oncept series- anthology of works collected for undisclosed reasons

Anthology of Works

Collected for

Undisclosed Reasons

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Foreword

An anthology is defined as a collection of works chosen by a compiler. The compiler arranges the works in a deliberate way as he or she fits.

This anthology is no different than any other anthology, except that the works collected here were collected for a reason/ a set of reasons that the compilers refuse to disclose. The reader is free to read and interpret this anthology in any manner or mode. Most importantly, the lack of intent and purpose of this anthology also gives the readers the freedom to not read it, thus giving priority to the agency of the reader in the process of reading over the authors' claims of literary or curatorial self-importance.

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Table of Contents

The Federal Court Database: New Research Opportunities..............................1by Terence Dungworth

Positive Environmental Externalities of Livestock inMixed Farming Systems of India..............................................................11by A.K. Dikshit and P.S. Birthal

The Need for Audiologic Habitation..................................................................20by E.J. Hardick and S.A. Lesner

The Signature of Line Graphs and Power Treesby Long Wang et al....................................................................................30

Estimation of the Equilibrium Exchange Real Exchange Rate for South Africa................................................................39by Ronald MacDonald and Lucca Ricci

The Efficient Method for Simultaneous Monitoring ofthe Culturable as Well as Nonculturable Airborne Microorganismsby Barbara Hubad.....................................................................................63

Attachment Styles at Hogwarts: From Infancyto Adulthoodby Wind Goodfriend...................................................................................72

Endocrine and metabolic manifestations in inflammatory bowel diseaseby Stelios Tigas and Agathocles Tsatsoulis...............................................88

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Agricultural Economics Research ReviewVol. 26(No.1) January-June 2013 pp 21-30

Positive Environmental Externalities of Livestock inMixed Farming Systems of India

A.K. Dikshita* and P.S. BirthalbaCentral Institute for Research on Goats, Makhdoom - 281 122, Uttar Pradesh

bNational Centre for Agricultural Economics and Policy Research, New Delhi - 110 012

Abstract

Livestock are often criticized for their negative externalities to environment. However, in the mixedfarming systems followed in India, the livestock help in saving natural resources through their synergisticrelationship with cropping activities. This paper has quantified the positive environmental externalitiesassociated with livestock production in Indias mixed farming systems. These include: land saving due torecycling of agricultural by-products as animal feed and also due to use of dung- cake as domestic fuel;saving of chemical fertilizers due to use of dung as manure and prevention of carbon dioxide emissiondue to use of animal energy in agriculture. Land saving from livestock production system due to recyclingof crop by-products as animal feed and use of dung as domestic fuel has been estimated as 42 Mha. Theuse of dung as manure saves 1.2 Mt of soil nutrients. Likewise, use of animal energy as a substitute formechanical energy has potential to save diesel consumption to the extent of 13 Mt and prevents greenhousegas emission due to burning of diesel.

Key words: Livestock, environment, mixed farming system, India

JEL Classification: Q51, Q20, Q0

*Author for correspondenceEmail: [email protected]

IntroductionLivestock, despite their significant contributions

towards enhancing food and nutritional security andreducing poverty, are often criticized for the negativeexternalities they cause to environment throughemission of greenhouse gases, overgrazing/deforestation and water pollution (Steinfeld et al.,2006). Impacts of livestock on environment, however,differ across production systems. Industrial livestockproduction systems cause more harm to environment,while mixed crop-livestock systems are benign toenvironment (Sere and Steinfeld, 1996). In the mixedfarming systems, animals draw their energyrequirements from environment in the form of feedfrom by-products of crops, from cultivated green fodder

and from grazing, and in turn, give back that energy inthe form of food (milk, meat, and eggs), draught power,fuel, and manure. With this process of energy exchangeare associated a number of environmental externalities,negative as well as positive. Negative externalities oflivestock to environment are well documented andquantified (Steinfeld et al., 2006); but their positivecontributions have remained less documented and non-quantified. The prominent positive environmentalcontributions include prevention of carbon di-oxideemission due to use of animal energy in place of fossilfuel, saving of natural resources mainly land as a resultof recycling of agricultural by-products and residuesas animal feed, and dung in place of firewood asdomestic fuel and as a substitute for chemical fertilizers.Evidence also suggests that managed grazing helps inimproving biodiversity (Pasha, 2005). In this paper,we have made an attempt to quantify some of the

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22 Agricultural Economics Research Review Vol. 26(No.1) January-June 2013

positive contributions of livestock to environment inIndia where livestock are largely raised in the mixedfarming systems.

Analytical ApproachInformation on feed consumption rates, by species,

is an important requirement in estimating the positiveenvironmental effects of livestock production. To ourknowledge, there is little information available on feedconsumption rates in India, except some localizedinformation generated through surveys undertaken bythe Indian Agricultural Statistics Research Institute(IASRI) during 1960s to early-1980s. This informationis quite aged now and also there are problems in poolingof the data from surveys spread over such a long period.

In this paper, we have used data on feedconsumption and several other attributes of livestock,viz. body size, grazing practices, dung production andits utilization, etc. from a nationally representativesurvey undertaken as part of a larger project, IndiasLivestock feed balance and its environmentalimplications, funded by the Indian Council ofAgricultural Research (ICAR) under the NationalAgricultural Technology Project (NATP), and carriedout jointly by the National Centre for AgriculturalEconomics and Policy Research (NCAP) and theSociety (now Centre) for Economic and SocialResearch (SESR), Delhi. The survey was conductedin 2001-02 in different agro-climatic regions of India.A brief description of delineation of regions, surveydesign, data collection procedure, feed consumptionestimation procedure and estimation of positivecontributions of Indias livestock production systemhave been given in the following sections.

Sampling Design

India has considerable heterogeneity intopography, soils, rainfall, irrigation, temperature,cropping pattern and livestock production systems.Hence, for any survey to qualify as a nationallyrepresentative sample, it must take into account thisheterogeneity. To ensure that survey estimates wererepresentative of the national situation, a multistagesampling framework was adopted to generate therequired information. The National Bureau of SoilSurvey and Land Use Planning (NBSS&LUP) anoffshoot of the Indian Council of Agricultural Research,

has mapped Indias territorial space into 20 agro-ecological zones with their further classification into60 sub-zones. However, for implementation of thesurvey, we have taken into consideration topography,climatic conditions and cropping pattern of 60 sub-zones, and re-organized these sub-zone into 11 broadregions, which we have termed as livestock regions.In doing so, it was ensured that a livestock region wascontiguous. These regions were: Western Himalayas,North-West Plains, Eastern Plains, Central Highlands,Eastern Plateau and Highlands, Deccan Plateau andHills, Rajasthan-Gujarat Plains, Eastern Ghats, WesternGhats, Assam-Bengal Plains and North-EasternHighlands.

The survey was conducted in 10 livestock regions,excluding North-Eastern Highlands. The stratifiedmultistage random sampling approach was adopted inthe study. From each livestock region, two districts (onefrom some regions) were selected at random; and fromeach selected district, two villages were selected againat random. A livestock census was conducted in eachselected village to know the ownership pattern ofdifferent livestock species. Having enumeratedlivestock-keeping households, a random sample of 20-25 livestock-keeping households was drawn from eachvillage to make up the total sample size of around 1000households. Excluding the un-surveyed zone, wecollected information from 864 households. The datawere collected during the years 2001 and 2002.

Information related to the households and livestockholdings was collected from the heads of samplehouseholds. Information that required measurement,e.g. amount of different types of feed to be fed todifferent categories of animals by age-group, sex andfunction; and animal characteristics, e.g. body weightwas generated by the field investigators at thehousehold premises. Investigators were required toweigh and record the types of feed every day in themorning and evening, for complete one year to captureseasonality in feed consumption rates and theircomposition which was likely because of theseasonality in production of different types feed andalso because of seasonal differences in the uses oflivestock or their outputs. Considering that it wasdifficult to weigh and record different feeds every day,each household was revisited every fortnight for oneyear to collect this information.

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Dikshit and Birthal : Positive Environmental Externalities of Livestock in India 23

Estimation of Feed Consumption Rates

Household level feed consumption rates serve asa base to estimate feed consumption rates at the nationallevel. These rates were estimated applying scale-upfactors at the levels of village, district and region. Fromthe survey, we gathered information on (i) number ofsample households having livestock, say buffalo in-milk and (ii) number of buffaloes in-milk observed,and (iii) amount of feed fed per day to these buffaloesin-milk. We then scaled-up information (ii) and (iii) tothe successive higher levels, that is to village, district,region and country.

From the livestock census of each village, we hadthe total number of households having buffaloes in-milk. We obtained a scale-up factor for each village bydividing the total number of households having ananimal species say buffaloe in-milk by the numberof sample households having buffaloes in-milk. Weapplied this factor to its sample estimates of (ii) and(iii) for each village.

Scaling-up factor for a district was obtained bydividing the total number of villages in that district bythe number of sample villages from that district. Letus consider any of the sample districts in a region. Forsample villages falling within it, we had alreadygenerated aggregate estimates of (ii) and (iii),respectively. We summed-up estimates of (ii) for thesample villages and multiplied this sum by the scale-up factor of that district to get district level aggregateof (ii). In the same way, we obtained district levelaggregate of (iii). Likewise, we worked out aggregateestimates of (ii) and (iii) for the other sample districtsin the region.

The scale-up factor for a region was obtained bydividing the number of districts in the region by thenumber of sample districts from that region. To obtainregion-level aggregates of (ii) and (iii) we followedthe same procedure as described for the district-levelaggregation. The district-level estimates of (ii) for thesample districts were summed up; and this sum wasmultiplied by the scale-up factor to obtain the region-level estimates of (ii). Likewise, by multiplying thesum of (iii) by the scale-up factor, we obtained regionalestimates of (iii).

