial models with fire count and anthromes groups Note that the reference variable is in italic

Pairwise Comparison Coefficients Standard Error t-Stat p-ValuesDense settlementsndashCroplands minus138688 043059 minus32209 00121

ForestedndashCroplands minus092198 006997 minus131762 0 RangelandsndashCroplands minus035406 026321 minus13452 07146

VillagesndashCroplands minus028199 032807 minus08595 09435 WildlandsndashCroplands minus229463 019565 minus117283 0

ForestedndashDense settlements 046491 042934 10828 08616 RangelandsndashDense settlements 103282 049872 20709 02552

VillagesndashDense settlements 110489 053579 20622 02593 WildlandsndashDense settlements minus090775 04666 minus19454 03214

RangelandsndashForested 056791 026118 21744 02076

Figure 7 Between group comparison Fire frequency by anthrome groups boxplots (left) Within groupcomparison Fire frequency boxplots within cropland anthrome (right)

Tukey pairwise comparison tests between anthromes groups (applied to the negative binomialmodel Table 3) highlight that six and seven pairwise comparisons are significantly different at 5 and10 level respectively Coefficients indicate relative increase or decrease of the expected log of firefrequency for categorical change in relation to the reference variable For instance there is a minus137decrease in the log of fire frequency when an observation is found in the dense settlements rather thanin croplands We find that fire frequency variable is useful to differentiate croplands with almost allcategories with the exception of Villages and Rangelands Both overlap substantially on the boxplots(Figure 7)

Tukey comparisons were also performed for fire frequency within the cropland anthromes groupto assess the potential of using fire frequency for finer definition of the human imprint of landscapeWe found that within croplands two out 10 and four out of 10 comparison results in significantdifferences in the log of fire frequency (Table 4) at 5 and 10 percent significance level respectivelyThis suggests that fire frequency is less useful at distinguishing within the cropland anthromes Thestrongest contrasts are found between ldquoresidential rainfed mosaicsndashremote croplands mosaicrdquo andbetween ldquoresidential irrigated croplandndashremote croplandsrdquo Both indicate decreases in the log offire frequency for locations that are found in residential rainfed and irrigated cropland compared toremote croplands

Land 2017 6 61 13 of 19

Table 3 Between-anthromes Tukey pairwise comparison for the negative binomial models with firecount and anthromes groups Note that the reference variable is in italic

Pairwise Comparison Coefficients Standard Error t-Stat p-Values

Dense settlementsndashCroplands minus138688 043059 minus32209 00121ForestedndashCroplands minus092198 006997 minus131762 0

RangelandsndashCroplands minus035406 026321 minus13452 07146VillagesndashCroplands minus028199 032807 minus08595 09435

WildlandsndashCroplands minus229463 019565 minus117283 0ForestedndashDense settlements 046491 042934 10828 08616

RangelandsndashDense settlements 103282 049872 20709 02552VillagesndashDense settlements 110489 053579 20622 02593

WildlandsndashDense settlements minus090775 04666 minus19454 03214RangelandsndashForested 056791 026118 21744 02076

VillagesndashForested 063999 032644 19605 03129WildlandsndashForested minus137266 01929 minus71159 0VillagesndashRangelands 007207 041346 01743 1

WildlandsndashRangelands minus194057 031874 minus60882 0WildlandsndashVillages minus201264 037409 minus53801 0

Table 4 Within-anthrome Tukey pairwise comparisons using the negative binomial models with firecount and anthromes croplands categories Note that the reference variable is in italic

PairwisendashComparison Coefficients Standard Error t-Stat p-Values

Populated rainfed croplandndashPopulated irrigated cropland 025239 022555 1119 07646Remote croplandsndashPopulated irrigated cropland 0572 025835 2214 01453

Residential irrigated croplandndashPopulated irrigated cropland minus061118 041094 minus14873 05244Residential rainfed mosaicndashPopulated irrigated cropland 008091 022337 03622 09955

Remote croplandsndashPopulated rainfed cropland 031961 014756 2166 01615Residential irrigated croplandndashPopulated rainfed cropland minus086357 0352 minus24533 00827

Residential rainfed mosaicndashPopulated rainfed cropland minus017148 007017 minus24437 00848Residential irrigated croplandndashRemote croplands minus118318 037387 minus31647 00105

Residential rainfed mosaicndashRemote croplands minus049109 014421 minus34054 00043Residential rainfed mosaicndashResidential irrigated cropland 069209 035061 1974 02396

5 Discussion and Conclusions

Analysis of the spatial patterns of fire in the Yucataacuten using fire data visually reproduces thegeography of human land-based activities during 2000ndash2010 including the influence of roadssettlements and natural protected areas The intra-annual temporal dimensions of fire dataapproximate key moments of seasonal agriculture and other land-based activities (Figure 4) Thesefindings are consistent with studies finding higher fire frequencies in the proximity to roads andsettlements region [40] and with research about fire and deforestation in other tropical settings(eg [2862ndash64]) and more generally about the relationship between land change road developmentand market accessibility [53546465]

The multinomial model confirms the significance of fire intensity (defined as count of fire flaggedpixels over time) and landscape configuration (represented by the spatial lag variable CY) for thepeninsula for all three types of land changepersistence outcomes Notably all change is stronglyaffected by the presence of fire The odds of a forested area becoming non-forested multiply by sixin the presence of fire This is not surprising given that the cross-tabulation analysis showed thatnearly 87 of pixels that changed from 2000 to 2007 had been flagged as fire by MODIS at some pointThe dominance of no-fire observations over fire occurrence the (pseudo) absence of fire makes for abetter predictor of forest persistence than fire occurrence per se especially for large patches (high CYvalues) Predicting non-forest persistence proved more difficult signaling the diversity of ecologicaland land use practices and transitions between them that define the NFP category as discussed in thedata section What exactly accounts for the remaining 13 is difficult to determine We can speculate

Land 2017 6 61 14 of 19

however that possible factors include data error and accuracy mismatches As some have notedMODIS products do omit fires for various reasons [40] We can also speculate on some detected firesbeing non-agricultural Finally we can also imagine some fires starting as agricultural burns butbecoming large multiday forest fires as they grow out of control [40]

Fire also proves to be a reasonable indicator to distinguish between anthromes groups (Figure 7)but less among finer anthromes categories Our analysis shows that for example with the aidof a fire frequency croplands are separable from the rest of categories and that dense settlementsare clearly distinct from villages Other categories like rangeland prove more difficult to separatesince they present larger variance Some within-variation within anthropogenic categories is alsodistinguishable For example populated irrigated is clearly separable from populated rainfed andfrom remote croplands These two former categories however are not as separable from each otherwith the aid of fire frequency alone

Perhaps some insight about differences distinguishing between- and within-anthropogeniclandscapes can be gained by looking into the distinction between quemas (legally regulated agriculturalfires) from incendios (large escape non-regulated forest fires) Both can be addressed through the use ofMODIS active fire data but cannot be thoroughly distinguished with these data alone Within-variationexists in both categories On the one hand quemas can be due to subsistence and commercial agriculturesuch as sugar cane cultivation along the border with Belize (ie either rain fed or irrigated anthromecategories) or Mennonite corn fields in Bacalar( ie the populated irrigated anthrome category) astheir spatial and temporal signatures can differ quite noticeably (Figures 2 and 4) On the other handincendios can be truly accidental or be the result of purposeful burning with nonagricultural goals(eg forcing land zoning code changes for urban development hunting practices) Future researchshould exploit these differences in order to account for a more nuanced description of the relationshipsbetween fire and human-induced land change in the region

We conclude that in subtropical forest settings in which burning is a fundamental landscape toolfire is a reasonable proxy for land change Use of fire data improves the estimation of land change andexpands our understanding of human-environment relationships that produce complex mosaics ofhighly dynamic landscapes such as those in the Mexican Yucataacuten

Acknowledgments This study was part of the SYPR (httpsyprasuedu) and EDGY (httplandchangerutgersedu) projects SYPR received support from the NASA LCLUC program (NAG-56046 511134 and 6GD98G)and the NSF BCS program (0410016) EDGY was sponsored by the Gordon and Betty Moore Foundation underGrant 1697 The authors thank Drs Birgit Schmook (El Colegio de la Frontera Sur) Laura Schneider (RutgersUniversity) and Zachary Christman (Rowan University) for their support and advice The staff of Clark Labsfacilitated the work by creating and maintaining the Idrisireg software (httpwwwclarklabsorg) with whichpreliminary analysis was performed Subsequent and final analysis was performed with R packages NNetMASS multcomp and raster

Author Contributions Marco Millones John Rogan BL Turner II conceived and designed the original researchand fieldwork Marco Millones performed the fieldwork Marco Millones performed preliminary data analysiswith Daniel A Griffith Robert Clay Harris and Benoit Parmentier executed the final data analysis John RoganBL Turner II revised earlier versions of the manuscript Marco Millones Benoit Parmentier and Robert Clay Harriswrote the paper John Rogan revised the manuscript

Conflicts of Interest The authors declare no conflicts of interest

Land 2017 6 61 9 of 19

data We used the implementation of multinomial model in the R ldquonnetrdquo package (version 73-12)for analyses We also ran the negative binomial model using the ldquoMASSrdquo package (version 73-12)in R version 34 and used the glht method from the multcomp R package (14-6) to perform theTukey comparison

4 Results

41 Spatio-Temporal Patterns of Fire and Land Change

As a proxy indicator of human land use fire frequency can be interpreted as a quantitativemeasure of ldquodensityrdquo (in space and time) of land use in this case It corresponds to how actively ldquousedrdquoor ldquounder-usedrdquo a 1 km parcel of land is in relation to the types of land use that require burning(eg high for pasture and cultivation land)

Fire occurrence for the period 2000ndash2010 presents a distinct non-random spatial pattern across thestudy area (Moranrsquos I = 062) (Figure 2) The individual observations presenting the highest detectionfrequencies (gt3 per year) appear in spatial clusters and are concentrated in the northern and westernsection of the Peninsula in the states of Campeche and the Yucataacuten Quintana Roo has comparativelyfewer and less clustering fire detections Areas with less fire frequency are observed in Campeche andQuintana Roo especially in the presence of federal and state run natural protected areas (eg SianKarsquoan and Calakmul bioreserves) (Figure 1) and in locations where road and settlement density is lowThis road-settlement-fire co-location is more explicit in the Yucataacuten and northern Campeche and lessso in southern Campeche where road density decreases

Locations affected by fire (Figure 5 and Table 1) cover roughly 45 of the study area More thanhalf of the fire occurrences concentrate in NFP areas followed by 40 of FP and 2 in CH areas(1 of the total) Locations with no fire occurrence cover more than 50 of the study area No-fireoccurrences are two times more common in FP than in NFP and they are minimally present in CHareas Land changepersistence figures (total rows percentage in Table 1) indicate that roughly 23 ofthe FP shows no fire detections whereas 60 of NFP presents fire occurrence CH shows 86 of itsarea as having burned at some time (although it is hardly visible in Figure 5 because CH covers only1 of the total area)

Land 2017 6 61 10 of 19

Table 1 Cross-tabulation of fire occurrence and land changepersistence row column and total percentages per class Preliminary interpretation matrix(extendeddetailed legend for Figure 5)

Fire No Fire Row Total Total Study Area

Forest Persistence

293-Error resulting from database mismatch-Error of commission in MODIS ActiveFire product-Error induced by aggregation of landcover data

707-Core areas of mature forest that have persisted for at least 17years (1990ndash2007)-Protected areas with a predominance of mature forest-Areas of planned selective forest extraction that have not beenextracted in 17 years or longer (under rotation management)

100 54

Non Forest Persistence

608-Areas where fire is used to convert fromnon-forest vegetation land covers toother non-forest vegetation land covers(eg agriculture to urban)-Areas of active non-forest land-uses-Error resulting from databasemismatches

3918-Areas under intensive land-uses that do not require land clearingfor prolonged periods (eg citrus agriculture urban)-Secondary vegetation of at least 10 years including forest notconsidered mature by CAB 2009 This can include forest regrowth(forest transition)-Forested areas of forest communities that have been extracted inthe last 10 years and are growing back-Seasonal agricultural areas currently fallow (eg milpa)

100 43

Change (Forest toNon-Forest)

860-All land cover changes (conversion andsome modification) preceded by landclearing by fire (ie deforestation)-Core forest areas that are heavilydeforested with more intense use of landclearing by fire

137-Error of omission in MODIS Active Fire product-Error resulting from database mismatches-Land changes that do not require fire-Fringe areas that are cleared without fire after the core area hasbeen cleared with fire-Fringe areas that are cleared with low intensity fire that is notdetected by MODIS Active Fire product

