Fish and Fisheries. 2019;00:1–15.  | 1wileyonlinelibrary.com/journal/faf

Received:19October2018  |  Revised:16May2019  |  Accepted:18June2019DOI: 10.1111/faf.12391

O R I G I N A L A R T I C L E

Density‐ and size‐dependent mortality in fish early life stages

Leif Christian Stige1  | Lauren A. Rogers2 | Anna B. Neuheimer3,4 | Mary E. Hunsicker5 | Natalia A. Yaragina6 | Geir Ottersen1,7 | Lorenzo Ciannelli8 | Øystein Langangen1 | Joël M. Durant1

1DepartmentofBiosciences,CentreforEcologicalandEvolutionarySynthesis(CEES),UniversityofOslo,Oslo,Norway2AlaskaFisheriesScienceCenter,NationalMarineFisheriesService,NationalOceanicandAtmosphericAdministration,Seattle,WA,USA3AarhusInstituteofAdvancedStudies(AIAS),AarhusUniversity,AarhusC,Denmark4DepartmentofOceanography,SchoolofOceanandEarthScienceandTechnology,UniversityofHawai’iatMānoa,Honolulu,HI,USA5FishEcologyDivision,NorthwestFisheriesScienceCenter,NationalMarineFisheriesService,NationalOceanicandAtmosphericAdministration,Newport,OR,USA6PolarResearchInstituteofMarineFisheriesandOceanography(PINRO),Murmansk,Russia7InstituteofMarineResearch,Bergen,Norway8CollegeofEarth,Ocean,andAtmosphericSciences,OregonStateUniversity,Corvallis,OR,USA

ThisisanopenaccessarticleunderthetermsoftheCreativeCommonsAttributionLicense,whichpermitsuse,distributionandreproductioninanymedium,providedtheoriginalworkisproperlycited.©2019TheAuthors.Fish and FisheriesPublishedbyJohnWiley&SonsLtd.

CorrespondenceLeifChristianStige,DepartmentofBiosciences,CentreforEcologicalandEvolutionarySynthesis(CEES),UniversityofOslo,P.O.Box1066Blindern,N‐0316Oslo,Norway.Email:l.c.stige@ibv.uio.no

Funding informationResearchCouncilofNorway(RCN),Grant/AwardNumber:267577,280468and255460/E40;AarhusUniversityResearchFoundation(AarhusUniversitetsForskningsfond);EuropeanUnion'sSeventhFrameworkProgramme,MarieCurieActions,Grant/AwardNumber:609033;NationalScienceFoundationDivisionofEnvironmentalBiology,Grant/AwardNumber:1145200

AbstractTheimportanceofsurvivalandgrowthvariationsearlyinlifeforpopulationdynamicsdependsonthedegreesofcompensatorydensitydependenceandsizedependenceinsurvivalatlaterlifestages.Quantifyingdensity‐andsize‐dependentmortalityatdifferent juvenilestages is therefore important tounderstandandpotentiallypre‐dicttherecruitmenttothepopulation.Weappliedastatisticalstate‐spacemodel‐lingapproachtoanalysetimeseriesofabundanceandmeanbodysizeoflarvalandjuvenilefish.Thefocuswastoidentifytheimportanceofabundanceandbodysizeforgrowthandsurvivalthroughsuccessivelarvalandjuvenileageintervals,andtoquantifyhowthedynamicspropagatethroughtheearlylifetoinfluencerecruitment.Wethusidentifiedbothrelevantagesandmechanisms(i.e.densitydependenceandsizedependence insurvivalandgrowth) linkingrecruitmentvariabilitytoearly lifedynamics.Theanalysiswasconductedonsixeconomicallyandecologically impor‐tant fishpopulations fromcold temperate and sub‐arcticmarineecosystems.Ourresultsunderscoretheimportanceofsizeforsurvivalearlyinlife.Thecomparativeanalysissuggeststhatsize‐dependentmortalityanddensity‐dependentgrowthfre‐quentlyoccuratatransitionfrompelagictodemersalhabitats,whichmaybelinkedtocompetitionforsuitablehabitat.Thegeneralityofthishypothesiswarrantstestinginfutureresearch.

K E Y W O R D S

Bayesianstate‐spaceanalysis,comparativeanalysis,growth–survivalrelationships,populationregulation,predation,recruitmentdynamics

2  |     STIGE ET al.

1  | INTRODUC TION

Understanding how processes early in life influence year‐classstrength has been a central topic of fisheries research for morethanacentury.Thisisbecauseyear‐to‐yearvariationsinyear‐classstrengthattheagewhenthefishenterintothefisheries(“recruit‐ment”) isamaindriverofchanges inpopulationsizeofmanyhar‐vestedmarinefishesandakeydeterminantofthenewharvestablebiomass (Hjort, 1914;Houde, 2008).Quantifying associations be‐tween changes in abundance and body size distribution throughearlylifeisanimportantsteptoexplain,andpotentiallypredict,fishrecruitment. Specifically, such quantificationmay reveal intercon‐nectionsbetweengrowth,survivalandpopulationregulation,and,therebytherelevanceofgrowthandsurvivalvariationsatdifferentearlylifestagesforrecruitment.

Changesinabundanceandmeanbodysizeduringtheearlylifestagesofmarine fishareoftencorrelatedbecauseofassociationsbetween the mean mortality rate, which influences abundance,and growth and size‐dependent mortality, which influence meanbodysize (Figure1).Severalecologicalprocesses link thechangesinabundanceandmeanbodysize.Forexample,predationmaysi‐multaneouslyinfluenceabundanceandsizedistributionbycausingsize‐dependentmortality,whilecompetitionmaydosobycausingdensity‐dependent growth and mortality (Bailey & Houde, 1989;Cushing,1995).

For apopulation topersistovermanygenerations, compensa‐torydensitydependencehastooperateforat leastsomepointofthelifecycle,sothatthepopulationgrowthratetendstoincreasewhenabundanceislowanddecreasewhenabundanceishigh;suchregulationcanoccurbylong‐termmean“input”rates(birthandim‐migration)scalingnegativelywithabundanceand/orby“loss”rates(mortalityandemigration)scalingpositivelywithabundance(Hassel,1975; Hixon, Pacala, & Sandin, 2002; Rose, Cowan, Winemiller,Myers, & Hilborn, 2001). For example, intra‐specific competitionforlimitedresourcessuchasfoodorhabitatcanpotentiallyleadtoincreasedmortalityorreducedfecunditywhenabundance ishigh.Othermechanismsfordensity‐dependentmortalityincludenumer‐ical or behavioural responses of predators, parasites and diseases(Bailey&Houde,1989;Hixonetal.,2002).Thecompensatoryden‐sity dependence is commonly assumed to take place early in lifeformostmarine fishes and is typically embedded in the relation‐shipbetweenthebiomassofspawnersandthenumberofrecruitsinfisheriesmodels(e.g.Ricker,1954,Beverton&Holt,1957).Thisassumptionappears tobevalid formanypopulations (Lorenzen&Camp,2018;Zimmermann,Ricard,&Heino, 2018), althoughden‐sity dependencemay alsooccur later in life for somepopulations(Andersen,Jacobsen,Jansen,&Beyer,2017).When in thepre‐re‐cruitmentperiodthedensitydependenceoccurs,warrantsfurtherinvestigation.Quantifying atwhich life stage density dependenceoccurs is important, for example, to assess population conse‐quences of environmental influences on abundances of fish eggsand larvae,assuchenvironmentaleffects tendtobedampened if

thesubsequentjuvenilestagesshowstrongcompensatorydensitydependence(vanGemert&Andersen,2018;Ohlberger,Rogers,&Stenseth,2014).

Competition can affect survival directly, for example throughstarvation mortality, or indirectly, by leading to reduced growthand development—which has survival consequences if mortalitydependsonsizeorstage.Inparticular,thereisstrongevidenceforcompensatory density dependence in growth during the early ju‐venile stage,which contributes to regulationof recruitmentwhencombinedwithincreasedmortalityatsmallbodysize(Houde,2008).Competition can also hypothetically lead to increasedmeanbodysizeathighabundance.Specifically,ifcompetitioncausesmortalitythatdisproportionallyaffectssmallindividuals,meanbodysizemay

1INTRODUCTION 2

2CASESTUDIES 3

3METHODS 4

3.1Correlationanalysis 4

3.2State‐spacestatisticalmodelsofage‐resolveddynamics

5

3.3Estimatingmodelparameters 5

3.4Hypotheticalexample 6

3.5Observationdata 6

4RESULTS 7

4.1Correlationanalysis 7

4.2Modeldiagnosticsandsensitivityanalysesforage‐resolveddynamics

7

4.3Across‐populationcomparison 7

4.4BarentsSeacodage‐resolvedresults 8

4.5BarentsSeahaddockage‐resolvedresults 8

4.6ScotianShelfandBayofFundyhaddockage‐resolvedresults

9

4.7BarentsSeacapelinage‐resolvedresults 9

4.8EasternBeringSeapollockage‐resolvedresults 10

4.9GulfofAlaskapollockage‐resolvedresults 10

4.10Inter‐cohortdensitydependence 10

5DISCUSSION 10

5.1Whendoessizeinfluenceabundance? 10

5.2Whendoesabundanceinfluencesize? 11

5.3Whenismortalitydensity‐dependent? 12

5.4Inter‐cohortdensitydependence 12

5.5Methodologicallimitationsandprospectsforfuturestudies

12

6CONCLUSIONS 13

ACKNOWLEDGEMENTS 13

REFERENCES 13

SUPPORTINGINFORMATION 15

     |  3STIGE ET al.

increaseand thiseffectmaycounteract thegrowth rateeffectofcompetition.

Ingeneral,mortalityratesoflarvalandjuvenilemarinefisheshavebeenfoundtodeclinewithbodysize(Bailey&Houde,1989;Sogard,1997),althoughforsinglestages,size–mortalityrelationshipsmaybeabsentorevenpositive(e.g.Pepin,2015).Akeymechanismbehindthegeneralpatternislikelytobesize‐dependentpredationmortal‐ity,assmallindividualsaretypicallyexposedtomorepotentialpred‐ators than large individuals and escape ability typically increaseswithbodysize(Bailey&Houde,1989).Fastgrowththroughthevul‐nerablesizerangesofearlylifestagesmaythenleadtohighsurvival(the'stagedurationhypothesis',Houde,1987).Furthermore,mortal‐ityratesmaydeclinewithbodysizebecausetolerancetostarvationandphysical extremesmaybehigher for larger individuals (Miller,Crowder,Rice,&Marschall,1988;Sogard,1997).Insuchcases,fastgrowthpriortoaperiodwithadverseenvironmentalconditions,forexamplethefirstwinteroflifeformanyhigh‐latitudespecies,maybeimportantforsurvivalthroughthatperiod(Sogard,1997).

