Discriminating between possible foraging decisions using pattern oriented modelling : the case of pink footed geese in Mid Norway during their spring migration

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ContentslistsavailableatScienceDirect

Ecological

Modelling

j o u r n al ho me p ag e :w w w . e l s e v i e r . c o m / l o c a t e / e c o l m o d e l

Discriminating

between

possible

foraging

decisions

using

pattern-oriented

modelling:

The

case

of

pink-footed

geese

in

Mid-Norway

during

their

spring

migration

Magda

Chudzi ´nska

a,∗

_,

_Daniel

_Ayllón

b

_,

_Jesper

_Madsen

c

_,

_Jacob

_Nabe-Nielsen

a

a_Department_of_Bioscience,_Aarhus_University,_{Frederiksborgvej}_399,_DK-4000_Roskilde,_Denmark

b_Department_of_Ecological_Modelling,_Helmholtz_Center_for_{Environmental}_{Research—UFZ,}_{Permoserstrasse}_15,₀₄₃₁₈_Leipzig,_Germany c_Department_of_Bioscience,_Aarhus_University,_Grenåvej_14,_DK-8410_Rønde,_Denmark

a

r

t

i

c

l

e

i

n

f

o

Articlehistory:

Received29May2015

Receivedinrevisedform7October2015 Accepted11October2015

Availableonline15November2015

Keywords:

Agent-basedsimulationmodel

Anserbrachyrhynchus

Heterogeneouslandscape Learning

Optimalforaging

a

b

s

t

r

a

c

t

ForagingdecisionsandtheirenergeticconsequencesarecriticaltocapitalArctic-breedersmigrating insteps,becausethereisonlyanarrowtimewindowwithoptimalforagingconditionsateachstep. Optimalforagingtheorypredictsthatsuchanimalsshouldspendmoretimeinpatchesthatenablethem tomaximisethenetrateofenergyandnutrientgain.Thetypeofsearchstrategyemployedbyanimals is,however,expectedtodependontheamountofinformationthatisinvolvedinthesearchprocess.In highlydynamiclandscapes,animalsareunlikelytohavecompleteknowledgeaboutthedistributionof theresources,whichmakesthemunabletoforageonthepatchesthatenablethemtomaximisetheir netenergyintake.Randomsearchmay,however,beagoodstrategyinlandscapeswherepatcheswith profitableresourcesareabundant.Wepresentsimulationexperimentsusinganindividual-basedmodel (IBM)totestwhichforagingdecisionrule(FDR)bestreproducesthepopulationpatternsobservedin pink-footedgeeseduringspringstaginginanagriculturallandscapeinMid-Norway.Ourresultssuggested thatwhilegeeseemployedarandomsearchstrategy,theywerealsoabletoindividuallylearnwherethe mostprofitablepatcheswerelocatedandreturntothepatchesthatresultedinhighestenergyintake. Suchasociallearningisrarelyreportedforflockanimals.Themodelledgeesedidnotbenefitfromgroup foraging,whichcontradictstheresultsreportedbymoststudiesonflockingbirds.Geesealsodidnot possesscompleteknowledgeabouttheprofitabilityoftheavailablehabitat.Mostlikely,thereisnoone singleoptimalforagingstrategyforcapitalbreedersbutsuchstrategyissiteandspecies-specific.We discussedthepotentialuseofthemodelasavaluabletoolformakingfutureriskassessmentsofhuman disturbanceandchangesinagriculturalpractices.

1. Introduction

Themovementstrategythatanimalsusewhileforagingon spa-tiallydispersedresourcesiscrucialtotheirsuccessinexploiting them(Viswanathanetal.,1999;Bartumeusetal.,2005;Giuggioli andBartumeus,2010).Foragingdecisionsandtheirenergetic con-sequences are particularly important to capital Arctic-breeders migratinginsteps,astheyonlyhaveanarrowtimewindowwith optimalforagingconditionsateachstep.Hence,thespring migra-tionis regarded as anenergetic bottleneckin theannual cycle of capitalbreeders (AnkneyandMacInnes, 1978; Alerstamand

∗Correspondingauthor.

E-mailaddress:[email protected](M.Chudzi ´nska).

Lindström,1990;EbbingeandSpaans,1995;PropandBlack,1998; Drentetal.,2003)thathavetogarnerbodystoresinordertostart breedingsoonafterarrivalonthebreedinggrounds.Optimal for-agingtheorypredictsthatsuchanimalsshouldspendmoretimein patchesthatenablethemtomaximisethenetrateofenergyand nutrientgain(Killenetal.,2007;Hedenström,2008;Bartumeusand Catalan,2009;Stephensetal.,2014).Inheterogeneous,dynamic landscapeswhere theavailability andquality of foodresources varyboth spatially andtemporally,foraging atthemost proﬁt-ablepatchesrequiresthattheanimalshaveacompleteknowledge abouttheenvironment,whichisrarelythecaseandithasbeen widelysuggestedthatforaginganimalspossessincompleterather thancompleteknowledgeabouttheirlandscapes(Bernsteinetal., 1988;Pettiforetal.,2000;KoopsandAbrahams,2003;Amanoetal., 2006a;Noletetal.,2006;BartumeusandCatalan,2009;Matsumura etal.,2010;Kułakowskaetal.,2014).Thetypeofsearchstrategy

http://dx.doi.org/10.1016/j.ecolmodel.2015.10.005

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employedbyanimalsthereforestronglydependsontheamount of information that is availablein thesearch process. Random searchingisaprofitablestrategywheninformationislacking, con-fusingordifficulttogather(Bernsteinetal.,1988,Bartumeusand Catalan,2009).Animalscanalsolearnwheretheprofitablepatches arelocated andreturn to thesame areaorthe vicinityof that areaforconsecutiveforagingbouts(Charnov,1976;Amanoetal., 2006b).Migrantscanacquireinformationaboutresource availabil-ity,distributionandpredation/disturbancerisk directlythrough theirownexperience(asociallearning)orindirectlybyobserving orexchanginginformationwithotherconspecifics(social learn-ing),whichmaybeofparticularimportanceforanimalsmigrating inflocks.Social learningmayprovidea shortcuttoinformation acquisitionandatthesametimeallowsindividualstoavoidtime consumingandriskyexploratorybehaviour.However,social infor-mationispotentiallylessreliable,especiallywhenresourcesare very dynamic and/or patchy (Németh and Moore, 2014), than informationgatheredpersonally(asociallearning),largelydueto itssecond-hand nature(Némethand Moore, 2007), but it may befavouredif obtaininginformation individually is costlyor if migrantsaretime-restrictedandoptforfastfuellingrate.Group foraging,akeyelementofsociallearning,hasbeendemonstratedas animportantfactorinforagingdecisionmakingofvariousspecies (Amanoetal.,2006a;Kułakowskaetal.,2014),however,littleis knownabouttherole of asociallearning, especially for species frequentlyobservedinflocks.

Besidesthenutritionalandenergeticcontentoftheavailable foodresources,animalssearchingforoptimalforagingsitesneed to consider other factors such as the costs related to search-ingandmovement,predationordisturbancerisk,andinter-and intraspecificcompetitionbecausetheseaspectsmaysignificantly reducetheirintakerate(Lindström,1990;MooreandYong,1991; Ydenberget al.,2002; Olsson et al., 2008; Wood et al., 2013). Disturbance,whichcanalsoberegardedaspredationrisk(Beale andMonaghan,2004;Tombreetal.,2005;Klaassenetal.,2006), mightbean importantfactor influencing foraging behaviourof animalsthatforageinagriculturallandscapes, astheyarelikely tobefrequentlyexposed tohumanactivitiesand/ortheir pres-ence may conflict with agricultural interests. Disturbance can causebothanincreaseinenergyexpenditurebyforcinganimals tofrequentlymoveawayfromthesourceof disturbance,and a decreasein energyintakebypreventingthem fromforaging in thedisturbedarea(Madsen,1994;Klaassenetal.,2006;Stillman etal.,2015).It canbearguedthat duetolargenumber of fac-torsinfluencingforagingbehaviourofanimals,awidevarietyof strategies maybe optimaland suchstrategies are, most likely, environment-andspecies-specific(Turneretal.,1993;Grossetal., 1995).

Understandingthe relationship between processes, adaptive traitsofindividualsandpatterns,socalledbottom-upapproach, isfundamentaltoourunderstandingofthebehaviourand ecol-ogyofaspecies.Bottom-upsimulations,asopposedtotop–down approaches, allow the processes and mechanism behind the observedpatternstoberevealed.Individual-basedecology pro-videsaconceptualframeworkwherepopulationsandecosystems areviewedascomplexsystemswithpropertiesthatemergefrom thetraitsand interactions of theirlower-level, individual com-ponents.Modellingoftenallowsforrevealingpatternswhichare difﬁculttodirectlyobserveinnature,likelearningprocessesof ani-mals.Severalstudiesattemptedtouncovertheroleofdifferent factorsaffectingthedistributionandforagingdecisionsofanimals throughanindividual-based modellingapproach (Amanoet al., 2006a;Woodetal.,2013;Kułakowskaetal.,2014;Nabe-Nielsen etal.,2014).Forexample,modelsby Amanoet al.(2006a) and Kułakowskaetal.(2014)revealedtheimportnaceofgroupforaging indecisionmakingofbirds.