100 1

Column TOTAL 45 36 100 100

Land 2017 6 61 11 of 19

42 Effect of Fire and Patch Size on Land ChangePersistence A Spatial Multinomial Logit Model

Results from the spatial multinomial logit model agree with the analysis presented above(Section 41) and indicate that past fire occurrence (pre-2007) is a useful predictor of land changepersistence categories The resulting equations and model statistics are summarized in Table 2 and inthe supplementary Appendix A The Akaike information criterion (AIC) indicates that the model withcovariates (intercept + fire and lag + control variables) performs better than alternative models (seeAppendix A) The likelihood ratio (LR) has two degrees of freedom and is significant which confirmsthat at least one of the variables in the model improves the model description

Table 2 Spatial multinomial logit model summary of trends FP = forest persistence NFP = non forestpersistence CH = change INTE = Intercept Odds = Odds ratio effects point estimates This tablecontains only FIRE and CY variables the full variable list is available in the Appendix A

CAT REF INTE CY FIRE Odds CY Odds FIRE

CH (3) FP (1) minus467 minus355 192 003 679NFP (2) minus607 minus346 020 003 122

CH Average minus537 minus350 106 003 400

FP (1) CH (3) 467 355 minus192 3466 015NFP (2) minus438 007 minus172 107 018

FP Average 015 181 minus182 1787 016

NFP (2) CH (3) 905 348 minus020 3243 082FP (1) 438 minus007 172 094 559

FP Average 671 171 076 1668 320

The maximum pseudo-likelihood and odds ratio point estimates (Table 2 and Appendix A) showthe effect and relative importance of FIRE and CY for each land changepersistence outcome in themodel At a 5 level the difference between FIRE = 1 (fire occurrence) and FIRE = 0 is statisticallydifferent for all cases (FP NFP and CH) for all three states separately and the three-state aggregatedstudy area CY is a significant covariate in the model for all of these cases Additional models wererun with control variables These full model results are presented in the Appendix A and confirm theusefulness of fire as predictor

An inspection of the pseudo-likelihood estimates for the aggregated study area (Table 2 andAppendix A) indicates that for each unit increase in FIRE (intensity) the log of the ratio of p(CH)p(FP)increases by ~192 and the log of the ratio of p(CH)p(NFP) increases by ~02 In other words for eachunit increase in FIRE (intensity) in a given pixel (in Figure 2) the odds of that same pixel belonging tocategory CH (forest to non-forest change) rather than category FP (forest persistence in Figure 3) aremultiplied by ~67 Unit increases in FIRE also increase the odds of a pixel belonging to category CHrather than NFP (no forest persistence) by 122

For every increase in one unit of Fire the odds of a pixel belonging to category NFP instead of CHare multiplied by 082 For every increase in one unit of Fire the odds of a pixel belonging to categoryNFP instead of FP are multiplied by 559 For every increase in one unit of Fire the odds of a pixelbelonging to category FP instead of CH are multiplied by 015 (almost none)

For every increase in one unit of Fire the odds of a pixel belonging to category FP instead ofNFP are multiplied by 018 (almost none) Overall FIRE estimates are negative when predicting forestpersistence (FP) and positive when predicting CH

The calculated spatial lag (CY) terms are significant for all cases CY as mentioned earlier can beinterpreted as cohesiveness of land cover patches [61] Larger CY values correspond to more similarvalues among neighboring cells (ie a larger patches of a category) Estimates of the model for theaggregated peninsula indicate that a unit increase in CY decreases the log of p(FP)p(CH) by ~minus355while the log of p(FP)p(NFP) decreases by ~minus007 This finding indicates that persistent forestareas located in large patches are very likely to remain forest (34 times more than CH) (Table 2 and

Land 2017 6 61 12 of 19

Appendix A) FP is also 107 times more likely than NFP In general CH has a negative relationship withCY This relationship can be attributed to CH occurring more often in isolated pixels corresponding tofragmented patches Conversely FP and NFP occur in larger continuous areas (Figure 3)

43 Comparison of Fire by Anthromes

Boxplots of mean fire frequency by anthromes groups suggest that fire can be used to distinguishamong anthromes groups thereby serving as an additional potential variable to examine humanimprints in the context of the Yucataacuten region (Figure 6) The croplands anthromes group has a higherfire frequency on average compared to most other anthromes categories We note that rangelandsdisplay a very large variance and thus may be difficult to distinguish from croplands and villagesFiner anthropogenic categories within the cropland groups also appear to be contrasted by the firefrequency variable (see boxplots Figure 7)

Land 2017 6 61 12 of 19

corresponding to fragmented patches Conversely FP and NFP occur in larger continuous areas (Figure 3)

43 Comparison of Fire by Anthromes

Boxplots of mean fire frequency by anthromes groups suggest that fire can be used to distinguish among anthromes groups thereby serving as an additional potential variable to examine human imprints in the context of the Yucataacuten region (Figure 6) The croplands anthromes group has a higher fire frequency on average compared to most other anthromes categories We note that rangelands display a very large variance and thus may be difficult to distinguish from croplands and villages Finer anthropogenic categories within the cropland groups also appear to be contrasted by the fire frequency variable (see boxplots Figure 7)

Tukey pairwise comparison tests between anthromes groups (applied to the negative binomial model Table 3) highlight that six and seven pairwise comparisons are significantly different at 5 and 10 level respectively Coefficients indicate relative increase or decrease of the expected log of fire frequency for categorical change in relation to the reference variable For instance there is a minus137 decrease in the log of fire frequency when an observation is found in the dense settlements rather than in croplands We find that fire frequency variable is useful to differentiate croplands with almost all categories with the exception of Villages and Rangelands Both overlap substantially on the boxplots (Figure 7)

Figure 7 Between group comparison Fire frequency by anthrome groups boxplots (left) Within group comparison Fire frequency boxplots within cropland anthrome (right)

Table 3 Between-anthromes Tukey pairwise comparison for the negative binomial models with fire count and anthromes groups Note that the reference variable is in italic

Pairwise Comparison Coefficients Standard Error t-Stat p-ValuesDense settlementsndashCroplands minus138688 043059 minus32209 00121

ForestedndashCroplands minus092198 006997 minus131762 0 RangelandsndashCroplands minus035406 026321 minus13452 07146

VillagesndashCroplands minus028199 032807 minus08595 09435 WildlandsndashCroplands minus229463 019565 minus117283 0

ForestedndashDense settlements 046491 042934 10828 08616 RangelandsndashDense settlements 103282 049872 20709 02552

VillagesndashDense settlements 110489 053579 20622 02593 WildlandsndashDense settlements minus090775 04666 minus19454 03214

RangelandsndashForested 056791 026118 21744 02076

Figure 7 Between group comparison Fire frequency by anthrome groups boxplots (left) Within groupcomparison Fire frequency boxplots within cropland anthrome (right)

Tukey pairwise comparison tests between anthromes groups (applied to the negative binomialmodel Table 3) highlight that six and seven pairwise comparisons are significantly different at 5 and10 level respectively Coefficients indicate relative increase or decrease of the expected log of firefrequency for categorical change in relation to the reference variable For instance there is a minus137decrease in the log of fire frequency when an observation is found in the dense settlements rather thanin croplands We find that fire frequency variable is useful to differentiate croplands with almost allcategories with the exception of Villages and Rangelands Both overlap substantially on the boxplots(Figure 7)

Tukey comparisons were also performed for fire frequency within the cropland anthromes groupto assess the potential of using fire frequency for finer definition of the human imprint of landscapeWe found that within croplands two out 10 and four out of 10 comparison results in significantdifferences in the log of fire frequency (Table 4) at 5 and 10 percent significance level respectivelyThis suggests that fire frequency is less useful at distinguishing within the cropland anthromes Thestrongest contrasts are found between ldquoresidential rainfed mosaicsndashremote croplands mosaicrdquo andbetween ldquoresidential irrigated croplandndashremote croplandsrdquo Both indicate decreases in the log offire frequency for locations that are found in residential rainfed and irrigated cropland compared toremote croplands

Land 2017 6 61 13 of 19

Table 3 Between-anthromes Tukey pairwise comparison for the negative binomial models with firecount and anthromes groups Note that the reference variable is in italic

Pairwise Comparison Coefficients Standard Error t-Stat p-Values

Dense settlementsndashCroplands minus138688 043059 minus32209 00121ForestedndashCroplands minus092198 006997 minus131762 0

RangelandsndashCroplands minus035406 026321 minus13452 07146VillagesndashCroplands minus028199 032807 minus08595 09435

WildlandsndashCroplands minus229463 019565 minus117283 0ForestedndashDense settlements 046491 042934 10828 08616

RangelandsndashDense settlements 103282 049872 20709 02552VillagesndashDense settlements 110489 053579 20622 02593

WildlandsndashDense settlements minus090775 04666 minus19454 03214RangelandsndashForested 056791 026118 21744 02076

VillagesndashForested 063999 032644 19605 03129WildlandsndashForested minus137266 01929 minus71159 0VillagesndashRangelands 007207 041346 01743 1

WildlandsndashRangelands minus194057 031874 minus60882 0WildlandsndashVillages minus201264 037409 minus53801 0

Table 4 Within-anthrome Tukey pairwise comparisons using the negative binomial models with firecount and anthromes croplands categories Note that the reference variable is in italic

PairwisendashComparison Coefficients Standard Error t-Stat p-Values

Populated rainfed croplandndashPopulated irrigated cropland 025239 022555 1119 07646Remote croplandsndashPopulated irrigated cropland 0572 025835 2214 01453

Residential irrigated croplandndashPopulated irrigated cropland minus061118 041094 minus14873 05244Residential rainfed mosaicndashPopulated irrigated cropland 008091 022337 03622 09955

Remote croplandsndashPopulated rainfed cropland 031961 014756 2166 01615Residential irrigated croplandndashPopulated rainfed cropland minus086357 0352 minus24533 00827

Residential rainfed mosaicndashPopulated rainfed cropland minus017148 007017 minus24437 00848Residential irrigated croplandndashRemote croplands minus118318 037387 minus31647 00105

Residential rainfed mosaicndashRemote croplands minus049109 014421 minus34054 00043Residential rainfed mosaicndashResidential irrigated cropland 069209 035061 1974 02396

5 Discussion and Conclusions

Analysis of the spatial patterns of fire in the Yucataacuten using fire data visually reproduces thegeography of human land-based activities during 2000ndash2010 including the influence of roadssettlements and natural protected areas The intra-annual temporal dimensions of fire dataapproximate key moments of seasonal agriculture and other land-based activities (Figure 4) Thesefindings are consistent with studies finding higher fire frequencies in the proximity to roads andsettlements region [40] and with research about fire and deforestation in other tropical settings(eg [2862ndash64]) and more generally about the relationship between land change road developmentand market accessibility [53546465]

The multinomial model confirms the significance of fire intensity (defined as count of fire flaggedpixels over time) and landscape configuration (represented by the spatial lag variable CY) for thepeninsula for all three types of land changepersistence outcomes Notably all change is stronglyaffected by the presence of fire The odds of a forested area becoming non-forested multiply by sixin the presence of fire This is not surprising given that the cross-tabulation analysis showed thatnearly 87 of pixels that changed from 2000 to 2007 had been flagged as fire by MODIS at some pointThe dominance of no-fire observations over fire occurrence the (pseudo) absence of fire makes for abetter predictor of forest persistence than fire occurrence per se especially for large patches (high CYvalues) Predicting non-forest persistence proved more difficult signaling the diversity of ecologicaland land use practices and transitions between them that define the NFP category as discussed in thedata section What exactly accounts for the remaining 13 is difficult to determine We can speculate

Land 2017 6 61 14 of 19

however that possible factors include data error and accuracy mismatches As some have notedMODIS products do omit fires for various reasons [40] We can also speculate on some detected firesbeing non-agricultural Finally we can also imagine some fires starting as agricultural burns butbecoming large multiday forest fires as they grow out of control [40]

Fire also proves to be a reasonable indicator to distinguish between anthromes groups (Figure 7)but less among finer anthromes categories Our analysis shows that for example with the aidof a fire frequency croplands are separable from the rest of categories and that dense settlementsare clearly distinct from villages Other categories like rangeland prove more difficult to separatesince they present larger variance Some within-variation within anthropogenic categories is alsodistinguishable For example populated irrigated is clearly separable from populated rainfed andfrom remote croplands These two former categories however are not as separable from each otherwith the aid of fire frequency alone

