Functional Ecology. 2018;1–18. wileyonlinelibrary.com/journal/fec  | 1© 2018 The Authors. Functional Ecology © 2018 British Ecological Society

Received:29May2018  |  Accepted:30October2018DOI:10.1111/1365-2435.13241

E C O ‐ E V O L U T I O N A R Y D Y N A M I C S A C R O S S S C A L E S

Eco‐evolutionary feedbacks—Theoretical models and perspectives

Lynn Govaert1,2,3* | Emanuel A. Fronhofer4*  | Sébastien Lion5 | Christophe Eizaguirre6 | Dries Bonte7  | Martijn Egas8 | Andrew P. Hendry9  | Ayana De Brito Martins10 | Carlos J. Melián10 | Joost A. M. Raeymaekers11 | Irja I. Ratikainen12,13 | Bernt‐Erik Saether12 | Jennifer A. Schweitzer14 | Blake Matthews2

1LaboratoryofAquaticEcology,EvolutionandConservation,KULeuven,Leuven,Belgium;2DepartmentofAquaticEcology,Eawag:SwissFederalInstituteofAquaticScienceandTechnology,Dübendorf,Switzerland;3DepartmentofEvolutionaryBiologyandEnvironmentalStudies,UniversityofZurich,Zürich,Switzerland;4ISEM,CNRS,IRD,EPHE,UniversitédeMontpellier,Montpellier,France;5Centred'EcologieFonctionnelleetEvolutive,CNRS,IRD,EPHE,UniversitédeMontpellier,Montpellier,France;6QueenMaryUniversityofLondon,London,UK;7DepartmentofBiology,GhentUniversity,Ghent,Belgium;8InstituteforBiodiversityandEcosystemDynamics,UniversityofAmsterdam,Amsterdam,TheNetherlands;9RedpathMuseumandDepartmentofBiology,McGillUniversity,Montreal,Quebec,Canada;10FishEcologyandEvolutionDepartment,CenterforEcology,EvolutionandBiogeochemistry,Eawag:SwissFederalInstituteofAquaticScienceandTechnology,Dübendorf,Switzerland;11FacultyofBiosciencesandAquaculture,NordUniversity,Bodø,Norway;12DepartmentofBiology,CentreforBiodiversityDynamics,NorwegianUniversityofScienceandTechnology,Trondheim,Norway;13InstituteofBiodiversity,AnimalHealthandComparativeMedicine,UniversityofGlasgow,Glasgow,UKand14DepartmentofEcologyandEvolutionaryBiology,UniversityofTennessee,Knoxville,Tennessee

*Theseauthorscontributedequallytothiswork.

CorrespondenceEmanuelA.FronhoferEmail:emanuel.fronhofer@umontpellier.fr

HandlingEditor:CharlesFox

Abstract1. Theoreticalmodelspertainingtofeedbacksbetweenecologicalandevolutionaryprocesses areprevalent inmultiplebiological fields.An integrativeoverview iscurrentlylacking,duetolittlecrosstalkbetweenthefieldsandtheuseofdifferentmethodologicalapproaches.

2. Here,wereviewawiderangeofmodelsofeco-evolutionaryfeedbacksandhigh-lighttheirunderlyingassumptions.Wediscussmodelswherefeedbacksoccurbothwithinandbetweenhierarchicallevelsofecosystems,includingpopulations,com-munitiesandabioticenvironments,andconsiderfeedbacksacrossspatialscales.

3. Identifying the commonalities among feedbackmodels, and the underlying as-sumptions,helpsusbetterunderstandthemechanisticbasisofeco-evolutionaryfeedbacks.Eco-evolutionaryfeedbackscanbereadilymodelledbycouplingde-mographic and evolutionary formalisms.We provide an overview of these ap-proachesandsuggestfutureintegrativemodellingavenues.

4. Ouroverviewhighlightsthateco-evolutionaryfeedbackshavebeenincorporatedintheoreticalworkfornearlyacentury.Yet,thisworkdoesnotalwaysincludethenotionofrapidevolutionorconcurrentecologicalandevolutionarytimescales.We show the importance of density- and frequency-dependent selection forfeedbacks,aswellastheimportanceofdispersalasacentrallinkingtraitbetweenecologyandevolutioninaspatialcontext.

K E Y W O R D S

demography,eco-evolutionarydynamics,ecology,feedback,modelling,rapidevolution,theory

2  |    Functional Ecology GOVAERT ET Al.

1  | INTRODUC TION

Feedbacksarerelevanttomanybiologicalsystemsandarecentraltoecologyandevolutionarybiology(Robertson,1991).Whileecologyaims tounderstand the interactionsbetween individualsand theirenvironment,evolutionreferstochangesinallelefrequenciesovertime.Inthepast,bothfieldshave,toalargeextent,beenstudiedinisolation.Evolutionaryecology(e.g.Roughgarden,1979)isanotableexception,where links between ecology and evolution are key toempiricalandtheoreticalresearch.

One of the pioneering studies on feedbacks between ecologyandevolutiondatesbacktoPimentel’sworkon“geneticfeedback”(Pimentel,1961).Inthisfeedback,frequenciesanddensitiesofdif-ferent genotypes in ahostpopulation shift theoverall populationdensity.Thischange indensitymodifiesselectiononthehostandconsequentlyshiftsgenotypefrequencies.Anotherearlyfeedbackconceptofgreatimportanceisdensity-dependentselection(Chitty,1967)wherethestrengthofselectionchangesduetochangingpop-ulation densities and vice versa (crowding; see also Clarke, 1972;Travis,Leips,&Rodd,2013).

Inrecentyears,therecognitionthatevolutioncanberapidandoccur on similar time scales as ecology (Hairston, Ellner, Geber,Yoshida,&Fox,2005;Hendry&Kinnison,1999)haspromptedre-search at the interfacebetween the twodisciplines (often termed“eco-evolutionary dynamics”; Hendry, 2017) and renewed theinterest in feedbacks between ecological and evolutionary pro-cesses[“eco-evolutionaryfeedbacks”(EEF);seeFigure1a;Ferrière,Dieckmann,&Couvet,2004;Pelletier,Garant,&Hendry,2009;Post&Palkovacs, 2009]. Eco-evolutionary feedbacks involve situationswhereanecologicalpropertyinfluencesevolutionarychange,whichthenfeedsbacktoanecologicalproperty,orviceversa.Classicalem-piricalexamplesincludethatpredation(ecologicalproperty)canleadto selection on defence traits in prey (evolutionary change)whichinturnfeedsbackonpredator–preydynamicsandshiftsthephaseof predator–preyoscillations (feedbackonecological property; re-viewedinHiltunen,Hairston,Hooker,Jones,&Ellner,2014).

Contemporary theory aboutEEFsbuildsonmanyof the samefundamentalideasestablishedbyPimentel(1961)andChitty(1967),andfeedbacksremaincentraltothedevelopmentoftheoryinevo-lutionary ecology (for recent overview see Lion, 2018; McPeek,2017).Suchfeedbackshavebeenfoundtogeneratespatialvariationinbioticinteractions(geographicmosaicofcoevolution;Thompson,2005),impactpopulationregulationandcommunitydynamics(e.g.,Abrams &Matsuda, 1997; Patel, Cortez, & Schreiber, 2018), andlead to species coexistence via stabilizingmechanisms (Kremer &Klausmeier, 2017), to name but a few examples. Besides theoret-icalwork, empirical and especially experimental tests of eco-evo-lutionary dynamics and feedbacks have increased recently (e.g.,Becks,Ellner,Jones,&Hairston,2010,2012;Brunner,Anaya-Rojas,Matthews,&Eizaguirre,2017;Schoener,2011;Turcotte,Reznick,&Hare,2011;Yoshida,Jones,Ellner,Fussmann,&Hairston,2003),andhavestronglycontributedtoourunderstandingonEEFs.

TheincreasingevidenceontheimportanceofEEFshasresultedin a series of existing literature reviews (e.g. Bailey& Schweitzer,2016;Fussmann,Loreau,&Abrams,2007;Hendry,2017;Pelletieretal.,2009;Post&Palkovacs,2009;Shefferson&Salguero-Gómez,2015; Van Nuland etal., 2016). These reviews, however, havebeenratherattheintersectionofempiricalandtheoreticalstudies(Fussmannetal.,2007),focusonparticularsystems(e.g.,plant–soilfeedbacks Bailey & Schweitzer, 2016; terHorst & Zee, 2016; VanNuland etal., 2016) or very broadly discuss eco-evolutionary dy-namics (e.g. Hendry, 2017). None of these overviews include thetheoretical literature in its full diversity, neither do they explicitlycomparedifferentmodellingframeworksforstudyingEEFs.

