Selection on stability across ecological scales

Selection

on

stability

across

ecological

scales

Jonathan

J.

Borrelli

,

Stefano

Allesina

,

Priyanga

Amarasekare

,

Roger

Arditi

,

Ivan

Chase

,

John

Damuth

,

Robert

D.

Holt

,

Dmitrii

O.

Logofet

,

Mark

Novak

,

Rudolf

P.

Rohr

,

Axel

G.

Rossberg

,

Matthew

Spencer

,

J.

Khai

Tran

,

and

Lev

R.

Ginzburg

1_{StonyBrookUniversity,StonyBrook,NY,USA}

2_{UniversityofChicago,Chicago,IL,USA}

3_{UniversityofCaliforniaLosAngeles,LosAngeles,CA,USA}

4_{DepartmentofBiology,UniversityofFribourg,Fribourg,Switzerland}

5_{UniversityofCaliforniaSantaBarbara,SantaBarbara,CA,USA}

6_{UniversityofFlorida,Gainesville,FL,USA}

7_{LaboratoryofMathematicalEcology,A.M.ObukhovInstituteofAtmosphericPhysics,AcademyofSciences,Moscow,Russia}

8_{OregonStateUniversity,Corvallis,OR,USA}

9_{CentreforEnvironment,Fisheries,andAquacultureScience(CEFAS),Lowestoft,UK}

10_{UniversityofLiverpool,Liverpool,UK}

11_{Syngenta,Greensboro,NC,USA}

Muchofthefocusinevolutionarybiologyhasbeenon the adaptive differentiation among organisms. It is equally important to understand the processes that resultinsimilaritiesofstructureamongsystems.Here, wediscussexamplesofsimilaritiesoccurringatdifferent ecological scales, from predator–prey relations (attack ratesand handlingtimes)throughcommunities (food-web structures) to ecosystem properties. Selection among systemic configurations or patterns that differ in their intrinsic stability should lead generally to in-creased representation of relatively stable structures. Such nonadaptive, but selective processes that shape ecologicalcommunitiesofferanenticingmechanismfor generating widely observed similarities, and have sparkednew interest instability properties. This non-adaptivesystemicselectionoperatesnotinopposition to,butinparallelwith,adaptiveevolution.

Anexplanationforecologicalsimilarities

In recent years, there has been a great deal of ferment focusedontheintegrationofecologyandevolution[1]. Evo-lutionaryandecologicalprocessescangenerateavarietyof community configurations,butsome are observed in na-turemoreorlessfrequently thanothers.Notallofthese configurations will be equally feasible (see Glossary) or dynamically stable, such that all member species can persist insufficientlyhighabundances that extinctionof anyoneisunlikely.Wheninterpretingbroadpatternsin ecology, we must account for feasibility and stability. Feasibleandstableconfigurationsshould beobservedin

nature with ahigher frequencythan configurations that arestronglyintrinsicallyunstable.

Ifthereisnowayforagivensetofspeciestocoexist(not feasible), thenthe configuration isdoomed toextinction. For example, in the well-studied intraguild predation module,anintraguildpredatoranditsprey(bothofwhom share a third resource) are unlikely to coexist if both predators are equal competitors for the shared resource and not limited by other factors, such as interference competition (Box 1). Instead, we should only expect to observe thismodule when the intraguild prey isable to outcompeteits predatorforthesharedresource[2–4].In othercases,afeasibleequilibriumdoesexistbutis intrin-sicallyunstable.

Thisexampleillustrateswhatwesuggesttobeamore general principle. Namely, differences in the observed frequencyofalternativecommunitystructuresmighthave

Glossary

Adaptive selection: a selection process (such as neo-Darwinian natural selection)thatcancauseadaptationtoalocalenvironment,becausefitness differencesresultfromaninteractionbetweenphenotypesandthatshared localenvironment.

Environment(ofasystem):alllocalfactorsexternaltothesystem,bioticand/or abiotic(dependinguponthesystemdefinition).

Feasibility:theexistenceof anequilibriumpointorattractorsuchthatall speciesinthesystemcancoexist.

Intrinsicsystemproperties:theattributesandqualitiesofthesystemasa whole,suchaspatternsinandmagnitudesofinteractionsandthedensitiesof participatingspecies.

Nonadaptiveselection:anyselectiveprocessthatdoesnotacttoadaptthe membersofthepopulationonwhichitactstoaspecificlocalenvironment. System: the particular unit of interest, typically involving multispecies interactions but dependent upon the ecological scale of the study. At macroecologicalscales,wetypicallyrefertosystemsasmultispecies interac-tionnetworks(e.g.,foodorplant–pollinatorwebs).

Systemicselection:nonadaptiveselectiononsystemsbasedontheirintrinsic systemproperties.

Correspondingauthor:Borrelli,J.J. (borrejj@gmail.com). Keywords:stability;feasibility;selection;macroecology.