Long‐term monitoring surveys of eggs, larvae and juvenilesexistforanumberofcommercialfishpopulations.Thetimeseriesdatahaveoftenbeencollectedtogetanearlyindicationofyear‐class strength to inform fisheries management (e.g. Dragesund,Hylen, Olsen, & Nakken, 2008, Bailey, Zhang, Chan, Porter, &Dougherty, 2012, McClatchie et al., 2014, Megrey, Hollowed,Hare,Maclin,&Stabeno,1996).Analysesofsuchtimeserieshaveshownthatreasonablepredictionsofrecruitmentcansometimesbeobtainedasearlyastheeggstage(Helleetal.,2000;Mukhina,Marshall,&Yaragina,2003),althoughprocessesatlateragesalsocomeintoplay(Bogstad,Yaragina,&Nash,2016;Stige,Hunsicker,Bailey,Yaragina,&Hunt,2013).Moreover,ithasbeenshownthatnot only abundance but also body size distribution of early lifestagesprovidesinformationonfutureyear‐classstrength(Bailey,2000;Campana,1996;Ottersen&Loeng,2000;Stigeetal.,2015).Such data can provide valuable insights into the mechanisms

that determine year‐class strength, such as effects of densitydependence and the connections between growth and survival.However,measurementerrorsandincompletetimeseriescompli‐cate interpretations,as illustratedbythefindingthatabundanceindices of older pre‐recruit life stages sometimes provide lessaccurate predictions of recruitment than indices of younger lifestages(Stigeetal.,2013).

We applied a statistical state‐space analysis approach on sixcommerciallyandecologicallyimportantfishpopulationsfromcoldtemperateandsub‐arcticmarineecosystems.Foreachpopulation,wequantifiedhowdeviationsintheabundanceandmeanbodysizeof a year‐class during early life propagated through subsequentpre‐recruit age intervals. We thus identified both relevant agesandmechanisms (i.e. density and size dependence in survival andgrowth) linking recruitment variability to early life dynamics. Thestate‐spaceapproach iswellsuitedtoaccount forcommon limita‐tionsinlong‐termtimeseriesdatasuchasmeasurementerrorsandincompletedatacoverage,andprovidesonecoherentanalysisthatlinksprocessesoccurringthroughmultipleageintervals.Ourresultsidentifiedprocessesandagesthatareimportantininfluencingyear‐class strength, andwhichwarrant increased attention in terms ofmonitoringandanalysistobetterunderstandandultimatelypredictrecruitmentvariations.Specifically,theresultsunderscoredtheim‐portanceoflargebodysizeearlyinlifeforstrongrecruitment,butalsoshoweddifferencesinthesurvivalvalueoflargebodysizeandin density dependence across life stages and species thatwe hy‐pothesizeareexplainedbyvariationsinthehabitatandlifehistoriesofthepopulations.

2  | C A SE STUDIES

Toobtainanin‐depthunderstandingoftheintertwinedprocessesofgrowthandsurvivalatearly lifestages,weselectedanumberof case studies based on populations for which we had accessto long‐term fishery‐independent time series of abundance andmeanbodysize forseveralpre‐recruitmentagegroups (Table1).These populations included three economically and ecologicallyimportant,andthereforewell‐monitored,speciesinthesub‐arcticBarentsSea (BS).ThethreefisheswerethegadoidsAtlanticcod(Gadus morhua,Gadidae)andhaddock(Melanogrammus aeglefinus,Gadidae),andtheforagefishcapelin(Mallotus villosus,Osmeridae).Togeneratehypothesesofgeneralpatternsthatmaybevalidbe‐yondtheBS,wealso includedthreecomparable,well‐monitoredgadoidpopulationsfromothersub‐arcticandcoldtemperateeco‐systems, one population of haddock and two ofwalleye pollock(Gadus chalcogrammus,Gadidae).Allspeciesarehighlyfecundwithlargeinterannualvariabilityinthenumberofoffspringthatsurviveto recruitment.

TheBScod(alsoreferredtoasNortheastArcticcod)iscurrentlytheworld's largestpopulationofAtlanticcod.TheBScodspawnsalongthenorthandwestcoastsofNorway,fromwhereeggs,larvaeandpelagicjuvenilesdriftwiththecurrentsintotheBS,whichisthe

F I G U R E 1  Schematicoutlineofmainprocessesthatlinkabundanceandmeansizeofayear‐classatsubsequentagesorstages(e.g.j=0,1,2and3yearsofage)

NjNj–1

LL SjSj–1

bj

Cj

Bj

cj

Nj: Year-class abundance at age jSj: Mean body size at age jbj: Density-dependent survivalBj: Density-dependent growth + survivalcj: Size-dependent survivalCj: Size-dependent growth + survival

4  |     STIGE ET al.

nurseryareaandthefeedingareaofadults(reviewedbyOttersenetal.,2014).Atanageofaround6months,thejuvenilesmovefrompelagictomoredemersalhabitats,andataround3years,theyenterintothefishery.

TheBShaddock(alsoreferredtoasNortheastArctichaddock)spawnsalongthewestcoastofNorwayandthewesternshelfbreakof theBS to thenorthofNorwayat around300 to600mdepth(Olsenetal.,2010).Thepelagiceggs,larvaeandjuvenilesdriftwiththecurrentsintotheBS,wherethejuvenileslargelyswitchtoade‐mersallifestyleintheirfirstfall.

TheBScapelinisasmallpelagicfishthatplaysakeyroleintheecosystemas themainpredatoronmesozooplankton,andpreyofcodandhaddockaswellasseveralotherfishspecies,seabirdsandmarinemammals (Yaragina&Dolgov,2009).TheBScapelin isalsofishedcommercially,with themain fisheries in recentdecades tar‐getingspawners (mostly3‐and4‐year‐olds).EggsarespawnedontheseaflooralongthesoutherncoastsoftheBSwheretheydevelopandhatchintolarvae.ThelarvaearepelagicanddriftnorthwardsandeastwardsintothenurseryareasinthecentralBS,which,togetherwiththenorthernBS,arefeedingareasofadults(Gjøsæter,1998).

HaddockonthesouthernScotianShelfandintheBayofFundy(SSBF)aredemersalandoccupywatersfromaround50to250mdepth(DFO,2006).Thehaddockfromthispopulationspawninbottomwa‐tersonoffshorebanks,principallyBrown'sBankbetweenNovaScotiaandGeorgesBank (DFO,2003;Shackell,Frank,Petrie,Brickman,&Shore,1999).Eggsarepositivelybuoyantandrisetopelagicwaters(10to50m)(Cargnelli,Griesbach,Berrien,Morse,&Johnson,1999).Eggsand larvaeareeither retainedonBrown'sBank (due toaclockwisegyrecirculation)oradvected,ofteninshore,forexample,intotheBayofFundy(Campana,Smith,&Hurley,1989).Larvaemetamorphoseatabout30to42daysanddescendtobottomwaterhabitats(Cargnellietal.,1999).Whileseasonalmigrationsoccur,thereislittleexchangewithotherhaddockpopulations(DFO,2006).

Walleye pollock is an ecologically and commercially importantspecies in the Eastern Bering Sea (EBS) ecosystem. They provide

forageforothercommerciallyimportantfishesandspeciesofcon‐servationconcernandsupportthelargestcommercialfisheryintheUnitedStates (around1.2million tons and>US$1billion annually,Hiattetal.,2011,Ianelli,Honkalehto,Barbeaux,Fissel,&Kotwicki,2016).Pollockarepelagicspawners,andtheyspawnalongtheoutercontinental shelf in theearly spring. In general, theyare semi‐de‐mersalandbecomeincreasinglydemersalwithage,althoughage‐2pollock are thought to school higher in the water column thanage‐1 (Duffy‐Andersonetal.,2003). Inmostyears,pollockrecruitto the fishery at age 4. The EBS pollock population ismost likelycomposedofmultiplespawningaggregationsvaryingintiming.Theearlierspawningaggregations(March)occurintheBogoslofIslandandUnimakPass regions, near theAleutian Islands. Later spawn‐ingaggregations(March–May)occuralongtheAlaskaPeninsulaandPribilofIslandsregion(Bacheler,Ciannelli,Bailey,&Duffy‐Anderson,2010;Hinckley,1987).

WalleyepollockintheGulfofAlaska(GOA),whilenotasabun‐dant as in the Bering Sea, do play a nodal role in the ecosystemasbothpredatorandprey (Gaichas&Francis,2008), and supportaUS$40Mfishingindustry(Dornetal.,2016). InMarchandApril,GOApollockgathertospawnprimarilyintheShelikofStraitregionbetweenKodiakIslandandtheAlaskaPeninsula.AsintheEBS,pol‐lock occupy midwater habitat across the shelf as age‐0 juveniles(Brodeur&Wilson,1996),movingtodeeperwaterwithage.

3  | METHODS

3.1 | Correlation analysis

For each fish population, we first conducted a simple correlationanalysisbetweenyear‐classstrengthandmeanbodysizeattheear‐liestagewithavailabledata,andyear‐classstrengthandmeanbodysizearound theageof recruitment to the fisheries.Pearson's cor‐relationswere computed for log‐transformed time series, consist‐entwiththescaleusedinsubsequentanalyses.Thesecorrelations

Population Yearsa Age classes analysed Size metric

BarentsSeacod 1959–2015 Larvae(~3mo.),age‐0(~5mo.),age‐1(~10mo.),age‐2,age‐3

Length

BarentsSeahaddock 1959–2015 Larvae(~3mo.),age‐0(~5mo.),age‐1(~10mo.),age‐2,age‐3

Length

ScotianShelfandBayofFundyhaddock

1970–2013 Age‐0(onlysize),age‐1,age‐2,age‐3,age‐4

Weight

BarentsSeacapelin 1959–2015 Larvae(~3mo.),age‐0(~5mo.),age‐1(~18mo.),age‐2

Length

EasternBeringSeapollock

1982–2016 Age‐1,age‐2,age‐3,age‐4 Weight

GulfofAlaskapollock 1979–2017 Larvae(~2mo.),age‐0(~6mo.),age‐1(12mo.),age‐2,age‐3

Mixedb

aTotalyearrange.Therewerefrequentlygapsinseveralofthetimeseries.bLengthforlarvaeandage‐0,weightforages1–3.Tofacilitateinterpretationofresults,loglengthsweremultipliedwith3(equivalenttocubictransformationoflengths)tobeonacomparablescaleaslogweights.

TA B L E 1  Summaryofdataseriesanalysed

     |  5STIGE ET al.

servedasmotivation fordevelopingstatistical state‐spacemodelsthat showed indetail the linksbetweenabundanceandbody sizeacrossmultipleageintervalsleadinguptorecruitment.

