Towards the integration of niche and network theories

Towards

the

Integration

of

Niche

and

Network

Theories

Oscar

Godoy,

*

Ignasi

Bartomeus,

Rudolf

P.

Rohr,

and

Serguei

Saavedra

Thequestforunderstandinghowspeciesinteractionsmodulatediversityhas

progressedbytheoreticalandempiricaladvancesfollowingnicheandnetwork

theories.Yet,nichestudieshavebeenlimited todescribecoexistence within

tropiclevelsdespiteincorporatinginformationaboutmulti-trophicinteractions.

Networkapproachescouldaddressthislimitation,buttheyhaveignoredthe

structure of species interactions within trophic levels. Here we call for the

integrationofnicheandnetworktheoriestoreachnewfrontiersofknowledge

exploringhow interactionswithin andacross trophiclevels promotespecies

coexistence.Thisintegrationispossibleduetothestrongparallelisms inthe

historical development, ecological concepts, and associated mathematical

toolsofboththeories.Weprovideaguidelinetointegratethisframeworkwith

observationalandexperimental studies.

NicheTheoryMeetsNetworkTheory

Onecentralaiminecologyisunderstandinghowspeciesinteractionsmodulatebiodiversity.At theoriginofthisinterestisDarwin’slegacy;hereasonedthatspeciescoexistenceislesslikely amongcloselyrelatedspeciesastheytendtocompeteforsimilarresourcesforsurvivingand reproducing[1].Giventhisreasoning,ecologistsbuilttheconceptoftheniche(seeGlossary)to assessthe degree of resource overlapamong species[2,3],and earlywork exploredthe consequencesofcompetitionforasingle-resourcenichedimension[4,5].However, research-erssoon recognized that a species’ niche is composed ofmultiple dimensions [6,7]. For instance,plantscompetedirectlyandindirectlyforabioticresourcessuchaswater,nutrients, andlight[8–10],as wellasforbiotic resourcesintheformofmutualisticinteractions(e.g., pollinators,disperses,andmycorrhizae)[11–14].Inadditiontoresourcecompetition,parallel workhasshownthatantagonistinteractionswithinatrophiclevel(i.e.,intraguildpredation)

[15]aswellasthosecomingfromothertrophiclevels(e.g.,predation,herbivory,and parasit-ism)arealsopartofaspecies’niche[16–19].Moreover,positiveinteractionssuchasfacilitation canbeasimportantascompetitiveinteractionsforstructuringecologicalcommunities[20,21]. Thisbody of knowledge has revealedthat species coexistence is a muchmore complex processthanoriginallythought.

Paralleltodescribingthemultidimensionalnatureofspecies’niche,ecologistshaveobtained critical progress by revealing general principles of the consequences of multiple species interactions for species coexistence. For example, the concept of apparent competition

[22,23]hasbeenparticularlykeytounderstandingtheroleofindirectmulti-trophicinteractions incoexistencebydescribinghowcompetitionwithinaguildofspeciesismodulatedbyshared enemies(e.g.,predatorsandpathogens).Thisconceptrecentlysetthepathtorecognizethat competitionforresourcesandpredationcanbeofequalimportanceforlimitingorpromoting diversitywithinaguildofprimaryproducersorconsumers(e.g.,plantsorherbivores)[24,25].

Highlights

We propose to integrate niche and

network theories into a single

framework.

Thisintegrationispossiblethroughthe

strongparallelisms ofconcepts and

methodologiesofboththeories.

Feasibilityandstabilityconditionsare

thekeyconceptsthatcanallowthe

integration.

How species interactions across

trophiclevelsfulfillfeasibilityand

stabi-lityconditionsisyettobediscovered.

1

InstitutodeRecursosNaturalesy

AgrobiologíadeSevilla(IRNAS-CSIC)

Av.ReinaMercedes10,E-41080

Sevilla,Spain

2

EstaciónBiol ́ogicadeDoñana

(EBD-CSIC)CalleAḿ ericoVespucio26,

E-41092Sevillea,Spain

3

DepartmentofBiology–Ecologyand

Evolution,UniversityofFribourg

CheminduMuśee10,CH-1700

Fribourg,Switzerland

4

DepartmentofCiviland

EnvironmentalEngineering,MIT,77

MassachusettsAv.,02139

Cambridge,MA,USA

@

Twitter:@Eco_Godoy

*Correspondence:

ogodoy@irnas.csic.es(O.Godoy).

http://doc.rero.ch

Published in "Trends in Ecology & Evolution 33 (4): 287–300, 2018"

which should be cited to refer to this work.