Here, we provide an overview of theoretical work that in-cludesEEFs(foracomprehensiveoverviewofempiricalworkseeHendry,2017)asanattempttoprovideaconceptualunificationthatfurthersourgeneralunderstandingofeco-evolutionaryfeed-back theory. While this review is focused on theoretical work,theinsightslearntarevaluablefortestingpredictionsempirically.Currently,therelevanttheoryvariesinmethodologicalapproaches(e.g., quantitative genetics and adaptivedynamics) andbetweenthematic subdisciplines (e.g., evolutionary rescue or suicide andnicheconstruction)withmostlysubtle,andattimessemantic,dis-tinctionsbetweenthem(Matthewsetal.,2014).Inanattempttobridgetheseboundaries,weorganizeournonexhaustiveoverviewaroundtwoaxesofbiologicalcomplexity:community(fromsingletomulti-speciesmodels)andspatialcomplexity(fromnonspatialtospatiallyexplicitmodels).Ourreviewfocusesspecificallyonfeed-backsanddiscussesEEFs inatheoreticalcontextacrossabroad

F I G U R E 1  Eco-evolutionaryfeedbacks(EEF).(a)Genericrepresentationoffeedbacksbetweenecology(greybox)andevolution(greenbox)implyingthattheeffectofanecologicalproperty(e.g.,demography)canbetracedtoevolutionarychange(e.g.,shiftinallelefrequencies;eco-to-evo)andbackagaintoanecologicalproperty(evo-to-eco)orviceversa.(b)Examplesofdemographic(ecological)andevolutionarymodellingformalismsthatcanbecoupledtoanalyseEEFs.Ofcourse,ODEsandIBMscanbeusedtomodelevolution,but,strictlyspeaking,theywillmakeuseofsomeoftheevolutionarymodellingframeworks,likeQGorgeneticalgorithms(GA),todoso.Theboxtypesandcolourswillbeusedthroughoutthetexttoimplyecologicalorevolutionaryaspects,respectively.Foradetailedexplanationofabbreviations,seeBox1

Ecology Evolution

species distributions,demography

interactions, etc.

distribution oftraits and/or

alleles

(a) Generic eco-evolutionary feedback patterns

Ecology Evolution

ODEs, difference equations,

matrix models,IPMs, IBMs, etc.

QG, game theory, AD, genetic algorithms

(b) Examples of modelling formalisms

     |  3Functional EcologyGOVAERT ET Al.

scaleofbiological levelswithastrongmethodologicalfocus.WesummarizeavailableformalismsusedtostudyEEFstheoretically,highlight their underlying assumptions and give an overview ofexisting theoreticalwork tohighlight researchgaps.WeuseoursynthesistoexpandthegenericfeedbackloopshowninFigure1aand to suggest a more mechanistic representation. Lastly, wemakesuggestionsforfuturedirectionsandwaystoovercomethebarriersthathavesofarpreventedsynthesisoftheoryinthisfield.

2  | FORMALISMS USED FOR MODELLING EEFS

Theoreticiansuseavarietyofdemographicmodelstostudythein-terplaybetweenecologyandevolution,includingclassicalordinarydifferentialequationmodels(ODEs,e.g.,Lotka–Volterraequations,for explanations and abbreviations of recurring terms see Box1),

structuredmodels(matrixmodels,physiologicallystructuredpopu-lationmodels,integralprojectionmodels)orstochasticagent-basedmodels.Byintroducinggeneticvariation(viastandinggeneticvari-ation and/ormutations) inoneor several populations, themodelscancaptureEEFs (Figure1b).Becausesuchmodelsarenotalwaysanalyticallytractable,variousformalisms,suchasadaptivedynamics(AD)andquantitativegenetics(QG),havebeendevelopedtofurtherour understanding of EEFs. Typically, these approaches takeEEFsintoaccount throughsimplifyingassumptionsonthetimescaleofecologicalandevolutionaryprocessesandonthemutationregime(reviewedinLion,2018).

Models usingAD rely on a separation of time scales betweenecologicalandevolutionarydynamics.Specifically,thesemodelsas-sume thatmutations are so rare that the ecological community isalwaysonitsattractor,sothattheevolutionarydynamicstaketheformofatemporalsequenceofallelesubstitutions (i.e.,mutation-limitedevolution).Thesuccessofamutantalleleisthenmeasured

BOX 1 Explanation of terms and abbreviations

Adaptive dynamics (AD):ADisamathematicalformalismthatprovidesadynamicalextensionofclassicaloptimizationapproachesandevolutionarygametheorytoincludedensityandfrequencydependence(Diekmann,2004;Waxman&Gavrilets,2005).Thismakeseco-evolutionaryfeedbackscentraltoAD.Dispersal:Dispersalisthemovementofindividualsawayfromtheirparentswithpotentialconsequencesforgeneflow(Clobertetal.,2012).Eco‐evolutionary feedback (EEF):Areciprocalinteractionbetweenanecologicalandevolutionaryprocesses(seeFigure1a).Theecologicalpropertyinfluencedbyevolutionarychangeneednotbethesameecologicalpropertythatledtotheevolutionarychange(narrowandbroadsensefeedbackssensuHendry,2017).Evolutionary rescue (ER) and suicide (ES):ERistheideathatapopulationcanavoidextinctionthroughrapidadaptation(Gonzalezetal.,2013).Bycontrast,ESistheprocessbywhichevolutiondrivesapopulationbeyonditsviabilityregion,eventuallycausingextinction(Ferriere,2000).Evolutionary game theory:Abranchofmathematicsthatstudiestheinteractionsbetweenindividualsinwhichthestrategyexertedbyanindividualhasapay-off thatdependsonboth the individual’s strategyandthestrategiesof theother individuals involved (McGill&Brown,2007).Genetic algorithm (GA):Atypeofoptimizationalgorithmusingtechniquesfromevolutionarybiology(i.e.,mutation,inheritance,selectionandrecombination)tofindanoptimizedsolutiontoaproblem(e.g.,Fraser,1957).Individual‐based model (IBM):IBM(alsoagent-basedmodel,ABMs)arebottom-upmodelsinwhicha(meta)populationor(meta)communityismodelledasanumberofdiscreteinteractingindividuals,inwhicheachindividualischaracterizedbyasetofstatevariables(location,physiologicalorbehaviouraltraits).Theinteractionsbetweenindividualsresultin(meta)populationand(meta)communityor(meta)foodwebdynamics(DeAngelis&Mooij,2005;Grimm,1999).Integral projection model (IPM):IPMsdescribethedynamicsofapopulationbyprojectingitssizeortraitdistributionthroughtimeusingakerneldistribution that connects individual-levelvital rates suchas survival, reproductionanddevelopment topopulation-levelpro-cesses.IPMscanbecoupledwithADorQGapproaches(Rees&Ellner,2016).Lotka‐Volterra model (LV):TheLVmodel(namedafterAlfredLotkaandVitoVolterra)consistsofODEsdescribingpredatorandpreydy-namics.Modificationsofthebasicmodelinclude,forexample,theRosenzweig-MacArthurmodel.Matrix population model:Formalizesthelifecycleofapopulationinamatrixusingeitherdiscretelifestages(classicalmatrixpopulationmodels;Caswell,2006)oracontinuoustraitsuchasbodysize(see“integralprojectionmodel”above).Metapopulation and metacommunity:Ametapopulationsensu lato isaspatiallystructuredpopulation,connectedbydispersal (Hanski,1999;Harrison&Hastings,1996).Similarly,ametacommunityisaspatiallystructuredcommunity,connectedbydispersal(Leiboldetal.,2004).Quantitative genetics (QG):QGstudiesthegeneticbasisofphenotypicvariation,withafocusonthedynamicsofcontinuoustraitdistribu-tions(Lynch&Walsh,1998).

4  |    Functional Ecology GOVAERT ET Al.

byitsinvasionfitness(Geritz,Kisdi,Meszena,&Metz,1998;Metz,Nisbet,&Geritz,1992).Theseparationoftimescalesbetweenecol-ogy and evolution, however, does notmean that there is no EEF.The feedback ismaterialized by the fact that the invasion fitnessofamutantalleledependsontheecologicalconditionscreatedbythe residentcommunity. In fact, theconceptofa “feedback loop”between ecology and evolution has been central in the develop-mentofAD(Ferrière&Legendre,2012).Nevertheless,thefocusonecologicalattractorsmaybea limitation.RecentworkbyChesson(2017)suggeststhatthereplacementofecologicalattractorswithtime-dependent environmental functions towhich the populationconvergesmayrepresentawayforward.

Quantitativegeneticsmodels,bycontrast,startfromadifferentperspectiveandexplicitlyconsiderevolutionresultingfromexistinggeneticvariation.Foragivenquantitativetrait,thesemodelstrackthedynamicsofdifferentmomentsofthetraitdistributionsthatarecentraltoeco-evolutionarydynamics(mean,variance,etc.;Chevin,Cotto,&Ashander,2017).Often,additionalassumptionshavetobemade,toallowforsimplifications.ManyQGmodelsassumethatthetraitdistributionisGaussianandtightlyclusteredaroundthemean(smallvarianceorweakselectionapproximation).Inthatcase,itbe-comespossibletoapproximatetheecologicaldynamicsofthefocalpopulationasifall individualshadthemeantraitvalue,andtoun-derstand thechange inmean trait in relation toa selectiongradi-ent,where the selectiongradient itselfdependson theecologicaldynamics(e.g.,Abrams&Matsuda,1997;Lion,2018;Luo&Koelle,2013).Thisallowsthecouplingofecologyandevolution,similarlytoAD,withthedifferencethatecologicaldynamicsdonothavetobeatequilibrium(noseparationoftimescales;seeLande,2007;Lande,Engen,&Saether,2009,fortheimpactofenvironmentalvariation).Therefore, QG models can focus on short-term dynamics, whichmakes them potentially more applicable to experiments or fieldstudieswhererapidevolutionisakeyprocess.