Perhaps some insight about differences distinguishing between- and within-anthropogeniclandscapes can be gained by looking into the distinction between quemas (legally regulated agriculturalfires) from incendios (large escape non-regulated forest fires) Both can be addressed through the use ofMODIS active fire data but cannot be thoroughly distinguished with these data alone Within-variationexists in both categories On the one hand quemas can be due to subsistence and commercial agriculturesuch as sugar cane cultivation along the border with Belize (ie either rain fed or irrigated anthromecategories) or Mennonite corn fields in Bacalar( ie the populated irrigated anthrome category) astheir spatial and temporal signatures can differ quite noticeably (Figures 2 and 4) On the other handincendios can be truly accidental or be the result of purposeful burning with nonagricultural goals(eg forcing land zoning code changes for urban development hunting practices) Future researchshould exploit these differences in order to account for a more nuanced description of the relationshipsbetween fire and human-induced land change in the region

We conclude that in subtropical forest settings in which burning is a fundamental landscape toolfire is a reasonable proxy for land change Use of fire data improves the estimation of land change andexpands our understanding of human-environment relationships that produce complex mosaics ofhighly dynamic landscapes such as those in the Mexican Yucataacuten

Acknowledgments This study was part of the SYPR (httpsyprasuedu) and EDGY (httplandchangerutgersedu) projects SYPR received support from the NASA LCLUC program (NAG-56046 511134 and 6GD98G)and the NSF BCS program (0410016) EDGY was sponsored by the Gordon and Betty Moore Foundation underGrant 1697 The authors thank Drs Birgit Schmook (El Colegio de la Frontera Sur) Laura Schneider (RutgersUniversity) and Zachary Christman (Rowan University) for their support and advice The staff of Clark Labsfacilitated the work by creating and maintaining the Idrisireg software (httpwwwclarklabsorg) with whichpreliminary analysis was performed Subsequent and final analysis was performed with R packages NNetMASS multcomp and raster

Author Contributions Marco Millones John Rogan BL Turner II conceived and designed the original researchand fieldwork Marco Millones performed the fieldwork Marco Millones performed preliminary data analysiswith Daniel A Griffith Robert Clay Harris and Benoit Parmentier executed the final data analysis John RoganBL Turner II revised earlier versions of the manuscript Marco Millones Benoit Parmentier and Robert Clay Harriswrote the paper John Rogan revised the manuscript

Conflicts of Interest The authors declare no conflicts of interest

Land 2017 6 61 10 of 19

Table 1 Cross-tabulation of fire occurrence and land changepersistence row column and total percentages per class Preliminary interpretation matrix(extendeddetailed legend for Figure 5)

Fire No Fire Row Total Total Study Area

Forest Persistence

293-Error resulting from database mismatch-Error of commission in MODIS ActiveFire product-Error induced by aggregation of landcover data

707-Core areas of mature forest that have persisted for at least 17years (1990ndash2007)-Protected areas with a predominance of mature forest-Areas of planned selective forest extraction that have not beenextracted in 17 years or longer (under rotation management)

100 54

Non Forest Persistence

608-Areas where fire is used to convert fromnon-forest vegetation land covers toother non-forest vegetation land covers(eg agriculture to urban)-Areas of active non-forest land-uses-Error resulting from databasemismatches

3918-Areas under intensive land-uses that do not require land clearingfor prolonged periods (eg citrus agriculture urban)-Secondary vegetation of at least 10 years including forest notconsidered mature by CAB 2009 This can include forest regrowth(forest transition)-Forested areas of forest communities that have been extracted inthe last 10 years and are growing back-Seasonal agricultural areas currently fallow (eg milpa)

100 43

Change (Forest toNon-Forest)

860-All land cover changes (conversion andsome modification) preceded by landclearing by fire (ie deforestation)-Core forest areas that are heavilydeforested with more intense use of landclearing by fire

137-Error of omission in MODIS Active Fire product-Error resulting from database mismatches-Land changes that do not require fire-Fringe areas that are cleared without fire after the core area hasbeen cleared with fire-Fringe areas that are cleared with low intensity fire that is notdetected by MODIS Active Fire product

100 1

Column TOTAL 45 36 100 100

Land 2017 6 61 11 of 19

42 Effect of Fire and Patch Size on Land ChangePersistence A Spatial Multinomial Logit Model

Results from the spatial multinomial logit model agree with the analysis presented above(Section 41) and indicate that past fire occurrence (pre-2007) is a useful predictor of land changepersistence categories The resulting equations and model statistics are summarized in Table 2 and inthe supplementary Appendix A The Akaike information criterion (AIC) indicates that the model withcovariates (intercept + fire and lag + control variables) performs better than alternative models (seeAppendix A) The likelihood ratio (LR) has two degrees of freedom and is significant which confirmsthat at least one of the variables in the model improves the model description

Table 2 Spatial multinomial logit model summary of trends FP = forest persistence NFP = non forestpersistence CH = change INTE = Intercept Odds = Odds ratio effects point estimates This tablecontains only FIRE and CY variables the full variable list is available in the Appendix A

CAT REF INTE CY FIRE Odds CY Odds FIRE

CH (3) FP (1) minus467 minus355 192 003 679NFP (2) minus607 minus346 020 003 122

CH Average minus537 minus350 106 003 400

FP (1) CH (3) 467 355 minus192 3466 015NFP (2) minus438 007 minus172 107 018

FP Average 015 181 minus182 1787 016

NFP (2) CH (3) 905 348 minus020 3243 082FP (1) 438 minus007 172 094 559

FP Average 671 171 076 1668 320

The maximum pseudo-likelihood and odds ratio point estimates (Table 2 and Appendix A) showthe effect and relative importance of FIRE and CY for each land changepersistence outcome in themodel At a 5 level the difference between FIRE = 1 (fire occurrence) and FIRE = 0 is statisticallydifferent for all cases (FP NFP and CH) for all three states separately and the three-state aggregatedstudy area CY is a significant covariate in the model for all of these cases Additional models wererun with control variables These full model results are presented in the Appendix A and confirm theusefulness of fire as predictor

An inspection of the pseudo-likelihood estimates for the aggregated study area (Table 2 andAppendix A) indicates that for each unit increase in FIRE (intensity) the log of the ratio of p(CH)p(FP)increases by ~192 and the log of the ratio of p(CH)p(NFP) increases by ~02 In other words for eachunit increase in FIRE (intensity) in a given pixel (in Figure 2) the odds of that same pixel belonging tocategory CH (forest to non-forest change) rather than category FP (forest persistence in Figure 3) aremultiplied by ~67 Unit increases in FIRE also increase the odds of a pixel belonging to category CHrather than NFP (no forest persistence) by 122

For every increase in one unit of Fire the odds of a pixel belonging to category NFP instead of CHare multiplied by 082 For every increase in one unit of Fire the odds of a pixel belonging to categoryNFP instead of FP are multiplied by 559 For every increase in one unit of Fire the odds of a pixelbelonging to category FP instead of CH are multiplied by 015 (almost none)

For every increase in one unit of Fire the odds of a pixel belonging to category FP instead ofNFP are multiplied by 018 (almost none) Overall FIRE estimates are negative when predicting forestpersistence (FP) and positive when predicting CH

The calculated spatial lag (CY) terms are significant for all cases CY as mentioned earlier can beinterpreted as cohesiveness of land cover patches [61] Larger CY values correspond to more similarvalues among neighboring cells (ie a larger patches of a category) Estimates of the model for theaggregated peninsula indicate that a unit increase in CY decreases the log of p(FP)p(CH) by ~minus355while the log of p(FP)p(NFP) decreases by ~minus007 This finding indicates that persistent forestareas located in large patches are very likely to remain forest (34 times more than CH) (Table 2 and

Land 2017 6 61 12 of 19

Appendix A) FP is also 107 times more likely than NFP In general CH has a negative relationship withCY This relationship can be attributed to CH occurring more often in isolated pixels corresponding tofragmented patches Conversely FP and NFP occur in larger continuous areas (Figure 3)

43 Comparison of Fire by Anthromes

Boxplots of mean fire frequency by anthromes groups suggest that fire can be used to distinguishamong anthromes groups thereby serving as an additional potential variable to examine humanimprints in the context of the Yucataacuten region (Figure 6) The croplands anthromes group has a higherfire frequency on average compared to most other anthromes categories We note that rangelandsdisplay a very large variance and thus may be difficult to distinguish from croplands and villagesFiner anthropogenic categories within the cropland groups also appear to be contrasted by the firefrequency variable (see boxplots Figure 7)

Land 2017 6 61 12 of 19

corresponding to fragmented patches Conversely FP and NFP occur in larger continuous areas (Figure 3)

43 Comparison of Fire by Anthromes

Boxplots of mean fire frequency by anthromes groups suggest that fire can be used to distinguish among anthromes groups thereby serving as an additional potential variable to examine human imprints in the context of the Yucataacuten region (Figure 6) The croplands anthromes group has a higher fire frequency on average compared to most other anthromes categories We note that rangelands display a very large variance and thus may be difficult to distinguish from croplands and villages Finer anthropogenic categories within the cropland groups also appear to be contrasted by the fire frequency variable (see boxplots Figure 7)

Tukey pairwise comparison tests between anthromes groups (applied to the negative binomial model Table 3) highlight that six and seven pairwise comparisons are significantly different at 5 and 10 level respectively Coefficients indicate relative increase or decrease of the expected log of fire frequency for categorical change in relation to the reference variable For instance there is a minus137 decrease in the log of fire frequency when an observation is found in the dense settlements rather than in croplands We find that fire frequency variable is useful to differentiate croplands with almost all categories with the exception of Villages and Rangelands Both overlap substantially on the boxplots (Figure 7)

Figure 7 Between group comparison Fire frequency by anthrome groups boxplots (left) Within group comparison Fire frequency boxplots within cropland anthrome (right)

Table 3 Between-anthromes Tukey pairwise comparison for the negative binomial models with fire count and anthromes groups Note that the reference variable is in italic

Pairwise Comparison Coefficients Standard Error t-Stat p-ValuesDense settlementsndashCroplands minus138688 043059 minus32209 00121

ForestedndashCroplands minus092198 006997 minus131762 0 RangelandsndashCroplands minus035406 026321 minus13452 07146

VillagesndashCroplands minus028199 032807 minus08595 09435 WildlandsndashCroplands minus229463 019565 minus117283 0

ForestedndashDense settlements 046491 042934 10828 08616 RangelandsndashDense settlements 103282 049872 20709 02552

VillagesndashDense settlements 110489 053579 20622 02593 WildlandsndashDense settlements minus090775 04666 minus19454 03214

RangelandsndashForested 056791 026118 21744 02076

Figure 7 Between group comparison Fire frequency by anthrome groups boxplots (left) Within groupcomparison Fire frequency boxplots within cropland anthrome (right)

Tukey pairwise comparison tests between anthromes groups (applied to the negative binomialmodel Table 3) highlight that six and seven pairwise comparisons are significantly different at 5 and10 level respectively Coefficients indicate relative increase or decrease of the expected log of firefrequency for categorical change in relation to the reference variable For instance there is a minus137decrease in the log of fire frequency when an observation is found in the dense settlements rather thanin croplands We find that fire frequency variable is useful to differentiate croplands with almost allcategories with the exception of Villages and Rangelands Both overlap substantially on the boxplots(Figure 7)

Tukey comparisons were also performed for fire frequency within the cropland anthromes groupto assess the potential of using fire frequency for finer definition of the human imprint of landscapeWe found that within croplands two out 10 and four out of 10 comparison results in significantdifferences in the log of fire frequency (Table 4) at 5 and 10 percent significance level respectivelyThis suggests that fire frequency is less useful at distinguishing within the cropland anthromes Thestrongest contrasts are found between ldquoresidential rainfed mosaicsndashremote croplands mosaicrdquo andbetween ldquoresidential irrigated croplandndashremote croplandsrdquo Both indicate decreases in the log offire frequency for locations that are found in residential rainfed and irrigated cropland compared toremote croplands

Land 2017 6 61 13 of 19

Table 3 Between-anthromes Tukey pairwise comparison for the negative binomial models with firecount and anthromes groups Note that the reference variable is in italic

Pairwise Comparison Coefficients Standard Error t-Stat p-Values

Dense settlementsndashCroplands minus138688 043059 minus32209 00121ForestedndashCroplands minus092198 006997 minus131762 0

RangelandsndashCroplands minus035406 026321 minus13452 07146VillagesndashCroplands minus028199 032807 minus08595 09435

WildlandsndashCroplands minus229463 019565 minus117283 0ForestedndashDense settlements 046491 042934 10828 08616

RangelandsndashDense settlements 103282 049872 20709 02552VillagesndashDense settlements 110489 053579 20622 02593

