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Forest Ecology and Management

journal homepage: www.elsevier.com/locate/foreco

Tree spatial patterns and stand attributes in temperate forests: Theimportance of plot size, sampling design, and null model

Marco Carrera, Daniele Castagneria,⁎, Ionel Popab, Mario Pividoria, Emanuele Linguaa

a University of Padua, Department TeSAF, viale dell’Università 16, Legnaro, PD, Italyb National Institute for Research and Development in Forestry “Marin Drăcea” (INCDS), Calea Bucovinei 73bis, Câmpulung Moldovenesc, Romania

A R T I C L E I N F O

Keywords:Forest structurePermanent plotSampling designSpatial pattern analysis

A B S T R A C T

Detection of tree spatial patterns and structural attributes in a forest stand can provide critical information onoccurring dynamics, and steer management decisions. However, since tree spatial distribution depends on fac-tors that operate at different scales, including environmental heterogeneity and tree-to-tree interactions, boththe extent to which measurements are taken and the choice of null model for spatial analysis (including siteheterogeneity or not), can considerably influence investigation outcomes and related inferences.

In this study, we aim to evaluate the effect of plot size, sampling design (single or combined plots), and nullmodel for spatial analysis, on point pattern analysis and stand attribute assessment in temperate forests. Analyseswere performed on 4-ha plots in two old-growth and two previously managed stands in central Europe. For eachsite, we calculated tree density, mean diameter, mean height and basal area, and performed point patternanalysis (pair-correlation function) under complete spatial randomness (CSR) and heterogeneous Poisson (HP)null models. We then assessed stand attributes and spatial patterns on subplots, and calculated their deviationfrom the 4-ha reference plot.

As expected, accuracy of stand attribute assessment improved by increasing subplot size. However, whileaccuracy of small (0.25-ha) plots was quite high for basal area, it was rather low for tree density, especially in theold-growth stands. Outcomes of point pattern analysis in 0.25-ha plots were variable, generally presenting lowagreement with the reference. Larger plots assured more consistent results, but deviations from the referencewere still rather high when CSR null model was used. In all the sites, subplot agreement improved using HPmodel.

Our investigation indicates that 0.25-ha plots are mostly reliable for assessing stand attributes in previouslymanaged forests. However, tree distribution can be very variable both in these and in old-growth stands,therefore spatial patterns cannot be reliably detected with one small plot. Combining several small plots, andusing null models accounting for site heterogeneity, are efficient strategies to detect small-scale spatial patterns,but plot larger than 1-ha should still be used to assess large-scale patterns in high-diversity forest stands.

1. Introduction

In the natural environment, trees are not uniformly distributed, butform a complex mosaic with patches of different age, size, species,which reflect past endogenous and exogenous processes, and influencefuture ones (Watt, 1947; Dale, 1999; Stoyan and Penttinen, 2000).Spatial patterns in forests cover a wide range, which require adequateobservation scales (Dungan et al., 2002). Mapping forest canopy on aglobal or regional scale (e.g. Simard et al., 2011) certainly cannot beperformed with the same resolution as studies on microsite influence onseedling establishment (e.g. Germino et al., 2002). For studies on eco-logical processes such as tree recruitment, competition and mortality,

the perspective of individual stems is often the most appropriate (Songet al., 1997), and recording the position of each individual ensures theminimum grain size and maximum possible resolution (Zenner andPeck, 2009). The spatial extent generally corresponds to the foreststand, which can be defined as a more or less homogeneous patch of theforest (West, 2004). However, operating at single tree level with theaim of fully capturing ecological processes within a stand, would re-quire huge field sampling efforts. This leads to restricting investigationto a subsample, i.e. a relatively large plot representative of the stand, ormany smaller plots scattered over the area. The spatial scale issue inforest science is therefore closely related to the sampling strategy, inparticular to the size and number of plots.

http://dx.doi.org/10.1016/j.foreco.2017.10.041Received 30 August 2017; Received in revised form 20 October 2017; Accepted 20 October 2017

⁎ Corresponding author.E-mail address: daniele.castagneri@unipd.it (D. Castagneri).

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0378-1127/ © 2017 Elsevier B.V. All rights reserved.

