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Estimating demographic contributions to effective population size in an age-structuredwild population experiencing environmental and demographic stochasticityTrask, AE; Bignal, EM; McCracken, DI; Piertney, SB; Reid, JM

Published in:Journal of Animal Ecology

DOI:10.1111/1365-2656.12703

First published: 03/07/2017

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Citation for pulished version (APA):Trask, AE., Bignal, EM., McCracken, DI., Piertney, SB., & Reid, JM. (2017). Estimating demographiccontributions to effective population size in an age-structured wild population experiencing environmental anddemographic stochasticity. Journal of Animal Ecology, 86(5), 1082 - 1093. https://doi.org/10.1111/1365-2656.12703

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J Anim Ecol. 2017;1–12. wileyonlinelibrary.com/journal/jane  | 1© 2017 The Authors. Journal of Animal Ecology © 2017 British Ecological Society

Received:17October2016  |  Accepted:5May2017DOI:10.1111/1365-2656.12703

S T A N D A R D P A P E R

Estimating demographic contributions to effective population size in an age- structured wild population experiencing environmental and demographic stochasticity

Amanda E. Trask1  | Eric M. Bignal2 | Davy I. McCracken3  | Stuart B. Piertney1 |  Jane M. Reid1

1Institute of Biological & Environmental Sciences, School of Biological Sciences,UniversityofAberdeen,Aberdeen,UK2ScottishChoughStudyGroup,IsleofIslay,Argyll,UK3Future Farming Systems, Scotland’s Rural College,Ayr,UK

CorrespondenceAmandaE.TraskEmail:amanda.trask@bto.org

Funding informationNatural Environment Research Council; ScottishNaturalHeritage;EuropeanResearchCouncil

Handling Editor: Fanie Pelletier

Abstract1. Apopulation’seffectivesize(Ne)isakeyparameterthatshapesratesofinbreedingandlossofgeneticdiversity,therebyinfluencingevolutionaryprocessesandpopu-lation viability. However, estimating Ne,andidentifyingkeydemographicmecha-nisms that underlie the Netocensuspopulationsize(N) ratio, remains challenging, especiallyforsmallpopulationswithoverlappinggenerationsandsubstantialenvi-ronmentalanddemographicstochasticityandhencedynamicage-structure.

2. AsophisticateddemographicmethodofestimatingNe/N, which uses Fisher’s re-productive value to account for dynamic age-structure, has been formulated.However, thismethod requiresdetailed individual-andpopulation-leveldataonsex-andage-specificreproductionandsurvival,andhasrarelybeenimplemented.

3. Here,weuse the reproductive valuemethod anddetaileddemographic data toestimate Ne/N forasmallandapparently isolatedred-billedchough (Pyrrhocorax pyrrhocorax)populationofhighconservationconcern.Weadditionallycalculatedtwo single-samplemolecular genetic estimates ofNe to corroborate the demo-graphicestimateandexamineevidenceforunobservedimmigrationandgeneflow.

4. ThedemographicestimateofNe/Nwas0.21,reflectingahightotaldemographicvariance(σ2dg) of 0.71. Females and males made similar overall contributions to σ2dg. However,contributionsvariedamongsex-ageclasses,withgreatercontributionsfrom 3year-old females thanmales, but greater contributions from ≥5year-oldmales than females.

5. ThedemographicestimateofNe was ~30, suggesting that rates of increase of in-breeding and loss of genetic variation per generation will be relatively high.MoleculargeneticestimatesofNecomputedfromlinkagedisequilibriumandap-proximateBayesiancomputationwereapproximately50and30,respectively,pro-viding no evidence of substantial unobserved immigration which could bias demographicestimatesofNe.

6. Our analyses identify key sex-age classes contributing to demographic varianceand thus decreasing Ne/Ninasmallage-structuredpopulationinhabitingavariableenvironment.TheytherebydemonstratehowassessmentsofNecanincorporatestochastic sex- and age-specific demography and elucidate key demographic

2  |    Journal of Animal Ecology TRASK eT Al.

1  | INTRODUCTION

A population’s effective size, Ne, is a key parameter that shapespopulation-wideratesofinbreedingandlossofgeneticdiversityand,in combination with the strength of selection, determines mutation fixationprobabilities (Charlesworth,2009;Frankham,1995;Nunney&Elam,1994).EstimationofNe,andelucidationofkeyunderlyingpro-cesses that cause the observed Ne, is thereforecentral inpredictingevolutionary trajectories of finite populations (Charlesworth, 2009)andinevaluatingpopulationviability(Frankham,Bradshaw,&Brook,2014;Mace&Lande,1991),suchthatappropriatepopulationman-agementstrategiescanbedevised(Hareetal.,2011;Laikre,Olsson,Jansson, Hössjer, & Ryman, 2016).

NeisdefinedasthesizeofanidealizedWright-Fisherpopulationthatwouldexperiencethesamerateofgeneticdriftasanobservedpopulation (Wright, 1931, 1969). Such a Wright-Fisher populationis defined as a hypothetical population of constant finite sizewithno migration or selection and random mating between monoecious individuals in discrete generations, giving a Poisson distribution of reproductivesuccess(Crow&Kimura,1970;Wright,1931).However,mostnaturalpopulationsviolatekeyWright-Fisherassumptions.Thus,Ne can exceed the census population sizeN (i.e.Ne/N>1), up to atheoretical maximum of 2Ngivenuniformreproductivesuccess(Lande&Barrowclough,1987;butseeWaples,Luikart,Faulkner,&Tallmon,2013). However, Ne is frequently smaller than N(i.e.Ne/N < 1), mean-ing that a populationwill experience greater genetic drift than ex-pectedgivenitsN,potentiallyreducingitsviability(Frankham,1995;Nunney&Elam,1994;Waplesetal.,2013).

ManyfactorscanreduceNe below N, including varying N,skewedsex-ratio and high among-individual variance in reproductive suc-cess (i.e. high reproductive skew,Caballero,1994;Frankham,1995;Nomura, 2002; Ruzzante etal., 2016; Wright, 1931). Indeed, highvarianceinreproductivesuccess isadominantfactorreducingNe in diverse natural populations, spanning fish (e.g. red drum, Sciaenops ocellatus,Turner,Wares,&Gold,2002;steelheadtrout,Oncorhynchus mykiss,Araki,Waples,Ardren,Cooper,&Blouin,2007),mammals(e.g.woodrats, Neotoma macrotis, Matocq, 2004) and amphibians (e.g.Italian agile frog, Rana latastei, Ficetola, Padoa-Schioppa, Wang, &Garner,2010).Smallpopulations(i.e.smallN)canalsoexperiencesub-stantialdemographicstochasticity,whichcanexacerbatevarianceinreproductivesuccessandfurtherdecreaseNe(Melbourne&Hastings,2008;Palstra&Ruzzante,2008).Consequently,atsmallN, Ne might

commonly be very small, further increasing genetic drift and threaten-ingpopulationviability.