Published in 7UHQGVLQ(FRORJ\ (YROXWLRQ± which should be cited to refer to this work.

littletodowiththeparticular characteristicsofthelocal environmentsinwhichsuchsystemsexist.Instead, intrin-sicsystempropertiesdeterminingfeasibilityandstability underlie the relative success or persistence of different configurations,andtheycando somoreor less indepen-dently of local environmental variation. We expect that suchnonadaptivesystemicselectioncanproducemanyof those recurrent ecological patterns that have been ob-servedinnatureoverlargescalesofspaceandtime.

Systemicselectioncanbeapowerfulyetsimple expla-nation of many ecological patterns, including ecological allometries, species interaction strengths, food-web metrics,andmacroevolutionarypatterns(e.g.,[5,6]).This intellectualprotocolforunderstandingecologicalpatterns has long been implicit in community ecology [7,8], but recentadvancesintheorysuggestthatitistimetomake thisprinciplemoreexplicitandformal.Here,westartwith anoverviewofsystemicselection,inthehopesof generat-inga‘searchimage’forthistypeofprocessinecology.Then, wedivedeeperinto(mostly)communityecologytoexplore the role of systemic selection on stability in connecting localscalestomacroscales.

Systemicselectionisnonadaptive

Biologistsare usedtothinkingof‘selection’asaprocess that explains the adaptation of individuals to local conditions, through a selection regimen based on the

interactions of phenotypes with a shared environment. However,macroscalebiologicalsystems,suchas commu-nities,canalsochangebythepreferentiallossofinternal configurations that are relatively unstable. This elimi-nation of the unstable is a type of long-term selective process,butonewheretheselection regimen,insteadof beingbasedonaninteractionofthebiologicalsystemor its components with local conditions, derives primarily from fundamental properties of the system itself; the processdoesnot‘see’thelocalconditionsandneitherisit activated byenvironmental change(Box 2).

A theory that is based on such a systemic selection process canbe thought ofas ‘nonadaptive’, in the sense thatthe selectionprocessitdescribesdoesnotadaptthe systemtolocalconditions,eventhough(ifworkingalone)it changesthesysteminagiven direction.Weuse ‘adapta-tion’as iscommonlyunderstood,illustratedby Vermeij’s definition(p.364in[9]):‘...asaheritableattributeofan entitythat confersadvantages insurvivaland reproduc-tionofthatentityinagivenenvironment.’Vermeijgoeson tosaythat these‘advantages’ are‘context dependent’.A traitthatisanadaptationinoneenvironmentmightnotbe inadifferentone.Bycontrast,whatwerefertoassystemic selection involves‘advantages’ that are context indepen-dent.

Ofcourse,thepropertiesofthesesystemslikelychange insignificant waysby ordinaryadaptive selectionand/or

Box1.Theintraguildpredationsystem

Toillustratetheideaofnonadaptiveselection,consideranintraguild predationcommunitydepictedinFigureIwithfourslightlydifferent interaction strength configurations. For simplicity, weassume the interactionsmatchthesimpleLotka–Volterramodelassumedin[3]

(e.g.,nointraspecificinterferencecompetitionintheconsumers,etc.). Thickerarrowsindicatestrongerinteractionsasdefined,forexample, by theamount ofenergyflowing froma preypopulationtoeach predator.Wecouldexpecttoobtaineachoftheseconfigurationsin several ways. For example, interaction strengths may change as speciesidentitieschangethroughspeciation,orthecombinationof extinctionandinvasion.Or,theycouldchangefromadaptive coevolu-tionamongthespecies,duetovariationoverspace,time,orwithin populations,ortobehavioralchangesinindividualforagingdecisions. However,whilemanysuchprocessescouldleadtoanyofthefour configurations,feasibilityconstraintsdictatethatwearenonetheless likelytoobserveoneofthesefourconfigurationsmoreofteninnature thantheotherthree[4,75].

Thatis,whentheintraguildpredatorandpreyareequallyefficient competitorsforthesharedresource(FigureIA),weexpectthe intra-guild prey tobe driventowards exclusion because the intraguild predatorhastheadvantageofconsumingitscompetition.Likewise, the intraguild prey will be driven towards exclusion even more strongly when the intraguild predator is the superior competitor (FigureIB), or when theeffects of the intraguild predator on the intraguildpreyisstronger(FigureIC).Althoughdifferencesinmortality ratesandthepresenceofalternativeresourcescanweakenand,to somedegree,counteractthesefeasibilityrequirements,itiswhenthe intraguildpreyisthesuperiorcompetitor(FigureID)thatwearemost likelytoobserveallspeciescoexisting.

Therefore,wecansaythatcommunitiesA–CinFigureIare systemi-callyselectedagainst.Furthermore,becausesuchselectionisaresult ofthepropertiesofthecommunity(i.e.,theconfigurationof interac-tionstrengths)andnotduetoitsparticularenvironment,thisselection isnonadaptive(Box2).