We present simulation experiments using individual based models (IBMs)to test thepotential decision makingrules and the mode of acquiring information in Svalbard-breeding pink-footedgeeseduringtheirspringmigrationinakeystopoversite inMid-Norway,wheretheavailabilityofdifferentfoodresources is very dynamic (Chudzi ńska et al., 2015)and geeseare under pressure to store energy and continue migration towards the breedingarea. Hence, thesetting offersaninteresting possibil-itytotestoptimalforaging hypothesesandtrade-offsincluding foragingondifferenthabitattypesaccordingtotheiravailability (randomsearch),maximisingenergyintakebyforagingonhighly energetic habitat patches, which requires from birds complete knowledgeabouttheenvironment,andchoosingforagingpatches basedonasocialand/orsociallearning.Wealsoinvestigatehow dis-turbance,intraspecificcompetitionandphysiologicalconstraints influenceforagingbehaviour,energeticsandspatiotemporal dis-tribution of geese. To do so, we model five different foraging decision rules(FDR): (1) randomselection offields, where ani-malsdonotgainexperience,(2)completelyinformedgeese,(3) non-omniscientforagersthatgainfamiliarityoftheenvironment throughexperience,(4)non-omniscientsociallylearningforagers and (5)non-omniscientbut learning, bothsociallyand through experience.Ineach foraging decisionrulegeese areexposedto variousdisturbancelevelscorrespondingtothosefoundinnature. Theycompetewitheachotherforresources,andtheirforagingis constrainedbyphysiologicalaspects.ThefiveFDRsaredefinedin searchofasingleoptimalforagingdecisionrule,whichisthebest practiceaccordingtothespecificenvironmentinMid-Norwayand energyrequirementsof thegeese.Followingapattern-oriented modelling (POM) strategy (Grimm et al., 2005; Railsback and Grimm,2012),wetestthecapacityofthefiveaforementioned alter-nativeforagingdecisionrulestoreproducefivepopulationlevel patternsobservedinnature.InPOM,patternsobservedinreal sys-temsatdifferenthierarchicallevelsandscalesareusedtooptimise modelcomplexity,reduceuncertaintyandtestandcontrast theo-ries(Grimmetal.,2005).Thecontrastedpatternsincludechanges indailynetenergyintakewithinthestopoverseason,howmuchof thepotentialtimeavailableforforaginggeesespendresting, phen-ologyofgeese,spatiotemporalchangesingoosedistributionand numberofgeeseobservedatroostsitesduringtheirstayin Mid-Norway.Theobservedpatternsarebasedonlong-termstudiesand detailedsatellitetrackingofpink-footedgeeseinMid-Norway.

2. Materialsandmethods

2.1. Studypopulationandsite

TheSvalbard-breedingpopulationofpink-footedgeese over-wintersinBelgium,TheNetherlandsandDenmark.Duringtheir migration tothebreedinggroundsthe geesestopin Trøndelag inMid-Norway,andVesteråleninNorth-Norway(Madsenetal., 1999;Fig.1).ThegeesestartarrivinginMid-NorwayinearlyApril, and numbers peak during late April–early May (Madsen et al., 1999).IndividualgeesestayinMid-Norwayforanaverageof20 daysbeforemigratingfurthernorth(Baueretal.,2008).

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Fig.1. TheinitialmodellandscapeoftheMid-Norwaystopoversitewithdifferent habitattypesrepresentedbydots(grass—green,stubble—yellow,ploughed—black, potato—brownandothers—pink).Roostsitesarerepresentedbyredsquares,water byblueandtheactualshapeoftheagriculturalfieldsareshowingreyinthe background.Themapinthetoprightcornershowsspringmigrationflywayof pink-footedgeese:winteringareasintheNetherlands/BelgiumandDenmark(greydots), studysite(reddot)andthefinalstopoversiteinNorth-Norway(blackdot).(For interpretationofthereferencestocolourinthisfigurelegend,thereaderisreferred tothewebversionofthisarticle.)

geese.Geesearerarelyseen restingonthefieldsand therefore theabove-mentionedroostingsitesconstitutetheirmainresting places(Madsenetal.,1997).Roostsitesarealsothemainsource ofdrinkingwater.Thenumberofgeeseateachroostsiteandthe positionsofthesesitesaremonitoredinMid-Norwayeveryyear by trained observers. The daylengthincreases by 4hover the stopoverseason,and becausethegeesefeedexclusivelyduring daytimehours(Madsenetal.,1997),thetimeavailableforforaging increasesaccordingly.Therearefourmainforaginghabitats avail-abletogeese:grass,barleystubblefromtheprecedingautumn, newlysown/germinatingbarleygrainsandploughedbarley stub-ble,butgeesealsooccasionallyforageonwastepotatofields.These habitatsarehenceforthreferredtoasgrass,stubble,grain,ploughed andpotato.Time-activitybudgetsforpink-footedgeesein Mid-Norwayconductedbytheauthorsrevealedthatploughedfields aremainlyusedasrestingsites.Grassiswidelyavailableduring theentirestopoverseasonanditstartsgrowingattheendofApril (Bjerkeetal.,2014).Stubblefieldsaregraduallyploughedand sub-sequentlysownwithbarley,whichstartsgerminatingtowardsthe endofthestopoverseason(Madsenetal.,1997).Tostudychanges inbehaviourandenergeticsofgeeseoverthestopoverseason,we divideditintofourperiods,whichroughlycorrespondedtohabitat changesduetoagriculturalpractices.Period1wasfrom6th–25th April,period2:26thApril–3rdMay,period3:4th–11thMayand period4:12th–19thMay.Theposition,sizeandhabitattypeofeach fieldwasderivedfromregularhabitatmappingconductedduring fieldworkin2013(Chudzi ńskaetal.,2015).

Theforagingbehaviourofherbivoreslikepink-footedgeeseis influencedbytheirdigestiveconstraints(DemmentandVanSoest, 1985;KvistandLindström,2000).Geesethereforefeedaslongasit takesthemtofilltheirguts(timeofthefirstpassage),andstop feed-inguntilthefoodinthegutisprocessed(retentiontime)(Bednekoff

andHouston,1994).Timeofthefirstpassagehasbeenestimated tobebetweenoneandfourhoursforgeesefeedingongraminoids (Dorozunska,1963;Marriot,1970;Burtonetal.,1979).Forgeese, themeanretentiontimeis2–3hforgrass(Burtonetal.,1979)and probablylessthan2–3hforgrain,whichisdigestedfasterthan grassduetoitslowercellulosecontent(DemmentandVanSoest, 1985).Geeseatthestudyareaprefertorestanddigestfoodonroost sitesratherthanstayingonfields,probablytoavoiddisturbances (Chudzi ńska,unpubl.manuscript).

Pink-footedgeeseatthestudysiteareexposedtovarious dis-turbingevents(intentionalscaring,passingcars,dogsetc.).Studies conductedatthestudysite(Jensenetal.,2008;Chudzi ńskaetal., 2013)andinDenmark(Madsen,1985a),showedthatgeesetendto forageatplacesfurtherawayfromroadsandthusonlargerfields (generally>0.06km2_)._Geese_flee_as_a_reaction_to_a_disturbance_at anaveragedistanceof120mandafterbeingdisturbed,geeseare likelytoflydirectlytoaroostsiteifsucharoostsiteiswithina shortdistance(Madsen,1985a).

Flocksizesof10–20individualsweremostcommonduringa surveyconductedin2012(Chudzi ´nska,unpubl.manuscript).Each modelledgooserepresentstherefore20individualgeese.

2.2. Modeldescription

Wedevelopedaspatiallyexplicitindividual-basedmodel(IBM) thattracksthehour-to-hourspatiotemporaldistributionofgeese andthedynamicsofenergystoresofeachindividualthroughoutthe stopoverseason,untiltheanimalsleavethestudysite.Themodel descriptionfollowstheupdatedODD(Overview,Designconcepts, Details)protocolsuggestedbyGrimmetal.(2006,2010).Themodel wasprogrammedinNetLogo5.0.4(Wilensky,1999).

2.2.1. Purpose

Thepurpose ofthemodel is toinvestigatehow pink-footed geesedecidewhich ﬁelds toforagein duringspring migration. Itexplicitlyincorporatesmemory,disturbance,physiological con-straints,energeticsandintraspeciﬁccompetitionandproducesa rangeofemergentpatternsthatdependonthechoiceofforaging decisionrule(FDR).

2.2.2. Entities,statevariablesandscales

2.2.2.1. Entitiesandstatevariables. TheIBMincludesthreekindsof agents:geese,roostsandﬁelds.

Goose agents arecharacterised by theirlocation, energetics (kJh−1₎_(amount_of_metabolised _energy_intake,_energy expendi-tureandnetenergyintakerate),andtimeoftheﬁrstpassagetime (h)(cumulativetimespentfeedingduringaparticulardayuntil returningtoaroostsite).Eachgooseagentrepresents20 individ-ualgeese(eachreferredtoasasupergoosefromnowon)(Scheffer etal.,1995).

Roosts(resting placeslocated onwater) are representedas immobileagentscharacterisedonlybytheirlocation.Themodel includesall26roostsitesinthestudyarea(Fig.1).

Fields:Themodelworldincludesallagriculturalfieldswithin 5kmfromtheroostsites,whichistheareawheremostgeeseforage (Jensenetal.,2008;seealsoSection2.1fordetails).Thefieldsare representedbyimmobileagentswithpositionscorrespondingto thecentresoftheagriculturalfieldsinthestudyarea[fieldcentres obtainedusingArcGIS(ESRI,2010)].Theyarecharacterisedbytheir location,size(m2_),_habitat_type_(a_field_can_be_one_of_five_habitat types:grass,stubble,grain,ploughedorpotato)(Fig.1)andbiomass (gperfield).Therelativeproportionofthehabitattypeschangesat thebeginningofeachofthefourperiods(seeSection2.1;Table1).

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Table1

Valuesofinputparametersusedintheanalysisofforagingbehaviourofpink-footedgeesespringstaginginMid-Norway.Thedetaileddescriptionofthesub-models(marked withboldfont)isgiveninAppendixA.Valuesareshownasmean±SDwhereapplicable.