Having estimated feed consumption rate for alivestock category at the regional level, the national

level feed consumption rate was obtained as theweighted average of the regional feed consumptionrates; the weight being regions population of thatlivestock category. The regional populations ofdifferent animal categories are aggregates of theirdistrict level populations for 2007 obtained from the18th Livestock Census. The estimated consumptionrates of different types of feeds and their totalconsumption are given in Table 1.

Quantification of Positive Externalities ofLivestock to Environment

Land Saving due to Recycling of Crop Residues asAnimal Feed

Using the feed consumption rates reported in Table1, we quantified the positive contributions of Indiaslivestock production systems to the environmentfollowing the Environmental Model of LivestockProduction System of Mishra and Dikshit (2004). Theestimated positive effects included: resource (land)saving due to crop by-product recycled as animal feed,and due to use of dung as a domestic fuel; saving inchemical fertilizers due to dung-use as a manure; savingin fossil fuel (diesel) due to use of animal energy inagricultural operations. The model has been describedbelow.

The gross energy intake per animal per day fromby-product feed was estimated by summing up theenergy values of by-product feed on dry matter basis.Similarly, the energy value of green fodder fed to theanimals was also calculated on dry matter basis. Then,the annual quantity of green fodder required, in termsof energy to replace gross energy from by-product feed,was estimated as per Equation (1):

(1)

where, Gf is the quantity of green fodder required toreplace the by-product feed, gei is the gross energyintake from by-product feed (dry fodder andconcentrates), e stands for the energy (million calories)per unit of Gf; and d is the dry matter fraction of greenfodder. We then estimated the land area required toproduce Gf. Let y be the yield of green fodder perhectare of land, then the area L required to produce Gfmay be given by Equation (2):

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(2)

Land Saving due to Use of Dung as Substitute forFire-wood in Domestic Fuel

In rural households, fire-wood is used as a domesticfuel; for cultivation or perennial fire-wood trees coverland and deprive its use for farming. The use of dung-cake as fire-wood would result in the saving of thisland, which can be used for crop-cultivation. We,therefore, estimated the land saved due to use of dungcake as a domestic fuel. The dung-cake output on drymatter basis was worked out using dung evacuationrate and its dry matter fraction. Supposing as the rateof substitution of dry fuel-wood for dung cake (fuel-wood: dry dung cake) in terms of thermal energy, thetotal quantity of dry fuel-wood required to replace thesupply (output) of dung cake was calculated byEquation (3):

(3)

where, Fw is the quantity of fuel-wood required toreplace dung cake, and dc is the quantity of dung cakeoutput. Now, let us suppose that fuel-wood is produced

and used within the year, and its yield per hectare ondry matter basis is y, then the total land area that wouldbe required for producing Fw can be calculated byEquation (4):

(4)

The effect of gestation lag in the production of fuel-wood can be described as follows: The model assumesthat fuel-wood is produced and used within the sameyear. This is apparently an unrealistic assumption. Inreality, more than one year is required to cover thewhole process of fuel-wood tree plantation, growth andlogging of trees, drying and use of cut-out wood asfuel. Suppose it takes 3 years to complete the processbefore dry wood is made available for use at the end ofthe 3rd or the beginning of 4th year. This means thatwhereas the fuel wood made available can replaceequivalent amount of dung cake only in the fourth year,the necessary land area required for growing andharvesting of trees for making the fuel-wood availablewill have to be kept locked up during the preceding 3years. This implies that around 3-times as much landwill be required or saved if one years dung cake outputwas used in place of fuel wood as energy source.

Table 1. Feed consumption rates and dung evacuation rates, 2001-02

Livestock Type of feed consumed Dry matter Gross energy Wet dungcategory (kg/animal/ day) intake per intake, production

animal per animal per per animalGreen fodder* Dry fodder Concentrates day (kg) day per day

(MJ) (kg)

Cattle In-milk 4.75 5.50 0.64 7.01 108.44 6.63Dry 3.40 4.02 0.40 5.15 77.82 6.58Adult male 4.06 6.03 0.33 7.51 107.56 4.46Young stock 2.18 2.13 0.18 3.07 42.42 4.43

Buffalo In-milk 5.96 6.34 1.05 8.88 132.34 8.35Dry 5.44 4.95 0.52 7.35 101.96 8.49Adult male 4.04 7.47 0.36 8.83 127.95 6.65Young stock 2.29 2.22 0.19 3.69 44.33 4.43

Goat 1.50 0.20 0.06 0.61 10.58 0.30Sheep 1.66 0.20 0.04 0.63 10.97 0.80Others** 15.62 6.72 0.49 10.39 172.37 6.10

Notes: * includes grazing also** includes horses and camels

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Saving of Chemical Fertilizers due to Use of Dungas Manure

The extent to which dung manure substitutes thechemical fertilizers, is a saving of chemical fertilizers.Fresh cattle dung on an average contains 0.30-0.40 percent nitrogen (N), 0.10-0.20 per cent phosphorus(P2O5), and 0.10-0.30 per cent potassium oxide (K2O)(Anonymous, 1997). According to the recent estimatesof Ghosh et al. (2004), dung manure contains 0.71 percent N, 0.18 per cent P2O5 and 0.71 per cent K2O. Inthis study, we have used the fraction of soil nutrients(N,P and K) in dung-manure as estimated by Ghosh etal. (2004), and the total quantity of N, P and K wasworked out for the proportion of bovine dung used asmanure.

Saving of Fossil Fuel due to Animal Energy-use inAgriculture

If the working animals were to be replaced byagricultural machinery, it would require additional fueland lead to emission of CO2 from burning of the fossil-fuel. It is this emission that is prevented by thelivestock. It has been assumed in the study that tractorsare the only machine used and are of similar power;and also the working animals do not differ in their workcapacity.

In order to determine the saving of fossil fuel andprevention of greenhouse gasses due to animal energyuse, we need to know (i) the rate of substitution betweentractors and working animals, (ii) the amount of dieselrequired for running a tractor to perform agriculturaloperations, and (iii) the amount of CO2 that will beemitted from the burning of a unit of diesel. On thebasis of economic substitution rate, 10 working malesare required to replace a tractor. The number of tractorsrequired for replacing countrys bovine working stock,diesel use, and the associated emission of greenhousegasses have been estimated.

Results and DiscussionIndia has one of the largest livestock populations

in the world, and therefore its livestock sector has comeunder critical scrutiny of the internationalenvironmental monitoring agencies such as IPCC.According to the estimates of the Indian Network forClimate Change Assessment, the agricultural sectoremitted 334 Mt of CO2 in 2007, to which livestock

contributed about 63 per cent. A number of studies inthe past have quantified methane emission fromlivestock production. These studies have shown widevariations, ranging from 8.5 Mt to 10.5 Mt, dependingon the methods and data used and also the year forwhich the gas emission was estimated (Lerner et al.,1988; Ahuja, 1990; Bhattacharya and Mitra, 1998;Mishra and Dikshit, 2004; Singhal et al., 2005; Swamyand Bhattacharya, 2006; Singh et al., 2012).

Notwithstanding their negative externalities,livestock in the mixed farming systems also helpconserve natural resources and improve quality ofenvironment. The estimates of the positivecontributions of livestock to the environment arediscussed below:

Land Saving due to Recycling of Crop Residuesas Animal Feed

Livestock production in the mixed farming systemssaves land by utilizing or recycling crop by-products,viz. dry fodder and concentrates as animal feed. If theby-product feeds were to be replaced by feed grains orcultivated green fodder, vast additional land will berequired to produce that much feed and fodder. Thisland saving is a positive environmental effect. Theproblem here can be posed as follows. How muchcultivated green fodder or feedgrains will be requiredif the gross energy intake of the ruminant populationmade available from the by-product feed, concentratesand dry fodder, were to be replaced by the energy fromeither of the former feeds. We have consideredcultivated green fodder as the alternative source of feedenergy.

The gross energy intake by the ruminant populationfrom by-product feed was estimated by summing-upthe energy values of the by-product feed on dry matterbasis. Similarly, the energy value of green fodder fedto the animals was also calculated on dry matter basis.The energy value of dry fodder and feed concentrate(on dry matter basis) is 3.69 Mcal/kg and 4.38 Mcal/kg of feed. Using feed consumption rates given in Table1, we have estimated that the by-product feed provides169 million calories of energy per day to livestock. Ifthis much energy were to be obtained from thecultivated fodder, India would require 1701 milliontonnes of green fodder annually, and with an averagefodder yield of 42.5 t/ha, the total area required to

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produce this amount of fodder would be as large as 40million hectares (Table 2).

Land Saving due to Use of Dung as a Substitutefor Fire-wood in Domestic Fuel

Another way that livestock production saves landis through supplying of dung as a domestic fuel. Ofthe total wet dung produced (635 Mt), about 37 percent (235 Mt) is used as domestic fuel. Considering 80per cent moisture in the fresh dung, the total dry dung-cake production was estimated to be 47 Mt. At areplacement rate of 3.54 in terms of thermal energy, ifthis amount of dung-cake were to be replaced by fuelwood, India will require 13 Mt of fuel wood in additionto whatever quantity is produced otherwise. To producethis much amount of fuel wood, about 1.62 Mha of

land will have to be constantly put to cultivation offuel wood plants with 4.5 years of gestation lag (Table3).