3.2 | State‐space statistical models of age‐resolved dynamics

All populations were analysed using a state‐space modellingframeworkforanalysingtimeseriesofabundanceandmeanbodysizeatdifferentages.Thefocuswastoidentifytherolesofabun‐danceandbodysizeforgrowthandsurvivalfromoneagetothenext.Year‐to‐year changes in abundanceandmeanbody sizeofayear‐classweredescribedbyamultivariatediscreteGompertzmodel,whichhastheadvantagethatitcanbewritteninalinearform and is also a good first‐order approximation ofmore com‐plexdynamics(Ives,Dennis,Cottingham,&Carpenter,2003).TheGompertzmodel differs from the commonly used Rickermodelforfishrecruitment (Ricker,1954) inthatthedensity‐dependentmortalityrateisassumedtoscalewithlog‐abundanceratherthanwith abundance. The support in the data for using a Gompertzmodelwasassessedforallpopulationsandages(see“Estimatingmodelparameters”).ThemodelstructurewasbasedonFigure1andisdescribedbythefollowingequations:

Here,Ni,jistheabundanceofayear‐classborninyeariatanagej. Si,jisaveragebodysize(measuredaslengthorweightdependentonpopulation;seethesection“Observationdata”).PredictoreffectsinEquation1,describingchangesinlog‐abundance,haveastraightfor‐wardinterpretationintermsofeffectsoninstantaneousmortalityrate(e.g.Ivesetal.,2003).ThiscanbeseenbywritingEquation1onarithmeticscale:

Here,ri,jistheinstantaneousrateofchangeinabundance,thatis,immigration−(mortality+emigration)ratesforagivenyearandageinterval. If immigrationandemigrationcanbe ignored,Equation4captureslinearandadditiveeffectsoflog‐abundanceandlog‐sizeonthe instantaneousmortality rate.Correspondingly,Equation2canbewrittenonarithmeticscaleasfollows:

Here,gi,jistheinstantaneousrateofchangeinmeanbodysize,whichreflectsgrowthandsize‐dependentsurvival.Theage‐spe‐cificintercept(aj)inEquations1and4reflectsthelevelofdensity‐independent mortality and, if relative indices are used, scaling.Note that for convenience,we refer to effects of abundance as

densitydependence,assumingthatyear‐classabundanceisarel‐evantmeasureofcrowding.Inasupplementaryanalysis,wecon‐sidered, however, an alternative model that explicitly includedinter‐cohortdensitydependence(Ricard,Zimmermann,&Heino,2016),byaddingeffectsofyear‐class i−1toEquations1and6.Coefficientbjquantifiesdensitydependenceinmortality(withnodensitydependenceatb=1,completecompensationatb = 0 and overcompensationatb<0).Coefficientcjquantifiestheeffectofmeanbodysizeonsurvival.ThecoefficientBjinEquations2and6 quantifies the effect of abundance on the instantaneous rateofchangeinmeanbodysize.CoefficientCjquantifiescompensa‐tioninbodysizewithage(withnocompensationofanomaliesinbodysizeatC=1,completecompensationatC = 0 and overcom‐pensationatC<0).ε and ζ arenormallydistributed (potentiallycorrelated) process errors with means zero. The process errorscapture effects of environmental conditions not explicitlymod‐elled.Theequations for theyoungest age analysedonly includetheinterceptandprocessnoiseterms.

Apossibledrawbackofthismodelformulationisthatwithsomeparametervalues,year‐classabundancemaybepredictedtoincreasewithage.Inourempiricalanalysis,thisfeaturemainlyaffectsthein‐terpretationoftheresults,meaningthatposteriordistributionsmayincludebiologicallyunrealisticparametervalues(asisoftenthecaseinstatisticalanalyses).Thismodelformulationsimplified,however,theinclusionofrelativeabundanceindiceswithunknownscalingtotrueabundance,aswedidnothavetoestimatethescalingfactors(whichwouldhavebeenstronglycorrelatedwiththelevelsofden‐sity‐independentmortality).

Themodelwasfitinastate‐spaceframework,wherebyN and S wereconsideredunobservedstatevariablesthatwerelinkedtotheobservationsthroughanobservationmodel.Thisway,uncertaintiesaboutbiologicalprocessesandobservationnoisewereexplicitlyac‐countedfor,toprovideunbiasedparameterestimatesandappropri‐ateconfidencebands(Clark&Bjørnstad,2004).Theapproachalsoaccommodatedmissing values in the time series. Specifically, theobservedabundanceŃi,jandbodysizeŚi,jwerelinkedtoNi,j and Si,j accordingtoEquations7and8:

Here,e and z are independentandnormallydistributedobser‐vationerrorswithmeanszeroandstandarddeviationsσŃj and σŚj.

3.3 | Estimating model parameters

All parameters of the model were estimated jointly by using aBayesian Markov Chain Monte Carlo (MCMC) approach. For thispurpose,weusedtheprogramJAGS(JustAnotherGibbsSampler)andtherjagsandR2jagspackagesofR(Plummer,2016).Thelikeli‐hood functionwascreatedbasedon themodeland thedata, and

(1)ln(

Ni,j

)

=aj+bj ⋅ ln(

Ni,j−1

)

+cj ⋅ ln(

Si,j−1)

+ �i,j

(2)ln(

Si,j)

=Aj+Bj ⋅ ln(

Ni,j−1

)

+Cj ⋅ ln(

Si,j−1)

+ �i,j

(3)Ni,j=exp(

ri,j)

⋅ Ni,j−1, where

(4)ri,j=aj+(

bj−1)

⋅ ln(

Ni,j−1

)

+cj ⋅ ln(

Si,j−1)

+�i,j

(5)Si,j=exp(

gi,j)

⋅ Si,j−1, where

(6)gi,j=Aj+Bj ⋅ ln(

Ni,j−1

)

+

(

Cj−1)

⋅ ln(

Si,j−1)

+�i,j

(7)ln(

Ni,j

)

= ln(

Ni,j

)

+ei,j

(8)ln(

Si,j

)

= ln(

Si,j)

+zi,j

6  |     STIGE ET al.

in combinationwith thepriordistributionsof theparameters, theposteriordistributionswereestimated.

Wemodelledcorrelatedprocesserrorsbydrawingεi,j(Equation1) from a normal distribution with standard deviation σNj and by drawingζi,j(Equation2)fromanormaldistributionwithstandardde‐viation σSjandaddingρj · εi,j/σNj.Wethusestimatedthreevarianceparameters,σNj,σSj and ρj,foreachagej.Thevarianceofεi,jisσNj

2,thevarianceofζi,jisσSj

2+ρj2andthecovariancebetweenεi,j and ζi,j

isρj · σNj.AsrecommendedbyIvesetal.(2003),weusedbestguessesof

observationerrorvarianceswhenpossible.Toobtainconvergencewhenwehadnoinformationonthemagnitudeofobservationer‐rors,theobservationerrorvariancewasgenerallyassumedtobethesameforallyearsandidenticaltothecorrespondingprocesserrorvariance(i.e.σŃj

2 = σNj2,σŚj

2 = σSj2+ρj

2).Inasensitivityanal‐ysis,wemultiplied the observation error standard deviations byeither0.5or1.5andassessedeffectsonposteriorparameterdis‐tributions.Aspartofthesensitivityanalysis,standarddeviationsofobservationerrors thatwereassumedknownweremultipliedwith1.5(butnotwith0.5)toassesstheinfluenceofpossibleun‐knownerrorsources.Forsomeofthemostdata‐richpopulations(BScodandBScapelin),unknownobservationerrorvarianceswereestimatedfromthedata(independentofprocesserrorvariances).

Priordistributions forparameters in theprocessmodelwereuniformandbroadtoletthedatadrivetheinferences.Wechosethe following uniform prior distributions of model parameters.Interceptsaj,Aj: (−20,20),densitydependenceinsurvivalbj: (−1,1),densitydependenceinsizechangesBj:(−1,1),sizedependenceinsurvivalcj:(−20,20),sizedependenceinsizechangesCj:(−1,1),varianceparametersσNj,σSj,σŃj,σŚj: (0,10),ρj: (−10,10).Awiderprior distribution for size effects on abundance (cj) than abun‐danceeffectsonsize(Bj)wasusedbecauseofmuchlargerln‐scalevariance in abundance than size. Prior distributions for the val‐uesoftheunobservedstatevariablesatthefirsttimestep i = 1 (N1,j,S1,j)were uniform and bounded by the observed ranges ofthevariables.

We used three independent chains with 300,000 iterations,where the first 30%of the iterationswere used as “burn‐in” iter‐ations to ensure that the chains had converged. In addition, wethinnedthechainstoreduceautocorrelationintheposteriorsam‐plesandtoproduceareasonableamountofoutput,inthiscasere‐sultingin1,000samplesfromeachchain,intotal3,000.

We used the Gelman and Rubin R convergence diagnostics(Gelman&Rubin,1992)andvisual inspectionof thechains toen‐sureconvergence.TheRcompareswithin‐chainandbetween‐chainvarianceandshouldbecloseto1atconvergence(Gelman&Rubin,1992). If themultivariate R or theupper95%confidence limit forRforoneormoremodelparameterswaslargerthan1.03ortherewereothersignsofpoorconvergence,wefirstincreasedthenum‐ber of iterations from 300,000 to 1,000,000, and if that did notsolve the issue,we simplified themodel formulation as describedinthedescriptionofthemodeldevelopmentforeachpopulationinAppendixS2(SupportingMethods).

Wecheckedforviolationsofkeymodelassumptionsbyinspecting(a) timeseriesplotsof statevariables forabundanceandbodysize(posteriormediansand95%credibilityintervals)andobservations,(b)pairwiseplotsoflog‐abundanceandlog‐sizeattimetversuslog‐abun‐danceand log‐sizeat time t+1,whichshouldshowapproximatelylinearrelationshipsiftheGompertzmodelformulationisappropriateand(c)quantile–quantilenormalprobabilityplotsof“residuals”,cal‐culatedasdeviationsbetween log‐scaleobservationsandposteriormediansofstatevariables,whichwouldrevealpossibleoutliersandstrongdeparturesfromnormality.WeusedtheGrubbstest(Grubbs,1969) to assesswhether outlier residualsweremore extreme thanexpectedbychanceandrefittedthemodelwithoutthestatisticallysignificantoutlierstoassesstheirpossibleinfluenceonresults.

To identify correlated parameters that should be interpretedjointly, we computed correlations between posterior distributionsforallparameterpairsandplottedthoselargerthan0.4inabsolutevalue.

3.4 | Hypothetical example

Toillustratetheanalysisapproach,weanalysedsyntheticallygener‐ateddata.ThesyntheticdatawererandomlygeneratedbasedonthegenericmodelpresentedinFigure1andanalysedastherealdata.ComputercodeandresultsareshownintheonlineAppendixS1.

3.5 | Observation data

Thedataneededfortheproposedanalysesaretimeseriesofabun‐danceandmean lengthorweightatdifferentagesorstagespriortorecruitment,preferablyincludinguncertaintyestimates.Whethertopreferlengthorweightdataifbothareavailableisnotobvious.Bothlengthandweightcouldpotentiallybeimportantfordynamics.Weightmaybethebestindicatorofcondition,andlengthanindica‐tor of role as predator or prey in the foodweb.Measurement is‐suescanalsoinfluencewhichsizemeasuretoprefer.Forexample,asweightismoreseasonallyvariablethanlength,weightispotentiallymoresensitivetoyear‐to‐yeardifferencesinsamplingtime.Weightmayalsotoalargerdegreethanlengthbesusceptibletofluctuationsattimescalesfromhourstoweeks,whichmaybeoflittlerelevanceforinterannualdynamics.Theanalysisframeworkcanaccommodaterelative abundance indices, that is, with unknown scaling to trueabundance,andthetimeseriescanincludemissingvalues.Morethanoneindexofanage‐classcanalsobeused,ifavailable.Forthisanaly‐sis,weassembledtimeseriesofabundanceandsize(weightand/orlength,dependentondataavailability),forageclassesrangingfromtheearliestagemeasured(larvae,age‐0orage‐1)throughtotheageatwhichrecruitmenttothefisheryoccurs(age2to4;summarizedinTable1,withmoredetailedinformationaboutyearcoverage,datasourcesanduncertaintyestimatesprovidedintheonlineAppendixS2,TablesS1–S5;thetimeseriesareshowninAppendixS3,FiguresS1–S6,andprovidedinAppendixS4.Data).Changesinsurveycov‐erageormethodologycouldpotentiallybiasparameterestimatesifcoincidingwithtrends insizeorabundance.Wetook intoaccount

     |  7STIGE ET al.

that the survey coverage forBS cod andBShaddock at ages1–3changed in1993byaddinganextraparametertotheobservationequationsforabundance(EquationS1,AppendixS2).Alldataserieswerecentredtohaveameanofzeropriortoanalysis.