Description Unit Value References

Initialisation

Initialgraindensity(D) gm−2 ₂₂_±₂₂_(stubble);₁₇_(grain) _Baveco_(unpubl._manuscript)_and

Jensenetal.(2012)

Initialcompressedswardlength m 0.03(atthestartofthemodel),

0.01(forthenewlysowngrass)

Baveco(unpubl.manuscript)and Bjerkeetal.(2014)

Initialcompressedswardlengthofnewlysowngrassﬁelds m 0.01

Large/smallﬁeldsthreshold km2 _0.06 _{Chudzi ´nska}_et_al.₍₂₀₁₄₎_and

Madsen(1985)

Initialbodystores kJ 22048±3107(equivalentto

API=2±0.5)

Drentetal.(2003)andMadsen etal.(1997)

Numberofgrasspatches 2455(period1);2389(period2);

2334(period3);2274(period4)

Chudzinska(unpubl.manuscript)

Numberofgrainpatches 0(period1);153(period2);773

(period3);1269(period4)

Numberofstubblepatches 578(period1);272(period2);76

Numberofploughedpatches 554(period1);842(period2);491

Numberofpotatopatches 27(period1);20(period2);5

Numberofotherpatches 86(period1);24(periods2);21

Grassgrowth

Grassgrowth cmday−1 _0.038_(period_1);_0.126_(period_2);

0.279(period3),0.459(period4)

Bjerkeetal.(2014) Intakerateandupdatingenergetics

Timeoftheﬁrstpassage h 3 Parameterised

Energyexpenditure(EE) kJh−1 _54.28_(roost_sites_and_ﬁelds);

416.35(ﬂying)

Chudzi ´nska(unpubl.manuscript) andButlerandBishop(1999)

Averageﬂightspeed kmh−1 ₅₀ _Fox_et_al.₍₂₀₀₃₎_and_Green_et_al.

(2002) Proportionoftimestepspentonfeeding(mean±SD)(tf) 0(roostsitesandploughed);

0.66±0.12(grass,stubble,potato); 0.78±0.08(grain)

Chudzi ´nskaetal.(2013)

Grossenergycontentoffood(GF) kJg−1 _16.18_(grass);_14.55_(grain);_17.24

(stubble)

Chudzi ´nska(unpubl.manuscript)

Grossenergycontentofdroppings(GD) kJg−1 _12.82_(grass);_11.47_(grain);_13.97 (stubble)

Droppingproductionrate(DR) h 9.8(grass);4.5(grain);5.6

(stubble)

Metabolisedenergyintakeonpotatoﬁelds kJh−1 _879.5 _Baveco_(unpubl._manuscript)

Regressioncoefﬁcient1(b1) 0.28 Baveco(unpubl.manuscript)

Croppingtime(tc) H 1512 Baveco(unpubl.manuscript)

Maximumrateofchewing(Rmax) gh−1 _30.6 _Baveco_(unpubl._manuscript)

Attackrate(a) m2_h−1 _11.7_(stubble),_5.87_(grain); _Baveco_(unpubl._manuscript)

Handlingtime(H) hg−1 _0.022_(stubble);_0.050_(grain) _Baveco_(unpubl._manuscript)

Leavingaﬁeld

Smallradius km 1 Amanoetal.(2006a,b)

Memoryfactor(˛) 0.07 Parameterised

Probabilityofdisturbance % 0(nightsanddayroostsites);30

(onﬁelds<=0.06km2_);₂₀_(on ﬁelds>0.06km2₎

Roost-disturbanceradius km 1 Parameterised

Leavingthemodel

Starvationenergystoresthreshold kJ 9620(equivalenttoagoosewith

API=0)

MadsenandKlaassen(2006)

Movingnorthenergystoresthreshold kJ 45036±2128(equivalentto

API=4.25±0.25andaccountedfor efﬁciencyforutilisation metabolisableenergyintake(0.8))

Drentetal.(2003),Duriezetal. (2009)andLopezandLeeson (2008)

municipalitiesin theCountyofNord-Trøndelag inMid-Norway. Themodel’sspatialextentis571×675gridcells,each covering 0.05×0.05km2₍_Fig.₁_)._The_model_runs_in_1-h_time_steps_from mid-night6thApril2012,whentheﬁrstgeesearrive,andends20thof May,orwhenallgeesehavemigratednorthorstarvedtodeath.

2.2.3. Processoverviewandscheduling

Beforethesimulation starts,aforagingdecisionrule(FDR)is selected.Ateachmidnightofeachsimulationdaybetweentheﬁrst

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Fig.2.Flowdiagramdescribingthegeneraldailyforagingdecisionofpink-footedgeeseunderallforagingdecisionrules.Diamond-shapedsymbolsindicatedecisionsmade bygeeseandrectanglesindicatecalculations.istheexpectedgainrateandtfcumcumulativetimespentfeedingfromleavinganightroosttoacurrenttimestep.***_a_goose’s decisionwhichroostorﬁeldtomovetoistheforagingdecisionrule-speciﬁc.

movebetweenﬁeldswithinatimestep.Eachtimestepthebelow actionshappeninsequence.Eachsupergoosegoesthroughallthe actionsandafterwardsnextgooseproceeds.Theorderofthegeese israndomisedateverytimestep.Thegraphicaldescriptionofthe modelﬂowisshowninFig.2.

2.2.3.1. Updatefieldtypesandenergycontent. Atthetimestepwhen anewperiodbegins(seeSection2.1)habitattypeoneachfield isupdatedtomimichabitatchangeduetoagriculturalpractices observedinnature.Thebiomassofnewfieldsiscalculatedbased onfieldsizeandhabitattype.

2.2.3.2. Goose arrival. On each modelled day, an empirically derivednumberofsupergeesearrivetothemodeluntil30thof April.

2.2.3.3. Grassgrowth. Grassﬁeldsincreasetheirforagebiomass.

2.2.3.4. Intake rateandhabitat depletion.Ifona ﬁeld,thesuper gooseforagesanddepletesthehabitatproportionally.Theintake rateishabitatspeciﬁc.

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2.2.3.6. Leavingafield. Eachsupergoosedecideswhethertostay orleaveagivenfieldifoneormoreofthefourfieldleavingrules aremet(seesectionLeavingafieldinAppendixA):(1)itabandonsa fieldifthecurrentgainratefallsbelowtheexpectedgainratebased onitspreviousexperience,(2)ithasbeenforagingcontinuously foratimenecessarytofillitsgut(timeofthefirstpassage)and thereforeneedtotakeadigestivebreak,(3)itisdisturbedor(4)it issunsetandthesupergoosereturnstoaroostsite.

2.2.3.7. Leavingthemodel. Ifasupergooseobtainsanenergylevel thatissufﬁcienttomigratenorth,itleavesthemodel.Italsoleaves themodel if it cannot obtain energy stores above a starvation threshold(itdies).

2.2.4. Designconcepts

2.2.4.1. Basicprinciples. Thismodelbuildsontheassumptionthat geese optimise their foraging behaviour to prepare for further migrationandbreeding.Theydothisbyintensiveforagingonhigh qualityfood,reduction inenergy expenditureand avoidanceof perceivedpredationrisk.Themodelthereforeposesaclassical opti-malforagingproblem:howshouldanindividualdecidewhereto foragetomaximiseitsﬁtness?Weprovideinsightintothis prob-lembycontrastingﬁvealternativetheoriesforthisdecisionbased onhowwelltheyreproducetheobservedpattern.

2.2.4.2. Emergence. Thenetenergyintakeofgeeseemergesfrom abalancebetweenmetabolisableenergyintakeobtainedby forag-ingondifferentfieldsandenergyexpendedduringflyingbetween fields/roostsites,activitywhileinthefield,aswellasenergyused tomaintainbasicbodyfunctions.Theamountoftimegeesespend onroostsitesduringdaytimeemergesfromtheirneedtodigest afterhavingforagedandfromtheirresponsetodisturbances.The amountoftimegeeseneedtodigestisproportionaltotheamount oftimetheyspendfeedingonfields.Thespatialdistributionofbirds emergesfromtheirtendencytomovetodifferentfieldsat differ-entdistancesfromtheroostsitesandfromthefieldtheyoriginate from,fromthespatialdistributionofthefields,andfromresource depletion.Thenumberofgeeseatthestudysiteemergesfroma balancebetweennewgeesearrivingtothemodelandgeese leav-ingthemodelbyeithermigratingnorthorstarvingtodeath.Geese choosearoostingsiteforarestaccordingtodifferentrules speci-fiedforeachFDR.Thesechoicesdeterminehowmanygeeserestat eachroostingsite.

2.2.4.3. Adaptation. Geese’shabitatselection behaviour(i.e.,the decisionofwhichﬁeldtooccupyeverytimesteptoforageon)is theonlymodelledadaptivetrait.

2.2.4.4. Objectives. Whileanimalsattempttooptimisetheir for-aging behaviourdifferently for each foraging decision rule,the overallobjectiveofthegeeseistooptimisetheirforagingbehaviour toobtainenoughenergy storestomigratefarther northandto breed.ForallFDRspredation/disturbanceriskisanimportant fac-torperceivedbybirds:geesechoosedisturbance-freeroostsitesas theirprimaryrestingplaces.

2.2.4.5. Learning. InFDRs3and5geeselearnwherethemost prof-itableﬁeldsarelocated.

2.2.4.6. Prediction. When geese arrive to the model, they are assumedtoalreadyhavesomeknowledgeabouttheproﬁtabilityof differenthabitattypesandtobeabletopredicttheexpectedgain rateontheirﬁrstchoiceofforagingpatch(seeSection2.2.7).