Saving of Chemical Fertilizers due to Use of Dungas Manure

After meeting its demand as fuel, the remainingdung is used as manure to fertilize crops, whichindicates the savings in use of chemical fertilizers.About 76 Mt of dung (on dry matter basis) is used asmanure. The total availability of soil nutrients frommanure was worked out to be of 1.22 Mt comprising0.54 Mt of N, 0.14 Mt of P and 0.54 Mt of K; it isequivalent to about 6 per cent of the total nutrientsused in the country in 2007. These nutrients frommanure can replace 2.63 Mt of ammonium sulphate,

Table 2. Land saving due to use of crop by-products as animal feed

Parameters Parameter value Source

Energy value of by-product feed on dry matter basis (Mcal/kg) Krishna et al. (1978)Dry fodder 3.69Concentrate 4.38

Consumption of by-product feed and crop residues in terms of 168.8 Estimated by authorsenergy (Mcal)Green fodder to dry matter ratio 1.0:0.25 Sen et al. (1978)Yield of green fodder (t/ha) 42.5 Anonymous (1997)Total green fodder required to replace by-products feed (Mt) 1701 Estimated by authorsLand area required to produce substituted quantity of green fodder (Mha) 40.0 Estimated by authors

Table 3. Parameter values for land saving due to use of dung cake as domestic fuel: 2007

Parameters Parameter Sourcevalues

Production of wet dung (Mt)* 635.0 Estimated by authorsUtilized as domestic fuel (%) 37 CSO, GoI (1996)Proportion of moisture in wet dung (%) 80 Flote (2011)Fuel wood yield (t/ha) 36.8 Chaturvedi (1993)Replacement rate of fuel wood for dung cake in terms of thermal energy 1:3.54 KVIC (1983)Gestation lag between planting and harvesting of fuel wood saplings /trees (years) 4.5 GoO (2007)Production of dung cake (Mt) 46.99 Estimated by authorsFuel wood required to replace dung cake (Mt) 13.3Land required to produce fuel wood :

With 1 year gestation lag (Mha) 0.36With 4.5 year gestation lag (Mha) 1.62

*Bovine dung production

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Table 4. Saving of chemical fertilizers due to use of dung as manure: 2007

Parameters Parameter values Source

Proportion of wet dung utilized as manure (%) 60 CSO, GoI (1996)Proportion of moisture in wet dung (%) 80 Flote (2011)Fraction of plant nutrients in dung manure Ghosh et al. (2004)

Nitrogen 0.0071Phosphorus 0.0018Potash 0.0071

Fraction of N, P and K in chemical fertilizersAmmonium sulphate (N) 0.206 www.indiaagronet.comSuper phosphate (P) 0.444Murate of potash (K) 0.660Production of wet dung (Mt) 635.0 Estimated by authorsDung Utilized as manure (Mt) 381.0Dung manure on dry matter basis (Mt) 76.2Saving of soil nutrients (Mt)

Nitrogen (N) 0.541Phosphorus (P) 0.137Potash (K) 0.541Total (N, P & K) 1.219

Saving of chemical fertilizers (Mt)Ammonium sulphate 2.63Super phosphate 0.31Murate of Potash 0.82

0.31 Mt of super phosphate and 0.82 Mt of murate ofPotash (Table 4). The available amount of thesenutrients is apparently small, but its value in monetaryterms could be substantial. Further, its environmentalvalue can be gauged if we consider the associatedemission in the production and transportation of theequivalent amount of chemical fertilizers at the farm-gate.

Saving of Fossil Fuel due to Use of Animal Energyin Agriculture

To estimate the contribution of animals towardssaving of fossil fuel we need (i) substitution orreplacement rate between working animals and tractors,and (ii) fossil-fuel (diesel) required per tractor per yearto do the work of replaced animals. On an average, abullock is rated at 0.4-0.5 HP (horse power). A 35 HPtractor is, therefore, supposed to replace at least 70bullocks. It is a purely engineering rate of substitutionbetween working animals and tractors. Some farm-level studies carried out during 1970s and 1980s in the

north-western states of Punjab, Haryana and westernUttar Pradesh the sheet of green revolution in India have reported the replacement rates of three to fourbullocks per tractor (Binswanger 1978; Sharma 1987;Mishra and Sharma 1990). Dikshit and Birthal(2010a;b) using time series data on the number ofbullocks and tractors have arrived at a substitution rateof 10, that is, a tractor can replace 10 working animals.We have used this rate of substitution, and accordinglythe country will require 5.5 million tractors to replace55 million working animals. To use the services ofrequired number of tractor stock, approximately 13.13Mt of diesel would be required annually. Burning ofdiesel will emit about 4.17 Mt of carbon di-oxide or0.2 Mt of methane, which is the methane emissionprevented by the working animals.

ConclusionsLivestock have been singled out as one of the

largest sources of methane emission after rice.Nevertheless, livestock also help conserve natural

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resources, particularly in the mixed farming systemswhere there is a considerable synergy between cropand livestock activities. In this paper, we have identifiedand quantified the positive environmental contributionsof livestock production system. Some of the positivecontributions identified include: saving of land due torecycling of agricultural by-products as animal feedand also due to use of dung-cake as domestic fuel;saving in use of chemical fertilizers due to use of dungas manure; and prevention of carbon dioxide emissiondue to use of animal energy in Indian agriculture.

The study has found that there is enormous savingof land in the mixed farming system on account of useof agricultural by-products as feed and use of dung asdomestic fuel. If the by-product feed were to bereplaced by green fodder, as much as 1701 Mt of greenfodder will be required to supply the equivalent amountof energy. To produce the required amount of greenfodder, about 40 Mha of land will be needed. Further,to replace the quantity of dung cake used as domesticfuel by fuel wood, the required amount of fuel woodin terms of thermal energy would be 13.3 Mt. The landresource required with three year of gestation lag wouldbe 1.62 Mha. The total land saving from the livestockproduction system thus has been worked out to be 41.62Mha.

The saving of soil nutrients due to use of dung asmanure has been estimated to the tune of 0.541 Mt ofnitrogen, 0.137 Mt of phosphorus and 0.541 Mt ofpotash. If these quantities of soil nutrients are to bereplaced by the equivalent amount of chemicalfertilizers, then 2.63 Mt of ammonium sulphate, 0.31Mt of super phosphate and 0.82 Mt of murate of potash

would be required. A tractor can replace about 10working animals and at this rate, approximately 5.5million tractors would be required to replace theexisting stock of working animals, that will consumeabout 13 Mt of diesel annually. Burning of this muchdiesel would emit about 4.17 Mt of CO2, which isequivalent to 0.199 Mt of methane emission.

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(USEPA), Inventory of U.S. Greenhouse Gas Emissionsand Sink, 1990-98.

Anonymous (1997) Hand Book of Agriculture, IndianCouncil of Agriculture Research (ICAR), New Delhi.

Bhattacharya, S. and Mitra, A.P. (1998) Greenhouse GasEmission in India for the Base Year 1990. ScientificReport, No.11, Centre for Global Change, NationalPhysical Laboratory, New Delhi.

Chaturvedi, P. (1993) Bioenergy Production and Utilizationin India Expert Consultation on Biofuels forSustainable Development and their Potential asSuitable to Fossil Fuels and CO2 Emission Reduction,Food and Agriculture Organization, Rome.

Dikshit, A.K. and Birthal, P.S. (2010a) Indias livestock feeddemand: Estimates and projections, AgriculturalEconomics Research Review, 23: 15-28.

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Table 5. Quantity of diesel saved due to use of animal energy: 2007

Parameter Parameter Sourcevalues

Number of draught animals (millions) 55 GoI (2007)Replacement rate 10.0 Dikshit and Birthal (2010)Number of tractors required to replace existing stock of working 5.463 Estimated by authorsanimals (millions)Number of operating hours (hours/year) 801 Stephane et al. (2009)Consumption of diesel by required No. of tractors (Mt) 13.13 Mishra and Dikshit (2004)Total carbon released from burning of estimated diesel use (Mt) 11.38 Estimated by authorsEmission of carbon dioxide prevented (Mt) 4.17Emission prevention equivalent to methane (Mt) 0.198 IPCC (1995)

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Ghosh, P.K. et al. (2004) Comparative effectiveness of cattlemanure, poultry manure, phosphor compost andfertilizer-NPK on three cropping systems in Vertisolsof semi-arid tropics, Crop Yields and SystemPerformance, 95: 77-83.

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Krishna, G., Razdar, M.N. and Ray, S.N. (1978) Effect ofnutritional and seasonal variations on heat and methaneproduction in BosIndicus, Indian Journal of AnimalScience, 48(5): 366-370.

Lerner, J., Mathews, E. and Fung, I. (1988) Methaneemission from animals, a global high resolution data,Global Biogeochemical Cycles, 2: 139-156.

Mishra, S.N. and Dikshit, A.K. (2004) Environment andLivestock in India : With a Comparative Study of theIndian and US Dairy Systems, Manohar Publishers andDistributors, New Delhi.

Pasha, S.A.(2005) Livestock-Environment Interaction:Issues, Problems and Prospects, Institute for Social andEconomic Change (ISEC), Bangalore.

Sen, K.C., Ray, S.N. and Ranjhan, S.K. (1978) NutritiveValue of Cattle Feed and Feeding of Animals, IndianCouncil of Agricultural Research, New Delhi.

Sere, C. and Steinfeld, H. (1996) World Livestock ProductionSystem: Current Status, Issues and Trends. FAO AnimalProduction and Health Paper 127. Food and AgricultureOrganization of the United Nations, Rome.

Singh, G.P. (1997) Effect of greenhouse gases on climatechange and Indian ruminant livestock, Current Science,72: 7.

Singh, S., Kushwaha, B.P., Nag, S.K., Bhattacharya, S.,Gupta, P.K., Mishra, A.K. and Singh, A. (2012)Assessment of enteric methane emission of Indianlivestock in different agro-ecological regions, CurrentScience, 102(7): 1017-1027.