Onthedemographic (ecological)side,ODEs,matrixpopulationmodels(e.g.,integralprojectionmodels—IPMs)andindividual-basedmodels (IBMs) have been used to study population dynamics, buthavealsobeenusedtostudysimultaneouschangeinecological(e.g.,populationsize)andevolutionaryparameters(e.g.,strengthofselec-tion),withoutexplicitlyusingthetermEEF(seee.g.,Caswell,2006).However, ODEs and matrix population models can be combinedwith AD and QG approaches to investigate EEFs (Rees & Ellner,2016). Individual-basedmodelsmay rely on genetic algorithms tocaptureevolutionarydynamics(Fraser,1957).Inaddition,IBMslendthemselvesveryeasilytotheincorporationofcomplexitiessuchasstochasticity, spatial structure and kin competition (e.g. Poethke,Pfenning,&Hovestadt, 2007),which are often difficult to handleusinganalyticalmodels.

Whileallof theseapproachescanbeused toanswera similarquestion,thereareoftenbarrierstointegration,orstemming,forex-ample,fromthespecificvocabularyofthefield.Nevertheless,therehasbeensomerecentprogresstowardssynthesis(Abrams,Harada,&Matsuda,1993;Day,2005;Day&Gandon,2007;Lion,2018).Forexample,ithasbeenshownthatasadditivegeneticvarianceinQG

models becomes very small, resultswill converge to those of ADmodels,whichprovidesadirectlinkbetweenthesetwomethodol-ogies (e.g.,Kremer&Klausmeier,2013).Asanotherexample,Lion(2018)suggestedconsideringtheorganism–environmentfeedbackascentral toeco-evolutionarymodels. In this formalism, theenvi-ronmentalvectorcapturesbothfocalpopulationdensities,aswellasexternalvariablessuchasabioticenvironments,andresources.

Beyondthescopeofthisreviewarecomplexadaptivesystemsmodels such as Bruggeman and Kooijman (2007) or Leibold andNorberg (2004), to name but two examples. These models allowfordynamicssimilartotraitevolutionandsimultaneouslyconsiderlargenumbersofspecieswithphenotypesfinelyspacedalongoneormoretraitaxes.WenextprovideageneraloverviewonmodelsincludingEEFsandtheirresultsstartingfrompopulationstocommu-nitiestoendwithecosystemsandfoodwebs.

3  | EEFS WITHIN POPUL ATIONS

ManytheoreticalstudieshaveanalysedEEFswithinasinglepopu-lation in a temporal or spatial setting. In single-species nonspatialsettings, EEFs areusually consideredbetween changes inpopula-tionsizeandchangesinheritabletraits.Inaspatialsetting,EEFscanoccurbetweenlocalpopulationsizeandlocaltraitvalues,butalsoamongpatchesbetweenregional(meta)populationsizeandlocalorregionaltraitvalues.Inaddition,landscapestructure(topology,con-nectivity)mightinfluencelocalEEFs,butalsoinducefeedbacksonaregionalscale.Thisisbecausedispersal(demography)andgeneflow(populationgenetics)areintrinsicallylinked.

3.1 | Feedbacks in single populations

Feedbacksovertimecanbeintrinsictothepopulation,whenitoc-cursbetweenpopulationdensityandtraitvalues,orextrinsic,whenitoccursbetweentheavailabilityofresourcesandtraitvalues.Forexample, a quantitative trait subject to density-dependent or fre-quency-dependentselection (eco-to-evo)can influencepopulationgrowth rate (evo-to-eco; Engen, Lande, & Sӕther, 2013; Lande,2007;Travisetal., 2013).Density-or frequency-dependent selec-tionimpliesthatanindividual’sfitnessisnotonlydeterminedbyitstraitvalue,butalsobythepopulationdensityorbytheproportionofcertaingenotypes (Clarke,1972;Travisetal.,2013). Inthecaseofdensity-dependentselection,changingpopulationdensitiesshifttheselectionpressurefavouringdifferentgenotypesbecauseofdif-ferentialcompetitiveability. In turn,changingcompetitiveabilitiescreate varying ecological conditions leading to changes in density(Engenetal.,2013;Lande,2007;MacArthur,1962).

Lively (2012) used a one-locus two-allele genetic system (QGwith two types) to illustrate a feedback betweenpopulation den-sity and allele frequency change assuming density-dependent se-lection (Figure2a). Similarly, Lande (2007) and Engen etal. (2013)usedQGmodelslinkingtheevolutionofaquantitativetraittopop-ulationgrowth,strengthofdensitydependenceandenvironmental

     |  5Functional EcologyGOVAERT ET Al.

stochasticity.Theseauthorsfoundthatinaconstantenvironment,evolutionwillmaximizemean fitness andmean relative fitness inthepopulationwhichmaychangewhenpopulationsizes fluctuate(Sӕther&Engen,2015).Technically, theevolutionary responseofthe population due to a changing environment in thesemodels isdescribed using the phenotypic selection differential (accountingforindividualsurvivalandfecundity,butnotinheritance)orintermsoftheselectiongradient(Landeetal.,2009;Leon&Charlesworth,1978).

Theassumptionoffrequency-dependentselectionisparticularlyrelevantinthecontextofsexualselectionandmatechoice(Alonzo&Sinervo,2001).Evolutionarygametheorycanbeusedtomodelapopulationconsistingoffemaleandmalemorphswherefemalematepreferencedependsonthetotalpopulationsize(density-dependentselection),butalsoonfemalemorphfrequency(frequency-depen-dentselection;Figure2b).ThisleadstoanEEFbetweenpopulationsizeandmorphfrequenciesviadensity-andfrequency-dependentselection(eco-to-evo)andviafitnessdifferencesinthemorphs(evo-to-eco;reviewedinSmallegange,Rhebergen,VanGorkum,Vink,&Egas, 2018). Very similarmechanisms have been discussed in thecontext of the evolution of cooperation (e.g., Gokhale & Hauert,2016;Lehtonen&Kokko,2012).Forexample,ecologicalconditions,suchasresourcelimitationandvariability,mayselectfortheevolu-tionofcooperation (eco-to-evo),whichcanthenfeedbackonde-mography leadingto increasedpopulationsizes (“supersaturation,”

Fronhofer, Liebig,Mitesser, & Poethke, 2018; Fronhofer, Pasurka,Mitesser,&Poethke,2011).

Finally, a classical EEF over time is often termed evolutionaryrescue(ER,seeBox1;Gomulkiewicz&Holt,1995;Gonzalez,Ronce,Ferriere,&Hochberg,2013;Lynch,1993).Evolutionaryrescuemod-els haveeither used aQGapproach, focusingon thepopulation’scapacitytotrackgraduallychangingoptimaintime(Burger&Lynch,1995;Lande&Shannon,1996)orspace(Pease,Lande,&Bull,1989;Polechová, Barton, & Marion, 2009; Uecker, Otto, & Hermisson,2014) or a singlemutation approach inwhich a population is ex-posed toa suddensevereenvironmental change (Gomulkiewicz&Holt,1995;Orr&Unckless,2014;Uecker,2017).Interestingly,whileERleadstopopulationpersistence,adaptiveevolutionmightalsore-sultinevolutionarytrappingorsuicide(ES,Ferriere,2000;Parvinen&Dieckmann,2013).Inthelatter,traitchangedrasticallydegradespopulation viability leading to extinction (Engen & Sӕther, 2017;Ferrière&Legendre,2012)becauseselectionactingattheindivid-ualleveldoesnotnecessarilyoptimizepopulation-levelproperties.WhethertheresultisERorES,thesemodelsdemonstratethatEEFscanbeofapplied relevance toconservation, forexample. In sum-mary,feedbacksovertimeareusuallymediatedbyintrinsically(den-sity-/frequency-dependentselection)orextrinsically(environment)changingselectionpressures.Theconsequencesofthesefeedbacksmaybepositive (e.g., increaseddensitiesandsurvival)ornegative(ES)atthepopulationlevel.

3.2 | Feedbacks in spatially structured populations

SpatialmodelsallowforEEFsbetweenlocaldemographyormetap-opulationconditionsandanevolvingtrait.Thefeedbackcanbemod-ifiedbyexternalpropertiessuchaspatchdynamics(colonizationandextinctionrates;Hanski&Mononen,2011)or landscapestructure(Fronhofer&Altermatt,2017;Kubisch,Winter,&Fronhofer,2016).Inmodelswithdiscretehabitatpatches,dispersal isacentral traitconnecting local patches and can have important effects on bothecological (Clobert,Baguette,Benton,&Bullock,2012)andevolu-tionary(e.g.,canlimitorfavourlocaladaptation;Lenormand,2002;Nosil, Funk,&Ortitz-Barrientos, 2009; Räsänen&Hendry, 2008)processes.Theevolutionofdispersal likely is themost frequentlystudiedexampleofanEEFinfragmentedlandscapes(Legrandetal.,2017).

