Earthworm distribution and abundance predicted by a process-based model

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Earthworm distribution and abundance predicted by a

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Johnston, A.S.A., Holmstrup, M, Hodson, Mark Edward orcid.org/0000-0002-8166-1526 et

al. (3 more authors) (2014) Earthworm distribution and abundance predicted by a

process-based model. Applied Soil Ecology. pp. 112-123. ISSN 1873-0272

https://doi.org/10.1016/j.apsoil.2014.06.001

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Earthworm

distribution

and

abundance

predicted

by

a

process-based

model

A.S.A.

Johnston

a,

*

,

M.

Holmstrup

b

,

M.E.

Hodson

c

,

P.

Thorbek

d

,

T.

Alvarez

e

,

R.M.

Sibly

a a_{SchoolofBiologicalSciences,UniversityofReading,UK}

b_{DepartmentofBioscience,AarhusUniversity,Denmark} c_{EnvironmentDepartment,UniversityofYork,UK} d_{EnvironmentalSafety,SyngentaLtd.,Bracknell,UK} e_{EcoRiskSolutionsLtd.,Norwich,UK}

ARTICLE INFO

Articlehistory:

Received25March2014

Receivedinrevisedform11June2014 Accepted16June2014

Availableonlinexxx

Keywords:

Individualbasedmodel Earthworm

Energybudget Foodavailability Soilwaterpotential Localmovement

ABSTRACT

Earthwormsaresignificantecosystemengineersandareanimportantcomponentofthedietofmany vertebratesandinvertebrates,sotheabilitytopredicttheirdistributionandabundancewouldhavewide applicationinecology,conservationandlandmanagement.Earthwormviabilityisknowntobeaffected bytheavailabilityandqualityoffoodresources,soilwaterconditionsandtemperature,buthasnotyet beenmodelledmechanisticallytolinkeffectsonindividualstofieldpopulationresponses.Herewe present a novel model capable of predicting theeffects of land managementand environmental conditions onthedistribution andabundance ofAporrectodeacaliginosa,thedominant earthworm speciesinagroecosystems.Ourprocess-basedapproachusesindividualbasedmodelling(IBM),inwhich eachindividualhasitsownenergybudget.Individualearthwormenergybudgetsfollowestablished principles of physiological ecology and are parameterised for A. caliginosa from experimental measurementsunderoptimalconditions.Undersuboptimalconditions(e.g.foodlimitation,lowsoil temperaturesandwatercontents)reproductionisprioritisedovergrowth.Goodmodelagreementto independentlaboratorydataonindividualcocoonproductionandgrowthofbodymass,undervariable feeding andtemperatureconditions supportourrepresentationof A.caliginosaphysiologythrough energy budgets.Ourmechanistic modelis abletoaccurately predictA.caliginosa distributionand abundanceinspatiallyheterogeneoussoilprofilesrepresentativeoffieldstudyconditions.Essentialhere is the explicit modelling ofearthworm behaviour in thesoil profile. Local earthworm movement respondstoatrade-offbetweenfoodavailabilityandsoilwaterconditions,andthisdeterminesthe spatiotemporaldistributionofthepopulationinthesoilprofile.Importantly,multipleenvironmental variablescanbemanipulatedsimultaneouslyinthemodeltoexploreearthwormpopulationexposure andeffectstocombinationsofstressors.Potentialapplicationsincludepredictionofthepopulation-level effectsofpesticidesandchangesinsoilmanagemente.g.conservationtillageandclimatechange.

ã_{2014TheAuthors.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense}

(http://creativecommons.org/licenses/by/3.0/).

1.Introduction

Earthworms are major contributors to soil biodiversity, are significantecosystemengineersinterrestrialsoils,andrepresenta largecomponentofthestockofnaturalsoilcapitalfromwhicha rangeofecosystemservicesflow(KeithandRobinson,2012;Blouin etal.,2013).Earthwormscanbring c.40t/ha/yearofsoiltothe surface by casting and potentially change erosion rates by

increasingsurfaceroughness(Felleretal.,2003).Belowground, earthwormscreatesoilaggregateswhichmaintainsoilstructure, aidplantgrowthandpromotecarbonsequestration(e.g.LeBayon etal.,2002;Butenschoenet al.,2009).Earthwormsarealsoan important component of the diet of many European animal species, both vertebrate and invertebrate (Granval and Aliaga, 1988), andsoaresignificantinecosystemfoodchains.Thus, an ability topredict the spatiotemporal abundance of earthworm populations has important applications in forecasting how changing environmental conditions alter the provision of soil ecosystemservices.However,previousmodelshaveneglectedthe major ecological drivers affecting earthworm populations in naturalenvironments(e.g.movementinthesoil,soiltemperature, soilmoistureandresources)(SchneiderandSchröder,2012).

*Correspondingauthorat:Room405,PhilipLyleBuilding,SchoolofBiological Sciences,UniversityofReading,Reading,BerkshireRG66AS,UK.

Tel.:+4401183785049.

E-mailaddress:[email protected](A.S.A. Johnston).

http://dx.doi.org/10.1016/j.apsoil.2014.06.001

0929-1393/ã2014TheAuthors.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense(http://creativecommons.org/licenses/by/3.0/).

ContentslistsavailableatScienceDirect

Applied

Soil

Ecology

Topredicthowpopulationsrespondtoenvironmentalchanges, understandingisneededofhowtheunderlyinglifecycleprocesses of individuals are altered byecological factors present in _field conditions. Food supply is well recognised as a major factor limitinganimalpopulations(Solomon,1949;Sinclair,1989)andis instrumental in structuring earthworm communities (Curry, 2004).Boththequantityandthequalityofthefoodsupplyare important (Lee, 1985). For example, earthworm population abundancein the _field has been found tovary in response to changes in soil organicmatter (SOM) content,associated with habitatqualityandlandmanagementpractices(e.g.Edwardsand Bohlen,1996; El-Duweini and Ghabbour, 1965; Hendrix et al., 1992). Soil moisture is also a key factor in determining the abundanceanddistributionofearthwormpopulations(Lee,1985). Clearrelationshipsbetweensoilwaterpotentialandearthworm physiology(A.caliginosaactivity,growthandreproductionrates) wereidentifiedbyHolmstrup(2001).Inthefield,Gerard(1967)

demonstrated how soil water potential governed the vertical movementofearthwormpopulationsinthesoilpro_file.