2.2.4.7. Sensing. InallFDRsgeeseareabletosensethehabitat qual-ityoffieldswithin5kmradius.InFDR2-maxenergygeeseareable tosensewherethemostprofitablefieldsarelocated.InFDRs2–5 geeseareabletosensethedistancebetweentheircurrentlocation andtheclosestroostsite.InFDRs4and5,geeseareabletosense whichfieldswithinacertainradiusarealreadyoccupiedbyother individuals.

2.2.4.8. Interaction. Themodelledbirdsinteractindirectlyviatheir competitionforfood.InFDRs4and5geeseforageinplaceswhere othergeesearealreadypresent.

2.2.4.9. Stochasticity. Theinitialamountofgrainvaries stochasti-callybetweenstubblefields.Whengeesearrivetothemodel,they distributethemselvesrandomlyamongroostsitesandtheyhave theirinitialenergystoresandtheamountofenergynecessaryto leavethemodelassignedwithintherangesgiveninTable1.During eachrun,thevaluesofthefollowingparametersaresetrandomly: thenextfieldorroost(inFDRs1,and3–5),proportionoftimespent feedingandbeingvigilantoneachfield,numberoftimestepsgeese stayonaroostsitewhenfollowingfieldleavingrules2and3(see sectionLeavingafieldinAppendixA),probabilityofasupergoose beingdisturbedfromafield.

2.2.4.10. Observation. The number of animals, their net energy intake, and total time spenton roost sites during daytime are recordedattheendofeachday.Thedistanceofgeesetothe clos-estroostsite(ifgeeseareonaﬁeld)isrecordedateachstep.The numberofgeeseoccupyingeachroostsiteisrecordedateachtime step.

2.2.5. Inputdata

Twoinputdatafilesfromexternalsourcesareusedinthemodel: numberofnewsupergeesearrivingtothemodelanddistribution ofhabitattypeswithinthemodelledarea.Thenumberofarriving geesewasassessedbasedoncountsofgeeseontheroostsitesinthe years2005–2012andnewgeesearrivetothemodelasdescribed inSection2.2.3andAppendixA.Newhabitatmapisloadedtothe modelatthebeginningofeachperiodasdescribedinSection2.2.3 andAppendixA.Theposition,sizeandhabitattypeofeachfieldwas derivedfromregularhabitatmappingconductedduringfieldwork in2013(Chudzi ńskaetal.,2015)(AppendixA).

2.2.6. Sub-models

Adescriptionofthesub-modelscorrespondingtotheprocesses listedinSection2.2.3presentedinAppendixA.

2.2.7. Initialisation

Themodelisinitialisedbyloadingahabitatdistributionmapin thebeginningofperiod1andbyassigninghabitatbiomass,grass lengthorgraindensitytoeachfieldagent(Table1).Asobservedin thefield,initialgrasslengthandinitialgraindensityonnewsown fieldsdonotvarybetweenthefieldswhereasthereisalarge varia-tioningraindensityonstubblefields.Theinitialnumberofbirdsis setto7040geese(352supergeese)thatarerandomlydistributed amongroostsites.Thisisanaveragenumberofgeeseobserved at6thofAprilbasedoncountsofgeeseontheroostsitesinthe years2005–2012(AppendixA).Eachsupergoosehasarealistic initialenergeticvaluerandomlyassignedwithinarangespecified inTable1.

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calculatetheinitial,expectedgainrate(seesectionLeavingaﬁeld inAppendixA),whengeesearrivetothemodelasfollows:

in=MEin−EE (1)

Heretheinitialmetabolisedenergyintakerate(MEin)was cal-culatedasinEq.(A4)(AppendixA)andenergyexpenditure(EE)was calculatedastheaverageenergyexpenditureforallfields(Table1). TheintakerateusedtoestimateMEinwascalculatedasanaverage intakefromallfieldswithina5-kmradiusfromtheroostsitethat thesupergoosearrivedtoforFDRs1and3–5.SinceinFDR2geese areexpectedtohaveacompleteknowledgeaboutprofitabilityof eachhabitattype,onlyfieldswherethehabitat-specificintakerate was>0wereusedtocalculateMEin.Theintakeratefromploughed fieldswasthereforeexcludedfromthecalculationoftheaverage intakefromallfieldswithin5km.

2.3. Realworldpatternscomparedtoemergentpropertiesofthe model

Toevaluatewhichforagingdecisionrulesbestcharacterisethe foragingbehaviourofpink-footedgeeseweanalysedwhethereach rulecausedthemodeltoreproducearangeofpatternsobservedin theﬁeldin2005–2007and2011–2013.Welistthepatternsinthe orderofdecreasingimportance:

(1)Theaveragedailynetenergyintake(dailymetabolisableenergy intake—daily energy expenditure) of pink-footed geesewas 1706±351kJday−1 (mean±SD)andthisvaluedidnotdiffer betweenperiods(Chudzi ´nska,unpubl.manuscript).

(2)Geesespentapproximately40%oftheirtimeavailablefor for-aging(i.e.,thedaytimehours)onroostsitesduringtheﬁrsthalf ofthestopoverseasonandaround25%ofdaytimeinthesecond half(Chudzi ´nska,unpubl.manuscript).

(3)The spatial distribution of geese fluctuated diurnally and betweenperiodsinresponsetochangesingoosedensitiesat thesetwotimescales.Inperiods1and4,whenthenumber ofgeeseatthestopoversitewaslowest,thediurnal distribu-tionofgeesedidnotdependondistancefromnearestroost site;geesewereobservedatthesamedistancefromtheroost sitesthroughouttheday.Duringperiods2and3,when densi-tiesofgeeseatthestopoversitewashighest,theprobability ofusing areasfurtheraway fromroostsitesdeclinedinthe morningbutincreasedintheevening.Inthemornings,when allgeeselefttheroostsitestoforagetheyhadahigherrelative probabilityofstayingclosetotheroost.Atmiddays,when den-sitiesonfieldswerelowestbecausemostgeesewereroosting, geeseusedhabitatindependentlyofthedistancetothe near-estroostsite.Intheevenings,whendensitiesincreasedagain, geeseselectedareasfurtherawayfromtheroosts(Chudzi ńska etal.,2015).

(4)Geesedeparturefrom Mid-Norwaybasedonweekly counts in years 2005–2007. The number of geese peaked at the endofAprilandallgeeseleftby20thMay(Baveco,unpubl. manuscript).

(5)Maximumnumberofgeeseobservedateachroostsitebased oncountsconductedbetween15thApriland8th May2013 (Baveco,unpubl.manuscript).

2.4. Geeseforagingdecisions

Wetestthemodel’sabilitytoreproducetheobservedpatterns (Section2.3)usingfivealternativeforagingdecisionrules(FDRs) thatdifferincomplexity.IneachFDR,eachsupergooseforageson thefieldsbetweensunriseandsunset,butwhichfielditchooses toforageondiffersbetweenFDRs.ForeachFDR,eachsupergoose staysonafielduntilconditionsofoneofthefourfieldleavingrules

aremet(seeSection2.2.3and AppendixA),andthenmoves to thenextfieldoraroostsite.Thefactorsthatforcebirdstoleave afieldanddefinefourleavingrulessuchasgainrate, physiolog-icalconstraints,disturbanceanddarknessdonotdifferbetween FDRs.Geesesearchfortheirforagingfieldswithinarelativelylarge areainthemorning(5kmasshownbyJensenetal.(2008);termed ‘largedisplacementradius’);however,oncetheygetfamiliarwith theirforaging area,theyrestricttheirsearchtoasmallerradius of1km(termed‘smalldisplacementradius’)(Turneretal.,1993; Grossetal.,1995;Amanoetal.,2006a).

2.4.1. Foragingdecisionrule1:Random(hereafter,FDR 1-random)

Thisforagingdecisionrulewasdevelopedfollowingarandom searchapproachasdescribedbyBartumeusandCatalan(2009).In thismodel,individualsareassumedtohavenopriorinformation oftheprofitabilityofavailablefieldsexceptatthetimewhenthey arrivetoMid-Norway,whentheyhaveacertainexpectedgainrate, presumablybasedontheirexperiencefrompreviousyear(see Sec-tion2.2.7).Eachfieldwithinacertainradiusisequallylikelytobe chosenbyasupergooseirrespectiveofwhetherithasbeenvisited beforeandregardlessofthebiomassofthisfield.Eachsupergoose leavestheroostafterciviltwilightandmovestoarandomfield within5kmfromthisroost.Itforagesonthisfielduntilleaving accordingtofieldleavingrules1–4(seesectionLeavingafieldin AppendixA,Table2).

2.4.2. Foragingdecisionrule2:Maximisingnutrient intake—Omniscientbirds(hereafter,FDR2-maxenergy)

This foraging decision rule was developed following a rate-maximising model approach used by, e.g., Goss-Custard et al. (1995),Pettiforetal.(2000)andAmanoetal.(2006a).Allgeese areassumedtohavecompleteknowledgeabouttheprofitabilityof allfieldswithintheradiusgeesenormallyforage(5kmfromroost sites,detailsinSection2.1ofSection2).Inordertomaximisetheir fuellingrates,thegeesemovebetweenthefieldsthatofferthe high-estintakeofmetabolisableenergy(ME).Eachsupergooseleaves theroostafterciviltwilightandmovestoafieldwithhighestME within5kmradiusfromthatroost.Ifthereismorethanonefield withthesameMEvalue,thesupergoosechoosesoneatrandom. Thesupergoosestaysonthisfieldaccordingtofieldleavingrules 1–4(Table2).