Conversely, somestudieshave foundan inverse relationshipbe-tween Ne/N and N,implyingthatsmallpopulationshavehigherNe than mightbeexpectedgiventheirN(Ardren&Kapuscinski,2003;Hedrick,2005;Palstra&Ruzzante,2008;Pray,Goodnight,Stevens,Schwartz,&Yan,1996;Watts,Saccheri,Kemp,&Thompson,2007).Suchpatternscanariseiftheamong-individualvarianceinreproductivesuccessde-creases at small N, forexamplebecauseenvironmental stochasticityreduces the reproductive success of all populationmembers, or be-cause male–malecompetitionformatesorbreedingsites isreduced(so-called‘geneticcompensation’mechanisms,Ardren&Kapuscinski,2003;Beebee,2009;Palstra&Ruzzante,2008).Given the rangeofpossiblevaluesandcausesofNe/N,pervasiveaimsacrossevolutionary,populationandconservationecologyaretoestimateNe/N in diverse naturalpopulationsandidentifythekeycontributingdemographicpro-cesses,andtherebyelucidategeneralrelationshipsbetweenNe, N, and underlying demography and population dynamics (Frankham, 1995;Palstra&Fraser,2012;Ruzzanteetal.,2016;Waplesetal.,2013).

For most natural populations, Ne cannot be measured directly andmustbeestimatedusingdemographicormoleculargeneticap-proaches. Demographic approaches estimate Ne as mathematical functionsofcausaldemographicparametersandprocessesthatgen-eratecontemporaryNe,suchasthevarianceinlifetimereproductivesuccess,breedersex-ratioorfluctuationsinN(Caballero,1994;Lande& Barrowclough, 1987). These demographic approaches estimatethevarianceeffectivesizeNev(i.e.thesamplingvarianceinallelefre-quencies per generation) and thereby quantifyNe for the offspringgeneration (Caballero, 1994; Kimura&Crow, 1963). Suchmethodsarevaluablebecause,beyondprovidingapointestimateofNe, they directlyidentifykeydemographicprocessesthatshapeNe.TheycanthereforeinformpopulationmanagementstrategiesaimingtoincreaseNeandreducefuturelossofgeneticdiversity(Nunney&Elam,1994;Ruzzante etal., 2016). However, many demographic methods relyonstrongsimplifyingassumptions,suchasdiscretegenerationswithnoage-structure,nodensity-dependenceandconstantN, which are typicallyviolated innaturalpopulations (Caballero,1994;Hill,1972;Nomura,2002;Nunney,1991).Even recentmethods forestimatingNeinage-structuredpopulationswithoverlappinggenerationsstillre-quirestrongassumptions,suchasconstantN and birth rate and hence stableage-structure(e.g.the‘AgeNe’method,Waples,Do,&Chopelet,2011)andconsequentlydonotincorporateeffectsofenvironmental

processesaffectingapopulation’sevolutionarytrajectoryandviability.Furthermore,our analyses show that Neforthefocalchoughpopulationiscriticallysmall,imply-ingthatmanagementtore-establishgeneticconnectivitymayberequiredtoensurepopulationviability.

K E Y W O R D S

conservationgenetics,evolutionarypotential,iteroparity,life-historyvariation,populationconnectivity,populationmanagement,reproductiveskew

     |  3Journal of Animal EcologyTRASK eT Al.

ordemographicstochasticityoradditionaldemographicheterogeneitythatgeneratedynamicage-structure.However,sincetheorypredictsthatenvironmentalanddemographicstochasticityandheterogeneitycould substantially affect Ne,especiallyatsmallN, such effects should be incorporated to avoid biased estimates ofNe (Engen, Lande, &Saether,2005;Engen,Lande,Saether,&Festa-Bianchet,2007).

Accordingly, Engen etal. (2005) and Engen, Lande, Sæther, andGienapp (2010) derived a novel demographic method that utilizestheconceptof‘reproductivevalue’torelaxtheassumptionofstableage-structureandtherebycaptureeffectsofenvironmentalandde-mographicstochasticityandadditionaldemographicheterogeneityonNe.Conceptually,thismethodconsidersthemeanandvarianceinthechangeinfrequencyofarareselectivelyneutralalleleateachtime-step in a hypothetical heterozygote subpopulation, given observedpatternsofage-specificdemographicvariance(Emigh&Pollak,1979;Engen etal., 2005).Overlapping generations and age-structure in avariable environment are incorporated using Fisher’s reproductivevalue(i.e.thecontributionofanindividualofagivenagetopopula-tion growth rate), which can be summed across individuals in all age classestogivethepopulation’stotalreproductivevaluegivenitsage-structure (Crow&Kimura,1970;Engen,Lande,Saether,&Dobson,2009;Fisher,1958).Changesintotalreproductivevaluecanthenbeusedtoobtainanestimateoftotalpopulationgrowthrate,andhencethe rate of increase of a neutral allele, thereby generating an estimate of Ne that is not biased by dynamic age-structure (Crow&Kimura,1970;Engen,Landeetal.,2007;Engenetal.,2010).

Thetotalvarianceinindividualcontributionstopopulationgrowthrate in a dynamically age-structured population stems from demo-graphicandenvironmentalvariances inage-andsex-specific fecun-dityandsurvivalwhich,inpractice,canbedefinedandestimatedasthe varianceswithin years and inmeans among years, respectively(Engen,Bakke,&Islam,1998).Therequiredvariancecomponentscanbeestimatedusingthedistributionof individualreproductivevaluesamong individuals within and among years, which can be used to es-timatethetotalpopulationdemographicvariance,σ2

dg.TheNe/N ratio

can then be estimated as:

where Tisthegenerationtime(AppendixS1;Engenetal.,2005).Thiscalculationispotentiallyveryinsightfulbutimposeschalleng-

ing data demands, requiring individual-level information on realizedsex- and age-specific reproductive success and survival alongsidepopulation-levelmean rates.Todate, it hasonlybeen implementedin a Siberian jay (Perisoreus infaustus) population (as amethodologi-calexampleconsideringthreeageclasses,Engenetal.,2010)andahouse sparrow (Passer domesticus) metapopulation (considering twoage classes, Stubberud et al., 2017) where genetic variation and in-breeding rates may be influenced by immigration rather than solely localdemography(e.g.Baalsrudetal.,2014).Indeed,immigrationcancause local Netoapproachthatforthewholemetapopulation,mean-ing that Ne/N is largely independentof localdemography (Gilbert&Whitlock,2015;Wang&Whitlock,2003).Consequently,studiesthat

apply the ‘reproductivevalue’estimatorofNe/N to isolatedpopula-tionsare required to identifykeydemographicprocesses that influ-ence Ne/N given environmental and demographic stochasticity andheterogeneity,andresultingdynamicage-structure.