Singhal, K.K., Mohini, M., Jha, A. K. and Gupta, P.K. (2005)Methane emission estimates from enteric fermentationin Indian livestock: Dry matter intake approach, CurrentScience, 88: 119-127.

Steinfeld, H., Gerber, P., Wassennar, T., Castel, V., Rosales,M. and de Haan, C. (2006) Livestocks Long Shadow:Environmental Issues and Options, Food andAgriculture Organization of the United Nations, Rome.

Stephane, de la Rue du Can, McNeil, Michael and Sathaye,Jayant (2009) India Energy Outlook: End Use Demandin India to 2020, Ernest Orlando Lawrence BerkeleyNational Laboratory, LBNL-XXXX, U.S. Departmentof Energy National Laboratory Operated by theUniversity of California.

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www.indiaagronet.com

Received: January 2013; Accepted: March 2013

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The signature of line graphs and power trees

Long Wang, Yi-Zheng Fan

School of Mathematics Sciences, Anhui University, Hefei 230601, P.R. China

Abstract: Let G be a graph and let A(G) be the adjacency matrix of G. The signature s(G)

of G is the difference between the positive inertia index and the negative inertia index of A(G).

Ma et al. [Positive and negative inertia index of a graph, Linear Algebra and its Applications

438(2013)331-341] conjectured that c3(G) s(G) c5(G), where c3(G) and c5(G) respectively

denote the number of cycles in G which have length 4k + 3 and 4k + 5 for some integers k 0,

and proved the conjecture holds for trees, unicyclic or bicyclic graphs.

It is known that s(G) = 0 if G is bipartite, and the signature is closely related to the odd

cycles or nonbipartiteness of a graph from the existed results. In this paper we show that the

conjecture holds for the line graph and power trees.

AMS subject classification: 05C50

Keywords: Line graph; power graph; inertia; signature

1 Introduction

Throughout this paper we consider only simple graphs. The adjacency matrix A(G) = [aij ]

of a graph G with vertex set V (G) = {v1, v2, . . . , vn} and edge set E(G) is defined to be a

symmetric matrix of order n such that aij = 1 if vi is adjacent to vj , and aij = 0 otherwise.

The positive inertia index p(G), the negative inertia index n(G) and the nullity (G) of G are

respectively defined to be the number of positive eigenvalues, negative eigenvalues and zero

eigenvalues of A(G). The rank of G, written as r(G), is defined to be the rank of A(G).

The signature of G, denoted by s(G), is defined to be the difference p(G) n(G). Obviously,

p(G) + n(G) + (G) = |V (G)|, p(G) + n(G) = r(G) and p(G) n(G) = s(G).

Motivated by the discovery that the nullity of a graph is related to the stability of the

molecular represented by the graph [1] and the open problem of characterizing all singular

graphs posed by Collatz [2], many authors discuss the nullity of a graph and obtain a lot of

interesting results. Here we particularly mention the results involved with the nullity of line

graphs. Sciriha [11] proved that all trees whose line graph is singular must have an even order.

Supported by National Natural Science Foundation of China (11071002, 11371028), Program for New Cen-

tury Excellent Talents in University (NCET-10-0001), Key Project of Chinese Ministry of Education (210091),

Specialized Research Fund for the Doctoral Program of Higher Education (20103401110002), Scientific Research

Fund for Fostering Distinguished Young Scholars of Anhui University(KJJQ1001).Corresponding author. E-mail address: [email protected] (Y.-Z. Fan), [email protected] (L. Wang)

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Gutman and Sciriha [5] showed that the nullity of the line graph of a tree is at most one. Li et

al. [7] proved that the nullity of the line graph of a unicyclic graph with depth one is at most

two. Gong et al. [4] improved the above results as: the nullity of the line graph of a connected

graph with k induced cycles is at most k + 1.

Recently some authors discuss a more general problem, that is, describing the positive or

negative inertia index of graphs or weighted graphs, especially of trees or their line graphs,

unicyclic or bicyclic graphs; see Ma et al. [9], Li et al. [8] and Yu et al. [12, 13]. In the paper [9]

the authors posed a conjecture as follows, and proved the conjecture holds for trees, unicyclic

or bicyclic graphs.

Conjecture 1.1. [9] The inequality c3(G) s(G) c5(G) possibly holds for any simple

graph G, where c3(G) and c5(G) denote respectively the number of cycles having length 4k + 3

(or length 3 modulo 4) and the number of cycles having length 4k + 5 for some integers k 0

(or length 1 modulo 4).

Theorem 1.2. [9] Let G be a tree, or a unicyclic graph, or a bicyclic graph. Then c3(G)

s(G) c5(G).

A weaker result was also given by Ma et al. [9] that |s(G)| c1(G) for any graph G, where

c1(G) denotes the number of odd cycles of G, or c1(G) = c3(G) + c5(G).

When G is bipartite, surely s(G) = 0 and the conjecture holds in this case. So, from Theorem

1.2 or Conjecture 1.1 (if it was true), we find that the signature is closely related to the odd

cycles or nonbipartiteness of a graph. In this paper we prove that the conjecture holds for the

line graphs and power trees.

2 Preliminaries

We first introduce some notations. Let G be a graph and let W V (G). Denote by GW the

subgraph of G obtained by deleting the vertices in W together with all edges incident to them.

If G1 is a subgraph of G, we sometimes write G G1 instead of G V (G1). In particular, if

W = {x}, we simply write GW as Gx. If G1 is an induced subgraph of G and x is a vertex

of G outside G1, denote by G1 + x the subgraph of G induced by the the vertices of G1 and x.

Lemma 2.1. [9] Let G be a graph containing path with four vertices of degree 2 as shown in

Fig. 2.1. Let H be the graph obtained from G by replacing this path with an edge. Then

p(G) = p(H) + 2, n(G) = n(H) + 2, (G) = (H), and hence s(G) = s(H).

G H

Fig. 2.1. The graphs G and H in Lemma 2.1

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Lemma 2.2. [7] Let Cn1,n2,...,nt be the graph obtained from a cycle Ct by attaching ni pendent

edges to each vertex vi of Ct, where ni 0. Let G be the line graph of Cn1,n2,...,nt, and let

m = |{i|ni > 0}|. Then the following results hold, where a zero chain of finite integer sequence

is defined to be a zero subsequence whose (cyclic) predecessor and successor are both nonzero,

and the length of the zero chain is defined to be the number of integers in that zero subsequence.

(1) (G) = 2 if and only if m = 0 and t 0 mod 4.

(2) (G) = 1 if and only if m 1 and either ni {0, 1} for i = 1, 2, . . . , t, the length of

any zero chain of (n1, n2, . . . , nt) is even, and t +m 0 mod 4; or t 0 mod 4 and one of

n1 = n3 = = nt1 = 0 and n2 = n4 = = nt = 0 must hold.

(3) (G) = 0 otherwise.

Lemma 2.3. [4] Let x be a cut vertex of a graph G and G1 be a component of Gx. If r(G1+x) =

r(G1) + 2, then r(G) = r(G x) + 2. If r(G1 + x) = r(G1), then r(G) = r(G1) + r(GG1).

Lemma 2.4. Let G be a graph and let x be a vertex of G. Then |s(G) s(G x)| 1. In

particular, if r(G x) = r(G) or r(G x) = r(G) 2, then s(G x) = s(G).

Proof. By the eigenvalues interlacing property of real symmetric matrices (or see [3]), we have

p(G) 1 p(Gx) p(G), and n(G) 1 n(Gx) n(G), which yields the required results

immediately.

Corollary 2.5. Let H be an induced subgraph of a graph G. If r(H) = r(G), then s(H) = s(G).

Proof. Note that H can be viewed as one obtained from G by sequently deleting some of its

vertices. The condition r(H) = r(G) implies that in each step the rank, and hence the signature

of the resulting graph keeps invariant by Lemma 2.4, which yields s(H) = s(G).

Corollary 2.6. Let x be a cut vertex of a graph G and let G1 be a component of G x. If

r(G1 + x) = r(G1) + 2, then s(G) = s(G x).

Proof. If r(G1 + x) = r(G1) + 2, then r(G) = r(G x) + 2 by Lemma 2.3, and hence

s(G) = s(G x) by Lemma 2.4.

Lemma 2.7. Let x be a cut vertex of a graph G and let G1, G2, . . . , Gk be all components of

Gx. If r(G1) = r(G1+x), then s(G) = s(G1)+ s(GG1). In particular, if r(Gi) = r(Gi+x)

for all i, then s(G) = s(G x).

Proof. Let = ki=2Gk. Write the adjacency matrix of G as follows,

A(G) =

A(G1) 0

T 0

0 T A()

,

where the middle 0 corresponds to the cut vertex x. As r(G1) = r(G1+x), the matrix equation

A(G1)X = has a solution, say , such that T = 0. Now, take Q as the following matrix

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with the same partition as A(G),

Q =

I 0

0 1 0

0 0 I

,

Then

QTA(G)Q =

A(G1) 0 0

0 0

0 T A()

.

So we have s(G) = s(G1) + s(GG1).

If r(Gi) = r(Gi + x) for all i, by induction on the number of components of G x, we have

s(G) =k1

i=1 s(Gi) + s(Gk + x). The result follows as s(Gk + x) = s(Gk) by Lemma 2.4.

Lemma 2.8. Let x be a cut vertex of a graph G and G1, G2, . . . , Gk be all components of G x.

If s(G) = s(Gx)+1, then s(Gl+x) = s(Gl)+1 for some l, and s(G) = s(Gl+x)+

j 6=l s(Gj).

Proof. Note that r(Gi + x) r(Gi) + 2 for each i. If r(Gi + x) = r(Gi) + 2 for some i or

r(Gi+x) = r(Gi) for all is, then s(G) = s(Gx) by Corollary 2.6 or Lemma 2.7; a contradiction.