Understandingthelinks betweenenvironmental factorsand populationdynamics is not possible using classical population models (e.g. matrix models) as these consider populations as collectiveentitiesandlandscapesashomogeneous(DeAngelisand Mooij,2005).However,aimingtocapturebiologicalrealismoften resultsinmodelswhicharecomplex,requireextensive parameter-isation,arehardtoevaluateandbecomespecies-andsite-speci_fic (Grimmetal.,2005).Instead,keydriversofthesystemshouldbe integrated with generic frameworks explaining biological responses.Thisrequiresa process-basedapproach(Evansetal., 2013).

A process-based approach ideally begins by modelling how individualphysiologicalprocessesrelatetoexternal environmen-tal drivers through energy budgets. Individual based models (IBMs) can then be used tosimulate the interactions between individuals and their environments, from which population dynamicsemerge(GrimmandRailsback,2012).Combiningthese approaches is necessary to mechanistically extrapolate from individuallifehistorytopopulationdynamicsinrealistic environ-ments(e.g.Siblyetal.,2013).Theresultingmodelscanthenbe usedtoanalysepopulationresponsestoavarietyofenvironmental conditionsandlandmanagementpracticesthroughmanipulation oflandscapevariables.

Aprocess basedmodelofearthworm populationswouldbe particularlybeneficial toagro-ecosystems,wherethefunctions provided byearthworm activity are replaced by chemical and mechanicalpractices(Chan,2001).Previousearthwormmodels havelargelyconcentratedoneasilyrearedspeciesofimportance in toxicity testing, vermiculture and waste management (e.g.

Jageretal.,2006;HobbelenandvanGestel,2007;Johnstonetal., 2014). However, the earthworm species considered are not commonly found in agricultural landscapes (Paoletti, 1999). Earthwormspeciesinhabitingagriculturalhabitatsarenormally adaptedtolowqualityfoodresourcesandregularperiodsoffood

limitation.TheendogeicearthwormA.caliginosaisthedominant earthworm in arable soils (Riley et al., 2008) and its global distributioniswiderthanthatofotherspecies(Blakemore,2002). Here we construct an energy-budget IBM for A. caliginosa and investigatethepotentialofthisprocess-basedapproachtopredict life histories and population dynamics under variable soil temperature, soil moisture and resource conditions in the laboratory and field. Although agricultural land management scenarios are not simulated here, we aim to capture the mechanisms governing the spatiotemporal distribution and abundanceofA.caliginosapopulationsinfieldconditions,sothat future exploration of agricultural management effects can be better understood. For example, the effects of pesticides on earthworm populationsare routinelytested inpasture(SANCO, 2002), and soit is important tounderstand these systems for applicationstoecologicalriskassessment.

2.Methods

ThepurposeofthemodelistosimulateA.caliginosapopulation dynamicsundervaryingenvironmentalconditions,representative ofthoseencounteredinthefield,particularlyfoodavailabilityand quality, soil water conditions and soil temperature. Population dynamics emerge from environmental conditions constraining energy allocationamongst individuals;thewaythis happens is representedbyan individualbasedmodel (IBM)in whicheach individual hasitsown energy budget.Here we give anoutline summary of the model. A full description, following the ODD protocolfordescribingIBMs(Grimmetal.,2010)ispresentedin AppendixAinSupplementarymaterialandJohnstonetal.(2014)

for Eisenia fetida. The model is implemented in Netlogo 5.0.4 (Wilensky,1999),aplatformforbuildingIBMs.

2.1.Energybudgetmodel

Individualsassimilateenergyfromingestedfoodandexpend availableenergyonmaintenance,growthandreproductioninthe orderofpriorityoutlinedinFig.1.

TheenergybudgetmodelwasparameterisedforA.caliginosa with data relating to species-specific growth and reproduction ratesunderoptimalenvironmentalconditionsasshowninTable1. Sub-optimalfeeding,temperatureandsoilwaterconditionsthen reduce metabolic rates. Iffood is limiting, the amountof food availableinapatch(g/0.01m2_{)isdividedbetweentheindividuals} livingthere.Aproportionofingestedenergy,determinedbythe energy content of food (Ex) and assimilation efficiency (Ae), becomesavailableforallocationtothevariousprocessesoutlined inFig.1.Ex(kJ/g)variesdependingonthedietoftheindividuals whilstAeisassumedtobeconstant.Iflessenergyisavailablethan isrequiredformaximumreproductionorgrowththenpriorities operateasinFig.1andreproductionand/orgrowtharereduced accordingly.Temperaturealtersindividualmetabolicrates accord-ingtotheArrheniusfunction(Fig.1).

Fig. 1.Structureoftheenergybudgetmodelforadultearthworms,withthethicknessofsolidarrowsindicatingprioritiesforallocationofenergyobtainedfromfood. Reproductionhaspriorityovergrowthinsexuallymatureindividuals.Energyremainingafterallocationenterstheenergyreserves.Equationsareusedtocalculatemaximum dailymetabolicrateswhichdependonmass,Mingrams;temperature,TinkelvinandparametersasdefinedinTable1forAporrectodeacaliginosa.A(T)istheArrhenius functionoftemperature,AðTÞ ¼e E=kð1=T1=TrefÞ _{, where kis the Boltzmann's constant (8.6210}5_eVK 1_).