However,theseadvancestogetherwithnichestudiesarelimitedintheirapproach,astheirgoal istounderstandtheroleofspecies interactionsinshapingspeciescoexistencewithin one singletrophiclevel[26].Therestofthespecieswithinacommunitythatdonotbelongtothe focaltrophiclevelisconsideredtobealwayspresentandstatic.Thiscriticallimitationofniche studies clasheswiththe increasinginterest of ecologistsin disentangling themechanisms maintainingspeciescoexistenceinmorethanonetrophiclevel(seeFigure1foraschematic representation).Indeed,partofthismotivationisduetohavingmulti-trophicinformationreadily available[27,28],butthe fundamentalquestionishowtoextend nichetheoryto studythe effects of species interactions on determining diversity across multiple trophic levels simultaneously.

To addressthis limitation,we call for the integrationof niche theory withnetwork theory. Networktheoryhasalreadypartiallyaddressedthechallengeofhowtoconsidertheroleof speciesinteractionsinshapingspeciescoexistenceacrossseveraltrophiclevels[29,30],butit hasmissedtheinformationwithintrophiclevelsthatnichetheoryincorporates.Inparticular, networkstudieshavefocusedontheassociationofthestructureofspeciesinteractionswith communitydynamics inmutualistic (e.g.,plant–pollinator and plant–disperser) [31–35] and antagonisticsystems(e.g.,host–parasite,prey–predator,andplant–herbivore)[34,36–38]Yet, becausenetworkstudiesemphasizespeciesinteractionsbetweentrophiclevels,theyconsider thatspecieswithinthesametrophicleveldonotdirectlyinteract,ortheyallinteractwiththe samestrength[33,35].

Becausenichestudies lack the ability to describespecies coexistencefor more than one trophiclevel,andnetworkstudiesignorethestructureofspeciesinteractionswithintrophic levels(Figure1),itissurprisingthatboththeorieshavenotspokenfluentlytoeachotherdespite

Glossary

Equilibriumpoint:afixedstateat

whichspeciesabundancesare

constantovertime.

Dynamicalstability:thepropertyof

anecologicalsystemtoreturntoan

originalequilibriumpointafterapulse

perturbation.

Intrinsicgrowthrate:therateat

whichapopulationincreasesinsize

intheabsenceofdensity-dependent

regulation.

Feasibility:thepropertyofan

ecologicalsystemtoholdan

equilibriumpointwithpositive

abundancesinallitsconstituent

species.

Feasibilitydomain:therangeof

conditions(e.g.,demographic

parameters)compatiblewithall

specieshavingpositiveabundance.

Feedback:theprocessbywhichthe

outputofasystemisroutedbackas

aninputofanothersystemforminga

loop.

Fitness:thespeciesabilitytomature

andproduceoffspring.

Fitnessdifferences:accordingto

Chesson(2000)[48],averagefitness

differencesbetweenspeciesarean

equalizingmechanismofspecies

coexistencethatreducecompetitive

imbalancebetweencompetitors.In

theabsenceofnichedifferences,

determinethesuperiorcompetitorin

acommunity.

Multi-trophicnetwork:anetwork

representingpatternsofmultiple

interactiontypesbetweenspecies,

includingcompetition,mutualistic,or

antagonisticrelationships.Also

knownasmultiplexnetworks.

Niche:theenvironmentalconditions

andresourcesaspeciesrequiresfor

livingandreproducing.

Nichedifferences:accordingto

Chesson(2000)[48],niche

differencesareastabilizing

mechanismofspeciescoexistence

bycausingintraspecificcompetition

toexceedinterspecificcompetition.

Percapitagrowthrate:therelative

contributiontothepopulation

increasesinsizeperindividual.

Speciesdynamics:changesin

species’populationoverspaceand

time.

Trophiclevel:aleveloforganization

withinthefoodchainofan

ecosystem,theorganismsofwhich

obtainresourcesinasimilarway.