WildlandsndashDense settlements minus090775 04666 minus19454 03214RangelandsndashForested 056791 026118 21744 02076

VillagesndashForested 063999 032644 19605 03129WildlandsndashForested minus137266 01929 minus71159 0VillagesndashRangelands 007207 041346 01743 1

WildlandsndashRangelands minus194057 031874 minus60882 0WildlandsndashVillages minus201264 037409 minus53801 0

Table 4 Within-anthrome Tukey pairwise comparisons using the negative binomial models with firecount and anthromes croplands categories Note that the reference variable is in italic

PairwisendashComparison Coefficients Standard Error t-Stat p-Values

Populated rainfed croplandndashPopulated irrigated cropland 025239 022555 1119 07646Remote croplandsndashPopulated irrigated cropland 0572 025835 2214 01453

Residential irrigated croplandndashPopulated irrigated cropland minus061118 041094 minus14873 05244Residential rainfed mosaicndashPopulated irrigated cropland 008091 022337 03622 09955

Remote croplandsndashPopulated rainfed cropland 031961 014756 2166 01615Residential irrigated croplandndashPopulated rainfed cropland minus086357 0352 minus24533 00827

Residential rainfed mosaicndashPopulated rainfed cropland minus017148 007017 minus24437 00848Residential irrigated croplandndashRemote croplands minus118318 037387 minus31647 00105

Residential rainfed mosaicndashRemote croplands minus049109 014421 minus34054 00043Residential rainfed mosaicndashResidential irrigated cropland 069209 035061 1974 02396

5 Discussion and Conclusions

Analysis of the spatial patterns of fire in the Yucataacuten using fire data visually reproduces thegeography of human land-based activities during 2000ndash2010 including the influence of roadssettlements and natural protected areas The intra-annual temporal dimensions of fire dataapproximate key moments of seasonal agriculture and other land-based activities (Figure 4) Thesefindings are consistent with studies finding higher fire frequencies in the proximity to roads andsettlements region [40] and with research about fire and deforestation in other tropical settings(eg [2862ndash64]) and more generally about the relationship between land change road developmentand market accessibility [53546465]

The multinomial model confirms the significance of fire intensity (defined as count of fire flaggedpixels over time) and landscape configuration (represented by the spatial lag variable CY) for thepeninsula for all three types of land changepersistence outcomes Notably all change is stronglyaffected by the presence of fire The odds of a forested area becoming non-forested multiply by sixin the presence of fire This is not surprising given that the cross-tabulation analysis showed thatnearly 87 of pixels that changed from 2000 to 2007 had been flagged as fire by MODIS at some pointThe dominance of no-fire observations over fire occurrence the (pseudo) absence of fire makes for abetter predictor of forest persistence than fire occurrence per se especially for large patches (high CYvalues) Predicting non-forest persistence proved more difficult signaling the diversity of ecologicaland land use practices and transitions between them that define the NFP category as discussed in thedata section What exactly accounts for the remaining 13 is difficult to determine We can speculate

Land 2017 6 61 14 of 19

however that possible factors include data error and accuracy mismatches As some have notedMODIS products do omit fires for various reasons [40] We can also speculate on some detected firesbeing non-agricultural Finally we can also imagine some fires starting as agricultural burns butbecoming large multiday forest fires as they grow out of control [40]

Fire also proves to be a reasonable indicator to distinguish between anthromes groups (Figure 7)but less among finer anthromes categories Our analysis shows that for example with the aidof a fire frequency croplands are separable from the rest of categories and that dense settlementsare clearly distinct from villages Other categories like rangeland prove more difficult to separatesince they present larger variance Some within-variation within anthropogenic categories is alsodistinguishable For example populated irrigated is clearly separable from populated rainfed andfrom remote croplands These two former categories however are not as separable from each otherwith the aid of fire frequency alone

Perhaps some insight about differences distinguishing between- and within-anthropogeniclandscapes can be gained by looking into the distinction between quemas (legally regulated agriculturalfires) from incendios (large escape non-regulated forest fires) Both can be addressed through the use ofMODIS active fire data but cannot be thoroughly distinguished with these data alone Within-variationexists in both categories On the one hand quemas can be due to subsistence and commercial agriculturesuch as sugar cane cultivation along the border with Belize (ie either rain fed or irrigated anthromecategories) or Mennonite corn fields in Bacalar( ie the populated irrigated anthrome category) astheir spatial and temporal signatures can differ quite noticeably (Figures 2 and 4) On the other handincendios can be truly accidental or be the result of purposeful burning with nonagricultural goals(eg forcing land zoning code changes for urban development hunting practices) Future researchshould exploit these differences in order to account for a more nuanced description of the relationshipsbetween fire and human-induced land change in the region

We conclude that in subtropical forest settings in which burning is a fundamental landscape toolfire is a reasonable proxy for land change Use of fire data improves the estimation of land change andexpands our understanding of human-environment relationships that produce complex mosaics ofhighly dynamic landscapes such as those in the Mexican Yucataacuten

Acknowledgments This study was part of the SYPR (httpsyprasuedu) and EDGY (httplandchangerutgersedu) projects SYPR received support from the NASA LCLUC program (NAG-56046 511134 and 6GD98G)and the NSF BCS program (0410016) EDGY was sponsored by the Gordon and Betty Moore Foundation underGrant 1697 The authors thank Drs Birgit Schmook (El Colegio de la Frontera Sur) Laura Schneider (RutgersUniversity) and Zachary Christman (Rowan University) for their support and advice The staff of Clark Labsfacilitated the work by creating and maintaining the Idrisireg software (httpwwwclarklabsorg) with whichpreliminary analysis was performed Subsequent and final analysis was performed with R packages NNetMASS multcomp and raster

Author Contributions Marco Millones John Rogan BL Turner II conceived and designed the original researchand fieldwork Marco Millones performed the fieldwork Marco Millones performed preliminary data analysiswith Daniel A Griffith Robert Clay Harris and Benoit Parmentier executed the final data analysis John RoganBL Turner II revised earlier versions of the manuscript Marco Millones Benoit Parmentier and Robert Clay Harriswrote the paper John Rogan revised the manuscript

Conflicts of Interest The authors declare no conflicts of interest

Land 2017 6 61 11 of 19

42 Effect of Fire and Patch Size on Land ChangePersistence A Spatial Multinomial Logit Model

Results from the spatial multinomial logit model agree with the analysis presented above(Section 41) and indicate that past fire occurrence (pre-2007) is a useful predictor of land changepersistence categories The resulting equations and model statistics are summarized in Table 2 and inthe supplementary Appendix A The Akaike information criterion (AIC) indicates that the model withcovariates (intercept + fire and lag + control variables) performs better than alternative models (seeAppendix A) The likelihood ratio (LR) has two degrees of freedom and is significant which confirmsthat at least one of the variables in the model improves the model description

Table 2 Spatial multinomial logit model summary of trends FP = forest persistence NFP = non forestpersistence CH = change INTE = Intercept Odds = Odds ratio effects point estimates This tablecontains only FIRE and CY variables the full variable list is available in the Appendix A

CAT REF INTE CY FIRE Odds CY Odds FIRE

CH (3) FP (1) minus467 minus355 192 003 679NFP (2) minus607 minus346 020 003 122

CH Average minus537 minus350 106 003 400

FP (1) CH (3) 467 355 minus192 3466 015NFP (2) minus438 007 minus172 107 018

FP Average 015 181 minus182 1787 016

NFP (2) CH (3) 905 348 minus020 3243 082FP (1) 438 minus007 172 094 559

FP Average 671 171 076 1668 320

The maximum pseudo-likelihood and odds ratio point estimates (Table 2 and Appendix A) showthe effect and relative importance of FIRE and CY for each land changepersistence outcome in themodel At a 5 level the difference between FIRE = 1 (fire occurrence) and FIRE = 0 is statisticallydifferent for all cases (FP NFP and CH) for all three states separately and the three-state aggregatedstudy area CY is a significant covariate in the model for all of these cases Additional models wererun with control variables These full model results are presented in the Appendix A and confirm theusefulness of fire as predictor

An inspection of the pseudo-likelihood estimates for the aggregated study area (Table 2 andAppendix A) indicates that for each unit increase in FIRE (intensity) the log of the ratio of p(CH)p(FP)increases by ~192 and the log of the ratio of p(CH)p(NFP) increases by ~02 In other words for eachunit increase in FIRE (intensity) in a given pixel (in Figure 2) the odds of that same pixel belonging tocategory CH (forest to non-forest change) rather than category FP (forest persistence in Figure 3) aremultiplied by ~67 Unit increases in FIRE also increase the odds of a pixel belonging to category CHrather than NFP (no forest persistence) by 122

For every increase in one unit of Fire the odds of a pixel belonging to category NFP instead of CHare multiplied by 082 For every increase in one unit of Fire the odds of a pixel belonging to categoryNFP instead of FP are multiplied by 559 For every increase in one unit of Fire the odds of a pixelbelonging to category FP instead of CH are multiplied by 015 (almost none)

For every increase in one unit of Fire the odds of a pixel belonging to category FP instead ofNFP are multiplied by 018 (almost none) Overall FIRE estimates are negative when predicting forestpersistence (FP) and positive when predicting CH

The calculated spatial lag (CY) terms are significant for all cases CY as mentioned earlier can beinterpreted as cohesiveness of land cover patches [61] Larger CY values correspond to more similarvalues among neighboring cells (ie a larger patches of a category) Estimates of the model for theaggregated peninsula indicate that a unit increase in CY decreases the log of p(FP)p(CH) by ~minus355while the log of p(FP)p(NFP) decreases by ~minus007 This finding indicates that persistent forestareas located in large patches are very likely to remain forest (34 times more than CH) (Table 2 and

Land 2017 6 61 12 of 19

Appendix A) FP is also 107 times more likely than NFP In general CH has a negative relationship withCY This relationship can be attributed to CH occurring more often in isolated pixels corresponding tofragmented patches Conversely FP and NFP occur in larger continuous areas (Figure 3)

43 Comparison of Fire by Anthromes

Boxplots of mean fire frequency by anthromes groups suggest that fire can be used to distinguishamong anthromes groups thereby serving as an additional potential variable to examine humanimprints in the context of the Yucataacuten region (Figure 6) The croplands anthromes group has a higherfire frequency on average compared to most other anthromes categories We note that rangelandsdisplay a very large variance and thus may be difficult to distinguish from croplands and villagesFiner anthropogenic categories within the cropland groups also appear to be contrasted by the firefrequency variable (see boxplots Figure 7)

Land 2017 6 61 12 of 19

corresponding to fragmented patches Conversely FP and NFP occur in larger continuous areas (Figure 3)

43 Comparison of Fire by Anthromes

Boxplots of mean fire frequency by anthromes groups suggest that fire can be used to distinguish among anthromes groups thereby serving as an additional potential variable to examine human imprints in the context of the Yucataacuten region (Figure 6) The croplands anthromes group has a higher fire frequency on average compared to most other anthromes categories We note that rangelands display a very large variance and thus may be difficult to distinguish from croplands and villages Finer anthropogenic categories within the cropland groups also appear to be contrasted by the fire frequency variable (see boxplots Figure 7)

Tukey pairwise comparison tests between anthromes groups (applied to the negative binomial model Table 3) highlight that six and seven pairwise comparisons are significantly different at 5 and 10 level respectively Coefficients indicate relative increase or decrease of the expected log of fire frequency for categorical change in relation to the reference variable For instance there is a minus137 decrease in the log of fire frequency when an observation is found in the dense settlements rather than in croplands We find that fire frequency variable is useful to differentiate croplands with almost all categories with the exception of Villages and Rangelands Both overlap substantially on the boxplots (Figure 7)

Figure 7 Between group comparison Fire frequency by anthrome groups boxplots (left) Within group comparison Fire frequency boxplots within cropland anthrome (right)

Table 3 Between-anthromes Tukey pairwise comparison for the negative binomial models with fire count and anthromes groups Note that the reference variable is in italic

Pairwise Comparison Coefficients Standard Error t-Stat p-ValuesDense settlementsndashCroplands minus138688 043059 minus32209 00121

ForestedndashCroplands minus092198 006997 minus131762 0 RangelandsndashCroplands minus035406 026321 minus13452 07146

VillagesndashCroplands minus028199 032807 minus08595 09435 WildlandsndashCroplands minus229463 019565 minus117283 0

ForestedndashDense settlements 046491 042934 10828 08616 RangelandsndashDense settlements 103282 049872 20709 02552

VillagesndashDense settlements 110489 053579 20622 02593 WildlandsndashDense settlements minus090775 04666 minus19454 03214