(A) (B) (C) (D)

TRENDS in Ecology & Evolution

FigureI.Fourhypotheticalintraguildpredationcommunities,atthetopistheintraguildpredator,themiddleistheintraguildprey,andthebottomistheshared resource.Arrowspointinthedirectionofenergyflowandtheirwidthrepresentsinteractionstrength.

coevolutionamongtheirmembers,andbyprocessessuch asmigrationanddrift,tendingtogeneratediversitywithin andamongsystems(e.g.,communities).However,because systemicselectionoperatesonintrinsicsystemproperties that do not vary with the environment, it can, if not significantlyoverwrittenbyotherprocesses,haveamajor role inexplaining the evolution and stable properties of macroscalebiologicalsystems.Suchnonadaptive process-estendtopromotesimilarityratherthandiversityamong ecologicalsystems.Abook-lengthtreatmentthatexplores nonadaptiveselectionmoregenerallyiscurrentlyin prep-arationbyDamuthandGinzburg.

Constraintsonattackratesandhandlingtimes

Nonadaptive systemic selection can act on whole com-munities and ecosystems, but we begin by describing how it can also act on the pairwise interactions of species. Each species in an interacting pair brings with it attributes that may affect the feasibility and stabilityofitsinteraction. Speciespairswithattributes that lead to extinction because they generate highly unstable dynamics are not likely to be observed, com-paredwithspeciespairswhoseattributes permitstable dynamics.

Thewell-studiedRosenzweigandMacArthurmodel[10]

provides aconceptualfoundation for understandinghow consumertraits,suchasattackratesandhandlingtimes, influenceoscillatory dynamicsin abroadarrayof preda-tor–preymodels[11].Inthis model,oscillations increase becausethehandlingtimeinducespositivefeedbackinthe per capita growth rate of the resource species, which enables prey to increase in abundance; the ensuing in-creaseinthepredatorpopulationleadstoprey overexploi-tationandadeclineintheabundanceofthepreyfollowed bythepredators[12].Oscillatorydynamicsaremorelikely to occur when prey are weakly self-limited (e.g., high

carrying capacity) and predatorshave high attack rates andlonghandlingtimes[11].

Oscillationsin populationabundancespredispose spe-cies, andtheinteraction modulesin whichtheyoccur,to stochasticextinctionsduringphasesoflowabundance.The disproportionateextinctionofinteractionsexhibitinglarge amplitudeoscillationsimposesselectionatthepopulation level.Theexpectationthatspecieswithoscillatory dynam-icsshouldthereforebeuncommoninnature[13]isborne out by analyses of time-series data, which show only approximately 30% of species with evidence of consum-er-drivencycles[14].However,suchcyclesareparticularly commonintightlycoupledinteractionsbetweenspecialist predatorsandtheirprey[15].

Given that systemic selection tends to cull predator– prey interactions inwhich oscillations lead toperiodsof low abundances, the attack rates andhandling times of predatorsshouldbeinverselyrelated;thatis,highattack ratesandshorthandlingtimes(greateroverexploitation), lowattackratesandlonghandlingtimes(lowexploitation potential), or low attack rates andshort handling times (short timedelay),whichdampen oscillations.

JohnsonandAmarasekare[12]establishtheveracityof this prediction through analysis of the attack rates and handling timesof57functionalresponse experimentsas well as the functional responses and self-limitation strengthoftwospecialistparasitoidsandtheirherbivorous insect host (Figure 1A) [16]. Likewise, estimating the attackratesandhandlingtimesoftwogeneralistintertidal whelkpredatorsfeedingon7–33differentpreyspecies[4], Novak (PhDthesis, UniversityofChicago,2008) showed that 181pairwise interactionsmeasured across six sites exhibitedcombinationsofattackratesandhandlingtimes consistentwiththepredictedinverserelation(Figure1B). Thus,empiricalevidencesupportsthetheoretical predic-tion that the stability of consumer–resource interactions

Box2.Nonadaptiveoradaptive?

Scientistsusetheterm‘adapt’anditsderivativesinvariousways.For ourpurposes,theprocessof‘adaptation’canbemostusefully con-sideredas‘adaptationtoaspecificlocallysharedenvironment’.Thisis themostcommonusageinevolutionarybiology.Inemphasizingthat, forsomesystems,therearesystemicselectiveprocessesthatimpose thesameselectiveforcesregardlessofvariationacrosslocal environ-ments,wehighlightthefactthattheseprocessesareselective,butfor reasonsthatdonotinvolveadaptationtolocalconditions.

This perspective contrasts witha more conventional approach toward the evolution of macroscale biological systems, accom-plished by expanding hierarchically the theory of adaptation by natural selection by identifying a hierarchy of units of selection

[76]. ‘Individual’ and ‘population’ are replaced with ‘population’ and‘community’(or‘community’and‘population-of-communities’), respectively,andanalogouspropertiesoftheseentitiesthat corre-spondtokeyelementsoforganismicnaturalselection(e.g., repro-duction, heritability, fitness, adaptation, or environment) are identified. Ithas long beenrecognized that such atheory ofthe adaptationofhigher-levelentitiestotheirenvironmentsislogically possible,althoughnotwithoutsignificantissues[76–79](J.KhaiTran, PhDthesis,StonyBrookUniversity,2011).