Metabolicprocesseshaveassociatedenergeticcosts:theenergy costofproducingonecocooniscalculatedas:Mc(Ec+Es)(Table1), whereMcismassofthecocoon,calculatedtogether withMbby regressionas described inAppendix B. Cocoon massis linearly relatedtothemassofthereproducingadultwhilstmassatbirth dependsonthemassofthecocoon(minimumtomaximumranges arepresentedinTable1).Energycostsofmovementareassumed tobeincludedaspartof“maintenance”.Someofthestudiesused toparameterisetheenergybudgetmodel areofA.turberculata, previouslyconsidereda sub-speciesof A.caliginosa(e.g.

Perez-Losadaetal.,2009).Herewedonotdistinguishbetweenthesetwo speciesastheyarecloselyrelated.

Ifanyassimilatedenergyremainsafterexpendituretorelevant lifecycleprocessesitisstoredinanindividual'senergyreserves, which may be utilised as an energy source when food is not availabletopaytheenergycostsofmaintenanceandreproduction. Maximumenergyreservesareproportionaltoanindividualsmass and are taken to be (M/2)Ec. Below a critical energy reserve threshold ((M/4)Ec), individual's catabolise tissue for energy, resulting in weight loss proportional to an individual's

Fig. 2. Partialenergyflowdiagramofearthworm(Aporrectodeacaliginosa)adults,showingtheprocesses(rectangles)eachindividualgoesthroughpertimestep,with diamondsindicatingdecisionpoints.Energyreservesareusedtopaymaintenancecostswhenfoodisunavailableandindividualsdieifweightlossunderstarvation continues.

Table 1

Defaultparametervaluesoftheearthworm(Aporrectodeacaliginosa)energybudgetmodelwithsources.Furtherdetailsoftheparameterestimatesareavailablein AppendixBoftheSupplementarymaterial.

Symbol Definition Value Unit Reference Notes

Ae Assimilationefficiency 0.19 – LavelleandSpain(2001) p.470

Bo Taxon-specificnormalization

constant

968 kJ/g/ day

Meehan(2006) CalculatedfromTable2,p.881andEq. (4)

E Activationenergy 0.25 eV Meehan(2006) p.880

Ec Energycontentoftissue 7 kJ/g Peters(1983) p.235

Es Energycostofsynthesis 3.6 kJ/g SiblyandCalow(1986) Calculatedfromp.54–55

Ex Energycontentoffood 0.56–

21.2

kJ/g Rangedependsondiet.Seesection2.3and

2.4.2fordetails. IGmax Maximumingestionrate 0.805 g/day/

g2/3

TaylorandTaylor(2014) Table 1,p.181

Mb Massatbirth 0.005–

0.026

g PedersenandBjerre(1991) Calculatedvialinearregressionwithmassof

cocoon.SeeAppendix B

Mc Massofcocoon 0.008–

0.035

g BoströmandLofs-Holmin(1986);Boström (1987)

Calculatedvialinearregressionwithadultmass(g). SeeAppendix B

Mp Massatsexualmaturity 0.50 g Lofs-Holmin(1983) Fig.6,p.35

Mm Maximumasymptoticmass 2.00 g Lofs-Holmin(1983) Fig.1,p.32

rB Growthconstant 0.049 /day Lofs-Holmin(1983) Fig.6,p.35

rm Maximumrateofenergyallocationto

reproduction

0.054 kJ/g/ day

Spurgeonetal.(2000) Table 2,p.1803

T0 Incubationperiod 62 days Holmstrupetal.(1991) Table 1,p.181

Tref Referencetemperature 288.15 kelvin Eriksen-HamelandWhalen(2006) Fig.1,p.211

m Backgroundmortalityrate 0.14 %/day p.210

maintenancecosts.Anindividualdiesofstarvationifitsenergy reservesaredepleted(Fig.2).

2.2.Individualbasedmodel

TheIBMcomprises A.caliginosaindividualsandamodelsoil profileconsistingoftwo-dimensional0.01m2_{patchesofsoil.In} simulations of laboratory experiments, patches represent the horizontalsoilsurface,whilstinthe_fieldtheyrepresentavertical cross-sectionofthesoilpro_file.Individuals arecharacterizedby life cycle stage (cocoon, juvenile or adult), mass and energy reserves, and patches by food availability, food quality, soil temperature, soil water content and soil texture. The model proceeds in discrete daily time-steps, at the end of which individual and patch variables are updated. Juvenile and adult movementbetweenpatchesdependsonfoodavailabilityandsoil waterconditionsin thesoilprofile,outlined inthe“Movement” sectionbelow.Variationinfoodavailabilitybetweenpatchesarises fromthemovementandfeedingofindividualsinthesoilpro_file. Soil water potential constrains individual ingestion rates and determinestheonsetofarestingphase(aestivation),outlinedin the“Soilwaterpotential”and“Aestivation”sectionsbelow.

2.2.1.Soilwaterpotential

Holmstrup(2001) founddecreasing soil water potentials to haveanegativeeffectonindividualA.caliginosalifecycletraits,as showninFig.3.Herewesupposesoilwaterpotential(

c

)reduces theingestionrateparameter(IGmax)as:

IGmaxð

c

Þ¼ðIGmaxÞekc (1)

whereIGmaxis theparametervalueat a soilwaterpotential of 2kPa(Table1)andktakesthevalue0.040.Thisresultsinless energybeingavailableforallocation togrowthorreproduction, than underoptimal conditions of soilwater potential ( 2kPa).

Fig.3presentsmodel resultswhenthemodel wassetupasin

Holmstrup(2001).Fulldetailsandresultsofthemodelsimulations areavailableinAppendixC.

2.2.2.Aestivation

Holmstrup(2001) reportedaestivationin A.caliginosato be inducedatsoilwaterpotentialsintherange 19to 29kPaata constant temperature of 15_{C, whilst Doube and Styan (1996)}

foundthecloselyrelatedspeciesA.trapezoidestoavoidsoilwater potentialsbelow 25kPa.Here,weassumedasoilwaterpotential of 25kPatriggersaestivation,independentoftemperature(e.g.