MARK

How to achieve precise and accurate estimates of forest attributesand structure, by efficiently reducing time and cost of field work, is asubject of debate in forest science (Bormann, 1953; Kenkel et al., 1989;Gray, 2003; Lynch, 2016). Previous studies have shown that some forestattributes, such as number of large trees (Zenner and Peck, 2009),deadwood elements (Lombardi et al., 2015), and abundance of rarespecies (Corona et al., 2011), require more and larger plots compared tocommonly investigated attributes such as stand basal area (Du et al.,2015). Other studies have investigated the effect of observation scaleson the spatial autocorrelation among stand characteristics (Král et al.,2014) and on tree size distribution (Alessandrini et al., 2011). However,to our knowledge, no study has specifically assessed the effect of plotsize on point pattern analysis (PPA). This approach has received in-creasing attention in forest ecology, being used to investigate re-generation (Kuuluvainen and Rouvinen, 2000; Janík et al., 2016),mortality (Castagneri et al., 2010; Aakala et al., 2012), intra and inter-specific competition (Doležal et al., 2006; Petritan et al., 2014) andfacilitation (Lingua et al., 2008; Muhamed et al., 2015) processes,spatiotemporal changes in the relationships between species and sizeclasses (Janík et al., 2014), and the influence of natural disturbances(Nagel et al., 2006) and management (Wolf, 2005) on forest structure.Just considering temperate forests (in subtropical and tropical forestssampling plots are generally larger, Getzin et al., 2014), the spatialextent of such investigations varies considerably, ranging from 0.25 hain pioneer studies (Kenkel, 1988) to 25 ha (Johnson et al., 2014). Smallplots cannot be expected to properly represent large forest patches re-lated to medium to large-scale disturbances (Nagel et al., 2006), butplots < 1 ha have been widely used to investigate tree spatial patternsin different environments (Svoboda et al., 2010; Aakala et al., 2012;Marzano et al., 2012; Petritan et al., 2014), as most inter-tree interac-tions are expected to occur within 10m scales (Stoyan and Penttinen,2000; Getzin et al., 2008). Nonetheless, small plots have intrinsic lim-itations, such as fewer trees compared to larger plots, and proportion-ally greater edge effect (Wiegand and Moloney, 2014). Combining in-formation from several plots, considered as pseudo-replications, hasbeen proposed (Illian et al., 2008; Wiegand and Moloney, 2014) andused (De Luis et al., 2008; Raventós et al., 2010; Petritan et al., 2014;Piermattei et al., 2016) to reinforce and stabilize results from smallplots, in order to obtain a more robust view of spatial patterns in theforest stand.

Beside plot size and arrangement, PPA can be deeply influenced bythe null model used (Dale, 1999). The simplest one, and still widelyused in ecological studies (Baddeley et al., 2014; Velázquez et al.,2016), is the complete spatial randomness (CSR). It considers that anypoint of the pattern has an equal probability of occurring at any loca-tion within the study plot, i.e., that the observed events are consistentwith a homogeneous Poisson process (Wiegand and Moloney, 2014). Ina forest stand, CSR implies that site (soil, topography, etc.) is homo-geneous, a condition that hardly occurs in practice (Velázquez et al.,2016). An alternative null model, widely applied to study plant spatialdistribution and relationships in a natural environment (such as trees inforest stands; Svoboda et al., 2010; Piermattei et al., 2016), whereenvironmental heterogeneity (e.g. different topography or soil condi-tions) can affect spatial distribution (Getzin et al., 2008; Baddeley et al.,

2014), is the heterogeneous Poisson (HP) null model. This differs fromCSR in that the intensity λ (x, y) of the process depends on location (x,y), but the occurrence of any point remains independent of that of anyother (Wiegand and Moloney, 2004). The selection of the null model isa critical step in PPA, influencing analysis outcomes and therefore in-terpretation of the observed patterns. Nonetheless, specific studiesevaluating the influence of the null model on PPA assessed from dif-ferent plot sizes, to our knowledge, are still lacking.

In this study, we evaluated how plot size, sampling design (single orcombined plots), and null model for spatial analysis, affect the assess-ment of tree spatial patterns and stand attributes in temperate forests.Analyses were conducted on four mountain forests in central Europe,including pure and mixed, even- and uneven-aged, old-growth andpreviously managed stands. We aimed at testing the following hy-potheses: (1) increasing plot size improves the accuracy of stand attri-bute and spatial pattern assessment; (2) combined information on standattributes obtained from four 0.25-ha plots is similar to that of 1-haplots, but less accurate on spatial patterns; (3) PPA accuracy of smallplots can be improved adopting a null-model accounting for spatialheterogeneity.