Inthisview,feasibilityandstabilityserveasanimportant compo-nent ofcommunity fitnessand are consideredto dependonthe environment. For example, the environment can influence the strengthandtypeofinteractionsbetweenspecies.Moreover,overall communityfitnessalsorelieson‘reproduction’intermsofa com-munitycolonizingnewareasorinfluencingthecompositionofother

communitiesthroughpropagulepressure.Althoughtheprocessis more nuanced, in oversimplifiedterms, adaptive selection atthe communityleveleliminates communitytypesthatonaverage do notpersistlongenoughtoproducealikecommunity(i.e.,absolute fitnesslessthan1).Thisislikelythefateofinfeasibleand highly unstableconfigurations,barringareproductiveratehighenoughto compensate.Furthermore,communityselectioncanfavoronestable communitytypeoveranotheraccordingtotheirrelativefitnesses. Similarityamongexistingcommunitiesisexplainedasthe conse-quenceofconvergence(limitedwaystosolveaproblem),withthe evolutionaryprocessbeinghigherleveladaptiveselection.

Despiteitslogicalappeal,aconsensushasnotemergedabouthow toput in practicesuch atheory so thatitboth avoidsconceptual difficultiesandprovidesrewardinginsightsintocommunityevolution. Fromtheperspectiveofnonadaptiveselection,astablecommunityis not necessarilya communitythatis‘better adapted’toitsspecific environment.Exploringnonadaptiveselectiondoesnotrequire resol-vingissuesaboutdefininglocaladaptationatthecommunitylevel.A usefulanalogyfromthephysicalsciencesillustratesthispoint. Pro-tons,thenucleiofhydrogenatoms,haveneverbeenobservedtodecay whilethemoststableisotopeoftheradioactiveelementfranciumis unstable(shorthalf-life).Hydrogenisthemostabundantelementin theuniverse,whereasfranciumisalaboratorycuriosity.Yet,wewould beunwillingtosaythathydrogenisbetteradaptedtotheuniverse. Eventually,afruitfuladaptivetheory ofcommunityevolution,asa counterparttothenonadaptiveprocesseswediscusshere,mightbe possible.

constrainsattackrateandhandlingtimecombinationstobe eitherlowand/orinverselyrelated.Animportanttaskfor futureworkwillbetoexaminethesimultaneousoperation ofsystemicselectionduetoinstability,andongoingnatural selectionwithineachofthecoevolvedspeciesthatinfluence attackratesandhandlingtimes[4].

Similar results have been found based on models of entire food webs. Nonadaptive systemic selection, throughstabilityandfeasibilityconstraints,canrestrict observedattack rates in a community to values where new consumers invade but do not overexploit their resources.Thepossibilityofsuchselectionamong other-wiseunconstrainedattackratesduringfood-web compo-sition turnover was first demonstrated in a model by Rossberget al. [17].

Community turnover is essential to this mechanism, because this enables species with a lower attack rate comparedwithcurrentresidentstoinvade,atleastwhen residentsandinvaderssufficientlydifferfromeachotherto notstrongly compete throughshared resources and con-sumers.Thiscouldresultfromtheimmigrationof individ-ualsfromalargespeciespool.Variantswithlowerattack ratescanhavehigherchancesofestablishinginafoodweb and persisting compared with those with higher attack rates,even thoughtheirinvasion fitness[18]is lower,if they avoid overexploiting and extinguishing their main resources.

Adetailedanalysisofthisphenomenonmustaccountfor the distribution of trophic interaction strengths among consumer–resource pairs, and trophic niche widths

[19]. Thus,this analysisidentifies an ‘optimal’ degreeof dietarydiversityforconsumers,wheretheriskofresource overexploitationisminimized, matchingwellthedietary diversity found for marine fish [19,20]. Another line of evidence for systemic selection of attack rates is that aquatic size spectra (the distribution of community bio-massoverindividualsofdifferentsizes[21])should theo-reticallyhavetheobservedpower-lawformsonlyifmean attackratesareconstrainedtoappropriatevalues,atleast toanorderofmagnitude[22].

Thus,systemic selection at thecommunity level, over longtimescales,canleadtopredictablechangesofattack ratesandnichewidths,becausethesetraitshavesimilar ecological implications across communities of different composition. Traitswithdynamicalimplicationsthat de-pendmoresensitivelyoncommunitycomposition,suchas somespecializedforagingordefensestrategies[23],might belesslikelytoexhibitpredictablepatternsacrossspaceor time.