4  | RESULTS

4.1 | Correlation analysis

Thecorrelationanalysisfocusedontherelationshipbetweenabun‐danceandmeansizearoundtheageofrecruitmenttothefisheriesand theyoungestagewithdata foreachpopulation.ThisanalysisshowedthatforBScodaswellasforBShaddock,age‐3abundancewassimilarlystronglycorrelatedwithabundanceandannualmeanlengthofthelarvaethreeyearspreviously(Figure2).ForSSBFhad‐dockandEBSpollock,age‐4abundancewassignificantlycorrelatedwith abundance but notmeanweight at age 1 three years previ‐ously.ForSSBFhaddock,weightbutnotabundanceat age0was

available,showingapositiveassociationofage‐0weightwithage‐4abundance(r=0.59,p=0.01)butnotwithage‐4weight(r=0.29,p =0.28) fouryears later. ForBScapelin andGOApollock, abun‐danceatage2(forcapelin)or3(forpollock)wasneithercorrelatedwithabundancenormeanlengthaslarvae.

Noneofthesixpopulationsshowedsignificantcorrelationsbe‐tweenbodysizeattheyoungestageanalysedandbodysizeattheoldestageanalysed.Fortwoofthepopulations,BScodandBScape‐lin,therewerestatisticallysignificantnegativecorrelationsbetweenlarvalabundanceandmeanbodysizeoftheyear‐classattheoldestageanalysed.ForBShaddock,thestatisticalpowerofthesecorrela‐tiontestsislowduetosmallsamplesize(N=12years).Hence,wealsoanalysedtheage‐0dataforthispopulation,findingthatmeanlength at age 3 was negatively correlated with age‐0 abundance(r=−0.42,N=33,p=0.02) aswell as length (r=−0.44,N=33,p=0.01)threeyearspreviously.

The age‐resolved state‐space analysis explored the links be‐tweenvariability in abundance andbody size early in life inmoredetail.

4.2 | Model diagnostics and sensitivity analyses for age‐resolved dynamics

Modeldiagnosticsandsensitivityanalysessuggestedthatthemainresults of the state‐space statistical analysis of age‐resolved dy‐namics were robust to the key model assumptions. Nonetheless,itshouldbenotedthatwhileresultsappearedqualitativelyrobust,theassumptionsmaderegardingmagnitudesofobservationerrorsdo influence some of the parameter estimates (see Appendix S3:SupportingResultsfordetails).

4.3 | Across‐population comparison

All populations with sufficient data showed low (close to 0) esti‐matesforeffectsofsizeaslarvaeorage‐0juvenilesonsizeatsub‐sequentages (2ndcolumn inFigure3, representingCjcoefficientsinEquation2.Lowestimatesforeffectsofsizeonsizemeanlittleconsistencyacrossagesinsizedeviations:meanbodysizeoflarvaeandage‐0 juvenilesarepoorpredictorsofmeanbodysizeat laterages—asalsoshownbycorrelationanalysis.

Three populations, BS cod, BS haddock and SSBF haddock,showedpositiveassociationsbetweenage‐0 sizeandage‐1abun‐dance(1stcolumninFigure3,representingcjcoefficientsinEquation1.Notethatwhileage‐0sizewasnotnecessarilyagoodpredictorofsizelaterinlifeforthesepopulations,itdidpredictabundance.

Forfourofthepopulations,BScod,BShaddock,BScapelinandGOA pollock, there was statistical evidence for negative effectsof abundance on size for at least one age interval (4th column inFigure3, representingBj coefficients inEquation2.Theredidnotseemtobeapatternofageintervalswithnegativeeffectsofabun‐danceonsize,theexpectedconsequenceofcompensatorydensitydependenceingrowth(4thcolumn),alsoshowingweakassociationsinabundance—theexpectedconsequenceofcompensatorydensity

F I G U R E 2  Correlationanalysisforassociationsbetweenabundance(N)andmeanbodysize(S)attheyoungestandoldestageanalysedforeachpopulation(subscriptsdenoteage).ThenumberbeloweacharrowisPearson'scorrelationcoefficientfortheassociationrepresentedbythearrow.Negativecorrelationsareshownbyredarrows,positivebyblue,witharrowwidthproportionaltocorrelationstrength.Dotted‐linedarrowsarenotstatisticallysignificantatp < 0.05

(b) BS haddock

(a) BS cod

(c) SSBF haddock

NLARV N3

SLARV S3

0.51

–0.11

–0.53 0.51

0.51

–0.29

NLARV N3

SLARV S3

–0.31 0.68

0.78

0.22

N1 N4

S1 S4

–0.20 –0.15

(e) EBS pollock

(d) BS capelin

(f) GOA pollock

NLARV N2

SLARV S2

0.23

–0.04

–0.47 0.02

0.41

0.12

N1 N4

S1 S4

0.07 –0.21

–0.11

–0.04

NLARV N3

SLARV S3

0.25 –0.01

8  |     STIGE ET al.

dependenceinsurvival(3rdcolumn,representingbjcoefficientsinEquation1.

4.4 | Barents Sea cod age‐resolved results

State‐spaceanalysisoftheprocessesthatlinkthelarvaetorecruit‐ment at age 3 for BS cod suggested that the positive associationbetweenlarvallengthandrecruitmentidentifiedinthecorrelationanalysiswasmainlyaresultofapositiveassociationbetweenage‐0

lengthandage‐1abundance(Figure4a,TableS6).Thenegativeas‐sociationbetweenlarvalabundanceandage‐3lengthwasexplain‐ablethroughanegativeassociationbetweenage‐0abundanceandage‐1 length.Age‐to‐age associations in abundancewere similarlystrong for all age intervals from larvae to age‐3while age‐to‐ageassociations in length were weakest at the earliest age intervals,with, in particular, age‐0 length being a poor predictor of age‐1length.Note thatparameters foreffectsofabundanceand lengthwerecorrelatedwitheachother,whichleadstohighervarianceof

F I G U R E 3  Parameterestimatesforstate‐spacestatisticalmodelresultsforthesixpopulationsanalysed.Pointsanderrorbarsrepresentposteriormeansand95%credibilityintervalsofparameters.Thefourcolumnsrepresent,respectively,parameterscj,Cj,bj and Bj in Equations1and2withthex‐axisrepresentingthesubscriptj

�

�

��

−20

010

BS

cod

on abundance

��

� �

−1.0

0.0

1.0

on size

�

�

��

−1.0

0.0

1.0

on abundance

�

�

�

�

−0.1

00.

000.

10

on size

�

�

��

−20

010

BS

had

dock

�

�

��

−1.0

0.0

1.0

�

�

�

�

−1.0

0.0

1.0

�

�� �

−0.1

00.

000.

10

�

� � �

−50

5

SS

BF

hadd

ock

�

�

� �−1

.00.

01.

0� �

�

−1.0

0.0

1.0

�� �

−0.3

0.0

0.2

�

�

�

−20

010

BS

cap

elin

�

��

−1.0

0.0

1.0

�

�

�−1

.00.

01.

0

�

�

�

−0.1

00.

000.

10

�

��

−50

5

EB

S p

ollo

ck

� ��

−1.0

0.0

1.0

�

��

−1.0

0.0

1.0

�� �

−0.3

0.0

0.2

� � �

−20

010

0 1 2 3 4

GO

A p

ollo

ck

�

�

�

�

−1.0

0.0

1.0

0 1 2 3 4

�

�

�

�

−1.0

0.0

1.0

0 1 2 3 4

�

��

−0.3

0.0

0.2

0 1 2 3 4

End age (years)

Para

met

er e

stim

ate

Effect of abundanceEffect of size

     |  9STIGE ET al.

eachparameterwheninterpretedalone(FigureS7inAppendixS3:SupportingResults).

4.5 | Barents Sea haddock age‐resolved results

Similar toBScod,wefoundthat thepositiveassociationbetweenlarvallengthandrecruitmentinBShaddockwasmainlyaresultofapositiveassociationbetweenage‐0 lengthandage‐1abundance(Figure4b,TableS7).Resultsalsoshowednegativeassociationsbe‐tweenabundanceandchangesinmeanlengthfromage0onwards,buttheseassociationswereweakerthanforBScod.Theuncertaintyin theseandotherparameterswas inflatedbecauseofcorrelationbetweenparameters (FigureS8 inAppendixS3). Interestingly, thenegativeassociationbetweenmeanlengthsofayear‐classatages0and3(whilenotstatisticallysignificantforlarvae,Figure2)seemedtobedue topositive associationsbetween lengthandchanges inabundance at early ages combinedwith negative associations be‐tweenabundanceandchangesinlengthatlaterages.

4.6 | Scotian Shelf and Bay of Fundy haddock age‐resolved results

The age‐resolved analysis for SSBF haddock showed that thepositive association between age‐0 weight and age‐4 abundance

identifiedinthecorrelationanalysiswascausedbyapositiveasso‐ciationbetweenage‐0weightandage‐1abundance(Figure4c,TableS8).However,withoutdataonage‐0abundance,itwasnotpossibletoassesswhether thisassociationmightbeconfoundedbyapos‐siblepositiveassociationbetweenweightandabundanceatage0.Wefoundnoevidenceforabundanceeffectsonweightorweighteffectsonabundancebetweenages1and4.Lackofassociationsbetweenweightsatages0and1withweightatage4wascausedbyweakage‐to‐ageassociationsinweightbeforeage2.

4.7 | Barents Sea capelin age‐resolved results

Consistentwiththecorrelationanalysis,wefoundnoevidenceforeffectsoflengthonsubsequentabundanceforBScapelin(Figure4d,TableS9).Thenegativeassociationbetween larvalabundanceandlengthatage2shownbythecorrelationanalysisseemedtobeex‐plained by a negative association between age‐1 abundance andage‐2 length.Note,however, thatparameters foreffectsofabun‐danceandlengthatage0onabundanceandlengthatage1werecorrelatedwitheachother,which leadstohighervarianceofeachparameterwheninterpretedalone(FigureS10inAppendixS3).Age‐to‐ageassociationsinabundancewereweakestfromage0toage1.Age‐to‐ageassociationsinlengthwereparticularlyweakfromlarvaetoage0anduncertainforlaterages.