EdwardsandBohlen,1996).Asfacultativediapauseisacondition thatmayterminateassoonassoilconditionsbecomefavourable (Lee,1985),weassumedasoilwaterpotentialof 20kPaprompts the re-emergence of individuals from aestivation. During

aestivation,individualsutilizeenergyreservestopaytheenergetic costs of maintenance according to the relationship between oxygenconsumption andcarbondioxide releaseof A.caliginosa atdifferentstagesofaestivationrecordedbyBayleyetal.(2010)

(Fig.4)

2.2.3.Movement

MajorfactorsdeterminingthelocalmovementofA.caliginosa innaturalsoilenvironmentsaresoilwatercontentandfoodquality (Lee,1985).AsA.caliginosaissensitive todecreasingsoilwater potentials,themovementofindividualsthroughthesoilprofileis primarilydrivenbysoilwatergradientswhensurfaceconditions aredry(Gerard,1967).Weassumethatbelowasub-optimalsoil waterpotentialof 10kPa(e.g.growthandreproductionarenot affectedat 10kPainHolmstrup(2001)),individualmovementis driven by the availability of higher soil water potentials in neighbouringpatchesinthemodelsoilpro_file(Fig.5).Burrowing activityofA.caliginosainthetop10cmofthesoilprofileisbelieved toreflectthepresenceofahigherSOMcontent(Jégouetal.,1998). Thus, if soil water conditions are non-limiting (greater than 10kPa)individualspreferentiallymovetopatchesofgreaterfood quality, representedby theparameterEx(Fig. 5).Neighbouring patchesoccurbothverticallyandhorizontallyandiftheydonot providebetterorworseconditionsindividualsmoverandomly.

Fig. 3. Theeffectsofsoilwaterpotential(lessthan 2kPa)ongrowthand reproductionoftheearthwormAporrectodeacaliginosa,withdata(points)from

Holmstrup(2001)togetherwithmodelsimulationoutputs(lines)forreproduction (dashed)andgrowth(solid).

Fig.4.Modelled declineinmaintenancerates oftheearthwormAporrectodea caliginosawithtimeaestivating(lineandleft-hand axis)comparedtooxygen consumptionandcarbondioxidereleasedatafromBayleyetal.(2010)(pointsand right-handaxis).

Fig.5.Conceptualmodelofearthworm(Aporrectodeacaliginosa)movementinthe individualbasedmodel,wherecrepresentssoilwaterpotentialandExtheenergy

contentoffood.Diamondsindicatedecisionpointsandrectanglesareprocessesper dailytime-step.

2.3.Laboratoryexperimentsimulations

The modelwas setuptomimic theconditionsof published laboratory experiments, for comparisons between modelled A. caliginosagrowthandreproduction(N=10)anddata.Estimatesof theenergycontentoffood(Ex)wereneededformeadowfescue, barleyandlucerneandthesewerebasedontheformula:

Ex¼

2:3CPþ4:1EEþ1:9CFþ1:8NFE

ð Þ

100 (2)

whereCPiscrudeprotein,EEisetherextract(mainlylipids),CFis crudefibreandNFEisnitrogen-freeextract,measuredinmg/gdry matter(Forbesand Watson,1992).Parametervaluesfor Eq.(2)

werederivedfromBoströmand Lofs-Holmin(1986)andForbes andWatson(1992)(Table2).Boström(1987)recordedtherelative massofparticlefractionsforeachplantmaterial.Here,wetook particlelengths<0.5mmtobedigestible,followingobservations byLoweandButt(2003).

Well-compostedcattlemanurewasprovidedasfoodinsome experiments.FollowingGunadietal.(2002)'sobservationsthat pre-compostingfor5weeksledtoa45%declineinreproduction

rates of E.fetida,we assumed that theenergycontentof well-composted cattle manure was one third that of fresh manure.

Wangetal.(2011)recordedtheenergycontentoffreshmanureto beapproximately21.2kJ/g,givinganExvalueof7kJ/gfor well-composted manure. The energy content of the soils in the experiments was calculated assuming that soil organic matter (SOM)hasanenergycontentof18.62kJ/g(Loustau,1984).Table3

outlinestheconditionsusedintheexperimentssimulatedhere.

2.4.Fieldtrialsimulations

To investigate the model's ability to predict earthworm population responses to land management, we simulated A. caliginosapopulationdynamicsina fieldexperimentby Gerard (1967)atRothamsted,UKandKnightetal.(1992)atNorthWykes Farm,UK.Gerard(1967) measured theverticaldistributionand population structure (adult, juvenile and cocoon density) of A. caliginosainthetop45cmofsoilunderpasture.Knightetal.(1992)

placed artificial cow pats on permanent grazed pasture and measuredtheearthwormbiomassresponse,whereA.caliginosa were the dominant earthworm species. The model soil profile Table 2

Estimatesfortheenergycontent(Ex)ofmeadowfescue,barleyandlucerneusingvaluesfromaBoströmandLofs-Holmin(1986);bForbesandWatson(1992)andcBoström

(1987).CPiscrudeprotein,EEisetherextract(mainlylipids),CFiscrudefibreandNFEisnitrogen-freeextract(mg/gdrymatter).

Analysisofdrymatter(mg/gDM) Digestibleportion(%) Ex

(kJ/g)

CP EE CF NFE

Meadowfescue 140a ₂₆b ₂₈₀a ₄₉₃b _56.4c _10.42

Barley 180a ₁₆b ₂₃₀a ₃₉₂b _30.4c _4.93

Lucerne 150a ₂₂b ₃₄₀a ₄₀₂b _43.8c _7.91

Table 3

ExperimentalconditionsusedinmodelsimulationsforcomparisonwithgrowthandreproductiondatafortheearthwormAporrectodeacaliginosa,whereSOMissoilorganic mattersandExisenergycontentoffood.