So r(Gi + x) r(Gi) + 1 for all is, with equality for at least one i.

Write the adjacency matrix of G as

A(G) =

0 T1 T2

Tk

1 A(G1) 0 0

2 0 A(G2) 0...

......

. . ....

k 0 0 A(Gk)

,

where the left upper 0 corresponds to the cut vertex x. Observe that for each i the equaiton

A(Gi)X = i has a solution i; otherwise r(Gi + x) = r(Gi) + 2; a contradiction. Taking Q as

the following matrix with the same partition as A(G),

Q =

1 0 0 0

1 I 0 0

2 0 I 0...

......

. . ....

k 0 0 I

,

we have QTA(G)Q = aA(G1)A(G2) A(Gk), where a = k

i=1 ii. The assumption

s(G) = s(G x) + 1 implies that a > 0. In particular, their exists some l such that ll < 0.

So, A(Gl + x) is congruent to (ll)A(G1)), which implies s(Gl + x) = s(Gl)+ 1. Therefore

s(G) = s(Gl + x) +

j 6=l s(Gj).

Corollary 2.9. Let x be a cut vertex of a graph G and let G1, G2, . . . , Gk be all components

of G x. If s(Gi) c5(Gi) and s(Gi + x) c5(Gi + x) for all is, then s(G) c5(G).

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Proof. By Lemma 2.4, s(G) s(G x) + 1. If s(G) s(G x), noting that s(G x) =ki=1 s(Gi) and s(Gi) c5(Gi) for all is, so we have s(G)

ki=1 c5(Gi) c5(G). If s(G) =

s(G x) + 1, by Lemma 2.8, s(G) = s(Gl + x) +

j 6=l s(Gj) for some l. By the assumption for

each Gi and Gi + x, we have s(G) c5(Gl + x) +

j 6=l c5(Gj) c5(G).

3 Signature of line graphs

The line graph of a graph G, denoted by LG, is the graph whose vertex set is E(G), where two

vertices of LG are adjacent if and only if the corresponding edges are incident in G.

Lemma 3.1. If G is one of the following graphs: a cycle with two pendant edges, two cycles

sharing a common vertex, two cycles sharing a common path of length at least 1, where all

cycles have length 2 modulo 4, then s(LG) c5(LG).

Proof. First suppose G is a cycle C of length 2 modulo 4 with two pendant edges e1 = x1y1

and e2 = x2y2, where y1, y2 are pendant vertices of G. If x1 = x2 or x1, x2 are connected by

paths on C of even length, by Lemma 2.2, LG is nonsingular. Note that LG has an even order

so that s(LG) is an even number. By Theorem 1.2, s(LC + e1) 0 as LC + e1 is bicyclic. Now

by Lemma 2.4, s(LG) s(LC + e1) + 1 1. So, s(LG) 0 = c5(LG).

If x1, x2 are connected by paths on C of odd length, then (LG) = 1 by Lemma 2.2. Note

that Cx1x2 consists of two disjoint paths P1, P2 both with order 0 or 2 modulo 4. By Lemma

2.1, it suffices to consider the line graphs G1, G2 in Fig. 3.1. We have s(G1) = s(G2) = 1 by

using Mathematica.

Next we consider the case that G is two cycles sharing a common vertex. Also by Lemma 2.1

it suffices to consider the line graph G3 in Fig. 3.1. By a direct calculation, we have s(G3) = 1.

Finally we consider the case that G is two cycles sharing a common path P of length at least

1. We stress all cycles have length 2 modulo 4. If the path P has length 1, then by Lemma 2.1 it

suffices to consider the line graph G4 in Fig. 3.1. By a direct calculation, we have s(G4) = 1.

If P has length greater than 1, then by Lemma 2.1 it suffices to consider the line graphs G5, G6

in Fig. 3.1. Also by calculation, we get s(G5) = s(G6) = 1.

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1G 2G

3G

4G

5G

6G

Fig. 3.1. The graphs in the proof of Lemma 3.1

Theorem 3.2. Let T be a tree with at least one edge, then s(LT ) c5(LT ).

Proof. We use induction on the number of internal edges (i.e. non-pendant edges) of T to

prove the result. If T has no internal edges, then T = K1,m (i.e. a star), and hence LT = Km,

a complete graph. The result holds in this case by a simple verification.

Suppose the result holds for all trees with k ( 0) internal edges. Let T be a tree with k+1

internal edges and let e be one of the internal edges of T . Then T e consists of two subtrees

T1, T2 of T . Obviously, each Ti and each Ti + e has fewer internal edges than that of T . By

induction we have s(LTi) c5(LTi) and s(LTi + e) c5(LTi + e) for each i = 1, 2. Noting that

e is a cut vertex of LT , so s(LT ) c5(LT ) by Corollary 2.9.

Theorem 3.3. Let G be a graph without isolated vertices. Then c3(LG) s(LG) c5(LG).

Proof. Without loss of generality we may assume G is connected. Let (G) be the set of edges

of G with at least one endpoint having degree greater than 2, and let (G) := |(G)|. We will

use induction on (G) to prove the left inequality. If (G) = 0, namely each vertex of G has

degree 1 or 2, then G is the disjoint union of paths and/or cycles. Thus, LG is the disjoint union

of paths and/or cycles. By Theorem 1.2, we have c3(LG) s(LG).

Assume that c3(LH) s(LH) for all graphs H with (H) k, where k 0. Let G be a

graph with (G) = k+1 and let x be a vertex of G with degree at least 3. Suppose e is an edge

incident to x. Then the vertex e of LG is contained in one triangle. So c3(LGe) = c3(LG e)

c3(LG) 1. By Lemma 2.4 and by induction,

s(LG) s(LG e) 1 = s(LGe) 1 c3(LGe) 1 c3(LG).

Next, set o(G) := |E(G| |V (G)| + 1, the dimension of G. We also use induction on o(G)

to prove the right inequality. If o(G) = 0, then G is a tree, and the result holds in this case by

Theorem 3.2. Assume the result holds for all connected graphs G with o(G) k, where k 0.

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Let G be a connected graph with o(G) = k + 1. Note that G must contain cycles. A cycle C of

G is said of type l if there are exactly l edges between C and G C.

Case 1: If G contains a cycle C of type l with l 3, letting m be the length of C and

letting e1, e2, e3 be three edges joining C and G C, then the line graphs LC , LC + e1, LC +

e1 + e2, LC + e1 + e2 + e3 contain cycles of length m,m + 1,m + 2,m + 3 respectively. Surely

one cycle among them must have length 1 modulo 4. Deleting an arbitrary edge, say e on the

cycle C, will break the cycle of length 1 modulo 4 and decrease the dimension of G. That is,

c5(LG e) c5(LG) 1, and o(G e) < o(G). Now by Lemma 2.4 and by induction,

s(LG) s(LG e) + 1 = s(LGe) + 1 c5(LGe) + 1 c5(LG).

Case 2: If G contains a cycle of type 1, say C, then C is connected to GC by an edge, say

e = xy, where x V (C) and y V (GC). Surely e is a cut edge of G. If G = C + y, then LG

is bicyclic and the result holds by Theorem 1.2. If G 6= C+y, then e is a cut vertex of LG, Ge

has two components: C and another subgraph say D, where o(D) < o(G) and o(D+x) < o(G).

So, by induction, s(LD) c5(LD) and s(LD + e) c5(LD + e). Observe that s(LC) c5(LC)

and s(LC + e) c5(LC + e) by Theorem 1.2. The result now follows by Corollary 2.9.

Case 3: If all cycles of G are of type 2, then G is either (i) one obtained from a cycle with

two pendant edges (denoted by H) by possibly attaching trees at the pendant vertices of H,

or (ii) two cycle sharing a common vertex or a common path of length at least 2, or (iii) G is

obtained from a tree by replacing some vertices of degree 2 by cycles.

If G is one of graphs in (i) and (ii), and in addition if one cycle has odd length or length 0

modulo 4, then we will find a cycle in G of length 1 modulo 4 containing the edges of the cycle.

Similar to Case 1, deleting an arbitrary edge on the cycle will break the cycle of length 1 modulo

4 and decrease the dimension of G. The result will follows by Lemma 2.4 and by induction.

Now assume G is one of graphs in (i) and (ii), and all cycles have length 2 modulo 4. If G

is exactly the graph H (a special case of (i)) or a graph in (ii), we get the result by Lemma 3.1.

If G is a graph in (i) obtained from H by attaching exactly one tree T at the pendant vertex

of a pendant edge say e, then G contains a cut edge say e such that G e has two components:

G1, T , where G1 is the cycle together with a pendant edge. Note that e is a cut vertex of LG, and

s(LT ) c5(LT ), s(LT +e) c5(LT +e) by Theorem 3.2. Also s(LG1) c5(LG1) by Theorem 1.2

as LG1 is bicyclic, s(LG1 + e) c5(LG1 + e) by Lemma 3.1. The result now follows by Corollary

2.9.

If G is a graph in (i) obtained from H by attaching two trees at the pendant vertices of

two pendant edge say e1, e2 respectively, Then G e2 has two components: G1, G2, where G1

contains the cycle and G2 is a tree. Note that in the graph G1 the cycle is of type 1, and hence

s(LG1) c5(LG1) by the result in Case 2. Also s(LG1 + e) c5(LG1 + e) by what we have

proved in this case. So the result also follows by Corollary 2.9.

If G is a graph in (iii), then there exists a cut edge e of G such that Ge has two components:

G1, G2, where G1, G2 both contain cycles. So o(Gi) < o(G), o(Gi + e) < o(G), and by induction

7

3639

s(LGi) < c5(LGi), s(LGi+e) < c5(LGi+e) for i = 1, 2. Note that e is a cut vertex of LG. The

result also follows by Corollary 2.9.