2.4.3. Foragingdecisionrule3:Asociallearning(hereafter,FDR 3-asociallearning)

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Table2

Movementofgeeseundereachforagingdecisionrule(FDR).MEstandsfrommetabolisableenergy.

FDR Fieldleavingrule1 Fieldleavingrule2 Fieldleavingrule3 Fieldleavingrule4

Currentgainrate<expectedgain rate

Digestivebreak Disturbed itisgettingdark

1 Movetoarandomﬁeldwithin

1kmfromthecurrentlocationc

Movetoarandomroostwithin 5kmfromthecurrentﬁelda_,_then

movetoarandomﬁeldwithin 1kmfromthatroost

If≤1kmfromanyroostb_,_move_to

thisroost,thenmovetoarandom ﬁeldwithin1kmfromthatroost sitec_;_if_>1_km_from_any_roost,

movetoarandomﬁeldwithin 1kmfromthecurrentlocationc

movetoarandomroostwithin 5kmfromthecurrentlocation

2 Movetoanextﬁeldoffering highestmetabolisableenergy(ME)

d,e

Movetotheclosestroostfromthe currentﬁelda_,_then_move_to_the

nextﬁeldwithhighestMEwithin 1kmfromthatroostd,e

thisroost,thenmovetothenext ﬁeldofferinghighestMEwithin 1kmfromthatroostsitec_;_if_>1_km

fromanyroost,movetothenext ﬁeldofferinghighestMEwithin 1kmfromthecurrentlocationd,e

movetotheclosestroostfromthe currentlocation

3 AsinFDR1 Movetotheclosestroostfromthe

currentﬁelda_,_then_move_to_a

randomﬁeldwithin1kmfromthat roostc

AsinFDR1 asinFDR2

4 Movetoarandomﬁeldwithin 1kmfromthecurrentﬁeldwhich isalreadyoccupiedbyatleastone supergoosef_.

Movetotheclosestroostfromthe currentﬁelda_,_then_move_to_a

randomﬁeldwithin1kmfromthis roostalreadyoccupiedbyatleast onesupergoosef

thisroost,thenmovetothenext, randomﬁeldalreadyoccupiedby atleastonesupergoosewithin 1kmfromthatroostsitef_;_if_>1_km

fromanyroost,movetoarandom ﬁeldwithin1kmfromthisroost alreadyoccupiedbyatleastone supergoosef

asinFDR2

5 AsinFDR4 AsinFDR4 AsinFDR4 asinFDR2

a_Each_super-goose_stays_on_this_roost_2–3_steps_before_moving_to_the_next_ﬁeld_mimicking_retention_time—time_when_food_is_processed_in_the_guts₍_Burton_et_al.,_1979; DemmentandVanSoest,1985).Numberofsteps(2or3)isassignedrandomlytoeachsuper-gooseandthisassignmentisdoneeverytimeasuper-goosevisitsaroost.

b _Each_super-goose_stays_on_this_roost₁_step_before_moving_to_the_next_field. c _If_there_is_no_field_within₁_km,_move_to_a_random_field_within₅_km.

d _If_there_is_no_field_of_any_type_within₁_km,_choose_a_field_with_highest_ME_within₅_km. e_If_there_is_more_than_one_field_with_the_same_ME_value,_choose_one_at_random.

f _If_there_is_no_field_within_that_radius_which_is_occupied_by_another_individual,_chose_the_next_field_at_random_within₁_km._If_there_is_no_field_at_all_within₁_km,_move_to_a

random,alreadyoccupiedﬁeldwithin5kmorarandomﬁeldiftherearenoothergeesewithinthatradius.

2.4.4. Foragingdecisionrule4:Sociallearning(hereafter,FDR 4-sociallearning)

Thisforagingdecision rulewasdevelopedfollowingtheidea thatbirdsmigratinginflocksrelyontheexperienceofother mem-bersoftheflock(e.g.NémethandMoore,2007;GuttalandCouzin, 2010).Birdsthereforeselectfieldswhereothergeesearealready foraging.Geeseleavetheroostsafterciviltwilightandmovetoa randomfieldwhereothergeese(atleastonemoresupergoose) arepresent,<5kmfromtheroost.Ifnoneofthefieldsarealready occupied,geesemovetoarandomfieldwithin5km.Thisrulealso appliesatthebeginningofeachday,whengeeseleaveroostsites simultaneously.Geesestayonthisfieldaccordingtofieldleaving rules1–4(Table2).

2.4.5. Foragingdecisionrule5:Socialandasociallearning (hereafter,FDR5-alllearning)

Thisforagingdecision rulewasdevelopedfollowingtheidea thatbirds livingin flocksrely onknowledgeand experienceof othermembersoftheflock;however,assuchinformationmay beinaccurateina patchyand dynamiclandscape (Németh and Moore,2014),geesealsoacquireinformationthroughtheirown experience(asocial learning).Such a combination of individual gatheringofinformationandinformationobtainedfromobserving thelocationsandactivitiesofotherscanimprovethespeedand accuracywithwhichindividualsassesseshabitatquality(Németh andMoore,2007).Accordingtothisrulegeeseleavethenightroost afterciviltwilightandgotothefieldthatresultedinthehighest MEthepreviousdayasinFDR3-asociallearning.Onthefirstday afterarrivaltoMid-Norwaygeeseleavetheirnightroosttoa ran-domfield<5kmaway.Geeseforageonthefieldsalreadyoccupied

byothergeesefortherestofthedayasexplainedforFDR4-social learning.Geesestayontheseﬁeldsaccordingtoﬁeldleavingrules 1–4asdescribedinTable2.

2.5. Parameterisation

Mostofthemodelparameterswereassignedusingvalues col-lected in the field, in thelaboratory or in publishedliterature (Table1).Theparametersthatwehadnofielddataforwere para-meterisedusingPOM.Thisincludedtimeofthefirstpassage,the distancebetweena fieldfromwhich geesewere disturbedand theclosestroost, whichdetermineswhethergeesemovetothe roostafterbeingdisturbedortoafield(termed‘roost-disturbance radius’,seeSection2.4andTable2),andthememoryfactorofthe geese(␣)(AppendixA,Eq.(A5)).WefollowedthePOMstrategy toidentifythecombinationofthesethree parametersthatbest reproducedthefiveobservedpatterns(seeSection2.3).Thesethree parametersweresettothefollowingvalues:timeofthefirst pas-sage:1–4hwith0.5intervals;roost-disturbanceradius:0.1–1km with0.1kmintervals;alpha0.001;0.01;0.03;0.05;0.07and1.We ran10simulationsforeachofthe420parametercombinationsfor eachFDR.Weusedanaveragevalueofagivenoutputofthese10 simulationsforfurtheranalysis.FollowingFrankandBaret(2013), weusedthesumofstandardisedsquarederrors(SSSE)toevaluate theagreementbetweentheobserved(obs)andpredicted(pred) valuesforeachFDRandeachobservedpattern.

SSSE_k,j=

n

i=1

({pred_i−obs_i)2

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Table3

Thelistofparametersandtheirminimumandmaximumvaluesusedinthe sensi-tivityanalysis.

Parameter Unit Min Max

Numberofgeeseinasuper-goose 15 25

Probabilityofdisturbance—smallﬁelds % 0 0.6

Probabilityofdisturbance—largeﬁelds % 0 0.4

Globaldisturbance % 0 0.5

Additionalmovingnorthstores kJ −11274 11274

Additionalinitialstores kJ −4735 4735

Fieldsizethreshold km2 _0.05 _0.08

Smallradius km 0.75 1.25

HerekiseachFDR,jeachofthefiveobservedpatternsandi iseachdayofsimulation.Theforagingdecision rulewhichbest fit a given observed pattern was indicated by thelowest SSSE value. Next, we followed a Monte Carlo Filtering approach, by whichtestedpatternswereappliedasfilterstoseparategoodfrom badsetsofparametervalues (Wiegand etal.,2003;Grimmand Railsback,2005).Todo this, quantitativecriteria for the agree-mentbetweenobservedandpredictedpatternsweredeveloped. Theobservedpatternswhererankedfromthemosttoleast impor-tantaspresentedinsectionSection2.3.Pattern1(dailynetenergy intake;DNEI)wasusedas thefirstfilter.We onlyretainedthe parametersetswhichreproducedtheobservedDNEI_±10%.We thereforeconsideredanobservedDNEIpatterntobeaccurately reproducedbyamodelsimulationwhenSSSEwaswithin±10% of themeanobserved DNEI forfour periods.Second,from this reducedset,weidentifiedparametercombinationsthatallowed ustoreproducepattern2(timespentonroostsites)within10%of themeanvaluesobservedinthefieldforallfourperiods.Finally, werepeatedthesameprocedure, retainingparametersets that allowedthemodeltoreproducepatterns3–5, one patternat a time.TheSSSEvaluecanbeartificiallyreducedwhenobservedor predicteddatashowlittleornovariation(Duriezetal.,2009).It wasthuscomplementedbyavisualinspectionofthefitbetween observedandpredicteddata.Weperformedthisfilteringapproach foreachFDRseparately.Fromthefinalsetsofparametersforeach FDR,weonlychosethissetwhichwascommonforallfiveFDRs. Thisledtoonesetofparameterswithtimeofthefirstpassage=3h; roost-disturbance radius=1km and alpha=0.07 (Table1). After identificationofFDRthatbestreproducedallfiveobservedpattern, weperformedadditionalparameterisationwiththesamemethod asdescribedaboveinordertocheckwhetherdifferentsetofthe threeparameterswouldresultinabetterfitbetweentheobserved patternsandthemodeloutcomeofthisFDR.