Study Numberofindividuals Foodresource SOM(%) Ex(kJ/g) Foodquantity(g)(dayprovided) Temp(C)

BoströmandLofs-Holmin(1986) 10 Barley 7 1.33 252(0) 15

Boström(1987) 1 Meadowfescue 5 1.018 252(0) 15

SpringettandGray(1992) 1 Standardmix 10 1.86 40(0) 12

Lofs-Holmin(1983) 5 Manure 10 5.76 20(0)40(30)80(60) 15

Boström(1988) 5 Meadowfescue 5.4 1.70 260(0) 15

Boström(1988) 5 Lucerne 5.4 1.64 260(0) 15

Boström(1988) 5 Barley 5.4 1.56 260(0) 15

Fig.6.DiagramofthemodellandscapeusedtosimulatethefieldexperimentsfortheearthwormAporrectodeacaliginosa,wherecissoilwaterpotential( kPa),estimated fromsoilwatercontent(cm3_/cm3_{)andsoiltexture.E}

xisenergycontentoffood,predictedfromsoilorganicmattercontent(%).Thedashedlinerepresentstheboundaryofthe

sampledarea(10.3m)andtheshadedarearepresentsthemodelledapplicationofmanuremixedintothetop10cmofsoilforsimulationoftheexperimentbyKnightetal. (1992).

spanned 20.5m whilst the area sampled in the model was 10.45mforGerard(1967)and10.3mforKnightetal.(1992)

(Fig.6).

Atthe start of Knight et al.'s (1992) experiment, fresh cow manure(Ex=21.2kJ/g;Wangetal.,2011)wasappliedatarateof 200g/m2_{andassumedtobemixedintothetop10cmofthesoil} pro_file(Fig.6).Thetimingofmanureapplicationisnotstatedinthe study but a sensitivity analysis(Appendix D) showed that the model was only sensitive to the timing of application during unfavourable soil water conditions (June–September) when aestivationis common.Here, we assume a manureapplication dateof1stApril1990.

Modelsimulationswereinitializedwith100individualsofeach lifecyclestage(adults,juvenilesandcocoons)andrunfor50years toallowthepopulationtostabilisebeforemakingobservationsin thesamplearea.Majorconsiderationsformodellingpopulations underundisturbed_fieldconditionsareseasonalvariationsinsoil temperature and soil water potential and the availability and qualityoffoodresources,outlinedinthenextsections.

2.4.1.Soiltemperatureandsoilwaterpotentialinthefield

Mean monthly values and standard deviations for soil temperature under grass at 10, 20 and 30cm and soil water contentestimateswereobtainedfromRothamstedExperimental Stationforbothfieldtrialssimulated.Thesoiltexturewasreported as a silty loamwith an underlying clay sub-soil, and we have assumedatransitionintexturefromsiltyloamtosiltclayloamto siltyclay,outlinedinFig.6.Weestimatesoilwaterpotential(

c

) from water content measurements

u

(cm3_/cm3_{) using the} parametricvanGenuchten(1980)modelintheform:

c

¼1 a uu us urr

_nn₁

1

1=n

(3)where

c

isinunits kPa,

u

rand

u

s aretheresidualandsaturatedwatercontentsrespectively,and

a

andnareparametersdirectlydependentonsoiltexture.Thevalues of

u

r,

u

s,

a

andnwereobtainedfromtheliteratureforthesoil texturesinthefieldtrialsimulated(Table4).

Seasonal variationsin soil water potential andtemperature for the soil depths sampled by Gerard (1967) for 1959 are presentedin Fig. 7.

2.4.2.Soilorganicmatterinthefield

Soilorganicmatterrepresentsakeyfoodsourceforendogeic earthwormslikeA.caliginosa(e.g.EdwardsandLofty,1977).Inthe model,weusesoilbulkdensityasaproxyforfoodavailabilityand SOMrepresentstheenergycontentofthefood.Althoughthisisa simplification of the diversity of resources available to earth-worms,particularlyepigeicandanecicspecieswhichfeedatthe soil surface, here we assume these details are sufficient for modellingthefeedingbehaviourofendogeic speciesinthesoil profileofundisturbedpastures.Knightetal.(1992)recordedsoil bulkdensitiesof0.75and1.06g/cm3_{inthetop10cmanddeeper} layers of the soil profile respectively and we assumed a bulk densityof 1.10g/cm3 _{for thesoil inGerard (1967).The feeding} dynamicsofA.caliginosainpastureweremodelledbyestimating variationsinSOMwithseasonanddepth.SOMcontentgenerally declineswithdepthinthesoilprofile(LavelleandSpain,2001).

Celik(2005)measuredtheSOMcontentofapasturesoiltorange from44.6g/kginthetop10cmto37.9g/kgatadepthof10–20cm. The soil carbon stock of a silty loam soil was measured by

Balesdentetal.(2000)as1.53,1.34and1.09kg/m2_{atdepthsof10,} 20and30cmrespectively,whichisinlinewithobservationsmade by Jenkinson (1969) at Rothamsted. From these values and consideringcarbontoaccountfor58%ofSOM(GuoandGifford, 2002),weassumed a maximumSOMcontentof 6%forthetop 30cm of the soil pro_file. Our estimate is in agreement with observationsfromRothamstedintherange5–7.1%SOM(Coleman etal.,1997;HarrodandHogan,2008).

Although no clear seasonal variations in SOM content have been identi_fied, some general patterns are evident in the literature for field soils (e.g. not sieved of macro-organic material). For example, McNaughton et al. (1998) found root biomassinundisturbedgrasslandstopeakinsummeranddecline inwinterwithadifferenceofaround300g/m2_{,whilstlevelsare} similarduringspringandautumn.Bardgettetal.(1997)recorded similarpatternsformicrobialbiomassingrassland,with differ-encesbetweensummerandwinterof200g/cm2_.Weusedthese general observations to model seasonal variations in SOM as shownin Fig. 8. Dailyvariationsin SOM, fromplant, rootand microbial growth and deathwere modelledby assigning each patchdailyenergycontents(kJ/g),takenatrandomfromnormal distributionsasinFig.8.Thisalsoproducedspatialheterogeneity insoilpro_files.