Case 4: If G contains a cycle of type 0 and contains no cycles of type 1 or type l with l 3,

then G itself is the cycle or the cycle with a chord (an edge with two endpoints on the cycle).

Clearly the result holds if G is a cycle. If G is a cycle with a chord, letting C1, C2 be two smaller

cycles containing the chord, if one cycle has odd length or length 0 modulo 4, then the result

follows by a similar discussion as in Case 3. Otherwise, C1, C2, and hence C all have length 2

modulo 4. In this case, we can get the result by Lemma 3.1.

4 Signature of power trees

Recall that the k-th power Gk of a graph G is obtained from G by adding edges between all

pairs of vertices within distance at most k. In particular G1 is exactly the graph G, and G2 is

called the square of G.

Lemma 4.1. Let G be a graph on at least 5 vertices. If k 2, then in the graph Gk every vertex

v is contained in at least one C3 and one C5. That is to say, c3(Gk v) c3(G

k) 1 and

c5(Gk v) c5(G

k) 1.

Proof. Let H be an arbitrary connected graph induced by five vertices of G. Then H contains

one of H1,H2,H3 as a subgraph; see Fig. 4.1. Thus G2, and hence Gk contains H21 as a subgraph

by considering the squares of H1,H2,H3. Note that in H21 each vertex is contained in at least

one C3 and one C5. The result follows.

1H

2H

3H

2

1H

Fig. 4.1. The graphs in the proof of Lemma 4.1

Theorem 4.2. If G is a tree, then c3(Gk) s(Gk) c5(G

k) for k 2.

Proof. If |V (G)| 4, the result follows by a direct calculation. Assume the result holds

for all trees on n vertices, where n 4. Let G be a tree on n + 1 vertices. By Lemma 4.1,

c3(Gk v) c3(G

k) 1 and c5(Gk v) c5(G

k) 1 for an arbitrary vertex v of G. Let u be a

pendant vertex of G. Then Gk u = (G u)k. So Lemma 2.4 and by induction,

s(Gk) s(Gku)+1 = s((Gu)k)+1 c5((Gu)k)+1 = c5(G

ku)+1 c5(Gk)1+1 = c5(G

k).

Similarly,

s(Gk) s((G u)k) 1 (c3(Gk u) + 1) c3(G

k).

The result follows.

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3740

Recall that the total graph TG of G is the graph with vertex set corresponding to union of

vertex and edge sets of G, with two vertices of TG adjacent if and only if the corresponding

elements in G are adjacent or incident. It is known that TG = S(G)2 (or see [6]), where S(G) is

the subdivision of G. If G is a tree, then S(G) is also a tree. So we have the following corollary.

Corollary 4.3. If G is a tree, then c3(TG) s(TG) c5(TG).

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The Efficient Method for Simultaneous Monitoring of theCulturable as Well as Nonculturable AirborneMicroorganismsBarbara Hubad, Ales Lapanje*

Institute of Microbial Sciences and Technologies, Domzale, Slovenia

Abstract

Cultivation-based microbiological methods are a gold standard for monitoring of airborne micro-organisms to determinethe occupational exposure levels or transmission paths of a particular infectious agent. Some highly contagiousmicroorganisms are not easily culturable but it is becoming evident that cultivation and molecular methods arecomplementary and in these cases highly relevant. We report a simple and efficient method for sampling and analyzingairborne bacteria with an impactor-type high-flow-rate portable air sampler, currently used for monitoring culturablebacteria or fungi. A method is reported for extraction of nucleic acids from impacted cells without prior cultivation andusing agarose as a sampling matrix. The DNA extraction efficiency was determined in spiked samples and, samples takenfrom a wastewater treatment plant and an alpine area. The abundance, diversity and quantity of total bacteria wereanalysed by a quantitative polymerase chain reaction, and by construction and analysis of clone libraries. The method doesnot interfere with downstream PCR analysis and can cover the gap between traditional culture and molecular techniques ofbioaerosol monitoring.

Citation: Hubad B, Lapanje A (2013) The Efficient Method for Simultaneous Monitoring of the Culturable as Well as Nonculturable Airborne Microorganisms. PLoSONE 8(12): e82186. doi:10.1371/journal.pone.0082186

Editor: Martin Rottman, Harvard Medical School, United States of America

Received May 10, 2013; Accepted October 22, 2013; Published December 20, 2013

Copyright: 2013 Hubad, Lapanje. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permitsunrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

Funding: This study was supported by the European Union Social Fund (grant no. P-MR-07/55) and the European Commission Seventh Framework program,projects MULTISENSE CHIP (grant no. 261810), KillSpill (grant no. 312139) and Patch (grant no. A-1087-RT-GC). The funders had no role in study design, datacollection and analysis, decision to publish, or preparation of the manuscript.

Competing Interests: The authors have read the journals policy and have the following conflicts: Patent number SI23434 Procedure for concentrating cellsand extraction of nucleic acids from polymer matrix for analysis of cells from the air was granted by The Slovenian Intellectual Property Office on 31.1.2012. Bothauthors confirm that this does not alter the authors adherence to all the PLOS ONE policies on sharing data and materials.

* E-mail: [email protected]

Introduction

Effective monitoring of bioaerosols requires efficient collection

of microorganisms and an appropriate technique for their analysis

[1,2]. There is no standard method for collecting bioaerosols, but

culture dependent methods are generally recognized as the gold

standard in monitoring clean rooms (e.g. pharmaceutical and

medical instrumentation production facilities, operating rooms

and hospital indoor air), since isolation and cultivation of a specific

organism is currently the only validated approach to link causative

agents to a particular disease. However, some bacteria, including

pathogens such as Legionella pneumophila, can be in a viable but

nonculturable physiological state and others, such as Mycobacte-

rium tuberculosis are initially hard to cultivate. Although cultivation

techniques can be used to isolate most of the microorganisms that

are of concern to humans, a majority of bacteria, which arguably

are the most environmentally relevant, cannot be cultivated at all

[37]. This suggests the need to improve current methods for

bioaerosol analysis. Introduction of molecular methods based on

DNA isolated directly from environmental samples of culturable

and non-culturable bacteria, is expected to provide more

information than each one separately [1,7].

Methods currently used to collect airborne bacteria include

sampling with filters, liquid impingement, impaction on solid agar

or passive sedimentation. However, when both culturable and

non-culturable fractions of bacteria are desired, liquid impinge-

ment is most frequently used [7,8]. The impingement samplers are

less robust which results in several disadvantages such as rapid

evaporation of sampling liquid, samplers are typically not battery

driven and can be used only in vertical position. In these samplers

the evaporation of sampling liquid limits sampling time and lowers

collection efficiency. Moreover, additional handling of liquid, such

as inoculation onto growth media, is needed. Impactor samplers

can overcome these obstacles, but are currently used mainly for

collection and analysis of airborne microorganisms, which can be

grown on agar growth media [9,10]. In favor of impactor based

sampling method, diversity of culturable bacteria was reported to

be higher then by air filtration method as well as by impingement

[9]. Despite the advantages of impactors used for collection and

characterization of culturable bacteria, only three studies have

been published that extend their use in molecular approaches

based merely on isolated DNA from collected airborne bacteria

without prior cultivation [9,11,12]. In each case, solid gelatin or

liquid mineral oil were used as an impactor matrix, which were

chosen based on low melting point or low evaporation rate,

respectively. Accordingly, mineral oil enables longer sampling

times, but it cannot provide solid support during impaction. This

results in uneven distribution of oil in impaction holders and liquid

loss during handling of the sampling liquid, which presumably

influences DNA extraction efficiency [12]. Gelatin however, has a

PLOS ONE | www.plosone.org 1 December 2013 | Volume 8 | Issue 12 | e821866366

solid structure at room temperature and low melting point (in a

range of 3037uC), which is beneficial for DNA extraction, since itsimplifies dissolution of the solid matrix [13]. Accordingly, the

solid matrix is the most preferable for sampling. However,

according to our knowledge the poorly defined chemical

characteristics of gelatin, which is composed of mixed size and

differentially branched polymeric matrix, as well as inhibition of

PCR due to high protein content, is especially pronounced in

samples with low numbers of cells [14]. If needed to use cultivation

in parallel to molecular methods, the low melting point of gelatin

limits its use at temperatures of 37uC and above, which isespecially problematic for incubation of pathogenic bacteria.

Additionally, gelatin can be degraded by many bacteria especially

eutrophic ones resulting in liquefied medium [15]. Therefore it is

of certain need to use alternative matrix with very similar

properties as gelatin but without drawbacks described above.

An ultimate approach to bioaerosol monitoring would be

simultaneous analysis of air samples by classical culturing methods

and by molecular methods without additional handling. One

favorable approach would be to use an impactor sampler with

classic growth media, from which in parallel one part of the sample

would be used in cultivation approach and the other for direct

DNA extraction. However, agar used to solidify nutrient media is

not molecular biology grade product and as such is inappropriate

to be used in DNA based analysis. Since this methodology is

currently unavailable, we have sought to develop and evaluate a

new method for monitoring total and culturable airborne bacteria,

adapted to the portable impaction based air sampler. The method

reported here is capable of speeding up the detection of the source

and identification of a particular microorganism.