In a spatial model without dispersal evolution, GomulkiewiczandHolt(1995)showthatERcanbestronglyhamperedbystochas-ticity, for example, as a consequence of low population sizes (seeGomulkiewicz,Holt,&Barfield,1999;foranotherexampleofspatialER). Interestingly, theprobability of rescue canbe a nonmonotonicfunctionofmigrationrates(Ueckeretal.,2014).Ifdispersalisallowedtoevolve(Ronce,2007),itmaybemodelledasadiscretetraitwithdis-persingandresidentgenotypes(e.g.,Hanski&Mononen,2011),asaquantitativetrait(Hanski,2011),orevenasanevolvingreactionnorm(Poethke &Hovestadt, 2002; Travis &Dytham, 1999; for an over-viewonthegeneticsofdispersalandhowdispersal is incorporatedintomodels,seeSaastamoinenetal.,2018).Forexample,combining

F I G U R E 2  Examplesofstudiesinwhichfeedbacksoccurinasingle-speciesnonspatialsetting.(a)InLandeetal.(2009)andLively(2012)population,densitydeterminestheselectionpressure,resultinginevolutionofsomequantitativetrait(Landeetal.,2009)orshiftsindiscretegenotypefrequencies(Lively,2012).(b)InAlonzoandSinervo(2001)notonlypopulationdensitybutalsothefrequencyofmorphsdeterminematechoice,whichinturndeterminestheoutcomeofmorphfrequenciesinthenextgenerationinfluencingthetraitofmatechoiceagain

PoMorph frequency

Mate choice

Population density

Trait evolutionGenotype frequencies

Density-dependent selection

Competition/defense (trade-o�)

(a)

(b)

Pay-off matrix(rock-paper-siccor)

Density- andfrequency-dependent

6  |    Functional Ecology GOVAERT ET Al.

stochasticpatchoccupancymodelswithdescriptionofmeanpheno-typicchangesinlocalpopulations,HanskiandMononen(2011)stud-iedanEEFbetweenpatchdynamics(colonizationandextinction)andthefrequencyofadispersergenotype(fordetailsseeFigure3a).

In spatial models, EEFs can link processes at different spatialscales.Forinstance,Poethke,Dytham,andHovestadt(2011)showthat theselective increase inpatchsize, forexample,asaconser-vationmeasure,canselectagainstdispersal(eco-to-evo)whichde-creasesre-colonizationprobabilitiesandcanleadtoES(evo-to-eco).Evolution can also rescue populations from extinction which willdepend on the rate of environmental change and landscape set-tings: ERmay be foundwhen environmental changes are not toofast (Schiffers,Bourne,Lavergne,Thuiller,&Travis,2013),but thecontraryhasalsobeenfound(Boeye,Travis,Stoks,&Bonte,2013).Similarly, in a range expansion context, Burton, Pillips, and Travis(2010)andFronhoferandAltermatt(2015)showedthattheecolog-icalprocessofarangeexpansioncanselectforincreaseddispersalatrangefronts(Travis&Dytham,2002)andmayfeedbackonthedistributionofpopulationdensitiesacrosstherangevialife-historytrade-offs.The importanceof landscape structure forEEFs is laidout inFronhoferandAltermatt (2017) (Figure3b).Taken together,spatialmodelsmayconsider local adaptation toabiotic conditionsasaheritabletraitandfixdispersalormayconsiderdispersalasanevolvingtrait.Altogether,thestudiesshowthatdispersalisanexcel-lentcandidatetolinkecology(demographyfromasinglepopulationormetapopulation)andevolution,makingdispersalcentraltoEEFs.

4  | EEFS INVOLVING T WO SPECIES

Inmulti-speciessystems,EEFscanbemediatedbyintra-andinter-specific densities that affect fitness and trait distributions (Travisetal.,2013).Inthefollowing,weconsiderfourmajorcategoriesoftwo-species interactions: interspecific competition, predator–prey,parasite–hostandmutualisticinteractions.

4.1 | Interspecific competition

Interspecific competition is a reciprocal interaction for a sharedlimiting resource (Dhondt,1989), suchas food. In this interaction,the competing species canevolvedifferent niches inorder to co-exist (Abrams,1986;Brown&Wilson,1956;Taper&Case,1992).Many studies have shown that competition-induced selection canresultinadaptivedivergencethroughecologicalcharacterdisplace-ment (Brown&Wilson,1956;Schluter,2000;Slatkin,1980;Taper&Case, 1992).However, other studies have shown that competi-tion could also lead to functional convergenceof the competitors(Abrams,1990; terHorst,Miller,&Powell,2010). In thesemodels,EEFsmay occur because competing species exert selection pres-sures that result in trait evolution (eco-to-evo) that might alterselection pressures on both species (evo-to-eco; e.g., Vasseur,Amarasekare,Rudolf,&Levine,2011;Figure4a).TheearliermodelsofcharacterdisplacementassumefixedvarianceandoftenassumeGaussianshapesforthespecies’characterdistribution(e.g.,Slatkin,1980).Recently,SasakiandDieckmann(2011)suggestedtheoligo-morphicapproximationasawaytodescribetheQGofanasexuallyreproducingpopulationthatconsistsofmultiplemorphs.SasakiandDieckmann(2011)thenusedthisapproachtogainamoredetailedunderstandingon thedynamicsofevolutionarybranching ina re-sourcecompetitionmodelandshowed,amongotheraspects,howtoobtainthresholdconditionsforevolutionarybranchingandhowmutationsaffecttheseconditions.

Models on interspecific competition include, for example,DieckmannandDoebeli(1999).ThisstudyusedanIBM,inwhichtheevolving trait determines the carrying capacity (competition), andinwhich individualssurviveanddieviadensityandfrequencyde-pendencegivingrisetoafeedbackbetweendensityandtraitevolu-tion,resultinginspeciationviaevolutionarybranching.Theauthorsshowedthatevolutionofassortativematingcanleadtoreproductiveisolation,resultinginincreaseddiversityandthatnonrandommatingisaprerequisiteforevolutionarybranching(seealsoThibert-Plante&Hendry,2009).Inasimilarmodel,Aguilée,Claessen,andLambert(2013)foundthatlandscapestructurehighlyinfluencestheoutcomeofdiversityresultingfromunderlyingdynamicsofcompetitionandassortativemating.ThelatterstudyusedanIBMassumingdensity-dependentresourcecompetitionandstrongercompetitionbetweenindividualswithsimilartraitvalues, inducingfrequency-dependentselectionandconsideredtraitslinkedtoresourceutilizationandtomatechoice.Last,amodelbyterHorstetal.(2010)foundthatevo-lutionary convergence could occur in amulti-speciesmodelwhenless resources thanspecieswerepresentandwhenthe intra-and

F I G U R E 3  Examplesofstudieswithspatialfeedbacks.(a)StudybyHanski(2011)andHanskiandMononen(2011)wherepatchdynamicsdrivenbycolonizationandextinctionmightinfluencedisperserfrequency(Hanski&Mononen,2011)orshiftsmeandispersalrate(Hanski,2011),whichinturninfluencespatchdynamics.(b)StudybyFronhoferandAltermatt(2017)inwhichlandscapetopologyinfluencesdispersalevolution,whichinturninfluencescolonizationprobabilitiesandmetapopulationdynamics(occupancy,turnover,geneticstructure,globalextinctionrisk)

(a)

(b)

     |  7Functional EcologyGOVAERT ET Al.

interspecific competition coefficients were equal. In this model,the rate of competitive exclusion slows down as species becomemoresimilartooneanother(evo-to-eco),givingspeciesmoretimetoevolve(eco-to-evo).Insummary,prominentexamplesofEEFsintwo-speciescompetitivesystems focusoncharacterdisplacementandpotentiallyspeciation.WhileanalyticalmodelsusingODEandtheADframeworkarewellestablished(seee.g.,Kisdi,1999),studiesontwo-speciesinteractionsoftenmakeuseofIBMscombinedwithGAtoincludearelativelyhighlevelofbiologicalcomplexity.

4.2 | Predator–prey interactions

In a predator–prey interaction, one species acts as a preda-tor feeding on the other species serving as prey. EEFs in

predator–preysystemsimplythatpredatordensitiesmayinducetraitevolution,forexample,inpreydefence(eco-to-evo)result-ing inconsequentshifts inpreyandpredatordensities (evo-to-eco;Figure4b).Manystudieshavefoundthatrapidevolutioninpreydefenceduetoshiftingpredatorabundancesresultsinan-tiphasecyclesratherthan1/4-lagcyclespredictedbynon-evo-lutionarymodels(Becksetal.,2010;Yoshidaetal.,2003,2007).Additionally,feedbackscanstabilizeordestabilizepredator–preydynamics depending on genetic variation and trade-off shapes(Abrams,2000;Abrams&Matsuda,1997;Cortez,2016;Cortez&Ellner,2010).

Predator–prey dynamics have been extensively studied usingmodelsoftraitevolutionoftheprey(e.g.Abrams&Matsuda,1997;Cortez,2016;McPeek,2017),thepredator(Cortez&Ellner,2010),or both (e.g. Cortez &Weitz, 2014; van Velzen & Gaedke, 2017;Figure4b). Inall three instances,EEFsweremodelledusingeitherseparate equations for the ecological and evolutionary dynamics(e.g. Abrams &Matsuda, 1997) or QG recursion equations or anapproximationofthose (vanVelzen&Gaedke,2017),usinganADapproach(Marrow,Dieckmann,&Law,1996)orbyusingmulticlonalLV equations (which are identical to “ecological selection”modelsCortez&Weitz,2014;Ellner&Becks,2011;Haafke,AbouChakra,&Becks,2016;Jones&Ellner,2007;Yamamichi,Yoshida,&Sasaki,2011).Includinglife-historytrade-offsbetweendefenceandfecun-ditymayleadtorecurrentEEFs(Huang,Traulsen,Werner,Hiltunen,&Becks,2017;Meyer,Ellner,Hairston,Jones,&Yoshida,2006).