2.6. Sensitivityanalyses

Althoughwe usedempiricallycollectedand literature-based valuestobuildthemodel,weperformedaglobalsensitivity analy-sistoevaluatehowthepatternsemergingfromthemodelwere affectedby variationsin theinputparameters. Theaimwasto decomposethemodeloutputs’varianceintovariancesattributable to each input parameter, but also to evaluate the interaction betweenparameters.WeranthesensitivityanalysisonlyonFDRs thatbestdescribedthebehaviourofgeeseandappliedthe vari-ancedecompositiontechniqueassuggestedbySobol’(1990),see thereviewbyThieleetal.(2014)forsummaryonsensitivity anal-ysis.Westartedbydeﬁningthelistwithvaluesofeachparameters usedinthesensitivityanalysisandwithallthepossible combina-tionsofthesevalues,whichwerelaterusedtorunthesimulations ofthegivenFDRs.Themodelsensitivitywasanalysedfor param-etervalues_±25%fromthevaluesusedintheﬁnalsimulationsof FDRs(Tables1and3).Wealsowantedtotesttherobustnessof themodeltodisturbanceperseandthereforeontopofthe±25%

variation indisturbanceprobability,weadded situationswhere disturbanceonsmallorlargefieldswasincreasedordecreasedby 100%(socalled‘Globaldisturbance’).Weranonesimulationwith parameters’combinationforeachFDR.WeusedthesensitivityR package(Pujoletal.,2014)usingtheformulasbyJansen(1999) andSaltellietal.(2010)todefinethefinallistofparameter com-binationandtoruntherestofthesensitivityanalysis.TheJansen formula(soboljansenformulainsensitivityRpackage)implements theMonteCarloestimationoftheSobolindicesforbothfirst-order andtotalindicesatthesametime.Sobol’sfirstordersensitivity indices(Si)measuretheeffectofvaryingafocusparameteralone, butaveragedovervariationsinotherinputparameters,thus pro-vidinginformation ontheaveragereduction ofoutputvariance whentheparameterisfixed.Sobol’stotaleffectsensitivityindices (STi)measurethecontributiontotheoutputvarianceofthefocus parameter,includingallvariancecausedbyitsinteractions,ofany order,withanyotherinputparameters.Thenumberoftested sett-ingswasgivenbym×(p+2),wheremisthesizeoftheMonteCarlo samplematrix(m=400inthisstudy)andpisthenumberof param-eterstoanalyse(p=8inthisstudy,Table3).Thisledto4000model runs.InordertoassessthesensitivityoftheFDRspredictionsto thevaluesofparameterestimates,weinvestigatedthechangesin dailynetenergyintake(pattern1)andproportionofdaytimespent onroostsites(pattern2).

2.7. Statisticalanalysesusedforevaluationofemergentpatterns basedonpattern-orientedmodellingapproach

Toﬁndoutwhichforagingdecisionrulebestmatchwithallthe observedpatterns,weusedtheSSSEasdescribedinSection2.5.For pattern3(spatiotemporaldistributionofgeese)weonlyusedvisual inspection.TheforagingdecisionrulewhichhadthelowestSSSE forthelargestnumberofpatternswasconsideredbestdescribing theforagingbehaviourofgeese.

InordertocomparechangesinDNEIbetweenperiodsfor dif-ferent FDRs we used ANOVA if there was no evidence of any signiﬁcantdifferenceinvarianceacrosstheoutputvaluesbasedon themodels’simulations,testedwiththeuseoftheFligner–Killeen testofhomogeneityofvariance(Conoveretal.,2011).Otherwise, weusedone-waytestwithWelch’scorrectionforvariance non-homogeneity(henceforthreferredtoasone-way;Welch,1951). Thesametestswereappliedtoanalysethediurnalandin-between periodchangesinthespatialdistributionofgeese.Weusedvisual inspection totest for normalityof model residuals (Quinn and Keough,2002;Zuuretal.,2007).BothresidualsofDNEIandthe diurnalandin-betweenperiodchangesinthespatialdistribution ofgeesewerenormallydistributed. Allstatisticalanalyseswere performedinR3.1.0(RDevelopmentCoreTeam,2013).Resultsare shownasmean±SDunlessotherwiseindicated.Thesigniﬁcance levelwassettop<0.05forallstatisticaltests.

3. Results

3.1. Comparisonofthepredictionsoftheﬁveforagingdecision rules

Weanalysed theabilityofthefiveforagingdecisionrules to reproducethefivedifferentpatternsobservedforfielddata:

3.1.1. Pattern1—Dailynetenergyintake

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Fig.3. Observedandpredictedin-between-periodschangesindailynetenergyintake(A)andproportionofdaylightspentonroostsites(B)forpink-footedgeeseat Mid-Norwayspringstopoversiteforﬁveforagingdecisionrules(FDR).ErrorbarsinAandBforFDRpredictionsshow±SDfrom100replicates.(Forinterpretationofthereferences tocolourinthisﬁgurelegend,thereaderisreferredtothewebversionofthisarticle.)

Fig.4.Diurnalandin-between-periodschangesinspatiotemporaldistributionofpink-footedgeesestaginginMid-Norwayinrelationtotheclosestroostsitepredicted foreachforagingdecisionrule(FDR).Solidlinesrepresenttheaverageof100replicates:black-morning(05:00–11:00),blue-midday(11:00–16:00),green-evening (16:00–21:00).Theshadedareasinmatchingcoloursaroundeachlineshow±SDfrom100replicates.Theredlinesshowtheobservedchangesingoosedistributionbased onthehabitatselectionanalyseswiththeuseofResourceSelectionFunction(RSF).TheresultsofRSFarerelativevaluesingeese’sdistancestotheroosthencetheobserved distributionisschematicwithnovaluesonthey-axis.(Forinterpretationofthereferencestocolourinthisﬁgurelegend,thereaderisreferredtothewebversionofthis article.)

learningthepredictedDNEIwasclosertotheobservedvaluesthan theotherfourFDRs,especiallyintheﬁrsttwoperiods(mean±SD observedandpredictedunderFDR3-asociallearningvaluesofDNEI respectively:1706±445kJday1_;₁₅₅₆_±₆₀₀_kJ_day1₎₍_Fig.₃_A)._This FDRhad thelowestSSSEvalue(Fig.7).ThevaluesofDNEI pre-dictedbyFDRs2and5weretheleastaccordantwiththeobserved values(Figs.3Aand7).ThepredictionsofFDR3-asociallearning showednobetween-perioddifferenceinDNEI(ANOVA:F3,39=1.08, p=0.38) which is inagreementwiththe observedpattern. The remainingfourFDRsshowedbetween-perioddifferenceinDNEI (ANOVA:F3,39=3.35,8.92,22.53,20.67respectivelyforFDRs1,2,4 and5;p<0.001forallfourFDRs).

3.1.2. Pattern2Timespentonroostsites

Inperiods1and2geesespentlesstimeonroostsitesduring daytimeunderallﬁveFDRsthanobserved,butforperiods3and4 predictionsofallﬁveFDRswerecomparabletotheobservedvalues

(Fig.3B).FDR3-asociallearninghadthelowestSSSEvalueamong allFDRsforthatpattern(Fig.7)

3.1.3. Pattern3—Spatiotemporaldistributionofgeese

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Table4

TheresultsofFligner–Killeentestofhomogeneityofvariance(Variance),ANOVAandone-waytestwithWelch’scorrectionsforvariancehomogeneity(one-way)testing statisticaldifferencesindiurnalandin-betweenperiodschangesinspatiotemporaldistributionofpink-footedgeeseinrelationtotheclosestroostsiteinMid-Norway predictedfortheﬁveforagingdecisionrules(FDR).IftheresultsoftheFligner–Killeentestdidnotindicateasigniﬁcantdifferenceinvarianceacrosstheresultsfromdifferent timeofday(ifp>0.05,Variance=N),weperformedANOVAonsuchresults.Otherwise(p≤0.05,Variance=Y),weusedone-waytest.

FDR Period Variance ANOVA(df=2,res=297) One-way

F p F p

1 1 Y 11.3 0.06

2 N 13.6 0.08

3 N 9.4 0.12

4 Y 11.7 0.06

2 1 N 5448 <0.001

2 N 5759 <0.001

3 Y 1259.6 <0.001

4 Y 2234.9 <0.001

3 1 Y 14315 <0.001

2 Y 13694 <0.001

3 Y 15735 <0.001

4 Y 9003 <0.001

4 1 Y 10119.9 <0.001

2 Y 7639.3 <0.001

3 Y 4135.6 <0.001

4 Y 1442.1 <0.001

5 1 N 996 <0.001

2 N 218.9 <0.001

3 N 16.2 0.05

4 N 13.1 0.08

3.1.4. Pattern4—Phenology

ForallFDRsalmostallgeese(92,96,97,94and99%,respectively) migratednorthbytheendofsimulationsasobservedintheﬁeld andthepredictedphenologyresembledtheobservedone(Fig.5). TheSSSEwaslowestforFDR1-random(Fig.7).Therewasnotmore than1supergoosestarvinginanyofthesimulations.

3.1.5. Pattern5—Distributiononroostsites

Theobservedandpredictedmaximumnumberofgeeseon dif-ferent roost sites agreedwellfor severalFDRs (Fig.6), butthe correspondencewasbestforFDR3-asociallearning(Fig.7).There wasnosigniﬁcant correlationbetween observedand predicted numbersforanyoftheFDRs(Pearson’scorrelation(pvaluesfor all FDRs>0.1, r for each FDR=−0.34, −0.19, −0.01, −0.21 and −0.20) indicatingthat theability ofeach FDRto reproducethe observed pattern was not related to the number of observed geese.