Communitymodules

Thestructureofecologicalnetworksstronglydiffersfrom random,particularlyatthelevelofsmall-scalestructures (networkmodulesormotifs),consideredtobethe‘building blocks’ of networks.Network patterns canbe altered by changingthenumberofspeciesthroughinvasion, specia-tion,andextinction,orbychangingthewayspecies inter-act (e.g., by changing trophic relations or interaction strengths).

In food webs, some modules are greatly over-repre-sented(e.g.,thetritrophicchain)[24–26].The preponder-ance of certain motifs could reflect their dynamical properties [25,27,28], andsimulations indeed show that motifprofileshavestronginfluenceonnetworkdynamics. Ifdifferentfoodwebconfigurationsvaryinstability, sys-temic selection should cull unstable configurations

[2,7].Such systemic selection could operatethrough two intertwined processes: network assembly anddynamical pruning[29,30].

The degree to which a community is stable can be determined through simulation [28], given assumptions abouttheequationsgoverningdynamics(e.g.,Box3).The networkmotifsthatareobservedinfoodwebsarealsothe structures with the greatest probability of being stable (Figure2)[25].Aside from motif patterns,food webs ex-hibitapatternofshortfoodchainsthatcanbeexplainedby stability constraints [8,31]. Food webs built with longer chains are less stable than those with shorter chains

[32].These resultsmatchwhat weexpectfrom systemic selectionagainstinstability.

Nonadaptivesystemicselectioncanactonnetworksvia dynamicalpruning,favoringconfigurationsthataremore likelytoleadtosystempersistence [31].Similar nonran-dommotifprofilescould alsoariseby networkassembly, the effectsof whichhavebeenfoundin bothmutualistic andtrophicnetworks[33–37].Only bydevelopingstrong modelsofnetworkassemblycanoneseparatetheeffectof dynamicalpruningfrom that ofnetworkgrowth and de-velopment. Assembly might not only involve systemic selection, but also include other processes (e.g., priority effectsorconstraintsoncolonization).

Limitsoffeasiblecoexistence

Whenmodelinglargenumbersofinteractingspecieswith arbitrary,yetbiologicallyplausible,combinationsoftraits andinteractions,itisdifficulttoachievecoexistenceofall species. During simulations, at least some species will inevitablydeclinetozeroabundance.Oftenthisisbecause there isnoequilibrium whereallspeciescancoexist (in-feasibility) rather than any existing equilibrium point beingunstable. 0 0.0 0.2 0.4 0.6 (A) (B) 8 8 6 4 2 0

0e+00 5e–04 1e–03

6 4 2 0 Handling me 1 2 3 4 0.00 Aack rate 0.05 0.10 0.15

TRENDS in Ecology & Evolution Figure1.The empiricalrelation between handlingtimeand attack rates. (A) Publishedattackrates(day1_ind1_{)andhandlingtimes(day}1_{)for57species;see}

[12]fordetails.(B)Empiricalrelationbetweenthespecies-specifichandlingtimes (days)andpercapitaattackrates(preyeatenpred 1_prey 1_m2_day1_)oftwo

predatorywhelkspeciesfeedingontheirprey(n=181;M.Novak,PhDthesis, UniversityofChicago,2008).Insetshowstherelationatlowattackrates.

Feasibility constraints canbe powerful modes of sys-temic selection. Models have shown that the number of speciesthatcancoexistinequilibriumcommunities(with no directcompetition within or between species [38,39]) cannotbegreaterthanthenumberofresourcesmediating indirectexploitativecompetition[40,41].When thereare morespeciesthanresources,somewillinvariably outcom-pete the others, resulting in afinal community with, at most,onespeciesperresource.

Only recentlyhasitbecome clear[19]that these con-straints canbecome tighter when the competing species

targetresourcesselectively,sothatmostspecieshavejust a few, but strong, competitors. In two-level food webs where a community of consumer species feeds on, and competesfor,membersofacommunityofresourcespecies, andsimilarly forhost–parasitecommunities,ithasbeen shown that feasible coexistence of the consumer species becomesunlikelyiftheirnumberexceedshalfthenumber ofresourcespecies[19].Beyondthispoint,smallchanges inmodelparametersleadtolargechangesinabundances. While coexistence ofmoreconsumers mightthenstill be possible,itwouldrequireadegreeoffine-tuningof param-etersthat isunlikely.

When several trophic levels are stacked upon each other, the feasibility constraint tightens even further, andonlyapproximatelyone-thirdofthenumberofspecies atonetrophiclevelarelikelytocoexistinthenexthigher trophiclevel.Thepotentialexplanatorypowerofthismode ofsystemicselectionmatchestheconsistentobservations ofa1:2species-richnessratioinhost–parasite communi-ties [19,42,43]and1:3richnessratiosatadjacenttrophic levelsinmultitrophicfoodwebs[19,44–46](Figure3).