F I G U R E 4  Schematicpresentationofstate‐spacestatisticalmodelresultsforthesixpopulationsanalysed.Theresultsshowassociationsbetweenabundance(N)andmeanbodysize(S)atsubsequentagesearlyinlife(subscriptsdenoteage).Negativeestimatesareshownbyredarrows,positivebyblue,witharrowwidthsproportionaltoparameterestimates.Dotted‐linedarrows:95%credibilityintervalsincludezero

NLARV N3N2N1N0

SLARV S3S2S1S0

(b) Barents Sea haddock

NLARV N3N2N1N0

SLARV S3S2S1S0

(a) Barents Sea cod

N0 N4N3N2N1

S0 S4S3S2S1

(c) Sco�an Shelf and Bay of Fundy haddock

N4N3N2N1

S4S3S2S1

(e) Eastern Bering Sea pollock

NLARV N3N2N1N0

SLARV S3S2S1S0

(d) Barents Sea capelin

NLARV N3N2N1N0

SLARV S3S2S1S0

(f) Gulf of Alaska pollock

10  |     STIGE ET al.

4.8 | Eastern Bering Sea pollock age‐resolved results

Consistentwiththecorrelationanalysis,wefoundnoevidenceforeffectsofweightonsubsequentabundanceorabundanceonweightfor EBS pollock (Figure 4e, Table S10). Age‐to‐age associations inabundancewereweakestfromage1toage2.Age‐to‐ageassocia‐tionsinweightwereuncertainforearlyageintervalsbecauseofcor‐relatedparametersforweightandabundanceeffects(FigureS11inAppendixS3).

4.9 | Gulf of Alaska pollock age‐resolved results

WhilethecorrelationanalysisforGOApollockrevealednosignifi‐cant linksbetween larval abundanceand lengthwith age‐3abun‐dance and weight, the age‐resolved analysis revealed a negativeassociationbetweenage‐1abundanceandage‐2weight(Figure4f,TableS11).Oneconsequenceofthisnegativeassociation(combinedwiththepositiveassociationbetweenabundancesatages1and2)isthatanegativecorrelationbetweenabundanceandsizeisestab‐lished at age2 (r = −0.73).As a result,model coefficients for thetransitionfromage2toage3areuncertain,because it isdifficulttoseparateeffectsofabundancefromeffectsofsize(FigureS12inAppendixS3).Ifweparsimoniouslyassumenoeffectsofage‐2sizeonage‐3abundance(c3)orofage‐2abundanceonage‐3size(B3),thecoefficients for the age‐to‐age associations in abundance (b3) andsize(C3)arebothbetween0.5and1(FigureS12).Thismeansthattheweakcorrelationsbetweenlarvalandage‐3abundancesandlengthsfoundbythecorrelationanalysisweremainlyexplainablebyweaklinksbetweenage‐0andage‐1abundancesandlengths.

We foundnoevidence for sizeeffectsonabundance; thiscon‐clusiondidnot change if the sparseage‐0datawereomitted fromthemodel, and associations between larval abundance and lengthandage‐1abundancewereassesseddirectly(shownasthe“baselinemodel”forGOApollockinFigureS15inAppendixS3).Whiletheef‐fectsoflarvalabundanceonage‐0lengthandoflarvallengthonage‐0abundance were not modelled, the available data did not suggeststrongcorrelations(larvalabundance—age‐0length:r=−0.21,N=9,p=0.58;larvallength—age‐0abundance:r=0.03,N=9,p=0.94).

Notethatparameterestimatesforeffectsonage‐0abundanceandlengthshouldbeinterpretedwithcautionastheyunrealisticallyassumednoprocesserrorsandknownobservationerrors (see thedescriptionofthemodeldevelopmentforGOApollockinAppendixS2).Basedonsimplecorrelationanalysis,theassociationsweresignif‐icant at α=0.10ratherthan0.05(larval—age‐0abundances:r=0.66,N=9,p=0.05;larval—age‐0lengths:r=0.60,N=9,p=0.09).

4.10 | Inter‐cohort density dependence

Modelsthat includedinter‐cohortdensitydependence(FigureS15inAppendixS3:SupportingResults)suggestedthatage‐2lengthinBShaddockwasmorestronglyandnegativelyassociatedwiththeabundanceofage‐2 fish theyearbefore thanwith theabundance

ofitsownyear‐class(i.e.age‐1theyearbefore).ThesamewasthecaseforBScapelin.Therewasnoindicationofnegativeeffectsofabundanceof theolder fishon survival; on theother hand, someestimateswerepositive.Theseresultsshouldbetreatedwithsomecaution due to slow convergence and several strongly correlatedparameters for inter‐ and intra‐cohort density dependence (notshown).

5  | DISCUSSION

Monitoringsurveysof fisheggs, larvaeand juvenilesareroutinelyconducted for a range of commercially important species to getearlyindicationsofyear‐classstrengthandtounderstandbetterthe“black‐box”recruitmentprocess(e.g.Dragesundetal.,2008).Here,wedemonstratehowwecangainnewinsightsintoearlylifedynam‐icspriortorecruitmenttothefisherybylinkingabundanceandsizeinformationatseveralpre‐recruitmentagesinonecoherentanalysis.Specifically,bymovingbeyondabundancecorrelations,weidentifyrelevantstagesandmechanismsthatshaperecruitmentvariability.Keyfindingsforthesixpopulationsanalysedareapossiblelinkbe‐tweenlifehistoryandwhensizemattersforsurvival,apossiblelinkbetweensize‐dependentmortalityanddensity‐dependentgrowth,andapossible“decoupling”betweendensitydependenceingrowthanddensitydependenceinsurvival.

5.1 | When does size influence abundance?

Our results suggest size‐dependent survival for three of the sixpopulations.Specifically,forBScod,BShaddockandSSBFhaddock,largemeanbody sizeas larvaeand/or juveniles is associatedwithhighsurvivalduringthefirstwinter(i.e.asexpressedashighage‐1abundance) andwith strong recruitment three to four years later.Theassociationsbetweenmeanbodysizeandchangesinabundancearemostparsimoniouslyexplainedintermsofsurvival,aswecon‐sider systematic associations between body size andmigration inandoutofthesurveyareasorwithcatchabilitylesslikely.ForSSBFhaddock,somecautionisneeded,aswelackabundancedatafromthefirstyearoflife,anditispossiblethatthesize‐abundancerela‐tionshipisalreadyestablishedattheonsetofthefirstwinter.TheseassociationsareconsistentwithearlierstudiescorrelatinglarvalandjuvenilesizeofBScodandBShaddocktorecruitment(e.g.Ottersen&Loeng,2000,Stigeetal.,2015)andwithfindingsthat largesizeoftemperatejuvenilefishesisfrequentlyassociatedwithenhancedwintersurvival(Sogard,1997).Oneimplicationofthesefindingsisthat inorder tounderstand andpotentially predict recruitment inthesepopulations,itisimportanttoinvestigatehowenvironmentalfactors influencesizeandabundanceduringthefirstgrowingsea‐son,incontrasttolaterageswhensizeappearstoberelativelyun‐importantforsurvival.

ForBScapelin,EBSpollockandGOApollock,wefoundnoasso‐ciationsbetweenbodysizeandsurvival.NotethatforEBSpollock,welackeddatapriortothefirstwinter.However,year‐classstrength

     |  11STIGE ET al.

ofEBSpollockhaspreviouslybeenassociatedwithtotalenergeticreserves acquiredby juvenile fishbefore the firstwinter, asmea‐suredby theproductofenergydensityandbodysize; thus,bodysize alonemay not be sufficient for high survival (Heintz, Siddon,Farley,&Napp,2013).Onepossibleexplanationforthelackofas‐sociationforGOApollockisalong‐termincreaseinpredationratesbyagrowingpredatorpopulation(arrowtoothflounder),whichhashadamajorimpactonjuvenilesurvival(Baileyetal.,2012),andmayhavemaskedanypatternsofsize‐dependentsurvival.Hence,lackofdetectedassociationinourstudydoesnotnecessarilyimplylackofabiologicallysignificantrelationship,asitwasnotfeasibleinourstudytocontrolforeffectsofenvironmentalchangesonsurvivalthatpo‐tentiallydominatedovertheeffectsofintra‐populationfactors.Thenon‐significanteffectofsizeonage‐0andage‐1abundance inBScapelinis,however,consistentwithanage‐resolvedanalysisthatdidaccountforeffectsofenvironmentalcovariates(Stigeetal.,2010).

One possible explanation for survival benefits of large size isthatlargeindividualsaremoretolerantofstarvationorphysicalex‐tremesthansmallerconspecifics(Milleretal.,1988;Sogard,1997).Large body size oftenmeans high energy reserves,which can in‐creasesurvival throughaperiodwithadverseenvironmental con‐ditions. The finding that size appears to be particularly importantforsurvivalduringthefirstwinteroflifesupportsthisexplanation:Thefirstwinteroflifemaybeenergeticallydemandingforhigh‐lat‐itude fishesdue to lower foodavailability than in summer, limitedlight available for visual feeding,unfavourable temperature condi‐tions and, formany species, needs for behavioural adaptations asthejuvenilesmovefrompelagictomoredemersalhabitats.Wenotethat lowrecruitment inBScodandBShaddock isassociatedwithlow temperaturesduring the firstwinterof life (Bogstad,Dingsør,Ingvaldsen,&Gjøsæter, 2013), indicating that environmental con‐ditions in this period of life are important for survival. However,predationregimesmayalsochangearoundthisperiodoflife,espe‐ciallyforspeciesthatmovefrompelagictodemersalhabitats.Forexample,atthistime,BScodandBShaddockbecomemoreexposedtopredationfromdemersalfish,includingfromtheolder,demersalstagesofcod,whichareknowntosignificantlyaffectrecruitmentofbothBScodandhaddock(e.g.Yaragina,Bogstad,&Kovalev,2009,Stigeetal.,2010).Suchincreasedpredationmaybesizeselective,aslargeindividualsarelikelytohavefewerpredatorsandbebetteratescapingthepredators thansmallerconspecifics (Bailey&Houde,1989;Houde,1987).Stomachcontentdatasuggestthatlargebodysizeat theendof the firstgrowingseasonmaypotentially reducepredation risk:codof10–14cm is themostabundantprey lengthgroupof cannibalisticBS cod (Yaragina et al., 2009),while annualmeanlengthsofage‐1BScodinourdatavaryfrom10to18cm(andofage‐1BShaddockfrom14to17cm).Itisthereforepossiblethatinyearswithhighmeanbody sizeof age‐0codandhaddock, thejuvenilesgrowmorerapidlyoutofthesizerangemostsusceptibletopredationfromoldercod,leadingtoincreasedsurvival.