RangelandsndashForested 056791 026118 21744 02076

Figure 7 Between group comparison Fire frequency by anthrome groups boxplots (left) Within groupcomparison Fire frequency boxplots within cropland anthrome (right)

Tukey pairwise comparison tests between anthromes groups (applied to the negative binomialmodel Table 3) highlight that six and seven pairwise comparisons are significantly different at 5 and10 level respectively Coefficients indicate relative increase or decrease of the expected log of firefrequency for categorical change in relation to the reference variable For instance there is a minus137decrease in the log of fire frequency when an observation is found in the dense settlements rather thanin croplands We find that fire frequency variable is useful to differentiate croplands with almost allcategories with the exception of Villages and Rangelands Both overlap substantially on the boxplots(Figure 7)

Tukey comparisons were also performed for fire frequency within the cropland anthromes groupto assess the potential of using fire frequency for finer definition of the human imprint of landscapeWe found that within croplands two out 10 and four out of 10 comparison results in significantdifferences in the log of fire frequency (Table 4) at 5 and 10 percent significance level respectivelyThis suggests that fire frequency is less useful at distinguishing within the cropland anthromes Thestrongest contrasts are found between ldquoresidential rainfed mosaicsndashremote croplands mosaicrdquo andbetween ldquoresidential irrigated croplandndashremote croplandsrdquo Both indicate decreases in the log offire frequency for locations that are found in residential rainfed and irrigated cropland compared toremote croplands

Land 2017 6 61 13 of 19

Table 3 Between-anthromes Tukey pairwise comparison for the negative binomial models with firecount and anthromes groups Note that the reference variable is in italic

Pairwise Comparison Coefficients Standard Error t-Stat p-Values

Dense settlementsndashCroplands minus138688 043059 minus32209 00121ForestedndashCroplands minus092198 006997 minus131762 0

RangelandsndashCroplands minus035406 026321 minus13452 07146VillagesndashCroplands minus028199 032807 minus08595 09435

WildlandsndashCroplands minus229463 019565 minus117283 0ForestedndashDense settlements 046491 042934 10828 08616

RangelandsndashDense settlements 103282 049872 20709 02552VillagesndashDense settlements 110489 053579 20622 02593

WildlandsndashDense settlements minus090775 04666 minus19454 03214RangelandsndashForested 056791 026118 21744 02076

VillagesndashForested 063999 032644 19605 03129WildlandsndashForested minus137266 01929 minus71159 0VillagesndashRangelands 007207 041346 01743 1

WildlandsndashRangelands minus194057 031874 minus60882 0WildlandsndashVillages minus201264 037409 minus53801 0

Table 4 Within-anthrome Tukey pairwise comparisons using the negative binomial models with firecount and anthromes croplands categories Note that the reference variable is in italic

PairwisendashComparison Coefficients Standard Error t-Stat p-Values

Populated rainfed croplandndashPopulated irrigated cropland 025239 022555 1119 07646Remote croplandsndashPopulated irrigated cropland 0572 025835 2214 01453

Residential irrigated croplandndashPopulated irrigated cropland minus061118 041094 minus14873 05244Residential rainfed mosaicndashPopulated irrigated cropland 008091 022337 03622 09955

Remote croplandsndashPopulated rainfed cropland 031961 014756 2166 01615Residential irrigated croplandndashPopulated rainfed cropland minus086357 0352 minus24533 00827

Residential rainfed mosaicndashPopulated rainfed cropland minus017148 007017 minus24437 00848Residential irrigated croplandndashRemote croplands minus118318 037387 minus31647 00105

Residential rainfed mosaicndashRemote croplands minus049109 014421 minus34054 00043Residential rainfed mosaicndashResidential irrigated cropland 069209 035061 1974 02396

5 Discussion and Conclusions

Analysis of the spatial patterns of fire in the Yucataacuten using fire data visually reproduces thegeography of human land-based activities during 2000ndash2010 including the influence of roadssettlements and natural protected areas The intra-annual temporal dimensions of fire dataapproximate key moments of seasonal agriculture and other land-based activities (Figure 4) Thesefindings are consistent with studies finding higher fire frequencies in the proximity to roads andsettlements region [40] and with research about fire and deforestation in other tropical settings(eg [2862ndash64]) and more generally about the relationship between land change road developmentand market accessibility [53546465]

The multinomial model confirms the significance of fire intensity (defined as count of fire flaggedpixels over time) and landscape configuration (represented by the spatial lag variable CY) for thepeninsula for all three types of land changepersistence outcomes Notably all change is stronglyaffected by the presence of fire The odds of a forested area becoming non-forested multiply by sixin the presence of fire This is not surprising given that the cross-tabulation analysis showed thatnearly 87 of pixels that changed from 2000 to 2007 had been flagged as fire by MODIS at some pointThe dominance of no-fire observations over fire occurrence the (pseudo) absence of fire makes for abetter predictor of forest persistence than fire occurrence per se especially for large patches (high CYvalues) Predicting non-forest persistence proved more difficult signaling the diversity of ecologicaland land use practices and transitions between them that define the NFP category as discussed in thedata section What exactly accounts for the remaining 13 is difficult to determine We can speculate

Land 2017 6 61 14 of 19

however that possible factors include data error and accuracy mismatches As some have notedMODIS products do omit fires for various reasons [40] We can also speculate on some detected firesbeing non-agricultural Finally we can also imagine some fires starting as agricultural burns butbecoming large multiday forest fires as they grow out of control [40]

Fire also proves to be a reasonable indicator to distinguish between anthromes groups (Figure 7)but less among finer anthromes categories Our analysis shows that for example with the aidof a fire frequency croplands are separable from the rest of categories and that dense settlementsare clearly distinct from villages Other categories like rangeland prove more difficult to separatesince they present larger variance Some within-variation within anthropogenic categories is alsodistinguishable For example populated irrigated is clearly separable from populated rainfed andfrom remote croplands These two former categories however are not as separable from each otherwith the aid of fire frequency alone

Perhaps some insight about differences distinguishing between- and within-anthropogeniclandscapes can be gained by looking into the distinction between quemas (legally regulated agriculturalfires) from incendios (large escape non-regulated forest fires) Both can be addressed through the use ofMODIS active fire data but cannot be thoroughly distinguished with these data alone Within-variationexists in both categories On the one hand quemas can be due to subsistence and commercial agriculturesuch as sugar cane cultivation along the border with Belize (ie either rain fed or irrigated anthromecategories) or Mennonite corn fields in Bacalar( ie the populated irrigated anthrome category) astheir spatial and temporal signatures can differ quite noticeably (Figures 2 and 4) On the other handincendios can be truly accidental or be the result of purposeful burning with nonagricultural goals(eg forcing land zoning code changes for urban development hunting practices) Future researchshould exploit these differences in order to account for a more nuanced description of the relationshipsbetween fire and human-induced land change in the region

We conclude that in subtropical forest settings in which burning is a fundamental landscape toolfire is a reasonable proxy for land change Use of fire data improves the estimation of land change andexpands our understanding of human-environment relationships that produce complex mosaics ofhighly dynamic landscapes such as those in the Mexican Yucataacuten

Acknowledgments This study was part of the SYPR (httpsyprasuedu) and EDGY (httplandchangerutgersedu) projects SYPR received support from the NASA LCLUC program (NAG-56046 511134 and 6GD98G)and the NSF BCS program (0410016) EDGY was sponsored by the Gordon and Betty Moore Foundation underGrant 1697 The authors thank Drs Birgit Schmook (El Colegio de la Frontera Sur) Laura Schneider (RutgersUniversity) and Zachary Christman (Rowan University) for their support and advice The staff of Clark Labsfacilitated the work by creating and maintaining the Idrisireg software (httpwwwclarklabsorg) with whichpreliminary analysis was performed Subsequent and final analysis was performed with R packages NNetMASS multcomp and raster

Author Contributions Marco Millones John Rogan BL Turner II conceived and designed the original researchand fieldwork Marco Millones performed the fieldwork Marco Millones performed preliminary data analysiswith Daniel A Griffith Robert Clay Harris and Benoit Parmentier executed the final data analysis John RoganBL Turner II revised earlier versions of the manuscript Marco Millones Benoit Parmentier and Robert Clay Harriswrote the paper John Rogan revised the manuscript

Conflicts of Interest The authors declare no conflicts of interest

Land 2017 6 61 12 of 19

Appendix A) FP is also 107 times more likely than NFP In general CH has a negative relationship withCY This relationship can be attributed to CH occurring more often in isolated pixels corresponding tofragmented patches Conversely FP and NFP occur in larger continuous areas (Figure 3)

43 Comparison of Fire by Anthromes

Boxplots of mean fire frequency by anthromes groups suggest that fire can be used to distinguishamong anthromes groups thereby serving as an additional potential variable to examine humanimprints in the context of the Yucataacuten region (Figure 6) The croplands anthromes group has a higherfire frequency on average compared to most other anthromes categories We note that rangelandsdisplay a very large variance and thus may be difficult to distinguish from croplands and villagesFiner anthropogenic categories within the cropland groups also appear to be contrasted by the firefrequency variable (see boxplots Figure 7)

Land 2017 6 61 12 of 19

corresponding to fragmented patches Conversely FP and NFP occur in larger continuous areas (Figure 3)

43 Comparison of Fire by Anthromes

Boxplots of mean fire frequency by anthromes groups suggest that fire can be used to distinguish among anthromes groups thereby serving as an additional potential variable to examine human imprints in the context of the Yucataacuten region (Figure 6) The croplands anthromes group has a higher fire frequency on average compared to most other anthromes categories We note that rangelands display a very large variance and thus may be difficult to distinguish from croplands and villages Finer anthropogenic categories within the cropland groups also appear to be contrasted by the fire frequency variable (see boxplots Figure 7)

Tukey pairwise comparison tests between anthromes groups (applied to the negative binomial model Table 3) highlight that six and seven pairwise comparisons are significantly different at 5 and 10 level respectively Coefficients indicate relative increase or decrease of the expected log of fire frequency for categorical change in relation to the reference variable For instance there is a minus137 decrease in the log of fire frequency when an observation is found in the dense settlements rather than in croplands We find that fire frequency variable is useful to differentiate croplands with almost all categories with the exception of Villages and Rangelands Both overlap substantially on the boxplots (Figure 7)

Figure 7 Between group comparison Fire frequency by anthrome groups boxplots (left) Within group comparison Fire frequency boxplots within cropland anthrome (right)

Table 3 Between-anthromes Tukey pairwise comparison for the negative binomial models with fire count and anthromes groups Note that the reference variable is in italic

Pairwise Comparison Coefficients Standard Error t-Stat p-ValuesDense settlementsndashCroplands minus138688 043059 minus32209 00121

ForestedndashCroplands minus092198 006997 minus131762 0 RangelandsndashCroplands minus035406 026321 minus13452 07146

VillagesndashCroplands minus028199 032807 minus08595 09435 WildlandsndashCroplands minus229463 019565 minus117283 0

ForestedndashDense settlements 046491 042934 10828 08616 RangelandsndashDense settlements 103282 049872 20709 02552

VillagesndashDense settlements 110489 053579 20622 02593 WildlandsndashDense settlements minus090775 04666 minus19454 03214

RangelandsndashForested 056791 026118 21744 02076

Figure 7 Between group comparison Fire frequency by anthrome groups boxplots (left) Within groupcomparison Fire frequency boxplots within cropland anthrome (right)

Tukey pairwise comparison tests between anthromes groups (applied to the negative binomialmodel Table 3) highlight that six and seven pairwise comparisons are significantly different at 5 and10 level respectively Coefficients indicate relative increase or decrease of the expected log of firefrequency for categorical change in relation to the reference variable For instance there is a minus137decrease in the log of fire frequency when an observation is found in the dense settlements rather thanin croplands We find that fire frequency variable is useful to differentiate croplands with almost allcategories with the exception of Villages and Rangelands Both overlap substantially on the boxplots(Figure 7)

Tukey comparisons were also performed for fire frequency within the cropland anthromes groupto assess the potential of using fire frequency for finer definition of the human imprint of landscapeWe found that within croplands two out 10 and four out of 10 comparison results in significantdifferences in the log of fire frequency (Table 4) at 5 and 10 percent significance level respectivelyThis suggests that fire frequency is less useful at distinguishing within the cropland anthromes Thestrongest contrasts are found between ldquoresidential rainfed mosaicsndashremote croplands mosaicrdquo andbetween ldquoresidential irrigated croplandndashremote croplandsrdquo Both indicate decreases in the log offire frequency for locations that are found in residential rainfed and irrigated cropland compared toremote croplands