Althoughotherpotentialmechanismsproducing corre-lationsofrichnessacrosstrophiclevelshavebeenproposed

[44,45,47], none to date predict specific values for the richness ratio. For size-structured food webs where the adultbodysizesofconsumersandresourcesarerelatedby acharacteristicpredator–preymassratio(PPMR), system-ic selectionarising from feasibilityconstraints impliesa declineofspeciesrichnesswithbodymassasapowerlaw withexponent log(3)/log(PPMR) 0.2,consistentwith numericalandempiricalobservations[48–51].

Systemicselectionatthecommunitylevelandbeyond Systemic selection at the scale of entire communities should result in patterns in ecological systems that are more feasible and stable than expected at random. One waytocharacterizeacommunityisthespeciesbyspecies communitymatrix,whose off-diagonalelementsquantify interspecificinteractions,specificallyhowfastthe popula-tionofonespecieschangesasaresultofsmalldeviations of another species from its equilibrium abundance. The

0.00 s1 s4 s5 s2 d3 Subgraph d4 s3 d2 d1 d5 d7 d6 d8 0.25 0.50

Mean relave frequency

0.75 1.00

TRENDS in Ecology & Evolution

Figure2.Themeanrelativefrequencyofthe13three-nodesubgraphs(picturedat thetopoftheplot)in50empiricalfoodwebsorderedbytheirstability.Formore detailsonmethodsanddata,see[25].

20 40 60

Number of prey species

Number of predator species

80 100 1:3 0 50 40 30 20 10 0

TRENDS in Ecology & Evolution Figure3.Predator–preyrichnessratiosinfreshwaterinvertebratecommunities after[44],comparedwiththepredictedratioof1:3(brokenline).

Box3.Modelingspeciesinteractions

Usually,interactionswithinfoodwebsaremodeledwithgeneralized Lotka–Volterraequations.However,althoughtheseequationscanbe acceptableinsomeconditions,theydonotapplyuniversally.The Lotka–Volterra functional response model assumes random and homogeneous mixingofprey andpredator individuals, andthat predatorsarerareenoughtoavoidinterference.Empiricalevidence andtheoretical considerationssuggestthatitisnecessarytouse differentmodels,particularlywithincorporationofpredator inter-ference. Extracaremustbetakenwhen usingnon-Lotka–Volterra interactions in food-web models to ensure that the generalized mathematicalexpressionremainslogicallyconsistent[80]

AnalternativetoLotka–Volterrafunctionalresponsemodels,the donor–controlmodel,isasimplecaseofratiodependencethathas oftenbeenobserved.Thistypeofinteractionmightresultnotonly from nonadaptive selection, but also from complexmechanistic models thatincorporateconventionaladaptive selection[81]. We can generalize the donor–control model to a multispecies case, whereseveralpredatorand/orpreyspeciesinteract.Fortwoprey specieshavingacommonpredator,onepreyspeciescanleadto indirectexclusionoftheotherspecies(apparentcompetition).Inthe caseoftwopredatorsalonecompetingforasinglepreyspecies,one speciesisalwaysexcludedbytheother,andthisistrueoftenevenin thepresenceofatoppredator.Thatis,akeystoneeffectisnever observedandtheconfigurationcollapsestoathree-levelfoodchain. Givendonorcontrol,simplefoodchainswillpersistornotbecauseof basalproduction,notbecauseoftop-downeffects.Intraguild preda-tioncan,insomeinstances,helpmaintainmorecomplexstructures.

diagonal entries describe the strengths of intraspecific densitydependencies.

Evenwithoutknowingthemagnitudeofthese interac-tions,onecanstilladdressthequestionofwhichkindsof structurehaveaselectiveadvantage(i.e.,aremorestable), by comparing structures of interactions formalized as signeddirectedgraphs.Such agraph describesthe com-munitymatrixinamagnitude-independent way;thatis, onlybythepatternofpluses,minuses,andzeroswithinthe matrix. Patternsof interactions that are sign stable (as magnitude-independentcommunitymatrices)are robust, inthatenvironmentalchangesaffectingstrengths(butnot signs)ofinteractionscannotflipasystemfromstabilityto instability.Thus,mathematicalresultsoncriteriaforsign stability (which are known, [52–55]) provide qualitative predictions about patterns in community structure that shouldresult.

Sign-stable configurations in nature are rare: simple trophicchains(withoutomnivory)orafewchainslinkedby amensalisticorcommensalisticlinkswithnocycles. Hori-zontally structured communities (i.e.,those without tro-phicinteractions)cannotbesignstable,butcanbestable dependingonthestrengthofinteractions.Theutilityofa particularconceptofstabilityofasystemdependsonthe levelofdetailinthesystemdescription.Whenafoodchain isused torepresentaseriesofstable,horizontally struc-tured aggregates of species, then the chain will be sign stable ifand onlyif omnivory isabsent. In a sense,one shouldexpectasign-stablecommunityofthiskindtobe

selectedbecauseitwillremainfeasibledespitevariationin parametervalues.