Phenotypicplasticityhasbeenfoundtoplayanimportantrolein predator–prey EEFs and has been incorporated for exampleby Yamamichi etal. (2011),who found that plasticity in prey de-fencepromotesstablepopulationdynamicsmorethanrapidevo-lutionary responses, although plasticitywas not advantageous in

F I G U R E 4  Examplesofstudiesinwhichfeedbacksoccurintwo-speciessettings.(a)StudybyVasseuretal.(2011)inwhichthecompetitioncoefficientsdeterminingthestrengthofintra-andinterspecificcompetitionaremodelledinfunctionofanevolvabletrait(growthordefencetrait)underdensity-andfrequency-dependentcompetition.(b)GeneralfigureonpossibleEEFsinpredator–preydynamics(detailedinCortez&Weitz,2014).Generally,atrade-offbetweengrowthandpredatordefenceisassumedinthepreypopulation,andatrade-offbetweenmortalityandoffenceisassumedinthepredatorpopulation.Densityofthepredatorandpreycanbothinfluencetraitevolutioninthepredatorandpreypopulation,whichduetothepreviouslydescribedtrade-off,determinespredatorandpreydensity.(c)Generalfigureonpossiblefeedbacksinhost–parasitedynamics(seeLuo&Koelle,2013).Inamodelofvirulenceevolution,densityofsusceptiblehostsdeterminesthedegreeofvirulencewhichfeedsbacktochangethedensityofsusceptiblehosts(stripedarrow).Inamodelonhostresistance,densityoftheinfectedhostsdeterminestheevolutionofhostresistance(dashedarrow),whichinturndeterminesthedensityofbothsusceptibleandinfectedhosts.(d)Generalrepresentationofpossiblefeedbacksinmutualisticinteractions.Changesintheecologicalinteractionsbetweenspeciesdeterminetheevolutionofamutualistictrait,which,inturn,canchangetheecologicalinteractionsbetweenspecies

Density- and frequency-dependent

Density- and frequency-dependent birth and death rates

(a)Densityspecies 1

Trait

Density species 2

coefficients

Densitypredator

Predator trait

Density prey

Prey trait

(b)

(c)

hosts

VirulenceHost resistance

Growth/defensetrade-off

Survival/offensetrade-off

Density infected hosts

(d)

Densityspecies 1

Density species 2

8  |    Functional Ecology GOVAERT ET Al.

stableenvironments.Theevolutionofplasticityhasbeenstudiedby Fischer etal. (2014), who extended an LVmodel allowing forvariationinplasticityamongmultiplegenotypesofprey.Theinclu-sion of such variation inmodels improved their ability to explainpredator–prey dynamics.Overall, predator—prey EEFs are a clas-sicalexampleof feedbacks involvingphaseshiftsand impactsonstability.TheseeffectsareclassicallymodelledwithODEs.Recentwork highlights the importance of incorporating both effects ofgenetic diversity and phenotypic plasticity to explain communitydynamics(Kovach-Orr&Fussmann,2013;Yamamichietal.,2011).

4.3 | Host–parasite interactions

In a host–parasite interaction, one of the species lives at the ex-penseoftheotherspecies.Similartopredators,parasitescan im-posestrongselectionpressuresontheirhosts,forexampleresultingin theevolutionofdefences that can in turn impose selectiononparasite traits. This process can lead to complex co-evolutionarydynamics inspatialandnonspatialsettings.Host–parasite interac-tions areoften characterizedbyoverlapping time scalesbetweenepidemiologicalandevolutionaryprocessesowingtotherapidevo-lution of those systems. Yet, evenwhen evolution is slower thanthespreadofdisease,selectioninhost–parasitesystemsischarac-terizedbystrongdensity-dependentfeedbacks,wherechanges indensitiesaffectselectionpressuresontransmission,virulenceandotherparasitetraits(eco-to-evo),andtheresultingtraitchangesinturnaltertheecologicaldynamics(evo-to-eco;Luo&Koelle,2013;Figure4c).

The studyofvirulenceevolution inparasites andpathogens isakeytopicinthetheoreticalliteratureinvolvingEEFs.TheseminalworkofAndersonandMay(1982)showedthatpathogenevolutionis shaped by the epidemiological dynamics of infectious diseasesthrough the density of susceptible hosts. Since then, a large lit-eraturehasbeendevoted tounderstanding theeffectofEEFsontheevolutionofparasitevirulenceandhost resistance (e.g.Boots& Haraguchi, 1999; Dieckmann,Metz, Sabelis, & Sigmund, 2002;Frickel, Sieber, &Becks, 2016; Lenski&May, 1994; Lion&Metz,2018; Van Baalen, 1998).Mostmodels of host–parasite EEFs useclassicalepidemiologicalmodels(compartmentmodelsthatincludesusceptible,infectedandpotentiallyrecoveredindividuals;SIRmod-els)todescribethechangesindensityorfrequencyofsusceptibleandinfectedhosts.TheseepidemiologicalmodelsarethencoupledwithAD (Dieckmannetal.,2002;Lion&Metz,2018)orQG (e.g.,Day&Gandon,2007;Day&Proulx,2004)approaches.

InthewakeofAndersonandMay(1982)’sseminalwork,manystudieshavefocusedontheevolutionofpathogentraits,undertheassumptionthathostevolutionismuchslowerandcanbeneglected.ThishasledtoagoodunderstandingofhowEEFsaffectpathogenevolution.Akey insight is that,even if thehost isassumednot toevolve,thetimescalesbetweenecologyandevolutionmayeitherbedecoupled[e.g.,thepathogenevolveswhilethepopulationisatanendemicequilibrium,seee.g.,Dieckmannetal.(2002);LionandMetz(2018)forareviewofADapproaches]oroverlap(e.g.,when

thepathogenevolvesduringanepidemic,seee.g.,Day&Gandon,2007;Day&Proulx,2004foraQGformalism).Whatgovernsthedifferenceintimescalesbetweenepidemiologyandpathogenevo-lutionwillthenbetheamountofstandinggeneticvariationorthemutationrate.

More generally, coevolution between hosts and parasiteswith overlapping generation times has been studied (Best etal.,2010;Eizaguirre,Lenz,Traulsen,&Milinski,2009;Nuismer,Otto,&Blanquart,2008),inparticularinthelocaladaptationliterature(Nuismeretal.,2008),butoftenundertherestrictiveassumptionoffixeddemography,whichsetsstronglimitstothetypesofEEFsthat are possible. In contrast, other studies of coevolution havedemonstratedhowthedimensionoftheenvironmentplaysacrit-icalroleingoverningevolutionarybranchinganddiversificationinboththehostandthepathogen(Bestetal.,2010).However, thestudy of EEFs in co-evolutionary host—parasite system remainsunderdeveloped.Interestingly,thosesystemsappeartobepartic-ularly amenable to experiments and should allow researchers tofurther tease apart theunderlyingeffectsofEEFs.For example,Brunneretal.(2017)demonstratedthatthesolepresenceofafishparasite inanexperimentalecosystemalterstheabioticenviron-mentofthehostintermsofnutrientcontentordissolvedoxygen.Thesealteredenvironmentswereshowntoimposeselectiononasubsequentgenerationofhosts,henceevidencingthatmacropar-asitescanmediateeco-evolutionaryfeedbacksbetweenfishandtheirenvironment.

Host–parasite interactions have also played a crucial roletowardsunderstandingspatialEEFs (e.g.,Boots&Sasaki,1999;Boots, Hudson, & Sasaki, 2004; reviewed in Lion & Gandon,2015). These studies have often modelled space as a regularnetworkofsites, inwhicheachsite iseitheremptyorcontainsa single host individual, which can be either susceptible or in-fected.Suchmodelscaneasilybeanalysedusing IBMs,butan-alytical insight is alsopossible to someextent, usingeitherADorQG(Lion&Gandon,2016).Duetotheinherentcomplexityofspatial models, however, we only have a partial understandingofhowthe feedbackbetweenspatialepidemiologicaldynamicsandtheevolutionofhostandparasitetraitsunfoldsinmorere-alistic host—parasite interactions (but see Nuismer, Thompson,& Gomulkiewicz, 2000, 2003). In summary, the host—parasiteliteraturehasa longtraditionofstudyingEEFs.Methodologicalapproaches differ depending on the level of complexity, fromsimpleODEstoIBMs.

4.4 | Mutualistic interactions

Amutualisticinteractionimpliesthattheinteractionisbeneficialforbothpartnersinvolved(e.g.,plant–pollinatororhost–symbiontinter-action).EEFsinthecontextofmutualismsareexpectedtostronglyimpacttheco-evolutionaryprocessbetweenmutualistsandexploit-ers(eco-to-evo)whichinturnshapestheecologicaldynamicsofthesystem (evo-to-eco; Figure4d; Doebeli & Knowlton, 1998; Jones,Ferriere,&Bronstein,2009).

     |  9Functional EcologyGOVAERT ET Al.

Eco-evolutionaryfeedbackswerefoundtoplayan importantroleindeterminingphenotypicandpopulationoutcomesinanADmodelonthecoevolutionofmutualistsandexploiterswhenlong-termcoexistenceofthespecieswaspossible(Jonesetal.,2009).In themodel by Jones etal. (2009), birth rates of themutualistandexploiterwereassumedtoevolveanddetermine thenatureof the mutualistic interaction. Ferrière, Bronstein, Rinaldi, Law,andGauduchon (2002) constructed amathematicalmodel com-biningsimpleLotka–Volterraequationsdescribing theecologicalmutualisticinteractionsbetweenthetwospecies,withdifferentialequationsdescribing theevolutionarydynamicsof themutualis-tictraits.Theseevolutionarydynamicsfollowthefitnessgradientshapedbytheunderlyingecologicaldynamics(eco-to-evo),whichinturndeterminethebenefitofthemutualistic interaction(evo-to-eco;Figure4d).