Figure1.ResearchDomainsofNicheandNetworkTheories.Nichetheory(leftside)hasbeensuccessfulin

incorporatingtheeffectofdirectandindirectinteractionswithinandbetweentrophiclevels(denotedbyblackarrows)on

determiningspeciescoexistencewithinasingletrophiclevel(lightgreenrectangle)[7,16,22,24].However,nichestudies

havenotaddressedhowthesedirectandindirecttrophicinteractionsmodulatecoexistenceacrosstrophiclevels.By

contrast,thistaskhasbeenaddressedbynetworkresearch(rightside).Whiletheareaofstudyisbigger(greenrectangle),

networkstudieshavenotconsideredthestructureofinteractionswithintrophiclevels(nounbrokenlinespresent).By

integratingnicheandnetworktheorieswecanstartconsideringexplicitlyandsimultaneouslyspeciesinteractionsacross

trophiclevelsandtheirrole(feedbacks)inmodulatingspeciescoexistence.Notethatarrowsaredouble-headed,indicating

theexistenceofsuchfeedbacks.Unbrokenandbrokenarrowsindicatewhethertheinteractioniswithinorbetween

trophiclevels,respectively.

theircomplementarities;doingsocanprovidenewresearchavenuesandunderstandingof howspeciesdiversityismaintained.Ouraimhereistoshowadirectintegrationofboththeories as they share strong similitudes in their theoretical motivations, ecological concepts, and mathematicaltools.Thispathofmutualunderstandingpavestheroadtocombinetheoretical conceptsandassociatedtoolboxesfromboththeoriesintoacommonmethodological frame-work. We believe the emerging framework is particularly useful for investigating species coexistenceinmulti-trophicnetworks,whichincludecompetitive,mutualistic,and antago-nisticinteractionssimultaneously.Additionally,weprovidearoadmapthataccommodatesthis newframeworktoexperimentalandobservationalstudies.

ConceptualParallelismsBetweenNicheandNetworkTheories

Obtainingacommontheoreticalframeworkfrom theintegrationofbothnicheandnetwork theoriesisstraightforwardasthesestudieshavestartedfromsimilarconceptualconstructs, andafterdecadesofresearchhaveindependentlyconvergedonequivalentconclusionsabout theconditionsleadingtospeciescoexistence.Toreachthemaximumaudience,weverbally detailthishistoricalconvergenceandexplainherewhyboththeoriesspeakthesamelanguage despite using different technical terms. We also aim to present a rigorous mathematical explanationofthisconceptualparallelism.Thisispossiblebecauseboththeoriesusesimilar population dynamics models to build ecological theory rooted in the Lotka-Volterra form

[4,24,25,35,38–41](Box1).WeareawarethatthedirectapplicationofLotka-Volterramodels todescribenaturalsystemsmightbelimitedassumingspecieslinearresponses,anddonot takeintoaccountmeta-communitydynamics.Partoftheselimitationswillbesolvedlaterwhen wepresentmoremechanisticmodelsthatcaptureadditionalnonlinearspeciesresponsesin orderto explain howto apply this emergingframework to experimentaland observational approximations[42,43].

Aswepreviouslymentioned,thenicheconceptwasafundamentalconstructtounderstand patternsofspeciesdistributionandco-occurrencewithinatrophiclevelbasedonhowspecies interact with the habitat they experience (Grinnellian niche), how they modify the habitat (Eltonianniche)andhowinteractwithotherspeciesinthecommunity(Hutchinsonianniche)

[44].Underclassicnichetheory,theonlyconditionmodulatingspeciescoexistencewasthe amount of niche overlap between species [4,45], which ecologists assumed to arise, for instance,from differences inphenology, billsize, shade tolerance,or feeding preferences. The rationale was that the smaller the niche overlap, the larger the chances of species coexistence[7,46,47].

However,subsequentwork[25,41,48]showedthatnichedifferencesalonearenotenough to determinespecies coexistence.Under recentadvancesof nichetheory (alsoknownas ‘moderncoexistencetheory’),nichedifferencesareonlyastabilizingmechanismthattendsto promotecoexistencewhenspecieslimitthemselvesmorethantheylimitothers[48].Modern coexistence theory has provided techniques to directly measure niche differences as the relative ratio between intra- and interspecific competition [25], and consider that neutral dynamicsoccurwhenspeciesdonotdifferintheirnichesbuthaveequivalentfitness[49]. Theestimationofnichedifferencesusingcoexistencetheorytechniquesremains phenome-nological(i.e.,thesourceofvariationisunknown),andrecentstudiesare,forinstance,mapping howspeciesfunctionaltraitdifferencesrelatetonichedifferences[50].