Wenote that all thepopulationswithevidenceof size‐depen‐dentsurvivalchangefrompelagictomoredemersalhabitatsasjuve‐niles,priortotheirfirstwinter(Bergstad,Jørgensen,&Dragesund,

1987;Cargnellietal.,1999). Incomparison,walleyepollock in theEBSandGOAappeartohaveamoregradualtransitionfrompelagictodemersalhabitats,withage‐0fishbeingpelagic,age‐4andolderfishbeingdemersal,andage‐1andage‐2 fishbeing found inbothhabitats (Duffy‐Anderson et al., 2003). Capelin are pelagic as lar‐vae,juvenilesaswellasadults(Gjøsæter,1998).Thetransitionfrompelagic todemersalhabitat is associatedwithhabitat‐linked shiftsindensity‐dependentmortality,dietandpredators (Juanes,2007).Asahypothesisforfurtherresearch,weproposethatourfindingsmayreflectageneralpattern,namelythatlargebodysizeatatran‐sition frompelagic to demersal habitatsmayoften give increasedsurvivalduetoeithersize‐dependentpredationbydemersalfishorincreasedenergyreserves.

5.2 | When does abundance influence size?

Our results suggest compensatory density dependence in growthforfourofthesixpopulations.Specifically,forBScod,BShaddock,BScapelinandGOApollock,wefoundthathighabundanceisasso‐ciatedwithlowmeanbodysizeatalaterage,mainlyatage1forBScodandBShaddockandage2forBScapelinandGOApollock.NosuchassociationswerefoundforSSBFhaddockorEBSpollock,butwenotethatwelackeddatatoanalysepossibleeffectsonsizeatage1forboththesepopulations.Theseassociationscanbeinterpretedascompensatorydensitydependenceingrowth,thatis,thatathighabundance, mean growth is reduced, and/or as a combination ofdensity‐dependentmortalityandsize‐dependentmortality,that is,thatincreasedmortalityathighabundancedisproportionallyaffectslarge individuals.Weconsiderthatcompensatorydensitydepend‐enceingrowthisthemostparsimoniousexplanation,asapatternofsize‐selectivemortalitydisproportionallyaffectinglargeindividualswouldbecontrarytowhatisexpectedundercrowding.

Thetimingoftheapparentdensity‐dependentgrowthofBScodandBShaddockcoincideswith thesize‐dependentsurvivalduringthefirstwinteroflifeandisconsistentwithcompetitionforsuitablespaceforfeedingaswellasshelterfrompredationwhenpelagicjuve‐nilessettletotheseafloor(Juanes,2007).Aswefoundnoindicationofsize‐dependentsurvivalafterage1,wedonotexpectthatreducedsizeatage1athighabundanceinfluencessurvivaltoages2and3(i.e.recruitment),althoughitcouldinfluence,forexample,reproductivepotentiallaterinlife.Unfortunately,welackdatatoassesswhetherSSBF haddock also show density‐dependent growth when theychangefrompelagictodemersalhabitat.Density‐dependentgrowthduringpelagic stagesofBScapelin is likelya resultofexploitativecompetition, as the capelinhavea strong top–downeffecton thebiomassoftheirzooplanktonprey,whichinturnhaveapositivebot‐tom‐upeffectoncapelinsizeatage(Gjøsæter,Dalpadado,&Hassel,2002;Stige,Kvile,Bogstad,&Langangen,2018).Thetimingofstrongintra‐specificcompetitionatage2 incapelin isconsistentwiththeaveragetotalbiomassdoublingfromage1toage2beforedeclininginages3and4(accordingto1972–2015surveydata).Interestingly,density‐dependent growth to age2 inBS capelin impacts popula‐tion dynamics by fast growth leading to earlier (size‐dependent)

12  |     STIGE ET al.

maturationandhighermortalityafterage2(asmostofthecapelinarethoughttodieshortlyafterspawning,Gjøsæter,1998).Resultssuggesteddensity‐dependentgrowthofGOApollockfromage1toage2,whileEBSpollockshowednodensitydependenceingrowth.WehypothesizethatthisdifferencemayberelatedtowintersbeinglongerandcolderintheEBSrelativetotheGOA.Hence,growthofEBSpollockmaymoreoftenbetemperaturelimitedratherthanfoodlimited (Laurel,Spencer, Iseri,&Copeman,2016),and thereby lesslikelytoshowdensitydependence.

Itshouldbeaddedthatthenegativeassociationsbetweenabun‐dance and changes in body size do not necessarily reflect causaleffectsof crowding, but couldbe causedbyextrinsic factors cor‐related with abundance. For example, the negative associationsbetween abundance and changes in body size in BS cod and BShaddockcanalternativelybeexplainedbyhightemperaturescaus‐ingbothhighsurvivalofeggs,larvaeandearlyjuvenilesandstrongcurrentstransportingthejuvenilesfarthereastwardsthannormalintheBarentsSea,whereambienttemperaturesarelowandindivid‐ualgrowth slow (Ottersen,Helle,&Bogstad,2002).The resultingcontrastbetweentemperaturesexperiencedatdifferentageswouldalsoexplainthenegativecorrelationfoundbetweenBShaddocksizeatages0and3.Analysesofspatiallyresolveddatawouldbeneededtoassessthishypothesis.

5.3 | When is mortality density‐dependent?

Ourstudyprovidesestimatesofthestrengthofcompensatoryden‐sitydependence in survival, a key factor forunderstandingpopu‐lation dynamics and how fishing and other factors influence fishpopulations(Roseetal.,2001).Tooursurprise,theageswithstrong‐estindicationsofcompensatorydensitydependenceingrowthwerenottheageswithstrongestindicationsofcompensatorydensityde‐pendenceinsurvival.Apossibleinterpretationisthattheremaynotbeadirectcorrespondencebetweendensitydependenceingrowthanddensitydependenceinsurvival.Forexample,forbothBScape‐linandGOApollockitappearsthatdensitydependenceinsurvivaloccursat ayoungerage thandensitydependence ingrowth.Thispatterncouldbecausedbylowenergystoragecapacityofsmallfish(Milleretal.,1988),whichmaymakeyoung lifestagesparticularlysusceptible tostarvationmortalityundercrowding,whereasolderlifestagesmaytoalargerextentbeabletogrowpoorlywhilestillsurvivingperiodsofstarvation.Thisresultmustbeinterpretedwithcaution,asourmethodmayprovideratherroughestimatesofden‐sity‐dependent survival. The pattern is, however, consistent withdensitydependenceearly in life typicallybeing reported toaffectabundance(i.e.recruitment),whereasdensitydependenceaftertherecruitment age mostly being reported to occur through growthratherthansurvival(Andersenetal.,2017;Zimmermannetal.,2018).

5.4 | Inter‐cohort density dependence

Our main models only considered within‐cohort density depend‐ence. When also considering the possible density effects of the

preceding year‐class, results suggested that growth of BS capelinandBShaddockwasmorestronglyregulatedbytheolderfishthanby theyear‐class itself.Wespeculate that this resultmight reflectasymmetriccompetition,forexamplebecausetheolderfishdisplacetheyounger fish to sub‐optimalhabitats (which is consistentwiththeage‐1andage‐2groupsofcapelindividingtheBarentsSeabyformingmigratorywavesthatmoveinoppositedirections,Fauchald,Mauritzen,&Gjøsæter,2006).Wenotethatalsothemainmodelssuggested density dependence in growth at these age intervals,but that the additional results providemore detailed insights intowhich density (which age) the growth depends on. The positiveestimates fordensityeffectsof theprecedingyear‐classonabun‐dance are likely caused by auto‐correlated effects of factors notexplicitlymodelled,suchaspredationeffectsonsurvival.Similarly,Ricardet al. (2016) foundpositive lag‐1autocorrelation in recruit‐mentresidualsforalargenumberofAtlanticfishstocks.Ricardetal. (2016)found,however,negativeautocorrelationinanumberofstocksattimelagsfromthreetofiveyears,suggestingcannibalismorinter‐cohortcompetition.Accountingforsuchinteractionsinthestate‐spaceanalysisofage‐resolveddynamicswouldrequirecarefulconsiderationofwhichagesarepotentialcompetitorsorpredatorsonotherages, forexample,basedondietdata.Ourconsiderationofonlytheone‐year‐olderage‐classmostlikelyaddressedthecom‐petitors,whilepotentiallymissingcannibalismbyolderfish.

5.5 | Methodological limitations and prospects for future studies

While the state‐space analysis approach here applied has poten‐tialtorevealnewinsights,themethodhaslimitations.Inparticular,theestimationofdensitydependencemaybestronglysensitivetoobservationerrorassumptions,thusnecessitatingsensitivityanaly‐sesunlessthemagnitudesofobservationerrorsareknown(Auger‐Méthéet al., 2016; Iveset al., 2003).As shownby the sensitivityanalysisweconducted(FigureS14inAppendixS3),uncertainmag‐nitudesofmeasurementerrorscontributetouncertaintyinthepa‐rameterestimates inourstudy,althoughourmainfindingsappearrobust.Further,factorsnotexplicitlymodelledcouldbiasparameterestimatesifcorrelatedwithabundanceorbodysize.Suchvariablesinclude climate factors, abundances of prey, predators and com‐petitors from other year‐classes or species, and unaccounted‐forchanges insurveycoverageormeshsize.Addingsuchvariables intheanalysiswouldleadtomoreunbiasedparameterestimates,butwithmorevariablesinthemodel,thecredibilityintervalsforthepa‐rametersmayincrease,andmodeldevelopmentwouldbemorecom‐plicated and computation timemight be restrictive. Alternatively,resultingpatternsrevealedbythestate‐spaceapproachcanbein‐terpretedwith respect to other possible factors (e.g. prey, preda‐tors,competitors)beforeunderlyingmechanismsaretheorized.Wechosenot toaddenvironmentalcovariates,butnotethat,as inallstatisticalmodelling,theresultsareinprinciplecorrelativeandneedtobeinterpretedaccordingly.Strongtrendsinthedata,dueto,forexample,overfishingorregimeshifts,wouldalsocomplicateanalysis

     |  13STIGE ET al.

andinterpretationofresults,bothforstatisticalreasons(theeffec‐tivedegreesoffreedomwouldbelow)andbecausethepopulationdynamicsmayhavechanged(becomenon‐stationary).Variabilityattimescalesofaround1–10yearsgenerallydominatedoverthelong‐termtrendsinourdata(FiguresS1−S6inAppendixS3),butwenotethatthenegativeassociationbetweenage‐0abundanceandage‐1lengthinBScodwaslikelydrivenbyalong‐termincreaseinage‐0abundanceandadecreaseinage‐1lengthsincethe1980s.

Despitetheselimitations,usingastate‐spaceanalysisapproachhasadvantagescomparedwithsimplecorrelationanalysis,byutiliz‐inginformationfromseveralagesorlifestagesinacoherentanalysisframework. For example, while the correlation analysis identifiedpositiverelationshipsbetweenlarvalorjuvenilesizeandrecruitmentinthreepopulations,theage‐resolvedstate‐spaceanalysisshowedatwhich age these relationshipswere established.Hence, our re‐sultsshedlightonthepossiblemechanismsthatlinkearlylifestagestorecruitment.Further,correlationresultsmightbeinconsistent,forexampleshowingstrongassociationbetweenabundanceatages1and3butnotbetweenages2and3,henceimplicitlypointingtoun‐certaintiesinthedata.Resultsfromastate‐spaceanalysisareeasiertointerpretassuchinconsistenciesareavoidedwhileuncertaintiesinthedataareexplicitlyaccountedfor.