SincesufficientdatatoimplementanydemographicestimatorofNe/N are often unavailable, Ne is commonly instead estimated from moleculargeneticdata.Single-sampleapproaches,whichrequireDNAsamplingatone time-point,aremostpractical forspecieswith longTandwherehistoricalsamplesarenotavailable(Palstra&Ruzzante,2008).SuchestimatorsgenerallymeasureinbreedingeffectivesizeNei (i.e.therateofchangeinheterozygosity)andthereforereflectNe of theparentalgeneration (Caballero,1994;Crow&Denniston,1988).Given varying N, NeiisexpectedtolagbehindchangesinN by at least onegeneration(Hill,1972;Kimura&Crow,1963;Waples,2005),andmight therefore give somewhat misleading estimates of current Ne. Additionally,moleculargeneticestimatesofNe are calculated from re-sultant effects of Neongeneticvariation,andhencedonottypicallyelucidate the ecological and demographic processes that cause theestimated Ne (butseeWang,Brekke,Huchard,Knapp,&Cowlishaw,2010).However, suchestimatorscancapture thegeneticeffectsofimmigration, which may remain undetected based solely on obser-vations of N and local demography (Baalsrudetal., 2014;Gilbert&Whitlock,2015;Hareetal.,2011).Consequently,togenerateoverallmechanistic understanding of Ne/N and Ne and hence elucidate sto-chastic evolutionary processes and inform population managementstrategies, molecular genetic estimators of Ne need to be calculated alongsideappropriatedemographicestimators.

Accordingly,weuseddetailedindividual-levelandpopulation-leveldemographicdata,andmoleculargeneticdata,toestimateNe/N and Ne in a small andapparently isolated red-billedchough (Pyrrhocorax pyrrhocorax Linnaeus, hereafter ‘chough’) population of major con-servationconcern.Weutilizedthe ‘reproductivevalue’demographicestimator (Engenetal.,2005) toaccount forenvironmentalandde-mographic stochasticity and heterogeneity and resulting dynamicage-structure,andtherebyidentifiedkeysex-andage-specificcompo-nentsofdemographicvariancethatcontributetoNe/N.Weaddition-allycomputedtwosingle-samplemoleculargeneticestimatesofNe to infereffectsofanyunobservedimmigration.Wetherebydemonstratehow Necanbeestimatedindynamicallyage-structuredpopulations,andidentifykeydemographicprocessesunderlyingNe, thus aiding our generalunderstandingofevolutionaryprocessesinfinitepopulationsand informing conservation strategy.

2  | MATERIALS AND METHODS

2.1 | Focal population

Choughs are of conservation concern in Europe and the UnitedKingdomduetosubstantialreductionsinrangeandpopulationsizeandresultingfragmenteddistribution(Eatonetal.,2015).Comprehensivecensusesundertakenevery3–6yearssince1982showthattheislandofIslayholdsmost(ca.84%)oftheremainingScottishchoughpopu-lation,yetnumberson Islayhavedecreasedfrom78breedingpairs

(1)Ne

N=

1

σ2dgT

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in1986to46pairsin2014(Finney&Jardine,2003;Hayhowetal.,2015;Trasketal.,2016;AppendixS2).Highneutralgeneticdifferen-tiationwith other British chough populations (Wenzel etal., 2012),andalackofobservedimmigration,suggestthatIslay’spopulationisisolated.ThisisolationandsmallN implythatinbreedingandlossofgeneticdiversitymaycompromisepopulationviability.

Islay’s choughs form territorial, socially monogamous breeding pairsandnestincavesorfarmbuildings(Bignal,Bignal,&McCracken,1997)withlittleextra-pairparentage(~5%chicks,Trasketal.,2016).Bothsexesbreedonceperyearstartingfromage2–4yearsandsur-vive to breed in multiple years (maximum breeding age: 17years),generatingoverlappinggenerations(Reid,Bignal,Bignal,McCracken,&Monaghan,2004).Reproductive successand survivalvaryamongages,years,cohorts,andnestsites (Reid,Bignal,Bignal,McCracken,&Monaghan,2003a,2003b,2006;Reidetal.,2004).Sub-adultandnon-breeding individuals aged 1year or older form flocks that oc-cupyknown locations,meaningthatallnon-breederscanbereadilyobservedandcensused(Bignaletal.,1997;Reidetal.,2006,2008).First-yearsurvival(fledgingtoage1year)forthe2007–2009cohortswas particularly low (Reid etal., 2011), causing low subsequent re-cruitment into the breeding population.Demographic estimation ofNe/Nthataccountsforenvironmentalanddemographicstochasticityanddemographicheterogeneity,andresultingdynamicage-structure,is therefore required.

2.2 | Demographic estimation of Ne

2.2.1 | Age- specific breeding success and survival

Demographic estimation ofNe using reproductive value to accountfor dynamic age-structure (e.g. Engen etal., 2005, 2010) requiresestimates of mean population-level sex-specific demographic ratesunderlying the deterministic asymptotic population growth rate (λ), definedforapre-orpost-breedingcensus.Therequiredratescom-prisethesex-specificprobabilitiesofattemptingtobreedateachage(ci),age-specificbreedingsuccessgivenabreedingattempt(mi), and juvenileandsubsequentage-specificannualsurvivalprobabilities(Pi, Caswell, 2001; Reid et al., 2004), where idenotesasex-ageclass.Suchestimation of Nealsorequiresindividual-leveldataonage-specificre-productivesuccessdefinedastherealizednumberofoffspringthatsurvivedtoage1year (b)andrealizedannualsurvival (J) from sam-plesofindividualfemalesandmalesinasampleofyears(Engenetal.,2005,2010).AllnotationsaresummarizedinAppendixS1(TableS1).