2. Materials and methods

2.1. Study sites

Our analysis was conducted on four temperate mountain forests incentral Europe (Table 1).

Giumalau (GIU), in the Romanian Carpathians, within the CodrulSecular Giumalau Forest Reserve (47°26′N; 25°28′E). The reserve, es-tablished in 1941, comprises 309.5 ha of pure Picea abies L. (Karst.)(Norway spruce) forest, including old-growth stands where the surveywas conducted (Lamedica et al., 2011).

Slatioara (SLA), in the Romanian Carpathians, on a mid-mountainslope within the Codrul Secular Slatioara Forest Reserve (47°27′N;25°37′E). The study was performed in an old-growth mixed forest standmainly composed of Norway spruce, Abies alba Mill. (silver fir) andFagus sylvatica L. (European beech).

Millifret (MIL), on the Cansiglio plateau, northern Italy, within thePian di Landro – Baldassare Nature Reserve (46°03′N; 12°20′E). This130-ha forest, protected since 1971, comprises pure even-agedEuropean beech stands, previously managed by the shelterwoodsystem.

Latemar (LAT), in the western Dolomites, eastern Italian Alps(43°22′N; 11°33′E). Mixed Larix decidua Mill. (European larch), Pinuscembra L. (Swiss stone pine) and Norway spruce subalpine forest wasaffected by extensive cutting and livestock grazing in the past centuries,but human activities have gradually decreased since the Second WorldWar.

2.2. Field data collection and stand attributes

In each site, we established one 4-ha (200×200m) permanentplot. All living trees with diameter at breast height (dbh)≥ 0.5 cm wereidentified and labelled, and stem base coordinates (x, y), dbh, and

Table 1Elevation, descriptive features and stand attributes of Giumalau (GIU), Slatioara (SLA), Millifret (MIL) and Latemar (LAT) (mean value in the 4-ha plots) sites.

Elevation (m a.s.l.) Category AgeStructure

SpeciesComposition

Density(n ha−1)

Dbh(cm)

Height(m)

Basal area(m2 ha−1)

GIU 1150 old-growth Uneven Pure 559 22.9b (20.8) 15.2c (12.4) 42SLA 1450 old-growth Uneven Mixed 1240 15.7c (17.9) 11.1d (9.6) 55.1MIL 1400 prev.manag. Even Pure 846 26.3a (9.1) 24.0a (4.4) 51.5LAT 1900 prev.manag. Uneven Mixed 453 29.6a (15.4) 16.9b (7.6) 39.7

For diameter (Dbh) and tree height (Height), standard deviation is reported in brackets, and different letters (superscript) indicate significant difference between the areas according toone-way ANOVA test with Tukey’s pairwise comparisons.

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height were recorded. For each plot, the following forest stand attri-butes were calculated: tree density (n ha−1), mean diameter at breastheight (cm), mean height (m), and basal area (BA) (m2 ha−1).Differences among the four sites were tested by one-way ANOVA, whenapplicable (on Box-Cox transformed data, to better approximate as-sumptions of normality and homogenous variance). In order to in-vestigate the role of plot size and sampling design in assessing standattributes, we virtually identified subplots within each site as follows(Fig. 1): two 2-ha plots; four 1-ha plots; eight 0.5-ha plots; 16 0.25-haplots; and 10 ‘combined’ 1-ha plots, assembled from four randomlyselected 0.25-ha plots. The random selection was done without re-placement and did not necessarily include adjacent subplots.

We then assessed, in all the study sites separately, the percentagedeviation of each attribute in each subplot from the 4-ha plot value,considered as the reference. Two-way ANOVA was applied to assess the(fixed) effect of subplot type (2-ha, 1-ha, 0.5-ha, 0.25-ha, combined) onthe percentage deviation, considering the random effect of site (GIU,SLA, MIL, LAT). Data were arcsine transformed prior to analysis. Allanalyses were implemented in R (R Development Core Team, 2016).

2.3. Spatial analysis

The spatial distribution of trees within the sites was assessed usingunivariate point pattern analysis (PPA). We used pair-correlationfunction (g) (Stoyan and Stoyan, 1994), a second order statistic closelyrelated to Ripley’s K-function (Ripley, 1977). We chose the g-functioninstead of K-function to avoid misinterpretation of results due to thecumulative effect of the latter (Perry et al., 2006). The univariate pat-terns were contrasted against two null models, the complete spatialrandomness (CSR), and the heterogeneous Poisson (HP) null model. Wecomputed the intensity function nonparametrically, applying the Epa-nechnikov kernel estimators (Stoyan and Stoyan, 1994; Wiegand andMoloney, 2014) using a 20m radius for the moving window estimator.