Conversely,speciescanalsodifferintheirfitness.Fitnessdifferencesarerelatedtospecies’ abilitytocaptureandtransformresourcesintooffspring,whichisgenerallyacombinationof demographicparameters(e.g.,fecundity,survival,andrecruitment)andthespecies’sensitivity

toreduce thesedemographicparametersinthepresenceofneighbors [25,43,49].Fitness differencesinessencedeterminethesuperiorcompetitorwithinaspeciespairintheabsenceof niche differences.It has been wellrecognized that coexistence is the result of a balance betweentherelativestrengthofnicheversusfitnessdifferences.Thatis,twospecieswillstably coexistwhentheirnichedifferencesovercometheirfitnessdifferences[48,49](seeTable1for examplesofbothspeciesdifferencesacrossawiderangeoforganisms).Thisconditionhas

Box1.ConceptualParallelismbetweenConditionsLeadingSpeciesCoexistenceforNicheand

NetworkTheory

Forapairofspeciesincompetition,thecoexistenceconditionsaccordingtonichetheoryaredefinedby:

ffiffiffiffiffiffiffiffiffiffiffiffiffiffi a11a22 a12a21 r ð1NichedifferenceÞ1 > r1 r2 ffiffiffiffiffiffiffiffiffiffiffiffiffiffi a22a21 a11a12 r Fitnessdifference > ffiffiffiffiffiffiffiffiffiffiffiffiffiffia12a21 a11a22 r 1Nichedifference [I]

wherer1>0correspondstotheintrinsicgrowthrate(demographicparameter)ofspecies1,anda12>0represents

thecompetitivepercapitaeffectofspecies2onthepercapitagrowthrateofspecies1.Thisequationstatesthatthe

fitnessdifference(i.e.,theratiobetweenintrinsicgrowthratesmodulatedbywhatisknownasthecompetitiveresponse

ratio)ofthetwospecieshastofallbetweenalowerandanupperbound,computedfromthenichedifference(i.e.,range

ofvaluesdefinedbytheratiobetweeninter-andintraspecificcompetition).Notethattheseinequalitiescanbealso

simplywrittenasa11/a21>r1/r2>a12/a22.Moreover,suchinequalitieshavealsotoassumethatthenichedifferenceis

smallerthanone,i.e.,

a12a21<a11a22 [II]

whichguaranteesthattheequilibriumpointisdynamicallystable(thesystemreturnstoitsoriginalequilibriumpointafter

apulseperturbation)inaLotka-Volterracompetitionmodeloftheform:

dN1 dt ¼N1ðr1a11N1a12N2Þ dN2 dt ¼N2ðr2a21N1a22N2Þ 8 > < > : [III]

whereN1andN2correspondtotheabundanceofspecies1and2,respectively.NotethattheinequalitiesinEquationI

correspondtoanequilibriumpointcalledfeasiblebecauseallspecieshavepositiveabundances(i.e.,N1*>0and

N2*>0)[35,52–54,99].Bycontrast,theinequalityofEquationIIonlygrantsthedynamicalstability(infact,inthat

specificcasetheglobalstability)byhavingintraspecificcompetitionstrongerthaninterspecificcompetition.Notethat

feasibilityisanecessaryconditionforspeciespersistenceinaLotka-Volterramodel[54].

Letusexplainhowdynamicalstabilityandfeasibilityconditionsariseinmulti-trophicsystemsbytakingasanexamplea

two-trophiclevelsystemdescribingthemutualisticinteractionsbetweenasetofplants(P)andasetofpollinators(A).

Notethatsimilarconclusionsareobtainedbyconsideringantagonistinteractionssuchasaprey–predatorsystem.This

mutualisticsystemcanbedescribedbythefollowingsetofdynamicalequations:

dPi dt ¼Pi r ðPÞ i  X j aðPÞ_ij Pjþ X j gðPÞ_ij Aj ! dAi dt ¼Ai r ðAÞ i  X j aðAÞ_ij Ajþ X j gðAÞ_ij Pj ! 8 > > > > < > > > > : [IV]

wherethevariablesPiandAidenotetheabundanceofplantandanimalspeciesi,respectively.Theparametersofthis

mutualisticmodelcorrespondtothevaluesdescribingintrinsicgrowthrates(ri),within-guildcompetition(aij>0),and

thebenefitreceivedviamutualisticinteractionsbetweentrophiclevels(gij>0).Alltheseinteractionstrengthscan,in

turn,beembeddedinatwo-by-twoblockmatrix;

b¼ _gaðPÞðAÞ gaðAÞðPÞ

 

[V]

Theconditionsforfeasibilitydependonboththespeciesinteractionsdefinedbybandthedemographicparametersof

speciesr(analogoustoEquationIabove)[71].Notethattheconditionsfordynamicalstabilityaremorecomplex[40].