However,omnivorouslinksare frequentlyobserved in trophicnetworks[56–58].Therefore,onemustlookmore closely toidentify incommunity matrices a signature of nonadaptive systemic selection through stability con-straints.Giventwo networkswithomnivorouslinksthat arebothstable(i.e.,willreturntoequilibriumfollowinga smallperturbation)thematrixflower(Box4)canbeused todeterminewhichismorelikelytobeeliminatedbecause ofinstability.

Wecanalsotrytodeterminehowlargethefeasibility domain(parameterspacecompatiblewith coexistence)is andhowthisdomainismodulatedbynetworkarchitecture and interaction strengths. In a competition system, for instance,wecanshowthatthelowerthelevelof interspe-cific competition, relative to intraspecific, the larger the domain of feasibility [59]. For mutualistic interactions, with a given number of species, links, and distribution ofinteractionstrengths,feasibilitydomainsincreasewith network nestedness [60]. A community pattern with a larger tolerance to perturbations in biotic and abiotic factors is, by definition, more structurally stable and, underthehypothesisofsystemicselection,shouldbemore frequentlyobserved.Aspredicted,nestednessiscommonly found in plant–frugivore and plant–pollinator networks (bothmutualistic)[61].

Theideathatsomethinganalogoustonaturalselection actsonecosystemshasbeenaroundforalmostaslongas

Box4.Thematrixflower

InadditiontothefamousconceptofLyapunovstabilitywithits well-knownmatrixcriterion,thereareseveralother,lesswell-known sta-bility concepts defined in matrix terms: D- and aD-stability, sign-stability,Volterradissipativeness,andothers.Thesestabilityconcepts dealwithstabilitydespitevariouskindsofuncertaintyorperturbation. However,fewsuchconceptshaveclearcharacterizationsviathematrix structureand/orelements,andsomejusthavedefinitions,withonly necessaryorsufficientconditionsfortheirverificationknown.Logical inclusionrelations(Venndiagrams)amongthespecialstability sub-sets ina generalspace ofrealn3nmatrices helpverify particular propertiesofagiven matrix.Addinga fewmoreconventionstoa standardVenndiagramturnsitintoa3Dmatrixflower[82],whose ‘petals’ represent the subsets of matrices with particular stability properties(FigureI).

Two,relativelysmall,petalsofsign-stablematricesarelocatedinthe very‘core’oftheflower,whiletheotherstabilitypetalssignifythe lowerlevelsinnonadaptiveselection.

We should keepin mindthathaving themoststable patternin interspecificinteractionsisonlyonesideoftheproblem.Theother sideisthefeasibilityofthecommunity,thatis,theexistenceofan equilibriumpointwhereallspecieshavestrictlypositiveabundances. Illustrating that feasibility is as crucial as the stability constraint, considerthesimpleexample given bya setofspeciescompeting for resources. Moreover, assume that the interspecific interaction matrix has been derived from species overlap in a niche space

[83].In this case,thematrix belongs automaticallytothepetalof beingVolterradissipative.Thisimpliesthatthecommunityis auto-maticallygloballystableaslongasthereexistsafeasibleequilibrium point.Therefore,theonlyremainingquestioniswhetherthesystem willbefeasible.Wecanshowthatthereexistsaspecificdomaininthe spaceofcarryingcapacities(orintrinsicgrowthrates),inwhichthe communityisfeasible[55,84].Anopenquestionishowtheseideas translateintosystemswherecoexistencearisesbecauseofnonlinear feedbacks(e.g.,Armstrong–McGeheeeffects[85,86]).

Stable D-stable D-stable Stable Sign-

Dissipa-ve _dominant

Quasi- M-Quasi-recessive Quasi-recessive Stable Normal -stable Totally stable

TRENDS in Ecology & Evolution FigureI.Logicalrelationsamongdifferenttypesofmatrixstability.Adapted from[82].

theideathatnaturalselectionactsonspecies.For exam-ple, Lotka[62]claimedthatnatural selectionmaximizes thetotalenergyfluxthroughanecosystem.Lotka’s argu-mentwasbasedonBoltzmann’s[63]statementthat entro-py, and not raw materials, is the limiting factor for all organisms. This intuition provided the foundation for a distinctiveschoolofecosystemecology(e.g.,[64,65]),whose ideasarenotcurrentlywidelyaccepted(althoughthisdoes notimplythattheyarewrong).

Takingadifferentapproach,Tansley[66]arguedthat‘a kind of natural selection’ will tend to favor more stable ecosystems.Thisviewhasremainedwidespreadin ecologi-caltheory.However,empiricallyevaluatingthedegreeto whichaparticularselectivemechanismmighthaveshaped ecosystem properties requires knowledge of transient states that have been selected against. Our sample of observed ecosystemsisunfortunately ‘length biased’: be-cause most observations come from single time points, ecosystemsthatare morepersistent arelikelytobe sys-tematicallyover-represented,relativetothetrue distribu-tionofhistoricalpersistencetimes.Ifecosystemstructure is shaped over time by stability constraints, we should expect unbiased samples (taken through time at fixed points ofspace) todiffer systematically from extant eco-systems,whichwouldrepresentthestableendproductsof historicalprocesses.