Fewerstudieshaveinvestigatedtheeffectofspatialheterogene-ityonmutualisticinteractions,butthosethathaveshowthatspatialheterogeneitycanleadtolong-termpersistenceofmutualism(e.g.,Doebeli&Knowlton,1998).Overall,mutualistic interactions inaneco-evolutionarycontexthavebeen studied less compared to theotherthreespeciesinteractiontypesdiscussedearlier.Nevertheless,studieshave shown thatEEFsmayplay an important role for thistypeofinteraction.

5  | EEFS IN A COMMUNIT Y AND ECOSYSTEM CONTE X T

The increasing interest in more complex ecological settings hasresultedinarapidgrowthofmodelsfocusingoncommunitiesandecosystemsthatcouldsimultaneouslyincorporateevolutionarydy-namics(Brännströmetal.,2012).Suchmodelsextendpreviousworkto include niche construction, plant–soil feedbacks, multi-speciescommunitiesandfoodwebs.

5.1 | Feedbacks between organisms and abiotic environments

Eco-evolutionary feedbacks with the environment have beenstudied in the context of niche construction (Kylafis & Loreau,2011; Lehmann, 2008; Odling-Smee, Odling-Smee, Laland,Feldman,&Feldman,2003),asinplant–soilfeedbacks,forexam-ple (Schweitzer etal., 2014;Wareetal., 2018;Figure5a).Gametheoryhasbeenusedtoinvestigateselectiononnicheconstruct-ingphenotypes(Lehmann,2008)wherethefeedbackariseswhenindividualsaffecttheirenvironmentbyreproducing(evo-to-eco),hencealteringtheselectionpressureonthepopulation (eco-to-evo). In plant–soil systems, plantsmight adaptively regulate soilfertility, resulting in positive, self-sustaining nutrient feedbacksthat influenceevolution.Forexample, increasingthedirectben-efitofsoilnutrientconditioningtoplantshasbeenpredictedtoincrease selection for higher values of soil conditioning traits(Kylafis & Loreau, 2008). Implicit in this model is a genetically

based plant trait that links plants with their soils. Subsequentmodelshave shown that thesegeneticallybasedplant–soil linkscan result in EEFs depending on thematchwith the soil gradi-entandthegeneticvariationpresentintheenvironment—alteringplanttrait(Schweitzeretal.,2014).

F I G U R E 5  Examplesofstudiesinwhichfeedbacksoccurbetweenabioticandbioticcomponentsorinamulti-speciessetting.(a)GeneralfigureofEEFsinnicheconstruction(Kylafis&Loreau,2011;Lehmann,2008)andplant–soilfeedbacks(Schweitzeretal.,2014).Innicheconstruction,theabioticenvironmentdeterminestheevolutionofatraitthatmodifiesthisabioticenvironment.Similarly,inaplant–soilsystem,aplanttraitcanmodifythesoil,whichdrivesevolutionofplanttraits.(b)StudybyMartínetal.(2016)inwhichtraitvaluesandspatiallocationsofspeciesdeterminecompetition,changinglocalselectionpressures,resultinginshiftinglocalandglobaltraitdistributionsandcommunitydiversity.(c)StudybyItoandIkegami(2006),inwhicheachspecieshasaseparatepreyandpredatorstrategywhichresultsinclustersoftrophicspeciesarisingfromchanginginteractionsbetweenspecies,whichinturncontinuouslychangetheposition,shapeandsizeofoccupiedareasinphenotypicspaceandchangetrophicinteractionsresultinginfurtherphenotypicevolutionandeventuallyevolutionarybranchingandtheemergenceoffoodwebstructure

(b)Community diversity

Trait species i

Physicain space

Environ(a)

Soil (community) property

Plant trait

(c)

Prey, predator strategy

Evo branching

Food web structure

10  |    Functional Ecology GOVAERT ET Al.

In plant–soil systems, evolutionary change in plant traits caninfluence ecological dynamics of soilmicrobes (evo-to-eco)whichinturncanchangeselectionpressuresonplanttraits (eco-to-evo).ThiscanbeinvestigatedusingIBMs(Schweitzeretal.,2014)orbyusinganextendedversionofclassicalresourcecompetitionmodels(Eppinga,Kaproth,Collins,&Molofsky,2011).Inthisspecificmodel,thedecompositionoflitterreleasesnutrientsthatcanbetakenupby the plants influencing competitive ability of the plant (eco-to-evo),resultingindifferentplantgenotypesthatmightgrowbetter.Thechangeinthegeneticcompositionoftheplantpopulationcaninturninfluencethelitterpool(evo-to-eco).

In analogy to negative niche construction (Odling-Smee etal.,2003), the spatial structureof localnegative feedbackscan resultinchangesinlocaldiversity(e.g.,Loeuille&Leibold,2014).Theen-vironmentbecomeslesssuitableforthespeciesoccupyingit(evo-to-eco),whichinducesachangeinselectionpressureonthespeciesto evolve towards amorematching trait–environment value (eco-to-evo).Overall,plant–soilinteractionsaregoodexamplesofnicheconstructionwherebyEEFscanbothbemodelledandobservedinnature.Themethodsemployedrangefromformalmathematicalap-proachestoIBMs.

5.2 | Feedbacks within communities

Theoretical studies on EEFs in multi-species communities can in-crease our understanding of biodiversity (Patel etal., 2018). Eco-evolutionary analyses have led to new insights into coexistencetheory, themaintenance of diversity, aswell as the structure andstability of communities (Kremer & Klausmeier, 2017; Patel etal.,2018). Moreover, studies have found that evolution might main-tain (Martín,Hidalgo,deCasas,&Muñoz,2016), increase (e.g. viaspeciation or ER Dieckmann & Doebeli, 1999; Gomulkiewicz &Holt, 1995; Rosenzweig, 1978) or decrease (Gyllenberg, Parvinen,&Dieckmann,2002;Kremer&Klausmeier,2013;Norberg,Urban,Vellend,Klausmeier,&Loeuille,2012)phenotypic,speciesandfunc-tionaldiversity.

Forexample,Martínetal. (2016) show thatEEFscanmaintainphenotypicdiversity.Theauthorscombineniche-basedapproacheswithneutraltheoryinaspatiallystructuredIBMwhereeachindivid-ualhasalocationinspaceandisconstrainedbyaspecifictrade-offbetweenresourceexploitationandcompetition.Similarindividualsexperience higher competition resulting in frequency-dependentselection.Competitiononly takesplacebetweenneighbouring in-dividuals,changing localselectionpressures,whichresults in localevolutionary shifts in phenotypic traits (eco-to-evo) that shift theglobal phenotypic trait distribution and influence species differ-entiation and thus community diversity (evo-to-eco; Figure5b).Bycontrast,Norbergetal. (2012)foundthattheeco-evolutionaryprocessesinducedbyclimatechangecontinuedtogeneratespeciesextinctions longafter the climatehad stabilizedand thus resultedinfurtherdiversityloss.Theseauthorsusedaspatiallyexpliciteco-evolutionarymodelbasedonpartialdifferentialequationstopredictspecies responses to climate change in amulti-species context in

whichtheyallowedgeneticvariationanddispersal to jointly influ-enceecological (competitionandspeciessorting)andevolutionary(adaptation)processes.Thefindingsofbothstudiesdiscussedabovecaneasilybeunderstoodinthelightofmoderncoexistencetheory(reviewedinChesson,2000)astheyrelatetostabilizing(concentrat-ing intraspecific interaction by dispersal limitation) and equalizingmechanisms(sorting).Insummary,EEFsincommunitiesemerge,be-causespecies’traitsmayaffectthecommunityand,viceversa,thecommunitycontextmayaffecttraitevolution(terHorstetal.,2018).Interestingly,fitnessmaynotonlydependondensities,butalsoontotalcommunitybiomass,totalproductivityorevenonspeciesrich-ness.Consequencesofevolutionary changecanbeunderstood inthelightofmoderncoexistencetheory.

5.3 | Feedbacks in food webs

Evolutionarydynamicshavebeensuggestedtodeterminefoodwebstructure(Rossberg,Matsuda,Amemiya,&Itoh,2006).Hence,therehasbeenanupsurgeinstudiesincludingevolutionarydynamicsintofoodwebmodels, by allowing a recurrent addition of new speciesormorphsintothefoodweb,basedonthetheoryofself-organizedcriticality (Allhoff&Drossel, 2013; Bak, Tang,&Wiesenfeld, 1987;Bolchoun,Drossel,&Allhoff,2017;Caldarelli,Higgs,&McKane,1998;Drossel,Higgs,&McKane,2001;Rossbergetal.,2006).Theseevolu-tionaryfoodwebmodelsoftendependonatraitthatshapesthebioticinteractionswhichdeterminethefoodwebstructure.Foodwebstruc-tureselectsthespeciesthatremaininthesystem(eco-to-evo),whichinturnaltersthephenotypictraitdistributioninthesystemonwhichmutationscanoccurtocreatenewspeciesormorphs.Theadditionofanewspeciesormorphchangesthepresentspeciesinteractions(evo-to-eco),hencechangingthefoodwebstructure(Bolchounetal.,2017).Thisinterplaybetweenpopulationdynamicsandmorphevolu-tiondeterminestheEEFandshapesthestructureof thefoodweb.SimilartotheADframework,itisassumedthatecologicaldynamicsoccurfastandreach(quasi)equilibrium,whileevolutionarydynamicsoccuronamuchslowertimescale(Allhoff&Drossel,2013;Guill&Drossel, 2008). Studies including both ecological and evolutionaryprocessesinfoodwebmodelsshowthatthiscanleadtonewinsightsintofoodwebdynamicsasopposedtomodelsthatonlyincludefixedecologicaldynamics(Bolchounetal.,2017).