Land 2017 6 61 13 of 19

Table 3 Between-anthromes Tukey pairwise comparison for the negative binomial models with firecount and anthromes groups Note that the reference variable is in italic

Pairwise Comparison Coefficients Standard Error t-Stat p-Values

Dense settlementsndashCroplands minus138688 043059 minus32209 00121ForestedndashCroplands minus092198 006997 minus131762 0

RangelandsndashCroplands minus035406 026321 minus13452 07146VillagesndashCroplands minus028199 032807 minus08595 09435

WildlandsndashCroplands minus229463 019565 minus117283 0ForestedndashDense settlements 046491 042934 10828 08616

RangelandsndashDense settlements 103282 049872 20709 02552VillagesndashDense settlements 110489 053579 20622 02593

WildlandsndashDense settlements minus090775 04666 minus19454 03214RangelandsndashForested 056791 026118 21744 02076

VillagesndashForested 063999 032644 19605 03129WildlandsndashForested minus137266 01929 minus71159 0VillagesndashRangelands 007207 041346 01743 1

WildlandsndashRangelands minus194057 031874 minus60882 0WildlandsndashVillages minus201264 037409 minus53801 0

Table 4 Within-anthrome Tukey pairwise comparisons using the negative binomial models with firecount and anthromes croplands categories Note that the reference variable is in italic

PairwisendashComparison Coefficients Standard Error t-Stat p-Values

Populated rainfed croplandndashPopulated irrigated cropland 025239 022555 1119 07646Remote croplandsndashPopulated irrigated cropland 0572 025835 2214 01453

Residential irrigated croplandndashPopulated irrigated cropland minus061118 041094 minus14873 05244Residential rainfed mosaicndashPopulated irrigated cropland 008091 022337 03622 09955

Remote croplandsndashPopulated rainfed cropland 031961 014756 2166 01615Residential irrigated croplandndashPopulated rainfed cropland minus086357 0352 minus24533 00827

Residential rainfed mosaicndashPopulated rainfed cropland minus017148 007017 minus24437 00848Residential irrigated croplandndashRemote croplands minus118318 037387 minus31647 00105

Residential rainfed mosaicndashRemote croplands minus049109 014421 minus34054 00043Residential rainfed mosaicndashResidential irrigated cropland 069209 035061 1974 02396

5 Discussion and Conclusions

Analysis of the spatial patterns of fire in the Yucataacuten using fire data visually reproduces thegeography of human land-based activities during 2000ndash2010 including the influence of roadssettlements and natural protected areas The intra-annual temporal dimensions of fire dataapproximate key moments of seasonal agriculture and other land-based activities (Figure 4) Thesefindings are consistent with studies finding higher fire frequencies in the proximity to roads andsettlements region [40] and with research about fire and deforestation in other tropical settings(eg [2862ndash64]) and more generally about the relationship between land change road developmentand market accessibility [53546465]

The multinomial model confirms the significance of fire intensity (defined as count of fire flaggedpixels over time) and landscape configuration (represented by the spatial lag variable CY) for thepeninsula for all three types of land changepersistence outcomes Notably all change is stronglyaffected by the presence of fire The odds of a forested area becoming non-forested multiply by sixin the presence of fire This is not surprising given that the cross-tabulation analysis showed thatnearly 87 of pixels that changed from 2000 to 2007 had been flagged as fire by MODIS at some pointThe dominance of no-fire observations over fire occurrence the (pseudo) absence of fire makes for abetter predictor of forest persistence than fire occurrence per se especially for large patches (high CYvalues) Predicting non-forest persistence proved more difficult signaling the diversity of ecologicaland land use practices and transitions between them that define the NFP category as discussed in thedata section What exactly accounts for the remaining 13 is difficult to determine We can speculate

Land 2017 6 61 14 of 19

however that possible factors include data error and accuracy mismatches As some have notedMODIS products do omit fires for various reasons [40] We can also speculate on some detected firesbeing non-agricultural Finally we can also imagine some fires starting as agricultural burns butbecoming large multiday forest fires as they grow out of control [40]

Fire also proves to be a reasonable indicator to distinguish between anthromes groups (Figure 7)but less among finer anthromes categories Our analysis shows that for example with the aidof a fire frequency croplands are separable from the rest of categories and that dense settlementsare clearly distinct from villages Other categories like rangeland prove more difficult to separatesince they present larger variance Some within-variation within anthropogenic categories is alsodistinguishable For example populated irrigated is clearly separable from populated rainfed andfrom remote croplands These two former categories however are not as separable from each otherwith the aid of fire frequency alone

Perhaps some insight about differences distinguishing between- and within-anthropogeniclandscapes can be gained by looking into the distinction between quemas (legally regulated agriculturalfires) from incendios (large escape non-regulated forest fires) Both can be addressed through the use ofMODIS active fire data but cannot be thoroughly distinguished with these data alone Within-variationexists in both categories On the one hand quemas can be due to subsistence and commercial agriculturesuch as sugar cane cultivation along the border with Belize (ie either rain fed or irrigated anthromecategories) or Mennonite corn fields in Bacalar( ie the populated irrigated anthrome category) astheir spatial and temporal signatures can differ quite noticeably (Figures 2 and 4) On the other handincendios can be truly accidental or be the result of purposeful burning with nonagricultural goals(eg forcing land zoning code changes for urban development hunting practices) Future researchshould exploit these differences in order to account for a more nuanced description of the relationshipsbetween fire and human-induced land change in the region

We conclude that in subtropical forest settings in which burning is a fundamental landscape toolfire is a reasonable proxy for land change Use of fire data improves the estimation of land change andexpands our understanding of human-environment relationships that produce complex mosaics ofhighly dynamic landscapes such as those in the Mexican Yucataacuten

Acknowledgments This study was part of the SYPR (httpsyprasuedu) and EDGY (httplandchangerutgersedu) projects SYPR received support from the NASA LCLUC program (NAG-56046 511134 and 6GD98G)and the NSF BCS program (0410016) EDGY was sponsored by the Gordon and Betty Moore Foundation underGrant 1697 The authors thank Drs Birgit Schmook (El Colegio de la Frontera Sur) Laura Schneider (RutgersUniversity) and Zachary Christman (Rowan University) for their support and advice The staff of Clark Labsfacilitated the work by creating and maintaining the Idrisireg software (httpwwwclarklabsorg) with whichpreliminary analysis was performed Subsequent and final analysis was performed with R packages NNetMASS multcomp and raster

Author Contributions Marco Millones John Rogan BL Turner II conceived and designed the original researchand fieldwork Marco Millones performed the fieldwork Marco Millones performed preliminary data analysiswith Daniel A Griffith Robert Clay Harris and Benoit Parmentier executed the final data analysis John RoganBL Turner II revised earlier versions of the manuscript Marco Millones Benoit Parmentier and Robert Clay Harriswrote the paper John Rogan revised the manuscript

Conflicts of Interest The authors declare no conflicts of interest

Land 2017 6 61 13 of 19

Table 3 Between-anthromes Tukey pairwise comparison for the negative binomial models with firecount and anthromes groups Note that the reference variable is in italic

Pairwise Comparison Coefficients Standard Error t-Stat p-Values

Dense settlementsndashCroplands minus138688 043059 minus32209 00121ForestedndashCroplands minus092198 006997 minus131762 0

RangelandsndashCroplands minus035406 026321 minus13452 07146VillagesndashCroplands minus028199 032807 minus08595 09435

WildlandsndashCroplands minus229463 019565 minus117283 0ForestedndashDense settlements 046491 042934 10828 08616

RangelandsndashDense settlements 103282 049872 20709 02552VillagesndashDense settlements 110489 053579 20622 02593

WildlandsndashDense settlements minus090775 04666 minus19454 03214RangelandsndashForested 056791 026118 21744 02076

VillagesndashForested 063999 032644 19605 03129WildlandsndashForested minus137266 01929 minus71159 0VillagesndashRangelands 007207 041346 01743 1

WildlandsndashRangelands minus194057 031874 minus60882 0WildlandsndashVillages minus201264 037409 minus53801 0

Table 4 Within-anthrome Tukey pairwise comparisons using the negative binomial models with firecount and anthromes croplands categories Note that the reference variable is in italic

PairwisendashComparison Coefficients Standard Error t-Stat p-Values

Populated rainfed croplandndashPopulated irrigated cropland 025239 022555 1119 07646Remote croplandsndashPopulated irrigated cropland 0572 025835 2214 01453

Residential irrigated croplandndashPopulated irrigated cropland minus061118 041094 minus14873 05244Residential rainfed mosaicndashPopulated irrigated cropland 008091 022337 03622 09955

Remote croplandsndashPopulated rainfed cropland 031961 014756 2166 01615Residential irrigated croplandndashPopulated rainfed cropland minus086357 0352 minus24533 00827

Residential rainfed mosaicndashPopulated rainfed cropland minus017148 007017 minus24437 00848Residential irrigated croplandndashRemote croplands minus118318 037387 minus31647 00105

Residential rainfed mosaicndashRemote croplands minus049109 014421 minus34054 00043Residential rainfed mosaicndashResidential irrigated cropland 069209 035061 1974 02396

5 Discussion and Conclusions

Analysis of the spatial patterns of fire in the Yucataacuten using fire data visually reproduces thegeography of human land-based activities during 2000ndash2010 including the influence of roadssettlements and natural protected areas The intra-annual temporal dimensions of fire dataapproximate key moments of seasonal agriculture and other land-based activities (Figure 4) Thesefindings are consistent with studies finding higher fire frequencies in the proximity to roads andsettlements region [40] and with research about fire and deforestation in other tropical settings(eg [2862ndash64]) and more generally about the relationship between land change road developmentand market accessibility [53546465]

The multinomial model confirms the significance of fire intensity (defined as count of fire flaggedpixels over time) and landscape configuration (represented by the spatial lag variable CY) for thepeninsula for all three types of land changepersistence outcomes Notably all change is stronglyaffected by the presence of fire The odds of a forested area becoming non-forested multiply by sixin the presence of fire This is not surprising given that the cross-tabulation analysis showed thatnearly 87 of pixels that changed from 2000 to 2007 had been flagged as fire by MODIS at some pointThe dominance of no-fire observations over fire occurrence the (pseudo) absence of fire makes for abetter predictor of forest persistence than fire occurrence per se especially for large patches (high CYvalues) Predicting non-forest persistence proved more difficult signaling the diversity of ecologicaland land use practices and transitions between them that define the NFP category as discussed in thedata section What exactly accounts for the remaining 13 is difficult to determine We can speculate

Land 2017 6 61 14 of 19

however that possible factors include data error and accuracy mismatches As some have notedMODIS products do omit fires for various reasons [40] We can also speculate on some detected firesbeing non-agricultural Finally we can also imagine some fires starting as agricultural burns butbecoming large multiday forest fires as they grow out of control [40]

Fire also proves to be a reasonable indicator to distinguish between anthromes groups (Figure 7)but less among finer anthromes categories Our analysis shows that for example with the aidof a fire frequency croplands are separable from the rest of categories and that dense settlementsare clearly distinct from villages Other categories like rangeland prove more difficult to separatesince they present larger variance Some within-variation within anthropogenic categories is alsodistinguishable For example populated irrigated is clearly separable from populated rainfed andfrom remote croplands These two former categories however are not as separable from each otherwith the aid of fire frequency alone

Perhaps some insight about differences distinguishing between- and within-anthropogeniclandscapes can be gained by looking into the distinction between quemas (legally regulated agriculturalfires) from incendios (large escape non-regulated forest fires) Both can be addressed through the use ofMODIS active fire data but cannot be thoroughly distinguished with these data alone Within-variationexists in both categories On the one hand quemas can be due to subsistence and commercial agriculturesuch as sugar cane cultivation along the border with Belize (ie either rain fed or irrigated anthromecategories) or Mennonite corn fields in Bacalar( ie the populated irrigated anthrome category) astheir spatial and temporal signatures can differ quite noticeably (Figures 2 and 4) On the other handincendios can be truly accidental or be the result of purposeful burning with nonagricultural goals(eg forcing land zoning code changes for urban development hunting practices) Future researchshould exploit these differences in order to account for a more nuanced description of the relationshipsbetween fire and human-induced land change in the region

We conclude that in subtropical forest settings in which burning is a fundamental landscape toolfire is a reasonable proxy for land change Use of fire data improves the estimation of land change andexpands our understanding of human-environment relationships that produce complex mosaics ofhighly dynamic landscapes such as those in the Mexican Yucataacuten