Indeed,severalmeaningfulnotionsofstabilityhavebeendefinedinecology,suchasVolterra-dissipative,D-stability,

sign-stability,andlocalstability.Sign-stability,Volterra-dissipative,andD-stabilityareonlydeterminedbytheinteraction

matrixb.Sign-stabilityhasthepropertyofgrantingglobalstabilityonlyonthedescriptionofwhoeatswhomandnoton

thestrengthofthetrophicinteractions.Volterra-dissipativeimpliestheglobalstabilityofafeasibleequilibrium,while

D-stabilitygrantsonlylocalstability.Finally,localstabilityinvolvesalsotheequilibriumdensitiesandthereforetheintrinsic

growthrates.Therelationsamongthesenotionsofstability(andmore)arewellrepresentedbyLogofet’sflower[53].

alsobeenreinterpretedasthelargerthenichedifferencebetweentwospecies,thelargerthe combinationoftheirfitnessdifferencescompatiblewiththeircoexistence[49,51](Box1).This reinterpretationiscriticalasit providesthemainbridgeofcommonunderstandingbetween nicheandnetworktheories,explaininghowspeciescoexistenceispossible.

Networkresearchonspeciescoexistencestartedbystudyingthestabilizingmechanismsfor entirecommunities[5],ratherthanfocusingonpairwiseinteractions.Thisstabilitywasdefined inadynamicalratherthanastaticway.Dynamicalstabilityisthepropertyofasystemto returntoanoriginalequilibriumpoint(ifitexists)afterapulseperturbation(e.g.,achangein speciesabundances)comingfromdemographicstochasticity,whichincludesmigrationand random changes in birth and death processes. Early network studies showed that this dynamicalstabilitydepends onspeciesinteractions(analogousto nichedifferences) within

Table1.ExamplesofNicheandFitnessDifferencesforDifferentOrganismsandTrophicLevelsa

Trophiclevel Evidencesofnicheandfitnessdifferences Refs

Niche Fitness

Plant–plant Spatialsegregation,phenology,orplantmorphology

differencesreducenicheoverlap.

Speciesabilitytodrawdowncommonlimitingresources

determinesspeciesfitness.

[4,8,48]

Plant–insect Fragmentedevidencessuggestthatdifferencesin

pollinatorscanstabilizeplantcoexistence.

Herbivorousinsectsandtheirnetworkofhyperparasitoids

cansignificantlyaffectplantfitness.

[11,70,83]

Plant–vertebrate Interactiveeffectsbetweenabioticstress,tolerancetoherbivory,andherbivorebodysizedetermineplantabundances

andrichness.

[84,85]

Plant–fungi Fungalpathogensmediatecoexistencethroughtrade-offs

betweencompetitiveabilityandresistancetopathogens

andthroughpathogenspecialization.

Lowspecificityoffungalpathogensdetermineslocal

abundanceofplantspeciesinatropicalforest.

[19,86]

Insect–insect Plantspecies,stemsize,andlocationwithinstem

determinenichedifferenceswithinaguildofherbivorous

insects.

Searchingability,femalefecundity,andresource

degradationandpreemptiondeterminefitnessdifferences

amongparasitoids,phytophagousinsects,and

arachnids.

[87,88]

Insect–plant Wildbeesspecializeintheirfloralrewardincludingnectar,

pollen,pollenresins,volatiles,lipids,andwaxes.

Foragingratesandfoodstoragedeterminefitness

differences(i.e.,droneproduction,wintersurvival)among

geneticallydiversehoney-beecolonies.

[11,89]

Insect–vertebrate Tickhabitatdiffersgreatlyamongspeciesfromrodent

burrowstocavesandbirdnests.

Thetiminganddurationofaquaticinsectemergenceis

regulatedbytemporalvariationinsalmondensity.

[90,91]

Vertebrate–vertebrate Differencesinbillshapeandbodysizestabilize

coexistencebetweenbirdsbytheuseofdifferent

resources.