2.5.Goodnessoffitofmodeloutputstorecordeddata

Weusedthecoefficientofdetermination(R2_{)toevaluatehow} wellthemodel'soutputsfittheobserveddata.R2_isde

finedas1– ((residual sum of squares)/(total sumof squares)), with values closerto1representingbetteragreementbetweenobservedand predictedvalues.NotethevalueofR2_{canbenegativeifthe}

fitis poor.ConventionalstatisticalmethodsofassessingtheR2values are not applicable here because the parameter values are not Table 4

Parametervaluesforestimatingthesoilwaterpotentialofdifferentsoiltextures.ur

istheresidualwatercontent,usisthesaturatedwatercontentandaandnarecurve fittingparameters.Valuesofur,usandnaretakenfromLeijetal.(1996)andafrom

Ghanbarian-Alavijehet al.(2010).

Depth(cm) Soiltexture ur us a N

0–20 Siltloam 0.061 0.43 0.565 1.39 21–30 Siltclayloam 0.098 0.55 0.500 1.41 31–50 Siltclay 0.163 0.47 0.600 1.39

Fig. 7. Seasonalvariationsinsoilwaterpotential(boldlinesandleft-handaxis: solid,dashedanddottedlinesrepresentmeanvaluesat15,30and45cmsoildepths respectively)withdepthandmeansoiltemperatureat10cm(faintsolidlineand right-hand axis)for(top)Gerard's(1967)and(bottom)Knightet al.(1992). Variationsinsoilwaterpotentialwithsoildepthresultfromdifferencesinsoil watercontent(cm3_/cm3_{)andchangesinsoiltexture.}

estimated from the data. However, we suggest that values of R2>0.5cangenerallybetakentoindicateagood_fit.

3.Results

Mechanisticmodelsforpotentialuseinpracticalapplications should be evaluated to ensure that they provide an adequate representationoftherealsystem.Here,weevaluateourmodel's predictionagainstmultipleindependentrecordsof A.caliginosa lifecycleprocessesinthelaboratoryandpopulationdynamicsin thefield.

3.1.Individuallifecycleprocesses

LifecycledataforA.caliginosafromexperimentalstudiesare presentedtogetherwithoutputsofmodelsimulationsrununder thesameconditions(Table3).Fig.9(a)and(b)showindividual changes in body mass under food conditions relevant to _field populations whenthe earthwormsare fedwithplant material.

Fig.9(c) and(d)showincreasedgrowth rateswhenindividuals werefedmoreenergyrichresourcessuchasmanure,underlining thedirectlinkbetweenenergyassimilationandexpendituretolife cycleprocesses.Themodeloutputsfitthedatawellasshownby theR2_{valuesinFig.9.}

Boström(1988)recordedgrowthandcocoonproductionof_five adult A. caliginosa maintainedfor 28 days on meadow fescue, lucerneorbarley(Fig.10).Modeloutputsagainfitwellwiththe recordeddata.

Cumulative cocoonproductionofA.caliginosaprovidedwith manureandmeadowfescueasfoodwasrecordedbyLofs-Holmin (1983)andBoströmandLofs-Holmin(1996);respectively.Thereis good model agreement with the data for variation of cocoon productionwithtemperature(Fig.11b:R2_{=0.92)andthedatafor} cocoon production do not differ significantly from the model outputs(ttest,p>0.05).

3.2.Fieldpopulations

TheverticaldistributionofanA.caliginosapopulationreported by Gerard (1967) is compared to model simulation results in

Fig. 12.InSeptember,Gerard(1967)didnot_findanyindividualsbut suggestedthatthewholepopulationwaspresentbelowthesoil depthsampled in theexperiment (45cm). In themodel, those individuals not aestivating were present below 31cm. Model outputsfitwellwiththerecordeddataatbothsoildepths.

Fig.9.Comparisonbetweentenmodelsimulationoutputs(lines)anddata(points)recordingchangesinindividualearthworm(Aporrectodeacaliginosa)biomassovertime providedwith(a)barley(fromBoströmandLofs-Holmin,1986),(b)meadowfescue(Boström,1987),(c)ahighlyorganicmix(SpringettandGray,1992)and(d)cattlemanure (Lofs-Holmin,1983)forfood.AverageR2_{valuesareshowninthebottomrightofeachpanel.}

Fig. 8. Estimatesofsoilorganicmatter(%)andequivalentenergycontents(kJ/ gsoil)inrelationtodepthandseasonforapasturesoilusedtosimulatethefield conditionsofGerard(1967)andKnightetal.(1992).Linesrepresentthemeanand SDistakenas10%.

Thepopulation densitiesof adults, juvenilesand cocoons were recordedeachmonthforthesampledyearinGerard(1967).Data from Gerard (1967) are presented alongside model outputs in

Fig.13.Althoughthemodelpredictsseasonalpatternsofjuvenile density reasonably well(Fig.13(b), R2_{=0.70), the}

fits for adult densitiesandcocoonsarepoor(Figs.13(a)and(c),R2=0.06and 0.08 respectively). However, the pattern of modelled adult densitiesreplicatesthatofthedata,withamaximuminspring,and aminimumin September(Fig.13(a))duetodrysoilconditions

drivingthepopulationtosoildepthsbelowthesampledarea(see above). The observed cocoon densities from January to June (453216/m2_{)arehigherthanpredicted(131}

57/m2_)duringhalf oftheyear(Fig.13(c)).However,theobserveddensitiesaremuch higherthanthoserecordedbyBoströmandLofs-Holmin(1996)in a meadow fescue lay, with a measured maximum density of 176cocoons/m2_inJune.