Moststudiesonfoodwebmodelsfocusonspeciation–extinc-tiondynamicswithspeciesbeingtheunitofthemodel,whilefewerstudies have investigated how the evolution of traits results infoodwebformation(Ito&Ikegami,2006;Takahashi,Brännström,Mazzucco,Yamauchi,&Dieckmann,2013).Both Itoand Ikegami(2006)andTakahashietal. (2013)havemodelledthebuildupofafoodwebthroughevolutionarydynamicsbyattributingtoeachindividual or phenotype a prey and predator trait (resource orvulnerability, respectively,utilizationorforaging). Individualsareassumedtoreproduceasexually,andoffspringmaydifferslightlybecauseofsmallrandommutations.ItoandIkegami(2006)showthatisolatedphenotypicclustersofspeciesandtheemergenceofhigher trophic levelsariseduetochanging interactionsbetween

     |  11Functional EcologyGOVAERT ET Al.

species(eco-to-evo),whichinturncontinuouslychangestheposi-tion,shapeandsizeofoccupiedareasinphenotypicspace.Thesechanges,inturn,altertrophicinteractions(evo-to-eco)resultinginfurtherphenotypicevolutionandeventuallyevolutionarybranch-ing (Figure5c).Takahashietal. (2013)usedan IBMtoshowthatinitial phenotypic divergence in the foraging trait relaxes inter-ferencecompetition(eco-to-evo),whichresultsintheemergenceofspeciesclusters.Theresultingchanges inspecies interactions(trophic levels; evo-to-eco)mediate further divergence in forag-ing traits and predator vulnerability (eco-to-evo). A study by deAndreazzi,Guimarães,andMelián(2018)explicitlyevaluatedtheeffects of network structure on eco-evolutionary dynamics forlong-term ecological network stability, by using different antag-onisticspeciesnetworks in theirsimulations.Populationdynam-icsweremodelledtodependonthephenotypictrait,whilemeantraitevolutiondependedontheenvironmentandtheantagonisticspecies interactions. The authors showed that EEFs resulted inspecific patternsof specializationwhich led to increases in spe-ciesmeanabundancesand todecreases in temporalvariation inabundances.

The effects of spatial dynamics on foodweb structure havealso been studied. For example, Loeuille and Leibold (2008),combined a simple foodweb structure (specialist and generalistherbivorespeciesfeedingontwoplantswhichinturnfeedonnu-trientresources),witha12-patchmetacommunitytoevaluatetheinteractionsbetweenevolutionaryadaptationandcommunityas-semblydynamicsasafunctionofdispersal.Thetwoplantspecieshadquantitativeandqualitativedefencetraitsthatwereheritable,uponoccurrenceofsmallmutationsbetweeneachtimesteps.Theauthors found that theoccurrenceofdispersalbetweenpatchesledtotheevolutionofdistinctmorphsoftheplantspecies(eco-to-evo),whichinfluencedthetrophicandfoodwebstructureinlocalpatches(evo-to-eco).

Overall,whileevolutionaryfoodwebmodelshaveallelementspresent forEEFstooccur,anexplicitanalysisof thesefeedbacksremains rare.This isprobablydue to themainassumptionof theseparationoftimescalesofecologyandevolution,withmutationbeingconsideredequivalenttospeciation(Takahashietal.,2013),and traits remaining constantwithin species. Exceptions exist ofcourse,suchasthefoodwebmodelusedbyLoeuilleandLeibold(2008). However, especially meta-food web models are scarce(Urbanetal., 2008). Evolutionary foodwebmodelshavepromis-ing features thatmay result inabetterunderstandingofEEFs inmore complex (natural) scenarios and likely representoneof thecurrent major challenges in eco-evolutionary modelling (Meliánetal.,2018).

6  | SYNTHESIS AND CONCLUSIONS

Throughoutthisoverview,wefoundthatEEFshavebeenincorpo-ratedintotheoreticalmodelsacrossawiderangeofdifferentlevelsof biological organization. The relevanceof theEEFmaynotonly

dependonthebiologicalsystem,butalsoonthespecifictraitsused:Differenteffectsmaybefounddependingonwhetherthetraitisin-fluencedbytheecologicalpropertyornot(e.g.,density-dependentversusdensity-independenttraits).Notsurprisingly,includingEEFsintheoreticalmodelssignificantlychangesourviewofwell-knownpatternsemergingfrompureecologicalorpureevolutionarymodels(e.g.,Dieckmann&Metz,2006;Poethkeetal.,2011).Morespecifi-cally,wehaveidentifiedmodelsthatincludeEEFs,whoseunderly-ingformalismsfallintoafewcategories(Figure1b).Inprinciple,anymodellingframeworkthatcouplesecologicaldynamics (e.g.,ODEsandIBMs)withanevolutionarymodel(e.g.,QG,ADorGA)canbeuseful for studying feedbacks. Studiesmodelling intertwinedeco-logicalandevolutionarydynamicsmostoftendifferintheirassump-tionofthetimescaleatwhichecologicalandevolutionaryprocessesoccur.Studiesassumingcontemporaryecologicalandevolutionarydynamicsoften coupleODEswithQGoruse IBMs,while studiesassumingevolutiontooccurwhenecologicaldynamicsareatequi-librium couple demographic models with AD to make analogousassumptions.

6.1 | Conclusions to date

BasedonournonexhaustiveoverviewoftheoreticalworkonEEFs,afewgeneralconclusionsemerge:First,EEFmodelsexplicitlyincludeecologicaldynamics in theanalysesofevolutionaryprocessesandviceversa.Density-dependentselectionandfrequency-dependentselection are often key ingredients for EEFs. Inmany cases, den-sitydependency and frequencydependency, aswell as ecologicalstochasticity, are not a priori assumptions, but emerge from eco-logicalsettingsandtraitcorrelations,forexample.Second,EEFsarenotnewtoevolutionaryecologytheory—theyaredeeplyrootedinthetheoryofmanysubdisciplines.Forinstance,thepredator–preyandhost–parasite literature, speciation literatureandevolutionarybranching, character displacement, andmetapopulationmodellingornicheconstructiontheorynaturallyincorporateEEFs.Strikingly,while the fieldof (meta)communityecology is rathernew (Leiboldetal.,2004),EEFsseemtohavebeenincludedin(meta)communityecologyvery rapidly, culminating in the recognition that thebasicdriversofevolutionandcommunityecologyareanalogous(Vellend,2010). Third, in a spatial setting, dispersal is a primary candidateforsuccessfuleco-evolutionary linkages,becausedispersal isbothan ecological process impacting densities and, at the same time,mediatesevolutionviageneflow. Inaddition, it is itselfsubject toevolution (Ronce, 2007). Movement can be similarly important(Hillaert,Vandegehuchte,Hovestadt,&Bonte,2018).Fourth,EEFsdonotnecessarilyrequirerapidorcontemporaryevolution(Post&Palkovacs,2009).Ofcourse,contemporaryevolutionhassparkedalotof interest inEEFs (Hendry,2017),butfeedbacksarealsopos-sibleoverlongertimescales(e.g.,asshowninADmodels).Fifth,ourshort overview of the eco-evolutionary modelling toolbox clearlyhighlightsthatthemaincharacterofaneco-evolutionarymodel isthecombinationofdemographicandevolutionarymodels, regard-lessoftheconcreteformalism.

12  |    Functional Ecology GOVAERT ET Al.

Becausedifferentformalismsoriginatefromdifferentfields,theyoftenrelyondifferingassumptions.Forinstance,thetimescalesonwhichprocessesoccurandthesourcesofgeneticvariationareim-portantconsiderationsofthedifferentmodellingformalisms(Lande,2007;Sӕther&Engen,2015).Thishasmadesomeformalismsmorefocussedonanalysingevolutionaryendpointandlong-termdynam-ics (AD),while others have focused on short-term dynamics fromonegenerationtothenext(QG).However,inbothformalisms,incor-poratingEEFsisfeasible.Theseparationoftimescalesalsomeansthattheformofthefeedbackmaychangewhenwemovefromonedynamicalregimetotheother,whichhasbeenwellstudiedinhost–parasitemodels(Day&Gandon,2007;Gandon&Day,2009;Lenski&May,1994;Lion,2018).However,most interestprobably lies inpredicting themid-termdynamics of anEEF system.To approachthisproperly,animportantissueforfuturetheoreticalworkwillbetodevelopmechanisticmodelsforthedynamicsofphenotypicandgenotypic variation in populations evolving at this mid-term timescaleof tens tohundredsofgenerations (seeFigure6 foran indi-vidual-basedperspective). Thiswould reveal for instancewhetherEEFs are time-dependent andhow common they are expected tobe.However,tocouplethesemodelstonaturalsystems,oneneedstomeasureheritabilityandgenetic(co)variancesoftraitswhichcanbechallenging.