Acknowledgments This study was part of the SYPR (httpsyprasuedu) and EDGY (httplandchangerutgersedu) projects SYPR received support from the NASA LCLUC program (NAG-56046 511134 and 6GD98G)and the NSF BCS program (0410016) EDGY was sponsored by the Gordon and Betty Moore Foundation underGrant 1697 The authors thank Drs Birgit Schmook (El Colegio de la Frontera Sur) Laura Schneider (RutgersUniversity) and Zachary Christman (Rowan University) for their support and advice The staff of Clark Labsfacilitated the work by creating and maintaining the Idrisireg software (httpwwwclarklabsorg) with whichpreliminary analysis was performed Subsequent and final analysis was performed with R packages NNetMASS multcomp and raster

Author Contributions Marco Millones John Rogan BL Turner II conceived and designed the original researchand fieldwork Marco Millones performed the fieldwork Marco Millones performed preliminary data analysiswith Daniel A Griffith Robert Clay Harris and Benoit Parmentier executed the final data analysis John RoganBL Turner II revised earlier versions of the manuscript Marco Millones Benoit Parmentier and Robert Clay Harriswrote the paper John Rogan revised the manuscript

Conflicts of Interest The authors declare no conflicts of interest

Land 2017 6 61 14 of 19

however that possible factors include data error and accuracy mismatches As some have notedMODIS products do omit fires for various reasons [40] We can also speculate on some detected firesbeing non-agricultural Finally we can also imagine some fires starting as agricultural burns butbecoming large multiday forest fires as they grow out of control [40]

Fire also proves to be a reasonable indicator to distinguish between anthromes groups (Figure 7)but less among finer anthromes categories Our analysis shows that for example with the aidof a fire frequency croplands are separable from the rest of categories and that dense settlementsare clearly distinct from villages Other categories like rangeland prove more difficult to separatesince they present larger variance Some within-variation within anthropogenic categories is alsodistinguishable For example populated irrigated is clearly separable from populated rainfed andfrom remote croplands These two former categories however are not as separable from each otherwith the aid of fire frequency alone

Perhaps some insight about differences distinguishing between- and within-anthropogeniclandscapes can be gained by looking into the distinction between quemas (legally regulated agriculturalfires) from incendios (large escape non-regulated forest fires) Both can be addressed through the use ofMODIS active fire data but cannot be thoroughly distinguished with these data alone Within-variationexists in both categories On the one hand quemas can be due to subsistence and commercial agriculturesuch as sugar cane cultivation along the border with Belize (ie either rain fed or irrigated anthromecategories) or Mennonite corn fields in Bacalar( ie the populated irrigated anthrome category) astheir spatial and temporal signatures can differ quite noticeably (Figures 2 and 4) On the other handincendios can be truly accidental or be the result of purposeful burning with nonagricultural goals(eg forcing land zoning code changes for urban development hunting practices) Future researchshould exploit these differences in order to account for a more nuanced description of the relationshipsbetween fire and human-induced land change in the region

We conclude that in subtropical forest settings in which burning is a fundamental landscape toolfire is a reasonable proxy for land change Use of fire data improves the estimation of land change andexpands our understanding of human-environment relationships that produce complex mosaics ofhighly dynamic landscapes such as those in the Mexican Yucataacuten

Acknowledgments This study was part of the SYPR (httpsyprasuedu) and EDGY (httplandchangerutgersedu) projects SYPR received support from the NASA LCLUC program (NAG-56046 511134 and 6GD98G)and the NSF BCS program (0410016) EDGY was sponsored by the Gordon and Betty Moore Foundation underGrant 1697 The authors thank Drs Birgit Schmook (El Colegio de la Frontera Sur) Laura Schneider (RutgersUniversity) and Zachary Christman (Rowan University) for their support and advice The staff of Clark Labsfacilitated the work by creating and maintaining the Idrisireg software (httpwwwclarklabsorg) with whichpreliminary analysis was performed Subsequent and final analysis was performed with R packages NNetMASS multcomp and raster

Author Contributions Marco Millones John Rogan BL Turner II conceived and designed the original researchand fieldwork Marco Millones performed the fieldwork Marco Millones performed preliminary data analysiswith Daniel A Griffith Robert Clay Harris and Benoit Parmentier executed the final data analysis John RoganBL Turner II revised earlier versions of the manuscript Marco Millones Benoit Parmentier and Robert Clay Harriswrote the paper John Rogan revised the manuscript

Conflicts of Interest The authors declare no conflicts of interest

Land 2017 6 61 15 of 19

Appendix A

Table A1 Multinomial Logistic Model Results (variable definitions below)

LN[p(NFP)(FP)]

Estimate Odds p-Value Standard Error z-Score

Intercept 438 7963 000 000 3001470CY minus007 094 000 000 minus53722

fire density 172 559 000 000 6661778distance to roads minus054 058 000 000 minus42823

Elevation minus001 099 000 000 minus7417slope (degrees) minus006 095 000 000 minus1575cattle density 006 106 000 000 5825

ejido lands minus039 068 000 000 minus426532population density change 000 100 087 000 017

precipitation 000 100 000 000 minus767protected areas 046 159 000 000 703454

Soil minus010 091 000 000 minus424804

LN[p(FP)(NFP)]

Estimate Odds p-Value Standard Error z-Score

Intercept minus438 001 000 000 minus2998184CY 007 107 000 000 53089

FIRE_intensity minus172 018 000 000 minus6720289dist_roads 054 172 000 000 42789Elevation 001 101 000 000 7414slope_deg 006 106 000 000 1574

cattledensity minus006 094 000 000 minus5813ejido 038 147 000 000 426107

popdens_chenge 000 100 071 000 minus037precip 000 100 000 000 765

protegidas minus046 063 000 000 minus704805soil 010 110 000 000 424483

LN[p(NFP)(CH)]

Estimate Odds p-Value Standard Error z-Score

Intercept 905 849841 000 000 12359353CY 348 3243 000 000 5569876

FIRE_intensity minus020 082 000 000 minus1493893dist_roads minus043 065 000 000 minus68767elevation 000 100 003 000 minus215slope_deg 058 179 000 000 32737

cattledensity 011 111 000 000 21822ejido minus025 078 000 000 minus533041

popdens_chenge minus006 095 000 000 minus4586precip 000 100 000 000 minus3916

protegidas 165 519 000 000 5011419soil 042 152 000 000 3598519

Land 2017 6 61 16 of 19

Table A1 Cont

LN[p(CH)(FP)]

Estimate Odds p-Value Standard Error z-Score

Intercept minus467 001 000 000 minus105272445CY minus355 003 000 000 minus77064397

fire density 192 679 000 000 141635673distance to roads minus011 090 000 000 minus443060

elevation minus001 099 000 000 minus357slope (degrees) minus064 053 000 000 minus6666661cattle density minus005 095 000 000 minus193187

ejido lands minus014 087 000 000 minus1687316population density chanve 006 106 000 000 4488

precipitation 000 100 000 000 3904protected areas minus118 031 000 000 minus135834349

soil minus052 059 000 000 minus42315699

LN[p(CH)(NFP)]

Estimate Odds p-Value Standard Error z-Score

Intercept minus607 000 000 000 minus197408165CY minus346 003 000 000 minus85153090

FIRE_intensity 020 122 000 000 21516066dist_roads 044 155 000 000 3489945elevation 000 100 003 000 215slope_deg minus047 062 000 000 minus4664659

cattledensity minus011 089 000 000 minus245785ejido 024 128 000 000 5127432

popdens_chenge 005 105 000 000 4132precip 000 100 003 000 221

protegidas minus159 020 000 000 minus242409475soil minus047 062 000 000 minus52636339

LN[p(FP)(CH)]

Estimate Odds p-Value Standard Error z-Score

Intercept 467 10673 000 000 6388224CY 355 3466 000 000 5698669

FIRE_intensity minus192 015 000 000 minus14804718dist_roads 011 111 000 000 16704elevation 001 101 000 000 357slope_deg 064 190 000 000 35884

cattledensity 005 105 000 000 10276ejido 014 115 000 000 303812

popdens_chenge minus006 095 000 000 minus4485precip 000 100 000 000 minus3910

protegidas 118 327 000 000 3591195soil 052 168 000 000 4459937

Intercept CY = spatial lag FIRE_intensity = fire flagged pixel count divided by five years dist_roads = distance toroads elevation = SRTM DEM derived elevation slope_deg = DEM derived slope cattle density = cattle densityejido = communal land property status (binary) popdens_change = population density change precipitation =precipitation derived from TRMM protegidas = natural protected areas (binary) soil = binary soil

References

1 Reid WV Chen D Goldfarb L Hackmann H Lee YT Mokhele K Ostrom E Raivio K Rockstroumlm JSchellnhuber HJ et al Earth System Science for Global Sustainability Grand challenges Science 2010 330916ndash917 [CrossRef] [PubMed]

2 Irwin EG Geoghegan J Theory data methods Developing spatially explicit economic models of land usechange Agric Ecosyst Environ 2001 85 7ndash24 [CrossRef]

Land 2017 6 61 16 of 19

Table A1 Cont

LN[p(CH)(FP)]

Estimate Odds p-Value Standard Error z-Score

Intercept minus467 001 000 000 minus105272445CY minus355 003 000 000 minus77064397

fire density 192 679 000 000 141635673distance to roads minus011 090 000 000 minus443060

elevation minus001 099 000 000 minus357slope (degrees) minus064 053 000 000 minus6666661cattle density minus005 095 000 000 minus193187

ejido lands minus014 087 000 000 minus1687316population density chanve 006 106 000 000 4488

precipitation 000 100 000 000 3904protected areas minus118 031 000 000 minus135834349

soil minus052 059 000 000 minus42315699

LN[p(CH)(NFP)]

Estimate Odds p-Value Standard Error z-Score

Intercept minus607 000 000 000 minus197408165CY minus346 003 000 000 minus85153090

FIRE_intensity 020 122 000 000 21516066dist_roads 044 155 000 000 3489945elevation 000 100 003 000 215slope_deg minus047 062 000 000 minus4664659

cattledensity minus011 089 000 000 minus245785ejido 024 128 000 000 5127432

popdens_chenge 005 105 000 000 4132precip 000 100 003 000 221

protegidas minus159 020 000 000 minus242409475soil minus047 062 000 000 minus52636339

LN[p(FP)(CH)]

Estimate Odds p-Value Standard Error z-Score

Intercept 467 10673 000 000 6388224CY 355 3466 000 000 5698669

FIRE_intensity minus192 015 000 000 minus14804718dist_roads 011 111 000 000 16704elevation 001 101 000 000 357slope_deg 064 190 000 000 35884

cattledensity 005 105 000 000 10276ejido 014 115 000 000 303812

popdens_chenge minus006 095 000 000 minus4485precip 000 100 000 000 minus3910

protegidas 118 327 000 000 3591195soil 052 168 000 000 4459937

Intercept CY = spatial lag FIRE_intensity = fire flagged pixel count divided by five years dist_roads = distance toroads elevation = SRTM DEM derived elevation slope_deg = DEM derived slope cattle density = cattle densityejido = communal land property status (binary) popdens_change = population density change precipitation =precipitation derived from TRMM protegidas = natural protected areas (binary) soil = binary soil

References

1 Reid WV Chen D Goldfarb L Hackmann H Lee YT Mokhele K Ostrom E Raivio K Rockstroumlm JSchellnhuber HJ et al Earth System Science for Global Sustainability Grand challenges Science 2010 330916ndash917 [CrossRef] [PubMed]

2 Irwin EG Geoghegan J Theory data methods Developing spatially explicit economic models of land usechange Agric Ecosyst Environ 2001 85 7ndash24 [CrossRef]

Land 2017 6 61 17 of 19

3 Agarwal C Green GM Grove JM Evans TP Schweik CM A Review and Assessment of Land-Use ChangeModels Dynamics of Space Time and Human Choice Technical Report NE-297 United States Department ofAgriculture (USDA) Burlington VT USA 2002

4 Turner BL Lambin EF Reenberg A The Emergence of Land Change Science for Global EnvironmentalChange and Sustainability Proc Natl Acad Sci USA 2007 104 20666ndash20671 [CrossRef] [PubMed]

5 Griggs D Stafford-Smith M Gaffney O Rockstroumlm J Oumlhman MC Shyamsundar P Steffen WGlaser G Kanie N Noble I Policy Sustainable development goals for people and planet Nature 2013495 305ndash307 [CrossRef] [PubMed]

6 Steffen W Sanderson RA Tyson PD Jaumlger J Matson PA Moore B III Oldfield F Richardson KSchellnhuber HJ Turner BL et al Global Change and the Earth System A Planet under Pressure SpringerBerlinHeidelberg Germany New York NY USA 2004