Toestimate the requiredpopulation- and individual-level demo-graphic rates, a sample of accessible chough nest sites across Islaywerevisitedeachyearduring1983–2014.Thenumberofnestlingsthatsurvivedtoca.3weekspost-hatchwasrecorded,andnestlingsweremarkedwithuniquecolour-ringcombinations(Reidetal.,2003b,2004).Adults breeding at nest sites across Islaywere subsequentlyidentifiedfromtheircolour-rings,andsexeswereassignedbasedonreproductivebehaviourandrelativesize(Bignaletal.,1997).Thean-nualbreedingsuccessofknown-ageindividualswastherebyrecorded.Colour-ringedadultsandsub-adultswereresightedacrossIslayduring

May-Juneeachyear,allowingage-specificannualresightingprobabili-tiesandapparentsurvivalprobabilitiestobeestimatedusingcapture-mark-recapture(CMR)models(Reidetal.,2003a,2004).

Initialyear-structuredCMRmodels showed that annual resight-ingprobabilitieswere typically less thanoneprior to2004,but ap-proached one subsequently due to increased resighting efficiency(estimateacross2004–2014of0.97±0.02SE,AppendixS1).Wecon-sequently focussed on live individuals and, of those breeding, whose offspringwereringedin2004–2013,sothatindividual-levelrealizedsurvival (J) and reproductive success (b) could be directly recorded. Separate age classes for individuals agedone to four, andapooledterminalage-classforindividualsaged5yearsorolder,weredefined(i.e.k=5ageclasses).Thisstructurecapturesage-specificvariationinkeydemographicrateswhilemaintainingsufficientsamplesizeswithineachsex-ageclass(AppendixS1).

Resightingsof individuals innon-breedingflocksvs.atnestsiteswereusedtoestimatethemeanprobabilityofbreeding(ci) for each sex-ageclass.Non-breeding individuals typicallypairedandshowedcourtshipbehaviourwithinflocks,allowingsexestobeassigned.Themean number of fledglings produced given that breeding was at-tempted (mi) was directly estimated from breeding records for each sex-ageclass.ConstrainedCMRmodelswerefittedtoestimatesepa-rateage-specificsurvivalprobabilities(Pi)for1983–2003and2004–2014 while retaining full encounter histories of all ringed individuals andmaximizingpowertoestimatePi for 2004–2014. Initial analyses showed thatmodels thatcontained threeageclasses, first-year (P1, fledgingtoage1year),second-year(P2, age one to age two) and adult (Pad,allsubsequentages)werestronglysupported,therebysettingPi equalacrossall individualsaged2yearsorolder(AppendixS1).Thisthreeage-classstructureisconsistentwithpreviousdetailedanalysesof age-specificPi in Islay’s choughs (Reid etal., 2004). Females andmaleswerepooledforCMRanalysesbecausesexesofindividualsthatdied before pairingwere unknown, and because previous analysesshowed that Paddoesnotdifferbetweenthesexes(Reidetal.,2003b,2004).Additionally,previousanalysesshowednoevidenceofstrongdensitydependenceinmeanbreedingsuccess,orinP1, P2 or Pad(Reidetal.,2003a,2008).

2.2.2 | Population projection matrix

Theasymptoticpopulationgrowthrate(λ),stableagedistribution(ui) andreproductivevalues (vi) were calculated from a 2k × 2k two-sexLesliematrix (l).Thematrixcomprised foursubmatrices, formulatedforabirth-pulsepopulationwithpre-breedingcensus,whichdescribethecontributionsoffemalesandmalestofemaleandmaleoffspring(AppendixS1).Toprowfecundityfi terms were calculated as:

where q istheprimaryproportionofthefocalsexandthefactorof1/2istheprobabilitythatahypotheticalrecessivealleleistransmit-tedtoeachoffspring,givenahypotheticalsubpopulationofheterozy-gotesthatonlymatewithdominanthomozygotes(Engenetal.,2010).

(2)fi=1

2q(cimiP1)

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SubdiagonaltransitionprobabilitiesP2 and Padweretheprobabilitiesof survival fromone age-class to the next (Appendix S1). Standardmatrixalgebrawasusedtocomputeui and vi from the right and left eigenvectors of l(Caswell,2001),scaledsothat∑ui=1and∑uivi = 1, and to compute the generation time,T, as themeanprojected ageofparentsofnewoffspring.Contributionstoλ from the female and male submatrices must be the same (Caswell, 2001; Engen etal.,2010;Mesterton-Gibbons,1993).λ was therefore initially calculated as the real dominant eigenvalue of the female and male submatrices separately to check that thesewere approximately equal, and thencomputedforthefulltwo-sexmatrix.

2.2.3 | Estimating demographic variance

Thetotalpopulationdemographicvariance,σ2dg,comprisesthesumof

thecontributions todemographicvariance fromeachsex-ageclass,σ2dgi

, weighted by the stable age distribution, ui:

Tocalculateeachσ2dgi,wefirstcalculatedthedemographicvariance

componentfromeachsex-ageclassineachyearusingthemeanb and Jofeachsex-ageclass i in each year, the mean sum of the squared difference of each individual’s b and J from its sex-age classmean(Sb

2 and SJ2),andthemeansumofsquaresofthecross-productsof

b and J(SJb)(AppendixS1,Engenetal.,2010).Thesecalculationsin-cludedall individualcolour-ringedchoughsalive ineachyearduring2004–2013 whose value of b could be quantified, either because they producedzero fledglings (i.e.b = 0) or because their fledglings were colour-ringedmeaningthatthenumberof1-yearoldoffspringalivein2005–2014wasobserved.Whethereachfocalcolour-ringedindivid-ualwasalivethefollowingyear(i.e.2005–2014),andhenceindividualJ, was also observed directly.

The expected contributions from females and males to demo-graphicvariancefromtheproductionofsonsanddaughterswasthencalculated, conditioned on b and J from the individuals and years sampled.Thebroodsex-ratiodoesnotdiffersignificantlyfrom1:1inIslay’s choughs, meaning that q=0.5(AppendixS3).Thecontributionstodemographicvariancefromtheproductionofsonsanddaughterswere consequently assumed to be equal (Appendix S1). These ex-pectedcontributionsandthereproductivevalues,vi,computedfroml,wereusedtocomputeσ2

dgiforeachsex-age-yearclass.Eachσ2

dgi was

thenweightedbysamplesize(Engenetal.,2010).Finally,Ne/N was calculated from Equation 1, and Ne was then calculated by defining Nasthetotalcensuspopulationsizewhichincludesbothadultsandsub-adults.Fulldetailsofallcalculations,underlyingdataandsamplesizesareprovidedinAppendixS1.