IntraguildpredationoflargecarnivoresonAfricanwild

dogsreducestheirpopulationsize.

[92,93]

Vertebrate–plant Strongoverlapofdietaryrequirementsbetweenwildand

domesticherbivores.

[94,95]

Insect–vertebrate Vertebratesdifferinthenumberandspecificityoftheir

parasiticinsects.

Ticksreduceoffspringandincreasemortalityinawide

varietyofanimalsincludingbirds,lizards,andmammals.

[90,96]

Trematode–mollusk Spatialheterogeneitystabilizescoexistenceofaguildof

saltmarshtrematodes.

Competition-colonizationtrade-offsdeterminetrematode

fitness.

[72]

Alga–alga Nicheandfitness:Phylogeneticrelatednessdoesnotpredictcompetitiveoutcomesbetweenfreshwateralgae. [58]

Bacteria–vertebrate SpecificimmunityofStreptococcuspneumoniae

serotypesstabilizescoexistence.

Acquiredimmunitytononcapsularantigensdetermines

serotypefitness.

[97]

Protist–bacteria Nicheandfitness:Differencesinmouthsizeofbacterivorousprotistspeciesreducescompetitiveexclusion. [46]

a

Someexamplesexplicitlyseparatethestudyofthespecies’nichefromthespecies’fitness,whileinotherexamplesresearchershaveonlystudiedonecomponent,or

bothnicheandfitnessdifferenceshavebeenconsideredtogether.Notethatformanytrophiclevels,informationofnicheandfitnessdifferencesisasymmetric,these

differencesarebetterknownforonetrophiclevelthanfortheother(e.g.,plants–fungiorinsects–vertebrate).

andbetweentrophiclevelcompartments(containedinbmatrix,Box1).Importantly,anumber ofinterestingquestionsemergedfromtheseconcepts,suchaswhethertheobservedstructure oflargemulti-trophicsystemsnecessarilyleadstomoredynamicallystablecommunities[5]. However,extensiveresearchshowedthatdynamicalstabilityalone(asnichedifferencesalone) isnotenoughtoguaranteestablecoexistenceofallspeciesinacommunity.Thismeansthatit canbepossibletohaveadynamicallystablecommunitywheretheequilibriumpointwillalways lead to one or more species withzero abundance (Ni*=0), even if reintroduced into the community[35,52,53].Inotherwords,thesystemisdynamicallystablebutcontainsonly a subsetofspeciesfromtheoriginalpool.

As it hashappenedwith the historicaldevelopment of nichetheory, subsequent work on networktheoryhasshownthatitisalsonecessarytoaccountforthespecies’fitnessinorderto evaluatetheconditionofwhetherspeciescanattainpositiveabundancesatequilibrium[54]. Networkstudiescalledthisconditionfeasibility,whichalsodependsonthespecies inter-actionscontainedinthematrix(b)andthespecies’demographicparameters(r)[35,52,55](Box 1).Importantly,theserecentadvanceshaveshownthatthestructureofspeciesinteractions betweentrophiclevelscanmodulatetherangeofcombinationsofdemographicparameters leadingtofeasiblesystems[35,55].Therefore,inlinewithnichetheory,networkstudiesalso found that species coexistence within communities depends on how the demography of speciesmatchtheconstraintsimposedbyspeciesinteractions.

This historical convergence shows the existence of a commontheoretical framework for understandinghowspecies interactionsmodulatediversity,whichhastwo keyingredients: (i)species’demographyand(ii)thestructureofspeciesinteractions.Thisstructureiscontained inthe bmatrix described in Box 1. Thetake-home messageof this framework isthat a communityofspeciescancoexistwhenbothingredientsarecombinedinthefollowingway:

Box2.EmergingPropertiesoftheIntegrationofNicheandNetworkTheory

Formulti-trophicdynamicalsystemsofthegeneralformdNi/dt=Nifi(N),annnblockmatrixemergesfordescribing

speciesinteractionacrossntrophiclevels:

b¼ a1 g12  g1n g₂₁ a2  g2n ... ... } ... gn1 gn2  an 2 6 6 6 4 3 7 7 7 5; [I]

wherethediagonalblocks (ai)correspondto thewithin-trophiclevel(i)interactions(i.e.,competition,intraguild

predation,facilitation)andtheotherblocks(gij)representthebetween-trophiclevelinteractions(effectoftrophiclevel

joniintheformofmutualismorantagonisminteractions).Asbisablockmatrix,eachelementofthematrixrepresentsa

submatrixofspeciesinteraction.Forinstance,a1isamatrixdescribingallspeciesinteractionwithinthetrophiclevel1,

andg12isanothermatrixdescribingallinteractiveeffectsofspeciesfromthetrophiclevel2onspeciesfromthetrophic

level1.