Our review also underlines the pervasive nature of EEFs. Itseemsatbestdifficulttodesignamodelthatincludesecologyandevolutionwithout anEEF (see alsoHendry, 2017; chapter 1 for adiscussion).However,itispossiblethatsometraitshavelittleeffecton the ecological dynamics, or that some ecological variableswillhavelittleeffectontheevolutionarydynamics.Forinstance,inadis-crete-timemodel,ifabsolutefitnessisproportionaltoafunctionofdensity,sayWi(t)=bi f(Nt),thenrelativefitnesswillnotdependonNt,sowecansaythatEEFsdonotmatterforevolutioninthisspecificcase.Inmodelswhereanoptimizationprincipleholds(sensuMetz,Mylius,&Diekmann,2008),wealsohaveverysimpleecologicalandevolutionary dynamics: The focal trait average steadily increases

andresourcedensitydecreasesuntilamaximum(resp.minimum)isreached.SuchsimplisticEEFshavebeentermedfrequencyindepen-denceinthebroadsensebyMetzandGeritz(2016).Overall,recentmodelshavebecomemoreelaborate.However,increasedcomplex-ityandrealismoftentradesoffwithtractability.Asaconsequence,thesestudiesmustprovideadditionalteststhateitherinvolvemod-elswherethepresumedfeedbackisabsentorprovideasimplifiedanalyticalmodel(e.g.,Branco,Egas,Elser,&Huisman,2018;Kubischetal.,2016,forexamplesinvolvingIBMs).

6.2 | The way forward

Thechallengetodayconsistsinpursuingnew,moreintegrativeandmechanisticmodellingavenueswhichhavethepotentialtoincludedifferent aspects of realism, such as genotype–phenotype map-ping,plasticityaswellaspopulationandspatialstructure(Figure6)andpredictsmid-termdynamicsofEEFsasoutlinedabove.Currenttheory has greatly increasedour understanding of EEFs (McPeek,2017), but these feedbacks have been primarily explored withinhierarchical levels of ecosystem organization, be they spatial ortemporalhierarchies,andhaveoften involvedonlysingleorafewindependentlyevolvingtraits.Whilethepresenceofahierarchicalorganizationofecosystemsiswellestablished(Meliánetal.,2018),itisanongoingchallengetoidentifytherelevanthierarchicallevelsandtheirinterdependenciestounderstandEEFs.

Currently,theleadinggraphicalmodeladoptsanimplicithierar-chywithfeedbacksbetweenlevelsfromgenes,totraits,topopula-tions, to communities and toecosystemprocesses (Hendry,2017;see also Figure1a for a simplification).Making such a conceptualmodelmoremechanistic requires understanding how interactionsat one scale (gene regulatory networks or complex traits) affectprocessesatdifferentscales(trait-dependentspeciesinteractions).OnesuchmodellingattemptbyMeliánetal.(2018)linksecologicalandevolutionarynetworksinameta-ecosystemmodel,takingintoaccountdemography, traitevolution,geneflowandtheecological

F I G U R E 6  MechanisticunderpinningsofEEFs.Ecologicaldynamics(left)aredrivenbyindividual-levelproperties(birth,death,dispersal).Interactionsbetweenindividualsofthesameordifferentspecies(bioticinteractions)impacttheseproperties,whichmayleadtodensitydependence,forexample.Individualsinteractwiththeabioticenvironmentandviceversa.Importantly,theseecologicalsettingswillimpactselection,driftandmigration(eco-to-evo).Evolutionisgovernedbytheinteractionbetweentheseprocesses,geneticconstraintsandmutations.Theresultingphenotypeissubsequentlydeterminedbythegenotype–phenotypemap.Ultimately,thephenotypewillimpactecology(evo-to-eco)bychangingbirths,death,dispersalandtheabioticenvironment.Plasticity(dashedlines)maymodulatethephenotypeand,hence,thedualeffectsoftheorganismonbioticandabioticenvironments

Genetic changeand map to phenotype

Abiotic environment

Selection, drift,

gene flow

Phenotype

Mutation

Birth, death, dispersal

Bioticinteractions

Plasticity

otypeotypeIndividual i

     |  13Functional EcologyGOVAERT ET Al.

dynamicsofnaturalselection.Suchprocess-basedmodelscanyieldnewinsightsintothemechanisticbasisofEEFsinmorecomplexnat-uralscenarios.Someofthemost importantprocessesaresumma-rizedinFigure6whichexpandstheconceptualmodelpresentedinFigure1atoamoremechanisticlevel.Withthisrepresentation,wepropose that feedbacksarebestconceptualizedasemerging fromindividual-levelinteractions(seealsoRueffler,Egas,&Metz,2006),withdispersalandinteractionswiththeabioticenvironmentleadingtotheemergenceoftherelevanthierarchicalcomplexity.

Besides theoretical advances, connecting theory to controlledlaboratoryor field experimentsmore tightlywill allow for the ex-perimentalassessmentoftheoreticalpredictionsaboutfeedbacks.For example, using rotifer–algae chemostats, Yoshida etal. (2003)experimentally tested predictions of a theoretical predator–preymodel thatallowed forpreyevolution.Thisexperimentconfirmedtheantiphaseoscillationspredictedfromtheorywhenpreyevolvesdefencestrategies.Whilesuchprominentexamplesoftheintegra-tionoftheoryandempiricaldataonEEFsexist (seeamongothersalso, Becks etal., 2012; Bonte&Bafort, 2018;DeMeester etal.,2018;Fischeretal.,2014;Fronhofer&Altermatt,2015;Huangetal.,2017; Litchman, Klausmeier, & Yoshiyama, 2009; Metcalf etal.,2008;Thomas,Kremer,Klausmeier,&Litchman,2012;VanNuland,Ware,Bailey,&Schweitzer,2018)breadthof the theoreticalworkhighlightedhere,thecouplingofempiricaldatafromnaturalandex-perimentalsettings,withtheoreticalmodels,needstobedeepened.Thisgapbetween theoryandempiricalworkmay, inpart,beduetodifferencesintechnicaljargonthatimpedeeffectivecommunica-tionbetweentheoreticiansandempiricistsaswellasmodellingspe-cializationsamongtheoreticianswhichimpedesynthesisoratleastslowdown progress. Isolation among subdisciplines and methodsleadstoconfusion,reducedinferenceandwillnotadvancethefield.Inthelattercase,effortssuchasthoseofQueller(2017)andLion(2018)atunifyingtheoreticalfieldsareurgentlyneeded.ToadvancetheoryonEEFs,weheresuggestthattakingamechanisticapproachfocusedon individual-level traits (Rueffleretal.,2006)asoutlinedin Figure6 can be productive for developing novel and synthetictheory.Keyingredientstosuchanindividual-levelapproacharethedescriptionoffocalorganismsintermsofindividualproperties(age,ecologically important traits, life-history parameters) and linkingthesetodemographicprocesses(seealsoTravisetal.,2014).Mostimportantly,scientistsneedtolearntoappreciatethestrengthsoftheirrespectiveapproaches,betheytheoretical,experimentallab-oratory-basedorcomparative,andnotfocusontheweaknessestodiscardpossibleavenuesofcollaborationandprogress.

Clearly, bridging between theory and empirical data is moredifficultwhenstudyingecologyandevolutioninthewild(Hendry,2018) and ecological pleiotropy may even cancel out EEFs(DeLong,2017).However,theoreticalmodelsarethebestavenuetoformulatehypothesesandgeneratetestablepredictionswhichstrengthen inference.Wesuggest thata three-wayapproach, in-tegrating theory, laboratory-based experiments and comparativedata from natural communities will enhance our understandingonhowprevalentEEFsare innature.Thisknowledgewillalsobe

criticalforcommunicatingtheimportanceofEEFstopolicymakers.Inthiscontext,itiscentraltoknowhowfeedbacksaffectbiodiver-sitydynamics,whether theevolutionof resistancemaybe fasterwithorwithoutfeedbacks,orwhetherpopulationsizecanbebet-ter controlledbymodifying certain componentsof feedbacks, toname but a few examples. Understanding the dynamical conse-quencesofEEFismoreimportantthaneverinarapidlychangingworld.

ACKNOWLEDG EMENTS

Theauthorswouldliketothanktheeditorsofthespecialissueforbringingustogetherandtwoanonymousrefereesforveryhelpfulcomments. This is publication ISEM-2018-232 of the Institut desSciencesdel’Evolution—Montpellier.

AUTHORS' CONTRIBUTIONS

L.G., E.A.F. and B.M. conceived the study and drafted themanu-script.L.G.andE.A.F.ledthestudy.Allauthorsperformedliteraturesearchandanalysisandcontributedtorevisions.

DATA ACCE SSIBILIT Y

Allpapersusedforthisreviewarecitedinthetext.

ORCID

Emanuel A. Fronhofer http://orcid.org/0000-0002-2219-784X

Dries Bonte http://orcid.org/0000-0002-3320-7505

Andrew P. Hendry http://orcid.org/0000-0002-4807-6667

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How to cite this article:GovaertL,FronhoferEA,LionS,etal.Eco-evolutionaryfeedbacks—Theoreticalmodelsandperspectives.Funct Ecol. 2018;00:1–18. https://doi.org/10.1111/1365-2435.13241