6  | CONCLUSIONS

Our study provides a novel perspective to study recruitment dy‐namicsbyfocusingin‐depthontheintertwinedprocessesofgrowthandsurvivalatearlyages.Theapproachpavesawayforabetter,moremeaningfulunderstandingofrecruitmentprocessescomparedwithdirectly linkingrecruitment to thebiomassofspawners,as isoftendoneinrecruitmentmodels.Weencourageotherstoapplythemethodpresentedinourstudytootherpopulationswheredataareavailable.Ourresultsunderscoretheimportanceofsizeforsurvivalearlyinlifeandsuggestthatsize‐dependentmortalityanddensity‐dependentgrowthfrequentlyoccuratatransitionfrompelagictodemersal habitats.Overall, these findings canbeused todevelopmechanisticallybasedhypothesesoflarge‐scalepatternsinearlylifedynamics,guidefutureresearchbyidentifyingstagesandprocessesthatareparticularlyimportantforrecruitmentandimproverecruit‐mentpredictions.

ACKNOWLEDG EMENTS

WethankGjertE.DingsørandElenaEriksenforhelpwithaccess‐ing Barents Sea capelin data. Esther Goldstein, Daniel Cooper,GeorgeHunt Jr and an anonymous reviewer provided construc‐tive feedback on earlier versions of this manuscript. We thanktheResearchCouncilofNorway(RCN)forfundingtheworkshopNAMOR (grant no. 267577). L.C.S. and J.M.D. were supportedby the RCN through the project SpaceShift (grant no. 280468).A.B.N. was supported by an AIAS‐COFUND Fellowship at theAarhusInstituteofAdvancedStudies,whichreceivesfundingfrom

theAarhusUniversityResearchFoundation(AarhusUniversitetsForskningsfond) and the European Union's Seventh FrameworkProgramme, Marie Curie Actions (grant agreement 609033).A.B.N.alsoreceivedsupportviatheNationalScienceFoundationDivisionofEnvironmentalBiologygrant#1145200.G.O.acknowl‐edgesthesupportfromRCNthroughtheprojectCoDINA(grantno. 255460/E40). This work is a contribution EcoFOCI‐0915 toNOAA's Ecosystems and Fisheries‐Oceanography CoordinatedInvestigationsProgram.

DATA AVAIL ABILIT Y S TATEMENT

Appendix S4 contains tables with all time‐series analysed in thisstudy. SeeAppendix S2 for a full description of data sources andoriginalcitations.

ORCID

Leif Christian Stige https://orcid.org/0000‐0002‐6808‐1383

Joël M. Durant https://orcid.org/0000‐0002‐1129‐525X

R E FE R E N C E S

Andersen,K.H.,Jacobsen,N.S.,Jansen,T.,&Beyer,J.E.(2017).Whenin lifedoesdensitydependenceoccur infishpopulations?Fish and Fisheries,18,656–667.https://doi.org/10.1111/faf.12195

Auger‐Méthé,M.,Field,C.,Albertsen,C.M.,Derocher,A.E.,Lewis,M.A.,Jonsen,I.D.,&MillsFlemming,J.(2016).State‐spacemodels’dirtylittlesecrets:Evensimple linearGaussianmodelscanhaveestima‐tionproblems.Scientific Reports,6,26677.https://doi.org/10.1038/srep26677

Bacheler, N., Ciannelli, L., Bailey, K., & Duffy‐Anderson, J. (2010).Spatial and temporal patterns of walleye pollock spawn‐ing in the eastern Bering Sea inferred from egg and larval dis‐tributions. Fisheries Oceanography, 19, 107–120. https://doi.org/10.1111/j.1365‐2419.2009.00531.x

Bailey, K. M. (2000). Shifting control of recruitment of walleye pol‐lock Theragra chalcogramma after a major climatic and ecosystemchange.Marine Ecology Progress Series, 198, 215–224. https://doi.org/10.3354/meps198215

Bailey,K.M.,&Houde,E.D.(1989).Predationoneggsandlarvaeofma‐rinefishesandtherecruitmentproblem.Advances in Marine Biology,25,1–83.https://doi.org/10.1016/S0065‐2881(08)60187‐X

Bailey,K.M.,Zhang,T.,Chan,K. S., Porter, S.M.,&Dougherty,A.B.(2012). Near real‐time forecasting of recruitment from larval sur‐veys: Application toAlaska pollock.Marine Ecology Progress Series,452,205–217.https://doi.org/10.3354/meps09614

Bergstad,O.A.,Jørgensen,T.,&Dragesund,O.(1987).LifehistoryandecologyofthegadoidresourcesoftheBarentsSea.Fisheries Research,5,119–161.https://doi.org/10.1016/0165‐7836(87)90037‐3

Beverton,R.J.H.,&Holt,S.J.(1957).On the dynamics of exploited fish pop‐ulations (fish and fisheries series, Vol. 11).Dordrecht,theNetherlands:SpringerScience+BusinessMedia.

Bogstad,B.,Dingsør,G.E.,Ingvaldsen,R.B.,&Gjøsæter,H.(2013).Changesintherelationshipbetweenseatemperatureandrecruitmentofcod,haddockandherring in theBarentsSea.Marine Biology Research,9,895–907.https://doi.org/10.1080/17451000.2013.775451

Bogstad,B.,Yaragina,N.A.,&Nash,R.D.M.(2016).Theearlylife‐his‐torydynamicsofNortheastArcticcod:Levelsofnaturalmortality

14  |     STIGE ET al.

andabundanceduringthefirstthreeyearsoflife.Canadian Journal of Fisheries and Aquatic Sciences,72,246–256.https://doi.org/10.1139/cjfas‐2015‐0093

Brodeur, R. D., & Wilson, M. T. (1996). A review of the distribution,ecology and population dynamics of age‐0 walleye pollock in theGulf of Alaska. Fisheries Oceanography, 5, 148–166. https://doi.org/10.1111/j.1365‐2419.1996.tb00089.x

Campana, S. E. (1996). Year‐class strength and growth rate in youngAtlanticcodGadus morhua. Marine Ecology Progress Series,135,21–26.https://doi.org/10.3354/meps135021

Campana,S.E., Smith,S. J.,&Hurley,P.C.F. (1989).Adrift‐retentiondichotomy for larvalhaddock (Melanogrammus aeglefinus) spawnedonBrownsBank.Canadian Journal of Fisheries and Aquatic Sciences,46,93–102.https://doi.org/10.1139/f89‐281

Cargnelli,L.,Griesbach,S.,Berrien,P.,Morse,W.,&Johnson,D.(1999).Essential fish habitat source document: Haddock, Melanogrammusaeglefinus, life history and habitat characteristics. NOAA TechnicalMemorandumNMFS‐NE‐128.WoodsHole,MA:NationalOceanicandAtmosphericAdministration.

Clark, J. S.,&Bjørnstad,O.N. (2004).Population time series:Processvariability, observation errors, missing values, lags, and hiddenstates.Ecology,85,3140–3150.https://doi.org/10.1890/03‐0520

Cushing,D.H. (1995).Population production and regulation in the sea. A fisheries perspective.Cambridge,UK:CambridgeUniversityPress.

DFO (2003). Haddock on the Southern Scotian Shelf and Bay of Fundy (Div. 4X/5Y).DFOCan. Sci. Advis. Sec. Sci. Advis. Rep. 2003/051.Dartmouth,Canada:DepartmentofFisheriesandOceansCanada.

DFO (2006). Haddock on the Southern Scotian Shelf and Bay of Fundy (Div. 4X/5Y). DFOCan. Sci. Advis. Sec. Sci. Advis. Rep. 2006/047.Dartmouth,Canada:DepartmentofFisheriesandOceansCanada.

Dorn,M.,Aydin,K., Fissel,B., Jones,D.,McCarthy,A.,Palsson,W.,&Spalinger,K.(2016).AssessmentofthewalleyepollockstockintheGulf of Alaska. In The Plan Team for the Groundfish Fisheries oftheGulf ofAlaska (Ed.),Stock assessment and fishery evaluation re‐port for the groundfish resources of the Gulf of Alaska (pp.119–136).Anchorage,AK:NorthPacificFisheryManagementCouncil.

Dragesund,O.,Hylen,A.,Olsen,S.,&Nakken,O. (2008).TheBarentsSea0‐groupsurveys;anewconceptofpre‐recruitmentstudies. InO.Nakken(Ed.),Norwegian spring‐spawning herring & northeast Arctic cod; 100 years of research and management(pp.119–136).Trondheim,Norway:TapirAcademicPress.

Duffy‐Anderson,J.,Ciannelli,L.,Honkalehto,T.,Bailey,K.M.,Sogard,S.M.,Springer,A.M.,&Buckley,T. (2003).Distributionofage‐1andage‐2walleyepollockintheGulfofAlaskaandeasternBeringSea:Sourcesofvariationandimplicationsforhighertrophiclevels.InH.Browman&A.Skiftesvik(Eds.),The big fish bang: Proceedings of the 26th annual larval fish conference (pp. 381–394). Bergen, Norway:InstituteofMarineResearch.

Fauchald,P.,Mauritzen,M.,&Gjøsæter,H.(2006).Density‐dependentmi‐gratorywavesinthemarinepelagicecosystem.Ecology,87,2915–2924.https://doi.org/10.1890/0012‐9658(2006)87[2915:DMWITM]2.0.CO;2

Gaichas,S.K.,&Francis,R.C.(2008).Networkmodelsforecosystem‐basedfisheryanalysis:AreviewofconceptsandapplicationtotheGulf of Alaskamarine foodweb.Canadian Journal of Fisheries and Aquatic Sciences,65,1965–1982.https://doi.org/10.1139/F08‐104

Gelman, A., & Rubin,D. B. (1992). Inference from iterative simulationusingmultiplesequences.Statistical Science,7,457–472.https://doi.org/10.1214/ss/1177011136

Gjøsæter,H.(1998).Thepopulationbiologyandexploitationofcapelin(Mallotus villosus)intheBarentsSea.Sarsia,83,453–496.https://doi.org/10.1080/00364827.1998.10420445

Gjøsæter,H.,Dalpadado,P.,&Hassel,A.(2002).GrowthofBarentsSeacapelin(Mallotus villosus)inrelationtozooplanktonabundance.ICES Journal of Marine Science, 59, 959–967. https://doi.org/10.1006/jmsc.2002.1240

Grubbs, F. (1969). Procedures for detecting outlying observations insamples. Technometrics, 11, 1–21. https://doi.org/10.1080/00401706.1969.10490657

Hassel,M.P.(1975).Density‐dependenceinsingle‐speciespopulations.Journal of Animal Ecology,44,283–295.https://doi.org/10.2307/3863

Heintz, R. A., Siddon, E. C., Farley, E. V., & Napp, J. M. (2013).Correlationbetweenrecruitmentandfallconditionofage‐0pol‐lock (Theragra chalcogramma) from the easternBering Sea undervarying climate conditions. Deep‐Sea Research Part II: Topical Studies in Oceanography, 94, 150–156. https://doi.org/10.1016/j.dsr2.2013.04.006

Helle, K., Bogstad, B., Marshall, C. T., Michalsen, K., Ottersen, G., &Pennington, M. (2000). An evaluation of recruitment indices forArcto‐Norwegiancod(Gadus morhuaL.).Fisheries Research,48,55–67.https://doi.org/10.1016/S0165‐7836(00)00119‐3

Hiatt,T.,Dalton,M.,Felthoven,R.,Fissel,B.,Garber‐Yonts,B.,Haynie,A.,…Seung,C.(2011).Stock assessment and fishery evaluation report for the groundfish fisheries of the Gulf of Alaska and Bering Sea/Aleutian Islands area: Economic status of the groundfish fisheries off Alaska. Anchorage,AK:NorthPacificFisheriesManagementCouncil.