Materials and Methods

Preparation of agarose matrixRCS High Flow plastic strips (impaction holders) (Biotest,

Germany) were used for agarose impaction matrix. The impaction

holders are comprised of two rows of 17 wells, each containing

250 mL of matrix. The impaction matrix was prepared withanalytical grade low melting point (LMP) agarose (Promega) in

DNase- and RNase-free 16TAE buffer (Sigma-Aldrich) and wassterilized by autoclaving for 20 min at 121uC. According to ourpreliminary studies, 0.7% (w/v) of agarose matrix was the most

appropriate concentration, which provided a stable solid gel

structure that withstanded air velocity during sampling. This

concentration of agarose also minimized the interference with

downstream methods since the large amounts of agarose in DNA

extracts can inhibit PCR [16,17]. Autoclaved agarose was kept

liquid by incubation at 60uC and then applied to the empty, sterileimpaction holders. A total of 8 mL of agarose was applied to each

holder and the holder was then closed with a sterile cover and the

contents were left to solidify at room temperature.

Extraction of DNA from agarose matrices spiked withbacterial cellsTo determine the most efficient protocol for extraction of DNA

from agarose matrices, a random amount of Escherichia coli (ATCC15597) and Staphylococcus aureus (ATCC 9144) in a range between107 and 108 CFU were used. Overnight cultures grown in Luria-

Bertani medium (Sigma-Aldrich) were applied to solid sterile

agarose matrices and left for 1 hour at 22uC to soak completelyinto the matrix. The efficiency and yield of DNA extraction was

determined by comparison of the obtained total DNA mass

extracted from spiked agarose matrices with the amount of DNA

extracted directly from bacterial cultures by the SmartHelixH

Complex samples Kit (Sekvenator Ltd., Slovenia) DNA extraction

protocol.

Development and optimisation of DNA extractionprotocolDissolution of the agarose matrix. To extract DNA from

the captured cells, it is (i) necessary to collect cells from the matrix,

(ii) to efficiently lyse the cells and (iii) to extract, purify and

concentrate the DNA. The most appropriate way to obtain

bacterial cells from the matrix is to completely dissolve and then

degrade the agarose into its monomeric units. However, in our

procedure, the amount of agarose that had to be dissolved

exceeded the volumes typically used (0.5 mL) for direct DNA

extraction. Therefore, adjustment of the reagent volumes and

times for incubation at elevated temperatures to completely melt

the agarose had to be determined from sample to sample. 0.7%

LMP agarose with spiked bacterial cells was transferred from

impaction holders into DNase- and RNase-free 10 mL tubes

(Sarstedt). Acid and enzymatic hydrolysis of agarose was tested in

combination with different temperatures to dissolve the agarose

completely and at the same time to minimize prolonged exposure

of sampled cells to elevated temperatures. Accordingly, for acid

hydrolysis, 1 mL of 5.5 M guanidinium thiocyanate (GuSCN,

pH 7) (Sigma-Aldrich) per 1 mL of agarose was added and then

incubated at 65uC for 10 min, 15 min or 30 min. For enzymatichydrolysis, agarose was first incubated at 65uC for 30 min or at100uC for 1 min, 1.5 min or 5 min to dissolve and then left for10 min to cool to 40uC. 7 U of b-agarase (Fermentas-ThermoScientific) per 1 mL of dissolved agarose was then added and the

mixture was incubated for 1 h or 1.5 h at 42uC.Concentrating bacterial cells from dissolved

agarose. The initial volume of agarose matrix expands to more

than 8 times the volume that is normally used in most

commercially available DNA extraction kits, and it was necessary

to concentrate bacterial cells and cell debris by filtration prior to

the DNA extraction. Accordingly, dissolved agarose samples from

bacterial spiking experiments were passed through PES membrane

filters (25 mm, pores 0.22 mm, Milipore). DNA was extracted fromthe filters by SmartHelixH Complex samples Kit (Sekvenator Ltd.,Slovenia), since PES is completely dissolved in phenol/chloro-

form/isoamyl alcohol, the solvent in this DNA extraction kit.

Concentrating DNA in filtrates. Since microbial cells

collected on the agarose matrix were exposed to elevated

temperatures during the agarose melting, it was expected that a

fraction of cells will have been lysed. Thus, DNA released from

lysed cells freely passes through the 0.22 mm pore size PES filtersduring the cell concentration procedure and is found in the filtrate.

Concentration of the DNA in the filtrate was achieved by

centrifugation of samples in ultrafiltration columns (10,000 Mw

cut-off, Vivaspin) at 9000 rpm for variable times, from 20 min to

60 min, until 100 mL of final DNA concentrate was obtained. TheDNA concentration was determined in all samples by Quant-iTTM

High-Sensitivity DNA Assay Kit Assay Kit using QubitTM

fluorometer (Invitrogen) and the total extracted DNA mass was

calculated.

Statistical analysis. Linear regression method was used to

model the total DNA mass extracted from spiked agarose matrices

as a function of total DNA mass extracted directly from bacterial

cells. The suitability of linear regression line was evaluated based

on random distribution of residual errors around the fitted values,

normal distribution of residuals errors and absence of laverage

points and outliers. The significance of correlation of was tested

based on Pearsons and Spearman correlation coefficients. All

statistical calculations were performed with the R software version

Method for Monitoring Airborne Microorganisms


2.14.1 according to the function lm from the R software package

[18]. Descriptive statistics was performed in R by deducer package

and graphs were visualised by ggplot2 package.

Evaluation of the procedure on environmental samplesSampling. To evaluate our procedure on actual samples,

outdoor sampling was performed at two locations, a wastewater

treatment plant (WWTP) which was predicted to have a higher

bacterial load [19,20], and an alpine mountainous area, which was

expected to have a lower bacterial load [21].

Impaction holders with sterile 0.7% LMP agarose as an

impaction matrix were inserted into portable RCS High Flow

air samplers (Biotest, Germany). For analysis based on culture-

independent methods, two air samples, designated Air1 and Air2,

each of 2 m3 were collected in the alpine mountain area

(Slovenian Alps, 46u2497.020N, 13u36926.540E, 760 a.s.l) and nineair samples, each of 2 m3 were collected at the WWTP (200,000

population units). In parallel, 0.5 m3 of air was sampled in

triplicate on the R2A growth media for alpine air and on nutrient

agar (NA) for samples taken at three locations in the WWTP to

permit characterisation of culturable bacteria from both locations

(Table 1).

Quantification. In samples from the WWTP, quantification

of total DNA concentrations and genes was performed by qPCR.

Two types of qPCR quantification were performed, a more

general method based on 16S rRNA genes and another specific

method targeting the Mycobacterium avium spp. hominisuis mtbA gene -because the WWTP is located next to a pig farm. DNA

concentrations were measured with Quanti-ItTM dsDNA HS

Assay Kit using QubitTM fluorometer (Invitrogen). In the same

DNA samples 16S rRNA genes were quantified in triplicate by

qPCR (7500 Real-Time PCR System, Applied Biosystems). The

20 mL volume reaction mixtures contained 200 nM primers U968and L1401 (Table 1, [22]), 10 mL of 26SYBR Green PCR mastermix (Applied Biosystems), 8.6 mL DNAse-free water and 1 mL ofgenomic DNA. Cycling conditions for real-time PCR were 2 min

at 50uC for prevention of DNA carryover, 10 min at 95uC forenzyme activation and initial denaturation, which was followed by

50 cycles of 15 s at 95uC for denaturation and 60 s at 60uC forannealing, extension and data acquisition. A final dissociation step

was added to exclude dimer interferences with the quantification.

A qPCR standard curve was determined with a series of 10-fold

dilutions of pCR2.1 plasmid with inserted partial 16S rRNA gene

of E.coli, amplified with the same primers. The detection limit wasset at a Ct value of 38 that corresponded to 15 copy numbers. 16S

rRNA gene copy numbers were calculated from triplicates of up to

500-fold dilutions of DNA samples.

For mbtA gene qPCR quantification the 20 mL reaction mixturescontained 600 nM primers mbtAPH_F and mbtAHA1_R

(Table 1), 10 mL of 26 SYBR Green PCR master mix (AppliedBiosystems), 7.8 mL DNAse-free water and 1 mL of genomic DNA.Cycling conditions for real-time PCR were 2 min at 50uC for

DNA carryover prevention, 10 min at 95uC for enzyme activationand initial denaturation, followed by 50 cycles of: 15 s at 95uC fordenaturation and 60 s at 61uC for annealing, extension and dataacquisition. A final dissociation step was added in order to assess

the potential occurrence of dimers. A qPCR standard curve was

determined with a series of 10-fold genomic DNA of Mycobacterium

avium spp. hominisuis, amplified with the same primers. The

detection limit was set at a Ct value of 36 that corresponded to 6

copy numbers. mbtA gene copy numbers were calculated from

triplicates of up to 100-fold dilutions of DNA samples.

Diversity. For culture-dependent analysis bacteria sampled

on R2A solid growth media, taken at the alpine mountain area,

were incubated at room temperature for 48 h. Colonies of bacteria

were enumerated and pure cultures from all grown colonies were

isolated. The culturable bacteria from one of three strips were

characterized by sequencing of 16S rRNA genes. The restriction

fragment length polymorphism (RFLP) analysis of 16S rRNA

genes was used on 33 and 39 colonies from Air1 and Air2,

respectively and the 16S rRNA genes from representatives of each

RFLP group were sequenced. Shannon-Wiener (H) index and

rarefaction analysis were calculated using Mothur software with a

97% OTU threshold [23].