Earthworm population biomasses reported by Knight et al. (1992)under_fieldconditionsarecomparedwithmodelsimulation Fig.10.Comparisonbetweenmodeloutputs(hatchedbars,mean+SEfrom10simulations)andrecordeddatafromBoström(1988)(solidbars)for(a)individualbiomassand (b)cocoonproductionofgroupsoffiveadultearthworms(Aporrectodeacaliginosa)maintainedontheindicatedplantfoods.AverageR2_{valuesare(a)0.96and(b)0.75.}

Fig.12.ComparisonbetweendatafromGerard(1967)(solidbars)fortheverticaldistributionofanearthworm(Aporrectodeacaliginosa)populationinpasturewithmodel simulationoutputs(hatchedbars,meanfrom10simulations)showingmonthlychangesintheproportionofthepopulationpresentat(a)0–15cmand(b)16–30cmofthesoil profile.AverageR2_{valuesare(a)0.87and(b)0.80.}

results for A. caliginosa in Fig. 14. Under control conditions (Fig.14(a))thereisnoconsistentvariationwithtime,butunder experimental conditions, population biomass increases for 9 weeks afterdepositionof an artificial cowpat(Fig.14(b)). The fielddataarehigherthanthemodeloutputunderbothconditions. However,A.caliginosaonlycomprisedonaverage44.5%ofthetotal population, and when this is taken into account agreementis better(Fig.14(c)and(d)).

Knight et al. (1992) recorded an earthworm density of 35473individuals/m2 _{in pasture. Considering}

A. caliginosa to comprise 44.5% gives a population density and biomass of 15833individuals/m2 _{and 20.6g/m}2_{. Model simulations} recorded a mean population density and biomass of 14723 individuals/m2_and20.9

4.1g/m2₍

SE,N=4),closelymatching theobservationsofKnightetal.(1992).

3.2.1.Sensitivityanalysis

The implications for modelling movement as a trade-off betweensoilwaterpotentialandfoodquality,asinFig.5,were evaluatedbycomparingmodel outputswhen themovementis assumed to be random for the Knight et al. (1992) manure experiment. Fig.15 showshow importantcapturing directional movementisforpredictingthedynamicsofearthworm popula-tionsfollowinglandmanagementscenarios.

ModeloutputsaresensitivetotheSOMcontentofthesoilas showninFig.16.Earthwormdensityandbiomasschangelinearly by14%foreach10%changeinSOMcontentinthemodelledKnight etal.(1992)pasturetrial.

4.Discussion

Ourmodel_fitswelltherecordsofindividualcocoonproduction andgrowthofbodymassinA.caliginosaforalltheexperimental studieswe knowof. It isthe first publishedmodel toconsider temperature,soilmoistureandresources,whicharefundamental ecological drivers for understanding earthworm populations (Schneider and Schröder, 2012). Simulated laboratory studies variedinthefoodsprovided(Figs.9–11)andwerecarriedoutat severaldifferenttemperatures(Fig.11(b)).Theabilityofthemodel Fig. 13.Comparisonofearthworm(Aporrectodeacaliginosa)populationdensity

datafrom Gerard(1967) (symbols)and model outputs(lines, meanfrom10 simulations)for(a)adults,(b)juvenilesand(c)cocoonsfortheyear1959inpasture atRothamsted,UK.AverageR2_{valuesare(a)0.06,(b)0.70and(c) 0.08.}

Fig.14.Comparisonbetweenmodelsimulationresults(hatchedbars,mean+SEfrom10simulations)andearthwormpopulationbiomassdata(solidbars)recordedby

Knightetal.(1992)for(a)acontrolplotundergrazedpastureand(b)acowmanuredepositionexperimentand(c)and(d)taking44.5%ofthetotalrecordedearthworm biomasstorepresentAporrectodeacaliginosa.AverageR2_{valuesare(a) 6.47,(b) 0.91,(c)0.85and(d)0.96.}

toadequatelyreproduceindividuallifehistorytraitsoverarangeof controlledconditionsinthelaboratory,supportsour representa-tion of individual physiology through energy budgets. In field trials, the model predicts the spatiotemporal distribution of A. caliginosa populations in the soil pro_file (Fig. 12), alongside seasonalpatternsinthepopulationstage-structure(Fig.13).The model'sabilitytoreproducethepatternsobservedinKnightetal. (1992)(Fig.14)illustrateshowenergybudgetIBMscanbeusedto make reliable predictions of population-level exposure and responses to changing soil conditions, and thereby support informedlandmanagementdecisions.

Variationsinsoilphysio-chemicalpropertiesareknowntoalter thedistributionand abundanceof earthwormsthroughthesoil profile(JiménezandDecaëns,2000).Here,synthesisofknowledge on the effects of food availability and soil water potential on individualA.caliginosamovementaccount,toalargeextent,forthe verticaldistribution offieldpopulations in pasture(Fig.12).In Gerard's(1967)_fieldtrialtheeffectsofsoilwaterpotentialonA. caliginosamovementarepredominantinSeptember(Figs.7and 12),whenindividualsmovetodeepersoillayerstoavoiddrysoil conditions.Themodelsabilitytoreplicatethesepatternssupport itsapplicationtopredicthowenvironmentalconditionsatthesoil surface affect the population's structure. However, modelling involvesa trade-offbetweenstructural realismand complexity, and so when factors not captured here (e.g. pH, chemical applications, and compaction) are important in understanding

earthwormpopulationdynamics,subsequentmodeldevelopment willberequired.