Therehaveoccasionallybeenclaimsthatnatural selec-tioncanoperatebetweenadjacent‘meta-ecosystems’,such thatthemoststableunitsleavethemostdescendants(e.g.,

[67]).However,itseemslikelythatsuchmechanismswill onlyworkifecosystemsreplicatethemselvesintheir en-tiretybyoccupyingnewunitsofspace.Nonadaptive selec-tiondoesnotrequireananalogofreproductionathigher levelsoforganizationthantheindividual,butdoesdepend upon persistence of definable configurations of species acrosstime.

Socialsystems

Here,wehavemainlyfocusedoncommunityecology.Yet, processesofnonadaptivesystemicselectionmightalsobe relevantinexplainingmanyotherbiologicalpatterns. Con-sider,forinstance,structurewithinpopulations,in particu-lar,theformationofanimalsocialsystems.Insmallgroups inmanyspecies(fromwaspstohumanchildren),dominance hierarchiesoftenreveallinearstructures.Inalinear hier-archy,oneanimal dominates allothers,being aggressive towardthemwithoutreceivingaggressioninturn.Asecond dominatesallbutthetop,andsoon.Allpossiblesubgroups ofthreeindividuals(triads)inagroupmusthavetransitive configurationsofattack(AattacksB,B attacksC,andA attacksC)forahierarchytobelinear.Ifahierarchyisnot linear,thenatleastonetriadhasintransitiveattack con-figurations(AattacksB,BattacksC,andCattacksA).

Traditionally,researchershaveexplained thispattern oforganization usingindividual-based, adaptive models. They have proposed that differences in individual attri-butes (e.g.,size,weaponry, or aggressiveness)determine ranks in the hierarchy [68,69]. Or, they have suggested thatfeedbackfromwinningorlosingcontestsduringgroup formationdeterminesindividualranks[70,71]:an individ-ualwinningacontestincreasesitsprobabilityofwinning

anothercontestwithanewindividual,andanindividual losingacontestincreasesitsprobabilityoflosing. Howev-er,bothexperimentalandanalyticalwork[72,73] demon-strate that these simple biological mechanisms of differences in attributes,orwinner andloser effects, are unableaccountfortheobservedstructureoflinear hierar-chies.Instead,theyarebetterexplainedbythedifferential stabilityratesofthebuildingblocksofthestructures.

Inanalysesofdynamical,peck-by-peckrecordsof chick-ensforminghierarchies,ChaseandLindquist[74] discov-ered that intransitive configurations of attacks were unstable, usually lasting only for brief periods of time beforechangingtotransitiveones.Bycontrast,transitive configurationslastedover20timesaslongasintransitive onesonaverage.Theyhypothesizedthatlinearhierarchies arecommonacrossmanyspeciesbecause,asinchickens, when intransitive configurationsof attacksappear, they convertquicklytotransitiveones,ensuringthathierarchy structuresarealmostalwayslinear.Thisrule(transitive configurationsaremorestablethanintransitiveones),plus therule thatallindividualsinteract,sufficestogenerate hierarchiesthatarealmostalwayslinear.

Concludingremarks

Amajorfocusofevolutionarybiologyisuponprocessesthat create and maintain diversity: how organisms become adapted to their various local environments (including otherorganisms).However,especiallywithregardto mul-tispecies interaction systems, it is alsoimportant to un-derstand the processes that result in similarity among systems. Here, we have argued that, because of system dynamics,thedeckisstackedinfavorofsome(stableand feasible) configurationsandagainst others,sothat what oneobservesisanonrandomdistributionofsystem archi-tectures, basedonintrinsicproperties sharedacross sys-tems. There is a resurgence of interest in stability and selectiveprocessesinshapingecologicalcommunitiesand theircomponentstructures(food webs,foodchains,etc.). Newtheoreticalapproachesandcomputationalresources revealthepotentialsignificanceof‘nonadaptive’systemic selectionprocessesandhighlightkeyattributespromoting stability. At the same time, stability and feasibility are themselves complex concepts that have not been fully explored. Identificationofstabilitycriteria for communi-tiesandcommunitymodulesmightdependsignificantlyon how researchersmodel smaller-scaleconsumer–resource interactions.Nevertheless,itislikelythatsystemic selec-tionprocesses(processesofpruningawayunstable config-urations) will increasingly be seen to underlie many recurrentstructuralfeaturesofbiologicalsystems,within which the more familiar processes of local adaptation operate.

Acknowledgments

Thisworkistheoutcomeofaworkshopgatheringalloftheauthorsatthe CentreInterfacultaireBernoullioftheEcolePolytechniqueFe´de´ralede Lausanne inSwitzerland (EPFL),with fundingof theSwiss National ScienceFoundation(http://cib.epfl.ch/prog.php?id=%271000000027%27).

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