The 99% confidence envelopes were computed from 99 Monte Carlosimulations (Wiegand and Moloney, 2004; Stoyan and Stoyan, 1994),and goodness-of-fit (GoF) test for null hypothesis was performed(Diggle, 2003; Baddeley et al., 2014). The univariate spatial pattern wasdefined as clumped, random or regular (overdispersed) if the g(r) valueswere greater than, equal to or lower than the confidence envelopes,respectively. We performed the g(r) analyses applying a 1m lag dis-tance and not exceeding half the minimum length of the plot to limit theinfluence of the margin effects (Haase, 1995). All analyses were donewith the grid-based software Programita (Wiegand and Moloney, 2004)adopting a grid size of 1m2 and a ring width of 5m.

For all four study sites, PPA was computed on the 4-ha plot, con-sidered as the reference, and on four 1-ha plots, 16 0.25-ha plots, and10 combined plots. The latter represent pseudo-replications of fourrandomly selected 0.25-ha plots (Wiegand and Moloney, 2014).

Besides visual comparison, PPA agreement of subplots with the 4-hareference plot was quantified with an agreement index, assessed on thefirst 25m (half the side length of the 0.25-ha plots). Values range from0 to 1, where 1 indicates perfect agreement, i.e. the subplot and thereference show the same pattern - clumped, random or overdispersed -on all 25 cases (i.e., 1-m distances), and 0 implies complete disagree-ment (Willmott, 1981). Three-way ANOVA was applied to assess theeffect of the subplot type (1-ha, 0.25-ha, combined), the null model(CSR, HP) and their interactions on the agreement, considering therandom effect of the site (GIU, SLA, MIL, LAT). Data were arcsinetransformed prior to analysis.

3. Results

A total of 12,393 trees were measured and mapped in the four sites(Fig. 2), which exhibited different stand characteristics (Table 1). Meandbh and height were smaller in SLA than in the other plots. However,SLA presented the highest BA, due to the much higher tree densitycompared to the other plots. Diameter distribution showed reverse-Jshape in SLA (Fig. 3). A similar pattern occurred in GIU, but small treeswere relatively less represented. MIL showed the typical diameter

Fig. 1. Sampling framework used in the study. The blue border delineates the 4-ha(200× 200m) plot. Red borders delineate four 1-ha plots, A, B, C and D. Within 1-haplots, four 0.25-ha plots, 1, 2, 3 and 4, are delimited by black borders. 2-ha plots arecomposed by two adjacent 1-ha plots (italic/not italic letters). 0.5-ha plots are composedby two adjacent 0.25-ha plots (underscored/not underscored letters within the same 1-haplot). Combined plots were formed by four 0.25-ha plots randomly extracted. (For in-terpretation of the references to colour in this figure legend, the reader is referred to theweb version of this article.)

GIU SLA MIL LAT200

150

100

50

020015010050 20015010050

Meters Meters

Meters

20015010050Meters

200150100Meters

50

Fig. 2. Maps of trees (green dots) in the four 4-ha (200×200m) plots at Giumalau (GIU), Slatioara (SLA), Millifret (MIL) and Latemar (LAT). (For interpretation of the references tocolour in this figure legend, the reader is referred to the web version of this article.)

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distribution of even-aged stands, while in LAT all classes< 50 cm weresimilarly represented.

Within the same site, subplot deviation from the reference 4-ha plotwas generally higher for tree density, and lower for basal area (Fig. 4,Supplementary Table 1). In general, subplots showed the highest de-viations at SLA, and lowest at MIL. For different subplot types, ANOVAanalysis indicated that deviations were highly different for density(F4,160= 5.50, P < .001), basal area (F4,160= 11.47, P < .001) andtree height (F4,160= 5.26, P < .001), and, to less extent, for dbh(F4,160= 3.54, P < .01).