Bootstrap confidence intervals (CIs) around estimates of demo-graphicvariance for each sex-age class (σ2

dgi), the total demographic

variance(σ2dg

) and Ne/Nwere initiallycomputedforthefullfiveage-classmodel,using10,000bootstrapsamples.However,CIsforvari-ancescanbedownwardlybiasedwhenbootstrapsamplesaredrawnfrom small sets of observationswith skewed distributions, because

rarehighvaluesmightnotbesampled(Manly,2007;Puth,Neuhauser,&Ruxton,2015;Schenker,1985).Thisislikelyforb, because few indi-vidualswereobservedforsomesex-age-yearclasses,andwhilemostbreeding attempts produced zero 1-year olds, a minority produced2–4. Indeed,bootstrapCIsforσ2

dg and Ne/Ncomputedfromthefull

fiveage-classmodelscarcelyincludedthepointestimate.Therefore,to adequately assess uncertainty around σ2

dg and Ne/N estimates, these

quantitieswere re-estimatedusing a reducedmodelwith three ageclasses (i.e.k = 3, ages 1, 2 and 3 years or older), thereby increasing samplesizesforadultsex-yearclasses.Bootstrapsamplesforrealizedsurvival(J)andbreedingsuccess(b)werejointlydrawn(withreplace-ment) at the level of individualswithinyears for each sex-age-yearclass.Thissamplingregimeisnecessarytomaintainanycovarianceinb and Jwithinindividuals,andtocapturestochasticvariationamongindividualswithinyears,whichgeneratesthedemographicstochastic-ityofinterest(Engenetal.,2010,AppendixS1).

Capture-mark-recapture models were fitted in program MARK(White&Burnham,1999).Other analyseswere run in rv2.15.2 (RDevelopment Core Team 2012), using package Popbio (Stubben &Milligan,2007)forpopulationprojections.

2.3 | Molecular genetic estimation of Ne

2.3.1 | DNA sampling and genotyping

Sinceadultchoughsmoultduringbreeding,DNAwasnon-invasivelysampledbycollectingmoultedfeathersfromnestsitesvisitedduring2007–2014.ThisprovidedDNAsamplesfromamixed-agesampleofadult individualsnestingacross Islay.DNAwasextracted from3to5mmclippingsofthelowerfeathercalamus,usingstandardammo-niumacetateprecipitation(Hogan,Cooke,Burridge,&Norman,2008;Trasketal.,2016).All samplesweregenotypedat13microsatellitelocideveloped forchoughsandpolymorphic in the Islaypopulation(Wenzel,Webster,Segelbacher,Reid,&Piertney,2011,AppendixS4).However,one locus (Ppy-005)didnotconformtoHardy-Weinbergequilibrium and hence was excluded from analyses (Appendix S4).Duplicatesamplesfromthesame individualwere identifiedandex-cluded to ensure that Ne estimates were not downwardly biased (AppendixS4).

2.3.2 | Genetic estimators of Ne

The best-evaluated single-sample molecular genetic estimator ofNe utilizes linkage disequilibrium (LD), andmeasures associationsbetween alleles at different neutral loci compared to expecta-tions given randommating and binomial sampling (Hill, 1981). Inisolated, finite populations with random mating, LD stems fromgenetic drift and can be used to estimate Ne (Hill, 1981).We im-plemented a single-sample LD estimator of Ne in NeEstimator v2.01(Doetal.,2014;Waples&Do,2008).Torelaxtheassump-tion of random mating given the chough’s mating system, a model that assumes random initial mating followed by lifelong monogamy (Waples,2006)wasused.Furthermore,sinceHill’s(1981)equations

(3)σ2dg=

∑

σ2dgiui

6  |    Journal of Animal Ecology TRASK eT Al.

can give downwardly biased estimates of Ne if the sample size isless than true Ne (England, Cornuet, Berthier, Tallmon,& Luikart,2006),abias-correctedanalysiswhichadjustsforsamplesizewasimplemented(followingWaples,2006).Finally,sincelowfrequencyalleles canupwardlybiasNe estimates, alleles at frequency <0.02 wereexcluded (followingWaples&Do,2010).Sensitivitytosuchexclusions was examined by repeating analyses with exclusionthresholdsof0.01,0.02and0.05.AlthoughtheLDmethodassumesdiscrete generations, it can give reasonably unbiased estimates of Neforspecieswithoverlappinggenerationsgivengenotypesfromamixed-age sample of adults, and if the number of cohorts rep-resented roughly equals the generation length (Waples, Antao,&Luikart,2014).Theseconditionsarefulfilledbygenotypedatafromadultchoughssampledduring2007–2014.

We additionally implemented an approximate Bayesian compu-tation(ABC)single-sampleestimatorofNeusingprogramONeSAMP(Tallmon,Koyuk,Luikart,&Beaumont,2008),whichcompareseightsummarystatisticscalculatedfromthefocalpopulationtothesamestatisticsfor50,000simulatedpopulationswithNe drawn from within

specifiedlowerandupperpriorboundaries.Twodifferentpriorswerespecified;2–180,withtheupperpriorreflectingthetheoreticalmax-imum Ne of 2N, and 2–100, as Ne is generally lower than 2N in wild populations (Frankham, 1995;Nunney& Elam, 1994). Since single-samplegeneticestimatorsofNeutilizesampledbreedingadults,N was takenasthetotalnumberofbreedingadultsinthepopulation(Palstra&Fraser,2012).As theeightONeSAMPsummarystatisticsmaybedifferently affected by Neofpreviousgenerations(Wang,2009)andpriorsweredefinedbycurrentN,genotypedatafromadultssampledduring 2012–2014 were used.

3  | RESULTS

3.1 | Mean demographic rates and projection matrix

Oneyear-oldchoughsneverattemptedtobreed,andtheprobabilityofbreeding(ci) increased to one in individuals aged 4 years or older in bothsexes(Figure1a,AppendixS1).Acrosssampledindividualsthatattemptedtobreed,meanbreedingsuccess (mi) increased from age

F IGURE  1 Age-andsex-classspecificestimatesof(a)annualsurvivalprobability(Pi,diamonds)with95%confidenceintervals,andprobabilityofattemptingtobreed(ci,greyfilledsymbols);(b)breedingsuccess(numberoffledglingsproduced)ofindividualsthatattemptedtobreed(mi),withassociatedstandarderrors;(c)reproductivevalues(vi),and(d)stableagedistribution(ui).Femalesandmalesare,respectively,indicatedby(a,b)circlesandtriangles,and(c,d)greyandwhitebars.SamplesizesaresummarizedinTableS2

Rep

rodu

ctiv

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Pro

babi

litie

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l &at

tem

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Sta

ble

age

dist

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ion

Bre

edin

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(b) (d)

(a) (b)

Age class

     |  7Journal of Animal EcologyTRASK eT Al.

twotothree,andtendedtobelowerin4-year-oldsandhigheragaininindividualsaged5yearsandolder(Figure1b,AppendixS1).Meanannual survival probabilities (Pi) increased from first-year throughsecond-yeartoadult(Figure1a,AppendixS1).