For culture-independent analysis, DNA was extracted from

agarose according to the established protocol (see final protocol)

and a clone library was constructed based on PCR-amplified and -

cloned 16S rRNA genes in the pCR 2.1 vector. Accordingly,

25 mL of a PCR mixture consisting of 106 PCR buffer,31.25 nmol MgCl2, 2.5 nmol dNTPs, 1.5 U of Ampli Taq

polymerase (Applied Biosystems), 10 pmol of each primer U968

and L1401 (Table 1, [22]), DNAse-free water and 1 mL ofgenomic DNA were used in PCR amplification. During PCR

amplification the following cycling conditions were used: 3 min of

denaturation at 92uC, followed by 35 cycles of 30 s at 92uC, 30 sfor primer annealing at 54uC, 1 min at 68uC for extension, and afinal cycle at 72uC for 7 min on TProfessional temperature cycler(Biometra, Goettingen, Germany). PCR products of 433 bp were

separated on the 1% agarose gels, excised and purified through

silica columns according to the manufacturers instructions

(Wizard SV Gel and PCR Cleaning System, Promega). Clone

libraries were constructed by ligation of purified PCR products in

TOPO TA vector pCR2.1 and transformed in electrocompetent

E. coli Top10 strain (Invitrogen) according to the manufacturers

instructions. From each constructed clone library, 60 clones were

randomly selected and 16S rRNA gene inserts in pCR2.1 plasmids

were sequenced by using M13f primer (Macrogen, Korea). The

closest relatives for given sequences were determined by using the

BLAST tool in the GenBank sequences databank and SeqMatch

in the RDPII database [24]. The sequences were grouped into

operational taxonomic units (OTUs) using a threshold of $97%sequence similarity. Shannon-Wiener (H) index, rarefaction curves

and Libshuff analysis were calculated using Mothur software [23].

Table 1. Primers and amplification conditions for the detection of mbtA or 16S rRNA gene.

Oligonucleotide Name Sequence (59R39) Target gene Amplicon size

Forward primer U968 AACGCGAAGAACCTTAC 16S rRNA 433 bp

Reverse primer L1401 CGGTGTGTACAAGACCC 16S rRNA 433 bp

Forward primer mbtAPH_F CGACGACGCCCGTGTGATC mbtA 65 bp

Reverse primer mbtAHA1_R GCCATCCCGAACACCTGCT mbtA 65 bp

doi:10.1371/journal.pone.0082186.t001



Negative controlsNegative controls on DNA contamination of 0.7% LMP

agarose, membrane PES filters and all chemicals, were done

simultaneously for bacterial spiking and outdoor sampling. These

controls were treated in the same way as samples, total extracted

DNA concentrations were measured and 16S rRNA genes

detection was performed by PCR and qPCRs.

Results

Optimization of DNA extraction from agarose matricesTo sufficiently dissolve 8 mL of 0.7% LMP agarose at least

30 min at 65uC or 1.5 min at 100uC was required, as determinedby the disappearance of agarose residuals, visible on the

membrane filters after the filtration procedure. Acidic and

enzymatic hydrolysis both prevented reverse gelling of agarose.

However, addition of GuSCN to the acid hydrolysis reaction

significantly increased the final sample volume by a factor of at

least 2 of the initial sample volume, to approximately 16 mL.

Increase in the overall volume after the addition of agarase was

,110 mL and was deemed to be negligible. Incubation withagarase for 1.5 h showed greater agarose degradation than 1 h

incubation, as determined by the higher viscosity in less degraded

Figure 1. Ratio of total DNA extracted either from retentate or filtrate. Ratio of total DNA extracted either from PES membrane filter(retentate) (N) or concentrated with ultrafiltration (filtrate) (m), after bacterial spiking of agarose followed by enzymatic hydrolysis in relation tothe sum of DNA extracted from each individual sample (abbreviated as total extracted DNA mass). The sum of the N and m percentages in eachvertical line is 100%, which is represented on the total extracted DNA mass axis. Black lines represent linear trend: filtrate (R2 = 0.331, slope coefficient20.03 and intercept 89.7) and retentate (R2 = 0.331, slope coefficient 0.03 and intercept 10.3). 95% confidence intervals for both fitted lines arepresented with grey area.doi:10.1371/journal.pone.0082186.g001

Figure 2. Total DNA mass extracted after bacterial spiking.Linear regression between total DNA mass extracted with developedprotocol from spiked agarose matrices and total DNA mass extracteddirectly from bacterial cells (R2 = 0.76, slope coeficient 0.68, intercept38.2). 95% confidence interval for fitted line is presented with grey area.doi:10.1371/journal.pone.0082186.g002



samples. After both acid and enzymatic hydrolyses, on average

32.5%611.3% and 19.5%68.5% (Figure 1) of total DNA masswere isolated from retentates, which showed that most of the cells

were lysed during the agarose melting procedure and the released

DNA successfully passed through the filter. The DNA in the

filtrate had to be extracted, and this was the most conveniently

achieved by ultrafiltration. Since the DNA in the filtrate was above

5 kbp, it was determined that ultrafiltration would be at least 50%

efficient. In samples treated by enzymatic hydrolysis in which

1.5 min at 100uC was used to dissolve agarose followed by 1.5 hincubation with agarase, the minimum centrifugation time needed

to concentrate the sample to a final volume 100 mL, was 20 min.All other samples had centrifugation times between 30 min and

60 min, especially in samples treated with GuSCN. In these cases,

the centrifugation time was in excess of 45 min since the overall

volume was up to twice that developed in the enzymatic hydrolysis

procedure.

Performance evaluationYield. A positive linear regression (R2 = 0.76, slope coefficient

0.68, intercept 38.2) was determined between the total DNA mass

extracted from spiked agarose matrix and total DNA mass

extracted directly from bacterial cells (Figure 2) as well as

significant positive correlation based on Pearsons and Spearman

coefficient (p,0.0001 for both). Residuals were randomly andnormally distributed (Figure S1). Since the coefficient of the

regression line is below 1, at higher values of total amount of DNA

the extraction yield is lower (Figure 2), while the ratio of DNA

mass extracted from retentate was higher (Figure 1). The

extraction efficiency was higher than 50% in all tested samples,

with an average value of 79.2%618.0%.

PCR amplification efficiency. The PCR amplification

efficiency was assessed in spiked as well as actual samples obtained

from air with low (alpine region) and high (WWTP area) amounts

of cells. The conventional amplification of 16S rRNA genes was

successful from spiked samples as well as samples collected

outdoors. Approximately 103 CFU/m3 were determined at

WWTP and 101 CFU/m3 at the alpine area (Table 2, Table 3).

For efficient amplification, dilutions of at least 10-fold had to be

applied to samples taken at the WWTP, whereas in samples

obtained from the alpine area or spiked, the PCR amplification

could be detected in non-diluted samples.

In all nine samples from the WWTP we extracted enough DNA

to measure fluorometrically the total DNA mass which was found

to be between 12.1 and 37.7 ng/m3 (Table 2). With real time

PCR, we detected 106109 copy numbers of partial 16S rRNA

gene per m3. Amplification was achieved within a linear range

from 50- to 500-fold dilution, with a dynamic range of Ct 2238,

extending from 330 to 1260 pg total DNA/m3 at a maximum to

24.2 to 75.5 pg of total DNA/m3 at a minimum.

By M. avium spp. hominisuis-specific qPCR we detected 215 to628 copy numbers of mbtA gene per m3 (Table 2). Amplificationwas achieved within a linear range from 50- to 100-fold dilution,

with a dynamic range of Ct 3136, extending from a maximum of

330 to 1260 pg total DNA/m3 to a minimum of 36.1 to 24.6 pg of

total DNA/m3.

Bacterial diversity. The diversity of culturable bacteria was

compared to the 16S rRNA gene diversity in the clone library.

According to the calculated rarefaction curves and H index, thebacterial diversity was higher in both clone libraries than was

determined by cultivation (Figure 3, Table 3). The taxonomic

assignment of clones and isolates showed sequences in common

Table 2. Total DNA mass, copy numbers of 16S rRNA gene and mbtA gene per m3 of sampled air at three locations inside WWTP.

16S rRNA geneMycobacterium aviumspp. hominisuis (mbtA)

Samplename Air sampling location and sampling time CFU/m3

Total DNA mass(ng/m3) Copy numbers/m3 Copy numbers/m3

AGC-1 Aerated grid chamber Day 1 - 37.7 2.1E+0967.3E+08 -

AGC-2 Aerated grid chamber Day 2 17136677 33.2 2.1E+0968.7E+08 215664

AGC-3 Aerated grid chamber Day 3 - 26.5 2.3E+0861.3E+08 -

AB-1 Aeration basin Day 1 - 14.6 3.8E+0763.7E+07 -

AB-2 Aeration basin Day 2 16296437 36.1 2.1E+0861.1E+08 3376134

AB-3 Aeration basin Day 3 - 27.3 6.3E+0765.7E+07 -

E-1 Entrance to the management building Day 1 - 12.1 4.2E+0763.7E+07 -

E-2 Entrance to the management building Day 2 859659 24.6 4.3E+0762.1E+07 8846115

E-3 Entrance to the management building Day 3 - 26.5 1.7E+0769.3E+06 -


Table 3. CFU per 2 m3 air sample size (CFU6SD) and H index determined in clones and isolates from alpine area. Values inbrackets are high and low 95% confidence interval.

H index

Sample name CFU/2 m3 isolates sequenced clones sequenced isolates clones

Air1 89622 31 50 1.63 (1.90, 1.37) 2.63 (2.26, 2.99)

Air2 96649 39 56 2.47 (2.75, 2.16) 3.57 (3.80, 3.35)




with the obtained isolates only among Methylobacterium, Acinetobacter

and Brevundimonas in Air1 and Air2, respectively (Figure S2, S3, S4,

S5). All other clones were found to be exclusive to clone libraries

or among isolates. Bacterial diversity of culturable bacteria and

clones were significantly different in each location (p,0.05) asdetermined by Cramer-von Mises test.

False positives and false negativesSince air samples contain relatively low quantities of bacterial

cells it was necessary to determine the purity of the reagents. After

DNA isolation from PES as well as from chemical reagents, the

total DNA concentrations were below the detection limit

oncept series- anthology of works collected for undisclosed reasons

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