The pair-correlation functions showed different tree spatial ar-rangements in the four sites (Fig. 5). In the 4-ha plots, GIU showedstrong aggregation at short distances, turning into a random pattern at33m under CSR null model, but already at 8m under the HP nullmodel. At SLA, where a strong density gradient occurs from west to east

(Fig. 2), tree spatial pattern was aggregated at all the distances underCSR, but only up to 9m under HP. MIL showed significant aggregationfrom 2 to 50m under CSR, but this pattern was not evidenced under HP.LAT showed significant aggregation in the first metres under both CSRand HP. However, aggregation at successive distances under CSR didnot show up under HP.

Despite the high variability among the four sites, some general in-dications emerged. ANOVA showed that the three subplot types havesignificantly different agreement with the reference (F2,231= 18.98,P < .001). In general, 0.25-ha plots provided the least agreement,while spatial patterns emerging from the 1-ha and combined plots weremore in agreement with the reference (Fig. 6, Supplementary Table 2).In most cases, 0.25-ha plots highlighted either a reduced range of ag-gregation with respect to the 4-ha plots, or none at all (Fig. 5).

Different null models not only influenced PPA results, but alsosubplot agreement with the reference (Fig. 6). ANOVA analysis re-vealed a strong influence of the null model (F1,231= 300.23,P < .001), and a significant effect of its interaction with the subplottype (F2,231= 3.72, P= .026). The subplot agreement to the referencewas generally higher using HP than using CSR (Fig. 6), but the differ-ence was more evident for 0.25-ha and combined plots than for 1-haones. Under CSR, 1-ha plots always had a better agreement compared tocombined plots, while under HP the agreement was similar.

4. Discussion

4.1. Stand attributes

Identifying a universally appropriate scale of investigation in forestecology, and thus an efficient sampling strategy to survey differentstand attributes in different forests, is unfeasible, as indicated by theextensive literature (Gray, 2003; Král et al., 2014; Lynch, 2016). In-deed, accuracy of sampling plots depends both on the target attributeand stand characteristics (Du et al., 2015; Lombardi et al., 2015). Somestructural features are more uniformly distributed within a stand thanothers, and require less sampling effort (Busing and White, 1993; Králet al., 2010). In the four sites, 0.25-ha and 0.5-ha plots usually providedquite accurate estimates for basal area (Fig. 4, Supplementary Table 1).Deviation from the reference was greater for tree density, due to thehigh within-site variation. For this attribute, combining informationfrom four 0.25-ha plots (combined plots) was an effective approach toimprove accuracy in the most heterogeneous site, SLA.

For most attributes, subplot deviation from the reference was

Fig. 3. Diameter distribution in 5-cm classes at Giumalau (GIU), Slatioara (SLA), Millifret(MIL) and Latemar (LAT). Note the different Y axis range between the plots.

Fig. 4. Subplot percentage deviation from the re-ference for tree density (Dens.) (n ha−1), mean dia-meter at breast height (Dbh) (cm), mean height(Height) (m), and basal area (BA) (m2 ha−1), atGiumalau (GIU), Slatioara (SLA), Millifret (MIL) andLatemar (LAT). Bar colours indicate the subplot type(see the legend).

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markedly higher in the old-growth GIU and SLA than in the other twosites. Structural complexity is one of the most indicative features of old-growth stands (McElhinny et al., 2005; Bauhus et al., 2009; Di Filippoet al., 2017). Most temperate old-growth forests in Europe comprise amosaic of small patches in different phases of development, due to in-termediate- to small-scale disturbance regimes (Král et al., 2010; Mottaet al., 2011). Plots< 1 ha cannot include such structural variability

within the stand (Busing and White, 1993). Younger, managed stands,or those affected by human activities in the past, are usually morehomogeneous, and present less variability in both size-related attributesand tree density (Carey, 2003). Our results, in agreement with otherstudies (e.g. Busing and White, 1993; Zenner and Peck, 2009), suggestto adopt larger (≥1 ha) or more (combined) plots in old-growth than inpreviously-managed stands.