Consequently,reproductivevalues,vi, increased with age and were slightlyhigherformalesthanforfemalesinallage-classes(Figure1c,Appendix S1).As expected, the proportional representation of age-classes measured by the stable age distribution values, ui, decreased acrossinitialageclassesbutwasgreatestforthepooled≥5age-class.Age-specificui values were equal for females and males because val-ues of Piweresetequal(Figure1a,d,AppendixS1).Populationgrowthratewas approximately equal for themale and female submatrices(λfem=0.964,λmale=0.967),sothatforthetwo-sexmatrixλ=0.965and generation time T = 6.7 years.

3.2 | Sex- age- year specific demographic rates

Reproductive success (bi), calculated as the number of 1year-oldsproducedperindividualperyear,variedamongsex-age-yearclasses(Figure2a,Appendix S1).Medianbiwas zero in all sex-age classes,

but higher values occurred most frequently in females and males aged 5yearsorolder(Figure2a,b).Realizedsurvival(Ji) also varied among sex-age-year classes; as expected given the estimated P2 and Pad, fewer 1year-olds survived to age two than survived througholderages (Figure2c,d,AppendixS1). Therewasno consistentlypositiveor negative covariance between J and b across individuals within each year(grandmeancovariance=0.04,AppendixS1).

3.3 | Demographic estimate of Ne

Given the two-sex five-ageclassmodel,Ne/N = 0.21 and σ2dg

= 0.71 (Figure3,AppendixS1).Giventhe2014censusofN = 141 choughs (including adults and sub-adults) and generation time T = 6.7 years, then Ne=30.Thereducedthree-ageclassmodelreturnedonlysmallchanges in the point estimates,with fairly tight 95%bootstrapCIs(Ne/N=0.23, 95% CI: 0.21–0.29; σ2

dg=0.67, 95% CI: 0.53–0.75,

AppendixS1).Thecontributiontototalσ2

dgvariedamongsex-ageclasses,such

that older age classes contributed more than younger age classes (Figure3). For 1-, 2- and 4-year-olds the estimated components of

F IGURE  2 Proportionsof(a)femalesand(b)malesineachage-classthatproduced0–41-year-oldoffspring(b),and(c)femalesand(d)malesineachage-classthatsurvivedtothefollowingyear(J).Onpanels(a)and(b),theinteriorx-axesshowtheb values and exterior x-axesshowthebreederageclasses,where‘5’includesindividualsaged≥5years.Nvaluesdenotesex-agespecificsamplesizesexceptforageonewheresexeswereunknownandhenceNdenotesthepooledsamplesize.Jisconsequentlyassumedtobeequalfor1-year-oldfemalesandmales(c,d)

Pro

port

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(c) (d)

(a) (b)

8  |    Journal of Animal Ecology TRASK eT Al.

σ2dgweresimilarforfemalesandmales.However,3-year-oldfemales

contributedmore than 3-year-oldmales toσ2dg (Figure3). This pat-

ternwasreversedforindividualsaged5yearsorolder,wheremalescontributed more than females to σ2

dg (Figure3), reflecting a strong

positivecovariancebetweenJ and bacrossmalesin1year(AppendixS1).Despitethesesex-ageclassdifferences,overallmaleandfemalecontributions to σ2

dgweresimilar(meansof0.61and0.57respectively,

Figure3,AppendixS1).

3.4 | Genetic estimates of Ne

Across the 13 microsatellite loci, the number of alleles per locusrangedfromtwotosixandobservedandexpectedheterozygositiesrangedfrom0.06to0.91and0.09to0.72respectively(fullmicrosat-ellitemarkersummarystatisticsareprovidedinAppendixS4).

Thesingle-sampleLDmethodestimatedNe=50(95%CI:37–69,usinggenotypesfrom93individualchoughs)givenacriticalallelefre-quency of 0.02. Neestimateswerelarger(upto38%larger),withwider95%CIs,whenlowfrequencyalleleswereincluded(AppendixS4).TheABCmethodestimatedNe=26(95%CI:21–36,usinggenotypesfrom71individualchoughs).Thisestimatewasrobusttothedifferentupperpriorboundaries(AppendixS4).

4  | DISCUSSION

Estimationofeffectivepopulationsize,Ne, and identification of un-derlyingcomponentsofdemographicvariancethatreduceNe below N,isrequiredtounderstandinter-relationsbetweendemographyandevolutionaryprocesses(Charlesworth,2009),andtopredictpopula-tionviabilityandinformpopulationmanagementstrategies(Frankhametal., 2014; Hare etal., 2011; Mace & Lande, 1991). However,

estimatingandinterpretingNeforwildpopulationsisextremelychal-lenging, particularly given overlapping generations, environmentaland demographic stochasticity and heterogeneity and resulting dy-namicage-structure,andgivengene-flowstemmingfromimmigration(Caballero,1994;Wang&Whitlock,2003;Waplesetal.,2011).Sucheffects could substantially impactNe but are often ignored (Engenetal., 2005; Engen, Lande etal., 2007), impeding understanding ofevolutionaryprocessesandpopulationviabilityanalyses.Weusedde-tailedindividual-andpopulation-leveldemographicdatatoestimateNe/N,anditsunderlyingcomponentsofsex-andage-specificdemo-graphicvariance,inasmallandapparentlyisolatedred-billedchoughpopulation, while accounting for environmental and demographicstochasticitybyconsideringreproductivevalue.Additionally,weusedtwosingle-samplegeneticestimatorsofNe toencompasseffectsofany unobserved immigration.