Hinckley,S.(1987).Thereproductivebiologyofwalleyepollock,Theragra chalcogramma, intheBeringSea,withreferencetospawningstockstructure. Fishery Bulletin, 85, 481–498. https://doi.org/10.1002/Grl.50726

Hixon,M.A.,Pacala,S.W.,&Sandin,S.A.(2002).Populationregulation:Historicalcontextandcontemporarychallengesofopenvs.closedsystems. Ecology, 83, 1490–1508. https://doi.org/10.1890/0012‐9658(2002)083[1490:PRHCAC]2.0.CO;2

Hjort, J. (1914). Fluctuations in thegreat fisheriesofnorthernEuropeviewedinthelightofbiologicalresearch.Rapports et Procès‐Verbaux Des Réunions Du Conceil International Pour L'exploration De La Mer,20,1–228. 11250/ 109177

Houde,E.D.(1987).Fishearlylifedynamicsandrecruitmentvariability.American Fisheries Society Symposium,2,17–29.

Houde,E.D.(2008).EmergingfromHjort'sshadow.Journal of Northwest Atlantic Fishery Science, 41, 53–70. https://doi.org/10.2960/J.v41.m634

Ianelli,J.N.,Honkalehto,T.,Barbeaux,S.,Fissel,B.,&Kotwicki,S.(2016).AssessmentofthewalleyepollockstockintheEasternBeringSea.InThePlanTeamfortheGroundfishFisheriesoftheBeringSeaandAleutian Islands (Ed.),Stock assessment and fishery evaluation report for the groundfish resources of the Bering Sea/Aleutian Islands regions (pp. 55–180). Anchorage, AK: North Pacific Fishery ManagementCouncil.

Ives, A. R., Dennis, B., Cottingham, K. L., & Carpenter, S. R. (2003).Estimating community stability and ecological interactions fromtime‐seriesdata.Ecological Monographs,73,301–330.https://doi.org/10.1890/0012‐9615(2003)073[0301:ECSAEI]2.0.CO;2

Juanes, F. (2007). Role of habitat in mediating mortality duringthe post‐settlement transition phase of temperate ma‐rine fishes. Journal of Fish Biology, 70, 661–677. https://doi.org/10.1111/j.1095‐8649.2007.01394.x

Laurel,B.J.,Spencer,M.,Iseri,P.,&Copeman,L.A.(2016).Temperature‐dependentgrowthandbehaviorof juvenileArcticcod (Boreogadus saida)andco‐occurringNorthPacificgadids.Polar Biology,39,1127–1135.https://doi.org/10.1007/s00300‐015‐1761‐5

Lorenzen,K.,&Camp,E.V.(2018).Density‐dependenceinthelifehis‐toryoffishes:Whenisafishrecruited?Fisheries Research,217,5–10.https://doi.org/10.1016/j.fishres.2018.09.024

McClatchie, S., Duffy‐Anderson, J., Field, J., Goericke, R., Griffith, D.,Hanisko, D., … Zapfe, G. (2014). Long time series in US fisheriesoceanography. Oceanography, 27, 48–67. https://doi.org/10.5670/oceanog.2014.86

Megrey, B. A., Hollowed, A. B., Hare, S. R., Maclin, S. A., &Stabeno, P. J. (1996). Contributions of FOCI research to

     |  15STIGE ET al.

forecasts of year‐class strength of walleye pollock in ShelikofStrait, Alaska. Fisheries Oceanography, 5, 189–203. https://doi.org/10.1111/j.1365‐2419.1996.tb00092.x

Miller,T.J.,Crowder,L.B.,Rice,J.A.,&Marschall,E.A. (1988).Larvalsize and recruitment mechanisms in fishes: Toward a conceptualframework. Canadian Journal of Fisheries and Aquatic Sciences, 45,1657–1670.https://doi.org/10.1139/f88‐197

Mukhina,N.V.,Marshall,C.T.,&Yaragina,N.A. (2003). Tracking thesignal in year‐class strengthofNortheastArctic cod throughmul‐tiple survey estimates of egg, larval and juvenile abundance.Journal of Sea Research, 50, 57–75. https://doi.org/10.1016/S1385‐1101(03)00046‐7

Ohlberger,J.,Rogers,L.A.,&Stenseth,N.C. (2014).Stochasticityanddeterminism:Howdensity‐independentanddensity‐dependentpro‐cessesaffectpopulationvariability.PLoS ONE,9,e98940.https://doi.org/10.1371/journal.pone.0098940

Olsen,E.,Aanes,S.,Mehl,S.,Holst,J.C.,Aglen,A.,&Gjøsæter,H.(2010).Cod,haddock,saithe,herring,andcapelinintheBarentsSeaandadja‐centwaters:Areviewofthebiologicalvalueofthearea.ICES Journal of Marine Science,67,87–101.https://doi.org/10.1093/icesjms/fsp229

Ottersen, G., Bogstad, B., Yaragina, N. A., Stige, L. C., Vikebø, F. B.,&Dalpadado, P. (2014). A reviewof early life history dynamics ofBarentsSeacod(Gadus morhua). ICES Journal of Marine Science,71,2064–2087.https://doi.org/10.1093/icesjms/fsu037

Ottersen, G., Helle, K., & Bogstad, B. (2002). Do abiotic mechanismsdetermineinterannualvariabilityinlength‐at‐ageofjuvenileArcto‐Norwegian cod?Canadian Journal of Fisheries and Aquatic Sciences,59,57–65.https://doi.org/10.1139/f01‐197

Ottersen,G.,&Loeng,H.(2000).Covariabilityinearlygrowthandyear‐classstrengthofBarentsSeacod,haddockandherring:Theenviron‐mentallink.ICES Journal of Marine Science,57,339–348.https://doi.org/10.1006/jmsc.1999.0529

Pepin,P.(2015).Deathfromnearandfar:Alternateperspectivesonsize‐dependentmortalityinlarvalfish.ICES Journal of Marine Science,73,196–203.https://doi.org/10.1093/icesjms/fsv1160

Plummer, M. (2016). rjags: Bayesian Graphical Models using MCMC. R packageversion4‐6.https://CRAN.R‐project.org/package=rjags

Ricard,D.,Zimmermann,F.,&Heino,M.(2016).Arenegativeintra‐spe‐cificinteractionsimportantforrecruitmentdynamics?AcasestudyofAtlanticfishstocks.Marine Ecology Progress Series,547,211–217.https://doi.org/10.3354/meps11625

Ricker, W. E. (1954). Stock and recruitment. Journal of the Fisheries Research Board of Canada, 11, 559–623. https://doi.org/10.1139/f54‐039

Rose,K.A.,Cowan,J.H.,Winemiller,K.O.,Myers,R.A.,&Hilborn,R. (2001). Compensatory density dependence in fish popula‐tions: Importance, controversy, understanding and prognosis.Fish and Fisheries, 2, 293–327. https://doi.org/10.1046/j.1467‐ 2960.2001.00056.x

Shackell,N.L.,Frank,K.T.,Petrie,B.,Brickman,D.,&Shore,J. (1999).Dispersalofearly lifestagehaddock(Melanogrammus aeglefinus)asinferredfromthespatialdistributionandvariabilityinlength‐at‐ageof juveniles.Canadian Journal of Fisheries and Aquatic Sciences,56,2350–2361.https://doi.org/10.1139/f99‐172

Sogard,S.M.(1997).Size‐selectivemortalityinthejuvenilestageoftele‐ostfishes:Areview.Bulletin of Marine Science,60,1129–1157.

Stige,L.C.,Hunsicker,M.E.,Bailey,K.M.,Yaragina,N.A.,&Hunt,G.L.Jr (2013).Predicting fish recruitment from juvenileabundanceandenvironmentalindices.Marine Ecology Progress Series,480,245–261.https://doi.org/10.3354/meps10246

Stige,L.C.,Kvile,K.Ø.,Bogstad,B.,&Langangen,Ø.(2018).Predator‐preyinteractionscauseapparentcompetitionbetweenmarinezoo‐plankton groups. Ecology, 99, 632–641. https://doi.org/10.1002/ecy.2126

Stige, L.C., Langangen,Ø., Yaragina,N.A.,Vikebø, F. B., Bogstad,B.,Ottersen, G., … Hjermann, D. Ø. (2015). Combined statistical andmechanistic modelling suggests food and temperature effects onsurvivalofearlylifestagesofNortheastArcticcod(Gadus morhua).Progress in Oceanography, 134, 138–151. https://doi.org/10.1016/j.pocean.2015.01.009

Stige, L.C.,Ottersen,G.,Dalpadado, P., Chan,K.‐S.,Hjermann,D.Ø.,Lajus,D.L.,…Stenseth,N.C.(2010).Directandindirectclimateforc‐inginamulti‐speciesmarinesystem.Proceedings of the Royal Society B: Biological Sciences, 277, 3411–3420. https://doi.org/10.1098/rspb.2010.0602

vanGemert,R.,&Andersen,K.H.(2018).Implicationsoflate‐in‐lifeden‐sity‐dependentgrowthforfisherysize‐at‐entryleadingtomaximumsustainable yield. ICES Journal of Marine Science, 75, 1296–1305.https://doi.org/10.1093/icesjms/fsx236

Yaragina,N.A.,Bogstad,B.,&Kovalev,Y.A. (2009).Variability incan‐nibalism in Northeast Arctic cod (Gadus morhua) during the pe‐riod 1947–2006. Marine Biology Research, 5, 75–85. https://doi.org/10.1080/17451000802512739

Yaragina,N.A.,&Dolgov,A.V. (2009).Ecosystemstructureandresil‐ience–AcomparisonbetweentheNorwegianandtheBarentsSea.Deep‐Sea Research II, 56, 2141–2153. https://doi.org/10.1016/j.dsr2.2008.11.025

Zimmermann, F., Ricard,D.,&Heino,M. (2018).Density regulation inNortheastArctic fishpopulations:Densitydependence is strongerinrecruitmentthaninsomaticgrowth.Journal of Animal Ecology,87,672–681.https://doi.org/10.1111/1365‐2656.12800

SUPPORTING INFORMATION

Additional supporting information may be found online in theSupportingInformationsectionattheendofthearticle.

How to cite this article:StigeLC,RogersLA,NeuheimerAB,etal.Density‐andsize‐dependentmortalityinfishearlylifestages.Fish Fish. 2019;00:1–15. https://doi.org/10.1111/faf.12391