ThestudyareaisonlypartofMid-Norwayandinreality pink-footedgeesealsoforageinareasoutsidethestudysite.Thenumber ofgeeseonroostsitesobservedintherealworldmaythereforebe inﬂuencedbyforagingareasnotincludedinthestudyarea,and thiseffectmaybemostpronouncedattheroostsiteslocatedat theedgeofthemodelledarea(‘edgeeffect’).Thesimulated num-bersmaythereforenotmatchtheobservedvalues attheedges of thestudysite due toreasonsother than processesincluded in themodel. We testedfor theedge effect byﬁtting a gener-alised additivemodel (GAM)using a non-parametric smoother with the predicted values of each FDR as a response and the observedvaluesandlatitudeandlongitudeofeachroostsiteas predictors.OnlyFDR1-randomshowedthe‘edgeeffect’bothalong latitudeand longitude axis(Flat=31.9, plat<0.01;Flong=8.1 and plong=0.007).

3.2. Summaryofresults

FDR3-asociallearninghadthelowestdifferencebetweenthe simulatedandobservedpatterns(asmeasuredwithSSSE)forthree out of ﬁvepatterns (Fig.7), includingpatterns 1 and 2, which

we considerthemostimportantones.FDR1-random best pre-dictedpattern3describingchangesinspatiotemporaldistribution ofgeeseandresultedinthelowestSSSEforpattern4(phenology ofgeese).

3.3. Sensitivityanalysisandpost-resultparameterisation

HerewepresenttheresultsofsensitivityanalysisonFDR 3-asociallearning,asthisFDRbestdescribedtheforagingbehaviour ofpink-footedgeese.However,thepredictionsofFDR1-random weremoreaccuratethanFDR3-asociallearningfortwopatterns; andthereforewepresentthesensitivityanalysisforthatFDRin AppendixB.

For FDR 3-asocial learning, the average DNEI over the four periods varied between 497 and 2620.8kJday−1 _(mean_±_SD: 1350±458.9kJday−1).Thisrangeis±68%oftheaveragevalue esti-matedbyFDR3-asociallearningwiththeuseofﬁnalparameter settings(1555.6kJday−1_)._The_sum_of_main_effect_indices,_S

iwas 0.96.Avaluecloseto1thatindicatesthatthemodelisalmostpurely additive,i.e.thereisanegligibleinteractionbetweenparameters, withastrongcontributionofthemaineffectofprobabilityof dis-turbanceonlargefields(responsiblefor41.3%ofthevariationof theDNEI,Fig.8)andsimultaneouschangesoftheprobabilityof dis-turbanceonallfields(‘Globaldisturbance’;57.7%ofthevariance, Fig.8).Whentheprobabilityofdisturbanceonallfields(‘Global dis-turbance’)wasincreasedbyapproximately100%,themeanDNEI forallfourperiodsdecreasedby60%incomparisontoDNEI esti-matedbyFDR3-asociallearning(withtheuseofthefinalparameter settings).SimulationswithalmostnodisturbanceinFDR3-asocial learningresultedinanincreaseofthemeanDNEIoverthefour periodsby52%incomparisontoDNEIestimatedbyFDR3-asocial learning.

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Fig.5. Observedandpredictedin-between-periodschangesinnumberofpink-footedgeeseatMid-Norwayspringstopoversiteforﬁveforagingdecisionrules(FDR).Shaded areasindicatedurationofeachperiod(P–P4).TheSDforeachFDRpredictionsfallwithin±2%ofthemeanvalueandarethereforenotshowninthegraph.(Forinterpretation ofthereferencestocolourinthisﬁgurelegend,thereaderisreferredtothewebversionofthisarticle.)

Fig.6.Observedandpredictednumberofpink-footedgeeseondifferentroostsites.Observedmaximumnumbersovertheentirestopoverseason(red)arecomparedwith predictionsforﬁvedifferentforagingdecisionrules(FDR).ErrorbarsforFDRpredictionsshow±SDfrom100replicates.They-axisofeachgraphshowsnumberofgeese multipliedby100.(Forinterpretationofthereferencestocolourinthisﬁgurelegend,thereaderisreferredtothewebversionofthisarticle.)

displacementradius’)wasresponsibleforalmosttheentire vari-ationintheoutput(95%,Fig.8).Whengeesewereallowedtomove onlyshortdistancesbetweenﬁelds(≤0.8km)theyspentmoretime ontheroost sites(26–28% of daytime),whereas a largervalue

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Fig.7.Thesumofstandardisedsquarederrors(SSSE)betweenobservedand pre-dictedvaluesforeachforagingdecisionrule(FDR)forfourtestedpatterns(1—daily netenergyintake,2—proportionofdaylightspentonroostsites,4—phenologyof geeseand5—distributionofgeeseamongroostsitesinMid-Norway.RelativeSSSE representsSSSEvaluesdividedbythevalueofFDRwiththelowestSSSEforeach speciﬁcpattern.Notethebreakinthey-axis.Theﬁtofthesimulatedvaluesfor pat-tern3—spatiotemporaldistributionofgeeseinrespecttotheclosestroostsitewas onlyevaluatedbasedonthevisualinspectionoftheresults.

andsmalldisplacementradius(Fig.8),indicating weak interac-tionsamongthem.Changesinglobaldisturbancehadasmalleffect ontheamountoftimegeesespentonroostsitesduringdaytime; themeanvalueoverfourperiodsforthemodelswithincreasedor decreaseddisturbancewasequaltothemeanvalueforall simula-tionsandwasequalto26%.

Thepost-resultparameterisationofFDR3-randomrevealedthat twosetsofparametersresultedinthebest,identical,fitbetween theobservedpatternsandthemodeloutcomeofthisFDR.Thefirst setwasidenticaltotheoneestablishedbytheinitial parameterisa-tion(timeofthefirstpassage=3h;roost-disturbanceradius=1km andalpha=0.07);thesecondwascomparable(timeofthefirst pas-sage=3h;roost-disturbance radius=1km andalpha=0.05).The finalresultsareshownwiththefirstset.

4. Discussion

Inthisstudyweusedanindividual-basedmodeltostudy forag-ingdecisionofpink-footedgeeseduringtheirspringmigration.Our resultssuggestthatwhilestudiedgeeseemployarandomsearch strategy,theyarealsoabletolearnbasedontheirownexperience wherethemostproﬁtablepatchesarelocatedandreturntothe patchesthatresultedinhighestenergyintake.

Thesefindingsarelikelyinfluencedbytheoverallhighquality ofthefoodresourcesavailableintheMid-Norwaylandscape,as grain(instubblefieldsandnew-sownfields)isagoodsourceof

energyandgrassisrichinprotein(PropandSpaans,2004).When resourcesareabundantacrossthelandscape,choosingoneforage resourceovertheotherdoesnotprovidemuchbenefitintermsof nutrientintake.Inthissituationrandomsearchwillbecloseto opti-mal(Turneretal.,1993).Resourceselectionfunctionanalysisalso revealedthatpink-footedgeeseinMid-Norwaychooseresources accordingtotheiravailability,andthereforeselectfieldsatrandom (Chudzi ńskaetal.,2015).Furthermore,thegeeseareforagingin ahighlydynamicagriculturallandscapewherethefoodtypeon agivenfieldmaychangewithinarelativelyshorttime.Insucha landscape,whereindividualsareunlikelytohavesufficient knowl-edgeabouttheenvironment(asalsorevealedbytheresultsofFDR 2-maxenergy),choosingpatchesatrandommaybemore benefi-cialthanreturningtoapatchvisitedfewdaysbefore,asthismay reducesearchtimeandenergyexpenditure(Amanoetal.,2006a,b). TheMid-Norwaystagingsiteisarelativelylargearea(50×30km2₎ andhabitatdepletionanddisappearance/appearanceoccur simul-taneouslyinvariousplacesbecauseofforagingand agricultural practices.Ontopofthat,bothvariabilityingraindensityonstubble fieldsandthefactthatgrainonnewsownfieldsissownatvarying depths,fromthesurfacetoseveralcentimetresbelow(Madsen, 1985b), hindertheassessmentoftheprofitability ofthesefield typeswithoutlandingthere.Thismakesitdifficultforthegeeseto obtainacompleteknowledgeaboutthespatialdistributionoffood andchoosingfieldsaccordingtotheiravailability(random)seems morebeneficial.Similarrandomchoiceofforaginghabitathasbeen foundforotherspecieslivinginhighlydynamiclandscapes(Focardi et al.,1996;Kułakowska etal.,2014).Outside springmigration seasongeese,however,havebeenreportedshowingselectionfor certainhabitattypesmainlybasedonnutritionalvaluesofthese habitats(NewtonandCampbell,1970;Owen,1973;McKayetal., 1996).