4.1 | Ne and demographic variance

OurdemographicestimateofNe/NforIslay’schoughpopulationwas0.21.This issubstantially lowerthanthemeanvalueof0.65±0.15SD estimatedacrossdiversebirdpopulations,whereNe/N was cal-culatedfrommeanlife-tabledataassumingconstantpopulationsizeandage-structureandhencenoenvironmentalordemographicsto-chasticityoradditionaldemographicheterogeneity(usingthe‘AgeNe’estimator,Waplesetal.,2013).The lowNe/N in choughs arose be-cause theestimated total demographic variancewas relativelyhigh(σ2

dg=0.71) compared to other bird species with similar generation

times.Specifically, the femaledemographicvariancecomponent forchoughs of σ2

d=0.57exceedsthevalueofσ2

d≈0.25forageneration

timeof7years(extrapolatedfromSæther,Engen,PapeMølleretal.,2004). Furthermore, the total σ2

dg estimated for choughs is notably

highforamonogamousspecies,wherereproductiveskewmightbeexpected to be relatively small (Sæther, Engen, Lande etal., 2004).This high σ2

dg is perhaps not surprising since first-year survival is

knowntovaryconsistentlyamongnestsitesonIslay,creatingaddi-tionaldemographicheterogeneityandinfluencingpopulationdynam-ics(Reidetal.,2006).Similarlyhighdemographicvariance,andsmallNe/N,might also arise in other populationswhere individual repro-ductive success varies with territory quality (e.g. Griffen &Norelli,2015;Sergioetal.,2009;VandePol,Bruinzeel,Heg,VanDerJeugd,&Verhulst,2006).However, commonlyusedsoftwares forpopula-tion viability analysis often assume a Poisson distribution of family sizes(e.g.RAMAS,Akçakaya,2002;althoughseeVORTEXv.10,Lacy&Pollak, 2014),meaning that demographic variancewill be under-estimated and Ne/Noverestimated(Frankhametal.,2014;Kendall&Wittmann,2010).Furthermore,ourestimateofNe = 0.21 for choughs mayitselfbeaslightoverestimate,becausetheEngenetal.(2010)de-mographicestimator,likeotherdemographicestimatorsthatconsiderage-structure(e.g.‘AgeNe’,Waplesetal.,2011,2013),assumeszerodemographiccovariancewithinindividualsacrossyears.Forrelativelylong-livedspeciesthatshownest-siteandmatefidelity,individualre-productivesuccessmightbepositivelycorrelatedacrossyears(Hamel,Gaillard,Festa-Bianchet,&Côté,2009;Lee,Engen,&Saether,2011).

F IGURE  3 Totalpopulationdemographicvariance(σ2dg,‘Total’),

sex-specificcomponentsofσ2dg(‘Sextotals’)andcontributionstoσ2

dg

fromeachsex-ageclass(Age1–5+years).Darkgreyandlightgreybarsindicatefemaleandmalecomponents,respectively.Whiskersdenote95%bootstrappedconfidenceintervals.Bootstrapconfidenceintervalsdidnotincludethepointestimatefor3-year-oldmalesandarenotshown(seeAppendixS1)

     |  9Journal of Animal EcologyTRASK eT Al.

Such persistent individual differences can create additional demo-graphicheterogeneity,whichcouldincreasethetotalvarianceinlife-timereproductivesuccessandtherebyfurtherreduceNe/N. Indeed, individualreproductivesuccess(b)wasmoderatelyrepeatablewithinindividualsacrossyearsinthefocalchoughpopulation(R=.22,95%CI: 0.00–0.40, Appendix S1). Future developments of demographicestimators of Neshouldaimtoincorporatesuchpersistentindividualdifferencesalongsideother formsofdemographic stochasticity andheterogeneity.

4.2 | Causes of demographic variance

AmajoradvantageofestimatingNe/Nusingdemographicestimatorsthatconsiderage-structure is thatsuchestimatorspotentiallyalloweach sex and/or age class’s contribution to total σ2

dg, and hence to re-

ducing Ne/N, tobeexplicitlyquantified(Engenetal.,2010;seealsoWaplesetal.,2013).Criticaldemographicclasses that influenceNe, andthereby influenceapopulation’sevolutionary trajectoryandvi-ability,canthenbeidentified.ThedetaileddemographicdataavailableforIslay’schoughpopulation,wheresurvivalandanyreproductionofadultsandsub-adultscanbedirectlyobserved,andimmigrationisap-parentlyveryrareorabsent,providesanunusualandextremelyvalu-ableopportunity topartition totaldemographicvarianceacrosskeysex-ageclasses.

Our analyses showed that 4-year-olds and the defined terminalage-class comprising adults aged 5years or older contributedmostto σ2

dg(Figure3).Thismightbeexpected,sincetheseclassesencom-

passmostbreedingadultsandhenceencompasssubstantialamong-individualvariationinreproductivesuccess.Overall,maleandfemalecontributions to total σ2

dgweresimilar(Figure3).Thisconcurswiththe

similar sex-specific components of demographic variance (0.16 and0.14 for females andmales respectively) estimated in Siberian jays(Perisoreus infaustus), a corvidwith a similar life-history to choughs(Engen etal., 2010). However, estimates of sex-specific demo-graphic variances in populations of other bird species have shownlargercontributionsfrommalesthanfemales(e.g.greatreedwarblerAcrocephalus arundinaceus,Sæther,Engen,Landeetal.,2004;housesparrow,Engen,Ringsbyetal.,2007).Further,althoughtotal femaleandmalecomponentsofσ2

dgweresimilarinchoughs,theage-specific

contributions differed between the sexes. Specifically, ≥5year-oldmales contributed more to σ2

dgthan≥5year-oldfemales,whereastwo

and 3-year-old females contributed more than two and 3-year-oldmales(Figure3).Thus,althoughoverallsex-specificcomponentsofσ2

dg

were similar, our analyses illustrate that theremay be key sex-age-specificprocessesactingatsmallpopulationsizesthatdriveevolution-aryprocessesandpopulationviability,throughtheirinfluenceonNe. Thesesex-agespecificdifferencesmayreflectpersistentpopulationor life-historycharacteristics,ormay reflect stochasticdemographicprocessesactingatsmallpopulationsizes.Ingeneral,estimatesofNe fromdemographicdatacommonlyonlyconsiderthefemalecompo-nentofdemographicvariance(Frankham,1995;Grant&Grant,1992;Nunney&Elam, 1994;Waples etal., 2013).Our results show that,even for monogamous species like choughs, sex-age-class specific

contributions to demographic variance should be incorporated intocalculations of Netoavoidbiasandidentifykeydemographicclasses,andhenceelucidatepotentialunderlyingecologicalmechanisms.