Fig. 5. Representation of univariate point pattern analysis at Giumalau (GIU), Slatioara (SLA), Millifret (MIL) and Latemar (LAT), using complete spatial randomness (CSR) andheterogeneous Poisson (HP) null models, assessed for 4-ha plots and subplots. For 4-ha plots (upper graph) and 1-ha plots (A, B, C and D, below), lines indicate the pair correlationfunctions g(r), and the shaded areas indicate the Monte Carlo envelopes (99% confidence). Values above confidence envelopes (clustering) are in green, values below confidenceenvelopes (overdispersion) are in red, values within the envelopes (random) are in black. For 0.25-ha plots (from A1 to D4), and combined plots (from Co.1 to Co.10), green circlesindicate clustering, red circles indicate overdispersion, white circles with black outline indicate random pattern. For all the analyses, the p value of the goodness of fitness (GoF) test isreported. All results are shown from 1 to 25m. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

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4.2. Small and large plots for spatial analysis

Scattered plots of between 0.01 and 0.1 ha are typically used inforest inventories to assess stand attributes (West, 2004; Zenner andPeck, 2009). However, such small plots are not useful for analyzing treespatial patterns, which are generally assessed on plots of at least 0.25 ha(Kenkel, 1988). Our hypothesis was that 0.25-ha plots would be lessaccurate than 1-ha plots for long-distance patterns (indicatively >10m), nonetheless we expected that they could provide reliable in-dications on short distances. Our analysis revealed high variability ofPPA outcomes among 0.25-ha plots, low accuracy with the reference,and scarce capacity to detect aggregation at all distances (Figs. 5 and 6).

Different aspects can be adduced to explain the low capacity of0.25-ha plots to detect aggregation: (i) small plots have few trees, thusadversely affecting PPA, particularly non-cumulative statistics such asthe g-function (Wiegand and Moloney, 2004). However, this probablyhad a minor effect in the study sites, as tree number was< 100 in just 7out of 64 0.25-ha plots, with a minimum of 68 trees, this being wellabove the lower thresholds we found in the literature (15–20 in-dividuals per class, Camarero et al., 2000; Zenner and Peck, 2009). (ii)The edge effect is proportionally larger in small plots (Wiegand andMoloney, 2014). Corrections accomplished by recent software (in-cluding Programita, Wiegand and Moloney, 2004) are generally con-sidered to be very effective (Velázquez et al., 2016), yet negative

Fig. 5. (continued)

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influence of edge effect for small plots cannot be completely ruled out.(iii) Small plots not only cannot include large tree clusters, and thus failto detect large-scale patterns, but small tree clusters can also be arti-ficially split by plot borders; this negatively affects small-scale patternsdetection. (iv) Especially in old-growth forests, stand structure and treespatial patterns can considerably vary within a large area. This playedan important role in all our sites, but GIU was probably the clearestcase. In this 4-ha plot (Fig. 2) there are a few tree clusters. However,they do not occur in several 0.25-ha plots, where tree distribution re-sults as being random. On these subplots, the analysis outcome (randomdistribution) was not an artefact due to the intrinsic limits of smallplots, but reflected the actual pattern within that particular part of the

stand. This differed from the reference pattern, which was aggregated(at some distances) due to the occurrence of sparse tree clusters.

In the combined plots, results were more consistent with the re-ference. In this subplot type, the edge effect is the same as in 0.25-haplots (same border/area ratio), indicating that this issue scarcely ex-plains the poor 0.25-ha plot performance. Rather, by increasing thetotal area under analysis, there was a higher probability of includingtree clusters. Remarkably, when just one of the four 0.25-ha plots in-cluded tree clusters (with significant aggregation detected), the com-bined plot showed significant aggregation.

One-ha plots had much better agreement than 0.25-ha ones, and insome cases than combined plots (see the next paragraph). However,

Fig. 5. (continued)

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even this type of subplot provided only partial agreement with the re-ference. Again, this was probably due to significant spatial patternvariations in the 4-ha plots: tree distribution in one hectare can sig-nificantly differ from that in four hectares. Handling such variationswith a null model that considers within-area heterogeneity, helped toimprove subplot agreement, as detailed below.

4.3. Null models

Using different null models led to quite different results in all thesites. Under HP null model, tree distribution was less aggregated than

under CSR, in all plot types. Besides, in all sites, subplot agreement withthe reference improved using HP, especially for 0.25-ha and combinedplots. This validates our initial hypothesis, since filtering out large-scaleheterogeneity helped in detecting small-scale interaction. Site condi-tions (i.e. soil parameters, water availability, occurrence of unsuitablespots) can vary all over the area, while tree interactions are supposedlymore consistent. Tree interactions are only expected to vary, e.g.shifting from negative (due to competition) to positive (facilitation)spatial interactions, on very large scales, including environmentalgradients (Callaway, 1998; Lingua et al., 2008). Furthermore, HP nullmodel probably filtered out variations in tree density related to stand

Fig. 5. (continued)

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history. Natural and human disturbances influence tree mortality andregeneration, causing a heterogeneous spatial arrangement that is notstrictly related to tree-to-tree interactions (Remmert, 1991; Dale, 1999).