7 Foley JA DeFries R Asner GP Barford C Bonan G Carpenter SR Chapin FS Coe MT Daily GCGibbs HK Global consequences of Land Use Science 2005 309 570ndash574 [CrossRef] [PubMed]

8 Turner BL II Skole D Sanderson S Fischer G Fresco L Leemans R Land-Use and Land-CoverChange ScienceResearch Plan IGBP Report No 35 The International Geosphere-Biosphere Programme IGBPStockholm Sweden 1995

9 Kates RW Clark W Corell R Sustainability Science KSG Working Paper No 00-018 John F KennedySchool of Government (KSG) Harvard University Cambridge MA USA 2000

10 Ellis EC Ramankutty N Putting people in the map Anthropogenic biomes of the world Front EcolEnviron 2008 6 439ndash447 [CrossRef]

11 Loveland TR Sohl TL Stehman SV Gallant AL Sayler KL Napton DE A strategy for estimatingthe rates of recent United States land-cover changes Photogramm Eng Remote Sens 2002 68 1091ndash1099

12 Rogan J Chen D Remote sensing technology for mapping and monitoring land-cover and land-use changeProg Plan 2004 61 301ndash325 [CrossRef]

13 Mertens B Lambin EF Land-cover-change trajectories in southern Cameroon Ann Assoc Am Geogr2000 90 467ndash494 [CrossRef]

14 DeFries RS Foley JA Asner GP Land use choices Balancing human needs and ecosystem functionFront Ecol Environ 2004 2 249ndash257 [CrossRef]

15 Csiszar I Justice CO Mcguire AD Cochrane MA Roy DP Brown F Conard SG Frost PGHGiglio L Elvidge C et al Land use and fires In Land Change Science Observing Monitoring andUnderstanding Trajectories of Change on the Earthrsquos Surface Gutman G Janetos AC Justice CO Moran EFMustard JF Rinfuss RR Skole D Turner BL II Cochrane MA Eds Springer Berlin Germany 2004pp 329ndash351

16 Brown D Band LE Green KO Irwin EG Jain A Lambin EF Pontius RG Seto KC Turner BL IIVerburg PH Advancing Land Change Modeling Opportunities and Research Requirements The NationalAcademies Press Washington DC USA 2013

17 Verburg PH Crossman N Ellis EC Heinimann A Hostert P Mertz O Nagendra H Sikor TErb K-H Golubiewski NE et al Land system science and sustainable development of the earth systemA global land project perspective Anthropocene 2015 12 29ndash41 [CrossRef]

18 Ronald Eastman J Sangermano F Ghimire B Zhu H Chen H Neeti N Cai Y Machado EACrema SC Seasonal trend analysis of image time series Int J Remote Sens 2009 30 2721ndash2726 [CrossRef]

19 Congalton RG Gu J Yadav K Thenkabail P Ozdogan M Global land cover mapping A review anduncertainty analysis Remote Sens 2014 6 12070ndash12093 [CrossRef]

20 McDermid GJ Franklin SE LeDrew EF Remote sensing for large-area habitat mapping Prog PhysGeogr 2005 29 449ndash474 [CrossRef]

21 Woodcock CE Ozdogan M Trends in Land-cover Mapping and Monitoring Remote Sens DigitImage Process 2004 6 367ndash377

22 Rogan J Franklin J Roberts DA A comparison of methods for monitoring multitemporal vegetationchange using Thematic Mapper imagery Remote Sens Environ 2002 80 143ndash156 [CrossRef]

23 Justice CO Giglio L Korontzi S Owens J Morisette JT Roy D Descloitres J Alleaume SPetitcolin F Kaufman Y The MODIS fire products Remote Sens Environ 2002 83 244ndash262 [CrossRef]

Land 2017 6 61 18 of 19

24 Neeti N Rogan J Christman Z Eastman JR Millones M Schneider L Nickl E Schmook BTurner BL Ghimire B Mapping seasonal trends in vegetation using AVHRR-NDVI time series in theYucataacuten Peninsula Mexico Remote Sens Lett 2012 3 433ndash442 [CrossRef]

25 Parmentier B Eastman JR Land transitions from multivariate time series Using seasonal trend analysisand segmentation to detect land-cover changes Int J Remote Sens 2014 35 671ndash692 [CrossRef]

26 Friedl MA McIver DK Hodges JC Zhang XY Muchoney D Strahler AH Woodcock CE Gopal SSchneider A Cooper A et al Global land-cover mapping from MODIS Algorithms and early resultsRemote Sens Environ 2002 83 287ndash302 [CrossRef]

27 Miller J Rogan J Using GIS and remote sensing for ecological mapping and monitoring In Integration ofGIS and Remote Sensing Masev V Ed Wiley and Sons West Sussex UK 2007 pp 233ndash268

28 Morton DC Defries RS Randerson JT Giglio L Schroeder W Van Der Werf GR Agriculturalintensification increases deforestation fire activity in Amazonia Glob Chang Biol 2008 14 2262ndash2275[CrossRef]

29 Pausas JG Keeley JE A burning story The role of fire in the history of life BioScience 2009 59 593ndash601[CrossRef]

30 Bowman DM Balch J Artaxo P Bond WJ Cochrane MA Drsquoantonio CM DeFries R Johnston FHKeeley JE Krawchuk MA et al The human dimension of fire regimes on Earth J Biogeogr 2011 382223ndash2236 [CrossRef] [PubMed]

31 Butsic V Kelly M Moritz MA Land use and wildfire A review of local interactions and teleconnectionsLand 2015 4 140ndash156 [CrossRef]

32 Lutz W Prieto L Sanderson WC (Eds) Population Development and Environment on the Yucatan PeninsulaFrom Ancient Maya to 2030 International Institute for Applied Systems Analysis Luxemburg 2000

33 Turner BL II Geoghegan J Foster DR (Eds) Integrated Land Change Science and Tropical Deforestation inthe Southern Yucataacuten Final Frontiers Oxford University Press Oxford UK 2004

34 Rogan J Schneider L Christman Z Millones M Lawrence D Schmook B Hurricane DisturbanceMapping using MODIS EVI Data in the South-Eastern Yucataacuten Mexico Remote Sens Lett 2011 2 259ndash267[CrossRef]

35 Islebe GA Calmeacute S Leoacuten-Corteacutes JL Schmook B Biodiversity and Conservation of the Yucataacuten PeninsulaSpringer International Publishing New York NY USA 2015

36 Vester HF Lawrence D Eastman JR Land change in the southern Yucataacuten and Calakmul biospherereserve Implications for habitat and biodiversity Ecol Appl 2007 17 989ndash1003 [CrossRef] [PubMed]

37 Schmook B Shifting Maize Cultivation and Secondary Vegetation in the Southern Yucataacuten Forest Impactsof Temporal Intensification Reg Environ Chang 2010 10 233ndash246 [CrossRef]

38 Schmook B van Vliet N Radel C de Jesuacutes Manzoacuten-Che M McCandless S Persistence of swiddencultivation in the face of globalization A case study from communities in Calakmul Mexico Hum Ecol2013 41 93ndash107 [CrossRef]

39 Xolocotzi H Baltazar EB (Eds) La Milpa de Yucataacuten Un Sistema de Produccioacuten Agriacutecola Tradicional Colegiode Postgraduados Montecillo Mexico 1995 Tome II

40 Ressl R Lopez G Cruz I Colditz RR Schmidt M Ressl S Jimeacutenez R Operational active firemapping and burnt area identification applicable to Mexican Nature Protecion Areas using MODIS andNOAA-AVHRR direct redout data Remote Sens Envrion 2009 113 1113ndash1125 [CrossRef]

41 Comision Nacional Forestal (CONAFOR) Los Incendios Forestales en Mexico Technical Report ComisionNacional Forestal Mexico City Mexico 2005

42 Cheng D Rogan J Schneider L Cochrane M Evaluating MODIS active fire products in subtropicalYucataacuten forest Remote Sens Lett 2012 4 455ndash464 [CrossRef]

43 Giglio L Descloitres J Justice CO Kaufman YJ An enhanced contextual fire detection algorithm forMODIS Remote Sens Environ 2003 87 273ndash282 [CrossRef]

44 Giglio L MODIS Collection 6 Active Fire Product Userrsquos Guide Revision A Unpublished ManuscriptDepartment of Geographical Sciences University of Maryland Available online httpslpdaacusgsgovsitesdefaultfilespublicproduct_documentationmod14_user_guidepdf (accessed on 22 February 2016)

45 Schroeder W Prins E Giglio L Csiszar I Schmidt C Morisette J Morton D Validation of Goesand MODIS active fire detection products using ASTER and ETM+ data Remote Sens Environ 2008 1122711ndash2726 [CrossRef]

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46 Vaca RA Golicher DJ Cayuela L Hewson J Steininger M Evidence of Incipient Forest Transition inSouthern Mexico PLoS ONE 2012 7 e42309 Available online httpdoiorg101371journalpone0042309(accessed on 13 March 2017) [CrossRef] [PubMed]

47 Steininger MK Tucker CJ Ersts P Killeen TJ Villegas Z Hecht SB Clearance and Fragmentationof Tropical Deciduous Forest in the Tierras Bajas Santa Cruz Bolivia Conserv Biol 2002 15 1523ndash1739[CrossRef]

48 Ellis EC Ramankutty N Anthropogenic Biomes of the World version 1 Socioeconomic Data and ApplicationsCenter (SEDAC) National Aeronautics and Space Administration (NASA) Palisades NY USA 2008Available online httpdxdoiorg107927H4H12ZXD (accessed on 5 January 2017)

49 Instituto Nacional de Estadiacutestica Geografiacutea e Inofrmaacutetica (INEGI) Datos Baacutesicos de la Geografiacutea de MeacutexicoAvailable online wwwinegigobmx (accessed on 7 February 2015)

50 Getis A Ord JK The analysis of spatial association by use of distance statistics Geogr Anal 1992 24189ndash206 [CrossRef]

51 Anselin L Local indicators of spatial association-LISA Geogr Anal 1995 27 93ndash115 [CrossRef]52 Griffith DA Moran coefficient for non-normal data J Stat Plan Inference 2010 140 2980ndash2990 [CrossRef]53 Chomitz KM Gray DA Roads land-use and deforestation A spatial model applied to Belize World Bank

Econ Rev 1996 10 487ndash512 [CrossRef]54 Verburg PH Overmars KP Witte N Accessibility and land-use patterns at the forest fringe in the

northeastern part of the Philippines Geogr J 2004 170 238ndash255 [CrossRef]55 Agresti A Categorical Data Analysis 2nd ed John Wiley amp Sons New York NY USA 200256 Hosmer D Lemeshow S Applied Logistic Regression 2nd ed John Wiley amp Sons New York NY USA 200057 Millington JD Perry GL Romero-Calcerrada R Regression techniques for examining land usecover

change A case study of a Mediterranean landscape Ecosystems 2007 10 562ndash578 [CrossRef]58 Lyapustin AI Kaufman YJ Role of adjacency effect in the remote sensing of aerosol J Geophys Res 2001

106 11909ndash11916 [CrossRef]59 Griffith DA Spatial Autocorrelation and Spatial Filtering Gaining Understanding through Theory and Scientific

Visualization Springer BerlinHeidelberg Germany New York NY USA 200360 Griffith DA Layne LJ A Casebook for Spatial Statistical Data Analysis Oxford University Press Oxford UK

New York NY USA 199961 Turner MG Gardner RH Orsquoneill RV Landscape Ecology in Theory and in Practice Pattern and Process

Springer New York NY USA 200162 Walker R Moran E Anselin L Deforestation and cattle ranching in the Brazilian Amazon External capital

and household processes World Dev 2000 28 683ndash699 [CrossRef]63 Bradley AV Millington AC Spatial and temporal scale issues in determining biomass burning regimes in

Bolivia and Peru Int J Remote Sens 2006 27 2221ndash2253 [CrossRef]64 Munroe DK Wolfinbarger SR Calder CA Shi T Xiao N Lam CQ Li D The Relationships between

Biomass Burning Land-Cover Change and the Distribution of Carbonaceous Aerosols in Main Land Southeast AsiaA Review and Synthesis Department of Statistics Preprint 793 The Ohio State University Columbus OHUSA 2007

65 Pfaff AJ What drives tropical deforestation in the Brazilian Amazon Evidence from satellite andsocioeconomic data J Environ Econ Manag 1999 37 26ndash43 [CrossRef]

copy 2017 by the authors Licensee MDPI Basel Switzerland This article is an open accessarticle distributed under the terms and conditions of the Creative Commons Attribution(CC BY) license (httpcreativecommonsorglicensesby40)