4.3 | Genetic and demographic approaches

The demographic estimate of Ne/N = 0.21 yielded an estimate of Ne≈30,givenN≈141.Twodifferentsingle-samplegeneticestima-tors based on LD and ABC further supported the conclusion thatNe≤50.DirectquantitativecomparisonbetweendifferentNe estima-tors isdifficult (Robinson&Moyer,2013),not leastbecausedemo-graphicestimatorsofNereflectprocessesintheoffspringgenerationand estimate Nev(Kimura&Crow,1963),whilesingle-samplegeneticestimatorsreflectprocessesintheparentalgenerationandestimateNei (Crow&Denniston,1988).GeneticestimatesofNei may there-fore lag behind changes in N by at least one generation. Indeed, Nei estimated from LDmay be influenced by processes occurringmul-tiplegenerationspreviously,asLDcan takemultiplegenerations tobreakdown(Wang,2005;Waples,2005).Geneticestimatorsalsoin-corporateeffectsofimmigrationandgeneflow,whichdemographicestimatorsdonot(e.g.Baalsrudetal.,2014).However,effectsonNe estimateswilldependon theextentof immigration. Immigrationoffew genetically differentiated individuals could cause Ne to be under-estimated, because LD generated by immigrationwill be attributedtodrift.Conversely,highmigrationratescouldcauselocalpopulationNetoapproachmetapopulationNe(Gilbert&Whitlock,2015;Wang,2005;Waples&Do,2008).

Inpractice, theLDestimatorgavethe largestestimateofNe for Islay’schoughpopulation,whichmayreflectthesomewhatlargerpastpopulationsize(e.g.78breedingpairsin1986,Finney&Jardine,2003;AppendixS2).TheABCestimatorgaveasimilarestimateofNe to the demographic estimator. Since theONeSAMPABCapproachutilizesmultipledifferentsummarystatisticstoestimateNe, the exact num-berofpreviousgenerationstowhichtheestimateapplies isunclear(Wang,2009).However,thisestimatormightbelessbiasedbyNe of previousgenerationsthantheLDestimatorandmaythereforebetterapproximatecurrentNe inapopulationofvaryingN.Thealternativeexplanation that the LD estimator is detecting immigration seemsunlikely,asthis isnotsupportedbytheABCestimator.Additionally,fortheLDapproachtogiveanupwardlybiasedestimateofNe there would need to be considerable successful immigration into the Islay population,which is unlikely to have gone unobserved during pop-ulationmonitoring and ringing of all UK chough populations.Thus,there is likely tobe littleorno immigrationand resultinggene flowthat might act to increase genetic diversity and Ne in Islay’s chough populationbeyondthatcalculatedfromobservedNanddemography.

4.4 | Conservation management implications

OurinsightsintothemagnitudeanddemographiccausesofNe/N given dynamicage-structurearealsodirectlyrelevanttoconservationstrat-egy for the focal choughpopulation. The demographic and geneticestimators all showed that Ne≤50,whichisbelowtherule-of-thumb

10  |    Journal of Animal Ecology TRASK eT Al.

minimum recommended to ensure short-term population viability(Frankhametal.,2014;Mace&Lande,1991).Specifically,thebase-line per-generation increase in inbreeding, and the correspondingexpectedrateoflossofgeneticdiversitypergeneration,canbecal-culated as:

(Falconer & Mackay, 1996). From the demographic estimate ofNe≈30,ΔFwillbe≈0.02perinitialgenerationinthecontinuedab-senceofimmigration.Thisvalueisrelativelyhigh,implyingincreas-ingexpressionof inbreedingdepressionand reducedevolutionarypotential,andhencereducedpopulationviabilityinboththeshort-termandlong-term(Frankhametal.,2014;Keller&Waller,2002).Genetic management should therefore be urgently considered. Since the observed high σ2

dg stems partly from spatial variation in

offspring survival to age one (Reid etal., 2006), future strategiescould aim to reduce this variation through targeted management of territorieswith current low productivity (e.g. through targetedhabitat improvement or supplementary feeding of specific breed-ingadults).Additionally,observedsex-agespecificcontributionstoσ2dgsuggeststrategiestoalleviatedemographicvariancecouldfocus

on different age classes in females vs. males. However, strategies to decrease σ2

dg and hence increase Ne/N may be insufficient to en-

sure futureviabilityof Islay’schoughpopulation,ascurrent levelsof inbreeding and genetic diversity would not be decreased and in-creased,respectively.Furthermore,becauseλ < 1, N will continue to decrease. Indeed, the low λmaypartlyreflectinbreedingdepressioninsurvivalandreproduction(e.g.Libergetal.,2005;O’Gradyetal.,2006).Translocationsmayconsequentlyberequiredtore-establishconnectivity between Islay andotherUK choughpopulations andthereby increase genetic diversity and ameliorate inbreeding. Re-establishment of gene-flow in small, fragmented populations hasbeen associated with increased fitness and λ (‘genetic rescue’) indiversespecies(Frankham,2015;Hostetler,Onorato,Jansen,&Oli,2013; Laikre etal., 2016). Such pro-active genetic management,alongsidehabitatmanagement,mightbeessential toensure long-termpopulationviability.

ACKNOWLEDGEMENTS

WethankeveryonewhohelpedwithfieldworkonIslay,inparticularSueBignalandPatMonaghan,aswellasallland-ownersandfarmerswhoallowedaccesstonestsites.WethankBernt-ErikSӕther,SteinarEngen and Henrik Jensen for their generous help and discussions.A.E.T.wasfundedbytheNaturalEnvironmentResearchCouncilandScottish Natural Heritage. J.M.R. was supported by the EuropeanResearch Council.

AUTHORS’ CONTRIBUTIONS

A.E.T.andJ.M.R.conceivedtheideasandundertookthedemographicdataanalyses;A.E.T.undertookmoleculargeneticanalyses,andS.B.P.

assistedwithlabwork;E.B.,D.McC.,J.M.R.andA.E.T.collectedfielddata;A.E.T.wrotethemanuscript,assistedbyJ.M.R.

DATA ACCESSIBILITY

Alldataassociatedwith thisarticle is availableat theDryadDigitalRepository https://doi.org/10.5061/dryad.68kk0 (Trask, Bignal,McCracken,Piertney,&Reid,2017).

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How to cite this article:TraskAE,BignalEM,McCrackenDI,PiertneySB,ReidJM.Estimatingdemographiccontributionstoeffectivepopulationsizeinanage-structuredwildpopulationexperiencingenvironmentalanddemographicstochasticity. J Anim Ecol. 2017;00:1–12. https://doi.org/10.1111/1365-2656.12703