Stablecoexistenceofallspecies(Ni*>0)acrosstrophiclevelsdependsonwhetherthisinteractionmatrixbandthe

demographicparametersrisatisfiestogetherboththestabilityandfeasibilityconditions[53,54,71].Therearedifferent

classesofdynamicalstability.Forinstance,localstabilityisthepropertyofthesystemtoreturntotheequilibriumpointaftera

small pulseperturbation(changesin speciesabundances), whereasglobalstabilityisconcernedwithexternalperturbations

ofanygivenmagnitudeconvergingtothesameequilibriumpoint.Eachclassdemandsspecificpropertiestobefulfilledby

theinteractionmatrixbincombinationwiththespeciesdemographicparametersri[53,71],andwhichclassofstability

shouldbe studieddepends on boththeresearchquestionand knowledgeabout the system. The feasibilityofamulti-trophic

systemcorrespondstotheconditionsallowingallspeciestohavepositiveabundances,whichalsodependsonboththe

interactionmatrixbandthedemographicparametersri[35,52–54,71].Thefigurebelowillustratestheconditionsof

feasibilityinathree-speciessystem.Thegreenareaonthesphererepresents therangeofdemographic parameters leading

tofeasibilitygiventheinteractionstrengthsmatrix.Tosomeextent,FigureIoftheextensionofmoderncoexistencetheoryto

multispeciescoexistence;theborderofthegreenareaisthemultispeciesanalogousofthefitnessandnichedifference

inequality(seeEquationIinBox1)thatappliestospeciespairsonly.

speciesinteractionsdefinethecoexistencespace(i.e.thefeasibilityregion)andspeciescoexist whenthecombinationoftheirdemographicparameters(i.e.fitness)fallswithinthisspace(Box 2andFigure2).Onecrucialadvantageofthisframeworkisthatitisnotlimitedtoanyparticular typeofmulti-trophicinteractions,andcanbethereforeaccommodatedtobothmutualisticand antagonisticinteractions,suchasaplant–pollinatororapredator–preycommunity.Another keyimportantadvantageisthatthisframeworkisnotlimitedtotwotrophiclevels.Itcanbe extended to multi-trophic structures, where three or more trophic levels are considered simultaneously.Indeed,thesemulti-trophicstructuresaresimplythecombinationof competi-tive/facilitativeinteractionswithintrophiclevels,aswellasantagonisticandmutualistic inter-actionsbetweentrophiclevels[56](Box2).

CouplingtheIntegrationofNicheandNetworkTheoriesWithExperimental andObservationalWork

Weacknowledge thatone criticalstepto considerinfullis thatthis integrativeframework dependsonhoweasilyresearcherscanadaptittotheirparticularsystems.Thebasictaskisto

FigureI.IllustrationoftheFeasibilityDomainforaMulti-TrophicSystem.Thefigureshowsthenormalized

domainofdemographicparameters(feasibilitydomainrelativetotheunitsphere)thatatwo-trophicsystem(e.g.,two

pollinatorsandoneplant)cantheoreticallyhavetobecompatiblewithallspecieshavingpositiveabundances.This

normalizedfeasibilitydomain(greensphericaltriangle)isconstrainedbytheintra-andinterspecificinteractionmatrix(b).

Thecolumnsoftheinteractionmatrix(e.g.[b11,b12,b13])givetheboundariesofthefeasibilitydomain(threebluelines).

Thelargerthisvolumeis,thelargerthesetofdemographicvaluescompatiblewithfeasibility,andthelargerthelikelihood

ofspeciescoexistenceacrosstrophiclevels[55,71].

obtaininformationofdemographicparametersaswellasspeciesinteractioncoefficientswithin andbetweentrophiclevels.However,itisnotsoobvioushowthisinformationcanbeobtained andrelatedtotheory.Wecanstartlearningfromtheabilityofrecentadvancesinnichetheoryto coupletheorywithfieldandlabexperiments[42,57–60].