FDR3-asociallearningreproducedmostoftheobserved pat-ternsincludingpatternsdescribingdailyenergyintakeandtime spend onroost sites, the most important ones.Returning to a recently visited patchcan bebeneﬁcial because in the agricul-turallandscapetheprobabilitythattheresourcetypeonsucha patchremains thesameas onedaybeforeishigher thanifthe samepatchisvisitedafterlongerperiodoftime.Severalstudies have shown that animals may return to thesame areato for-ageiftheyexperiencedsuitableforagingconditionsatthatarea (e.g.,Charnov,1976;Bailey,1995;Baileyetal.,1996).Bernstein etal.(1988)revealedthatincompletelyinformedforagersselecting patchesrandomlycoulddistributethemselvesoptimallyby learn-inghabitatqualityandusingapatchdeparturerulebasedonthe

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marginalvaluetheorem(Charnov,1976)asisthecaseinthisstudy. Modelsincludingsociallearning(FDRs4and5)ledtolessrealistic energyintakeratesandspatialdistributionsofgeese.Thiscontrasts otherstudiesdemonstratingbenefitsofgroupforagingforgeese andotherspecies(Amanoetal.,2006a;NémethandMoore,2007; Kułakowskaetal.,2014).Inourmodel,oneagentconsistedof20 individuals.Ourmodeldoesnotruleoutthebenefitsofgeese forag-inginsmallflocksbutindicatesthatforaginginlargerflocksmay notbebeneficial. Thisislikely tobeinfluencedbythefactthat duetoalargenumberofpink-footedgeeseforagingatthestudy site(approx.80,000individuals,MadsenandWilliams,2012),large flocksconcentratedonasmallpatchwouldleadtoafasthabitat depletion,anditisthereforemorebeneficialforgeesetoforage inmorewide-spreadandsmallflocks.Althoughsociallygathered informationregardinglocationofprofitableforagingareasmaynot beaprimarytypeofinformationexchangedbetweenindividuals fromthesameflock,otherexchangeofinformation,likeoptimal timeofdeparturefromastopoversite,canstilltakeplace.Most studiesfocusingonspeciesfrequentlylivinginflocksoftenpoint outthebenefitsofsociallearning(RafaczandTempleton,2003; Amanoetal.,2006a;NémethandMoore,2007;Kułakowskaetal., 2014);however,ourstudyalsorevealedtherelevanceofasocial learningforsuchspecies.Althoughdetailedanalysisofhowsuch learningisaccomplishedbygeeseandwhichcuesarecrucialinthis processwasnottheaimofthiswork,thisisaninterestingaspect worthfurtheranalysis.

Thesensitivityanalysisrevealedthepervasiveroleofhuman disturbanceonforagingbehaviourofpink-footedgeesein Mid-Norway.Indeed,thebehaviourofpink-footedgeeseatthisstopover site,aswellasatotherstopoversitesalongthemigrationroute,is knowntobestronglyinfluenced bydisturbance(Madsen,1994, 1998;Klaassenetal.,2006;Jensenetal.,2008;Chudzi ńskaetal., 2013). Othergoosespecies are alsoknown tobesusceptive to humandisturbance(Owen,1973;Madsen,1994;Stillmanetal., 2015).Theforagingbehaviourofpink-footedgeeseinMid-Norway isinfluencedbyvarioustypesofdisturbances,someofwhichare predictable,suchasregular road traffic,while others are more unpredictable,suchasfarming activitiesor irregularpassageof walkingpeople.Thetypeofdisturbanceinfluencesforhowlong geeseforageandtheirhabitatselection(Chudzi ńskaetal.,2013, 2015).Thedifferencebetweentheresultsofthesensitivity analy-sisofpattern2(timespendonroostsites)ofFDR1-randomand FDR3-asociallearningmayindicatethatthelocationofhigh qual-ityareasinrelationtotheclosestroostsitesmaydeterminegoose behaviour,inagreementwithpreviousstudies(Jensenetal.,2008; Chudzi ńskaetal.,2013,2015).

AlthoughIBMscan bepowerful toolsfor analysingwhether differentbehaviouralmechanismscanleadtorealisticemergent properties,theyhaveoftenbeencriticisedforbeingtoocomplex ortoosimpleanddatadeficient,makingitdifficulttotesttheir validity(Grimmetal.,1999;GrimmandRailsback,2005;Evans etal.,2013).Inthefollowingparagraphswediscusshowourmodel canbeimprovedbyaddingormodifyingsomeaspectsof forag-ingbehaviourofthestudiedgeese.Noneofthepredictionsofthe FDRswereinagreementwiththeobservedpatterndescribingthe proportionofdaytimegeesespentonroostsitesforthefirsttwo periodsofthestopoverseason.AstudybasedonGPS-tagged pink-footedgeeserevealedthatinMid-Norwaygeesespentmoretime onroostsitesthannecessaryfordigestion,andhumandisturbance wassuggestedasthemainreasonwhygeesereturnedtoroostsites duringaday(Chudzi ńska,unpubl.manuscript),althoughlittleis knownaboutthemechanismthatdrivessuchbehaviour.Inthe beginningofthestopoverseason,geesemaynotbefamiliarwith factorscausingdisturbanceandhencespendlongertimeonroost sitesthanattheendoftheseasonwhentheymayhavelearnedhow toavoidorhabituatetodisturbances.Suchadaptivebehaviourhas

notbeenincludedinthemodelandmoreinformation,preferably experimental,shouldbegathered.

Noneof thepredictionsoftheFDRs wereabletoaccurately mimichowthedistancebetweentheforagingpatchusedbygeese andtheroostsiteschangedalongthedayandbetweenperiods.The spatiotemporaldistributionofgeesecanbeinfluencedbymany factors,severalofwhichare notincludedinthecurrent design ofthemodel.Geesemayexplorepatchesinthevicinityoftheir currentpatchandonlywhenthesepatchesaredepleted,moveto anotherarea.InthecurrentdesignofFDR3-asociallearningand FDR5-alllearning,geeseonlyreturntothepreviouslyvisitedpatch onceperdayin themorningbutthesearch rulethenceforthis random(FDR3-asociallearning)ordependsonthedistributionof othergeese(FDR5-alllearning).Inourmodel,geeseleaveapatch notonlybasedontheirenergyintakeonthatpatchbutalsodueto physiologicalandexternalfactors(disturbance,timeofday).We donotincludeanyformofadaptationoradditionallearninginour modelandthereforegeesedonotreturntoarecentlyabandoned patch(e.g.neithertheforagingpatchthatresultedinhighenergy intake,norapatchwheretheyexperiencedlowdisturbancelevel) at any time of day other than in the morning, unless they do sobychance. Theanalysis ofhow thestudied speciesselected foraginghabitatsusingresourceselectionfunctionsrevealedthat spatiotemporalchangesinthegoosedistributionrelativetothe roost sites are largely shaped by density-dependent processes (Chudzi ńskaetal.,2015).Suchprocessesarerepresentedinour modelthroughhabitatdepletionbyotherindividuals (exploita-tive competition) and through a relationship between number of animals and the amount of time they spend foraging and beingvigilant.However,othercompetitiveprocesses,suchasthe behaviouralresponsesinducedbyaggressiveinteractions (inter-ference)thatmaylimitthemaximumnumberofgeeseoccupying acertainspace,arenotincluded.Moreempiricalstudiesaboutsite fidelityofgeese,density-dependentprocessesandtheadaptation bygeesetodisturbancearenecessary.

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environments(RailsbackandHarvey,2002;GrimmandRailsback, 2012).

The presented model has a potential for risk assessment whereinformationaboutspatialandtemporalaspectsofforaging and/or the effect of various external factor on energetics are necessary.DuetothefactthattheSvalbard-breedingpopulation ofpink-footedgeesehasincreaseddramaticallyinthelastdecade (Madsen and Williams, 2012), theconflict betweenagricultural ownersandgeeseforagingontheirfieldsincreasedandledtoan agriculturalsubsidyschemetoalleviatethisconflict(Tombreetal., 2013).Because geeseare allowed toforage undisturbed atthe subsidisedfields,geesearefrequentlychasedawayatremaining areasinordertoreducetheirdamagetocrops.Ourmodel,which incorporates humandisturbance, can be appliedto predictthe population-level and energetic consequences of, for example, increased scaring intensity or concentration of such scaring in certain areas.Our resultssuggest that when theprobability of disturbanceonallfieldswasincreasedby approximately100%, themeanDNEIforallfourperiodsdecreasedby60%.Ourmodel canbeusedtopredicttheconsequencesofdifferentmanagement scenariosandthushelpsolvecriticalpracticalquestions,suchas: cantheeffectofdisturbanceongeesebereducedifdisturbance variestemporallyand/orspatially?Ourmodelalsodemonstrated that pink-footedgeesestaging in Mid-Norway maynot benefit fromforaginginlargeflocks.Itcanthereforebeusedtosupport decisionmakingregardingthedefinitionofmanagementschemes of protected or subsidised areas by providing key information, forexample,abouthowbigtheareasshouldbeandhowcloseto eachothertheyshouldbeplaced.Ourmodelcanalsobeusedto predicttheeffectofchangesinhabitatavailabilityandalternative agricultural practices in Mid-Norway on population dynamics, revealing the optimal policies with regard to when to plough andre-sowfieldstoreduceagriculturalconflictsand/orpotential effectsofintroductionofnewcroptypessuchaswinterwheat.

Wethusbelievethatourandsimilarmodels(e.g.Kułakowska etal.,2014;Stillmanetal.,2015),whicharebasedonindividual behaviourandenergetics,canbevaluabletoolsformakingmore realisticandecologicallyrelevantriskassessmentsofhuman dis-turbanceandchangesinagriculturalpractices.

Acknowledgements

Thisstudywasapartof MC’sPhDprojectfundedbyAarhus University.D.AyllónwasfundedbyaMarieCurieIntraeuropean Fellowship (PIEF-GA-2012-329264)for theprojectEcoEvolClim. The data collectionwas supportedby the Norwegian Research CouncilprojectMIGRAPOP.WewouldliketothankPeterdeVries, BartNolet,JannikHansen,PerIvarNicolaisen,RobertPeeland Car-olineSimonsenfortheirhelpindatacollection.Wewouldspatially liketothankVolkerGrimmforhisadviceduringmodel design anddevelopment.WearealsogratefultoSantaClusterfromUFZ forspeedingupthesimulations.Twoanonymousreviewersmade severalhelpfulcommentsthatreallyimprovedthequalityofthe manuscript.

AppendixA. Supplementarydata

Supplementarymaterialrelatedtothisarticlecanbefound,in theonlineversion,athttp://dx.doi.org/10.1016/j.ecolmodel.2015. 10.005.

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