Theabundanceofearthwormsinpastureiscloselyrelatedto organicmatterinputs(e.g.EdwardsandBohlen,1996;El-Duweini and Ghabbour, 1965). Hence, predicting realistic earthworm population dynamics in the _field is dependent on accurate estimatesofSOM(Fig.16).Fraseretal.(1996)foundearthworm populations to decline with time under arable cultivation and increasewithtimeunderpastureproductioninNewZealand,due tochangesintheSOMcontent.Amaximumpopulationdensity andbiomassof950individuals/m2_and185.7g/m2_werereported inplotsusedaspasturefor6–9years.ArelativelylowSOMcontent of3%,incomparisontotheaverage6%assumedfortheKnightetal. (1992) fieldtrial,wasrecorded.Thehighearthwormpopulation abundancesreportedarelikelyduetoahighersoilbulkdensityof 1.4g/cm3_{,whichdeterminestheamountofsoilavailableasfood.} Whenourmodelis setupasin thesimulation ofKnightet al. (1992)butwithasoildensityof1.4g/cm3_{andSOMcontentof3%,} rather than 0.75–1.06g/cm3 _{and 6%, an average}

A. caliginosa population densityand biomass of 63660individuals/m2 _and 13013g/m2 _{were recorded respectively, which closely agrees} withFraseretal.(1996)'sobservations.Thissuggeststhattheuse ofsoilbulkdensityandSOMareusefulproxiesforfoodavailability andqualityforpredictingearthwormpopulationdynamics.

Manyauthors havereportedthe beneficial effects ofanimal wasteapplications to_fieldpopulationsof earthworms. Satchell (1955) reporteda three-foldincrease in earthwormpopulation densitywhenmanurewasappliedtograssland,whilstEdwards andLofty(1977)foundmanureapplicationstoarablelandresulted inearthwormabundances14timesthoseofunmanipulatedplots. AttheindividuallevelBarley(1959)foundtheprovisionofsheep manureatthesoilsurfaceincreasedA.caliginosabodyweightby 111%after40days.TheeffectsofprovidingindividualA.caliginosa with high quality foods, such as manure, on their life cycle processes can be seen in our simulations of the laboratory experiments of Lofs-Holmin (1983) in Fig. 9(d) and Fig.11(a). Comparingthesegrowthandreproductionratestothoserecorded when individuals were provided with plant material and soil mixtures(e.g.Fig.9(a)and(b)andFig. 10),highlightsthedirectlink betweentheenergycontentoffoodandindividualphysiology.

FieldpopulationresultsinFig.14(b)and(d)clearlyshowhow the quality of food resourcesaffects populationdynamics. The assumptions made about individual behaviour in the field, particularly movement,wereessential toachievinggood model fitstopopulationdata.Comparisonsbetweenmodeloutputsfor the cow manure experiment when movement was explicitly modelledasin Fig.5,andwhen movementwas assumedtobe randominFig.15suggestthatthemodeladequatelycapturesthe factors driving thespatial distribution of earthworms. Further-more, sensitivity analysisof SOM effects on the abundance of earthworm populations (Fig. 16) is in close agreement with observations by Hendrix et al. (1992); who found soil organic carbon(%)todescribeearthwormabundanceinconventionaland no-tillageagroecosystemsalongsidegrassmeadows.

Earthwormsareimportantsoilengineersandsotheabilityto predict their abundance has wide application in ecology, conservation and land management. Our mechanistic model is abletopredicttheabundanceanddistributionofthedominant earthwormspecies inagro-ecosystems,A.caliginosa,inspatially heterogeneoussoilprofilesofundisturbedhabitats.Wehopethe model will _find many applications because of the vital role earthwormsplayinagriculturalhabitats(Hendrix andEdwards, 2004).Forinstance,earthwormsarefocalorganismsfor environ-mentalriskassessmentofpesticidesinEurope(underRegulation (EC)No1107/2009; seeSANCO,2002), andourmodel canhelp assess the population consequences of pesticides application Fig. 16.Modelledresponsesofearthworm(Aporrectodeacaliginosa)population

biomassanddensityto10%incrementsinSOMcontentofthepastureplotsampled byKnightetal.(1992)at15weeks,presentedasapercentagechangecomparedto thecontrolpopulation.

Fig. 15.ComparisonbetweendatafromKnightetal.(1992);representingonly

Aporrectodeacaliginosa(44.5%ofthetotalpopulation),foracowmanuredeposition experiment(solidbars)andmodelsimulationresultswhenindividualmovement dependsonsoilwaterandfoodqualityconditions(hatchedbars:R2_=0.96)and

whenmovementisrandom(dottedbars:R2_{= 0.11).}

followinginclusionofatoxicologicalsubmodel(e.g.Johnstonetal., 2014).Thespatialdistributionofindividualsinfieldpopulationsis predictedbythemodelandso,ifthefateofappliedchemicalsis known, then the exposure of individuals to pesticides can be calculated.Forapplicationtoanecicearthworm species suchas Lumbricus terrestris, additional model development may be requiredtocapturemorespatiallyexplicitmovementandfeeding behaviour.Furthermorethemodelcouldbeused toinvestigate population level effects of multiple stressors (e.g. tillage and pesticide applications), or variation of pesticide application timings, or climatic conditions. Considerations for modelling tillageinagroecosystemsincludemortality,redistributionofsoil organic matter and the effects of compaction on the energy budgets and movement of individuals in the soil profile (e.g.

Kretzschmar,1990).Formorewidespreadapplication,themodel should also be tested in a variety of climatic conditions. The authorsarecurrentlyworkingonapplyingthepresentedmodelto investigatetheinteractionsbetweenvariablechemical, mechani-calandenvironmentalconditions.Alsoimportantistheabilityto predictthelocalfoodsuppliesof animalsthateatearthworms, includingspeciesofpotentialconservationconcernsuchaswading birds(e.g.thelapwingVanellusvanellus),andspeciessometimes regardedaspestssuchasflatworms(Bipaliumadventitium)and foxes(Vulpesvulpes).

Acknowledgements

We thank AnneVerhoeffor assistancemodellingsoil water potentialandRothamstedResearchforsupplyingweatherinput data. This research has been financially supported by BBSRC studentshipBB/1532429/1, with CASE support from Syngenta.

AppendixA.Supplementarydata

Supplementarydataassociatedwiththisarticlecanbefound,in theonlineversion,athttp://dx.doi.org/10.1016/j.apsoil.2014.06.001.

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