In the old-growth GIU and SLA, most aggregate patterns at longdistances (> 10m) under CSR turned into random patterns under HP inthe 4-ha, 1-ha and combined plots. Significant aggregation was pre-served under HP for the first 5–10m. Using HP instead of CSR improvedthe agreement of all subplot types. At MIL, differences within the plot inlogging activities a few decades ago obviously affect tree distribution.In addition, a narrow forest track crosses the stand (Fig. 2), probablyaffecting PPA in some subplots. Such heterogeneity likely explainsdifferences in the plots. However, after removing this “noise” by HP, thespatial patterns showed good agreement between most subplots and thereference. Different null models also affected analysis at LAT. Strongaggregation at short distance (typical of subalpine forests, Callaway,1998) was found in the 4-ha plot and in most subplots under both nullmodels. However, in the 4-ha plot, moderate but significant aggrega-tion under CSR at long distances turned into random under HP. Suchaggregation was likely not related to tree-to-tree interactions, whichoccur on shorter distances, but to environmental constraints (Wiegandet al., 2007; Getzin et al., 2008) or stand history, e.g. due to differentregeneration patches within the stand (Dale, 1999). Once again, het-erogeneity handling by HP improved the agreement of subplots.

These differences call for a careful selection of the null model forpoint pattern analyses. In all the stands, site topography was apparentlyhomogeneous. We could not establish whether significant aggregationat long distances under CSR were related to soil heterogeneity, or toprocesses related to forest dynamics (Dale, 1999; Getzin et al., 2008).Both these factors probably contributed to shape forest structure. Al-though CSR is generally considered to be unrealistic in a forest stand(Velázquez et al., 2016), this simple null model could help in identi-fying large-scale patterns in spatially complex stands, such as most old-growth forests (Franklin and Van Pelt, 2004). HP better reflects het-erogeneous conditions of forests, and certainly provides a more realisticindication of tree-to-tree interactions when tree distribution is affectedby unsuitable micro-sites or stand history. We demonstrated that this

null model considerably increases consistency of subplots. Given theincreased analysis speed of recent software for PPA, we suggest testingtree spatial patterns against different null models, including both CSRand models that account for site heterogeneity.

4.4. Considerations on sampling strategies

Planning of forest field surveys, mainly those conducted for pro-duction, conservation, management, or research purposes, has to findthe best compromise between time and money spent in the field, andreliability of retrieved information (Gray, 2003; West, 2004; Coronaet al., 2011). Some stand attributes widely used in forestry, such asbasal area, can be reliably assessed by few small plots, especially in low-diverse even-aged forests such as many previously-managed stands inEurope. However, tree density and spatial distribution can considerablyvary also within these stands, thus affecting point pattern analyses.Using null models accounting for site heterogeneity can improve smallplot accuracy.

To investigate large-scale spatial patterns in old-growth mountainforests across Europe, which generally have higher structural and spa-tial complexity than managed or previously-managed stands (Franklinand Van Pelt, 2004; Lombardi et al., 2015), we suggest to use plotslarger than one hectare. Low performance of subplots in our analysisseemed to be only partially related to intrinsic problems of small plots(few trees, edge effect), but rather to their scarce representativeness ofthe complex tree spatial patterns in old-growth stands. However, whensurvey strategies require a large number of sampling points, combininginformation from small (e.g. 0.25-ha) plots, using null mpdels that ac-count for spatial heterogeneity, can be an efficient strategy to obtainconsistent and reliable information on small-scale spatial patterns.

Acknowledgments

We thank Davide Bazzanella, Nechita Constantin, Efrem Ferrari,Silvia Lamedica, Hannes Markart, Giai Petit, Boris Šašić, Luca Soraruf,and all the people involved in fieldwork over the last ten years, for theiressential contribution in the creation of the permanent plot network.We also thank Fabio Maistrelli from The Forest Planning Office of theAutonomous Province of Bolzano and Paola Berto from VenetoAgricoltura for providing logistic and technical support.

Appendix A. Supplementary material

Supplementary data associated with this article can be found, in theonline version, at http://dx.doi.org/10.1016/j.foreco.2017.10.041.

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