Thesestudiessuggestthatthemostrigorouswaytoproceedwouldbetoconductexperiments inordertoparameterizeandvalidateasystemofequationscontainingamodelofpopulation dynamicsforeachtrophiclevel.Technically,thisparameterizationiseasiertoobtainwhenthe

(A)

(D) (E) (F)

(B) (C)

Network Interacons with environmental variaon in me and space

Feasibility domain

Fitness differences

Coexistence Coexistence Exclusion

Figure2.EffectsofSpecies_’IntrinsicPropertiesandNetworkStructureonSpeciesCoexistence

ForaFigure360authorpresentationofFigure2,seethefigurelegendathttps://doi.org/10.1016/j.tree.2018.01.007

Speciestraitssuchasbodysize,phenologicaltiming,orfeedingpreferencesinteractwithenvironmentalvariationsin

spaceandtimetodetermine(i)networkstructureand(ii)species’fitness.Brokenlinesrepresentthestrengthofspecies

interactionswithintrophiclevelsandunbrokenlinesrepresentthesameacrosstrophiclevels.Obtaininginformationon

howsuchtrait–environmentinteractionsmodifiedthesetwoelementsinecologicalcommunitiesremainsfundamentalto

predicttheconsequencesofspeciesinteractionsforthemaintenanceofdiversity[98].Considerahypotheticalcaseofa

plant–pollinatorsysteminwhichenvironmentalvariationmodifiesthesetwoelementsinthreedifferentways(PanelsA–C).

Thesizeofthecirclesdenotestherealizedspecies’fitness,whicharisesasacombinationofspeciesinteractionsandtheir

demographicparameters(plantsingreenandinsectsinblue).Additionally,wehavelearnedfromtheintegrationofniche

andnetworktheoriesthatthestructureofspeciesinteractionswithinandbetweentrophiclevelsrendersthefeasibility

domain(hererepresentedintwodimensionsforsimplicity;darkgrayareainPanelsD–F).Notethateachnetworkstructure

givesadifferentsizeoffeasibilitydomain.Inprinciple,thelargerthefeasibilitydomain,themorelikelyspeciescoexistasit

allowsforalargercombinationoffitnessdifferences(seeFfeasibilitydomaincomparedwithDandE).However,itis

paramounttopointoutthatevenwithalargefeasibilitydomain,speciesmaynotcoexistifthepositionofthevector

containingspecies’fitness(redline)fallsoutsidethefeasibilitydomain(i.e.,fallswithinthelightgrayarea)[71].Thisisthe

caseofFwhereoneplantspeciesisexcluded.Conversely,thesystemcanbemaintaineddespiteshowingasmaller

feasibilityregionifthevectorofspecies’fitnessfallswithinthefeasibilitydomain(casesDandE).Therefore,thetake-home

messageisthatcoexistenceoccurswhenspeciesinteractionscreateafeasibilitydomaincompatiblewiththeobserved

fitnessdifferences.Recallthatfitnessdifferencesaremeasuredasthedistancebetweenthecenterofthefeasibilitydomain

andthepositionofthevectorcontainingspeciesfitness(redline).Importantly,systemswithlowfitnessdifferencesmay

facelargerperturbations.Forinstance,speciescancoexistincaseEbutcanbelessresistanttoperturbationscompared

withcaseD,giventhatthepositionofthevectorofspecies’fitnessisclosetotheexclusionregion.

life-spanbetweenorganismsissimilar.Inparticular,populationmodels describingspecies dynamicswithanannuallifecycleseemamongthebestapproximationstochooseforseveral reasons.Theydefinethenetworkstructureandspeciesfitnessintheexactsamewayasthe originaldefinitionusingtheLotka-Volterraframework[25,43],yettheyarecomplexenoughto includenonlinearmechanismsofspeciescoexistencesuchasthestorageeffect,and saturat-ingfunctionalresponsestocompetitive,mutualistic,andantagonisticinteractions(Box3).They canalsotakeintoaccounttheeffectofenvironmentalvariationinspaceandtimeonmodifying diversitymaintenanceduetochangesinintransitivecompetition[59],intraspecifictraitvariation

[61],orphenotypicplasticity[62].Moreover,annualspeciesarerelativelyeasytomanipulate, modelsdescribingpopulationdynamicshavebeensuccessfullyusedforplants[43,57],and canbeextendedtootherannualorganismsincludingpollinators(e.g.,wildbees),herbivores (e.g.,snails,grasshoppers),orpathogens(e.g.,fungalseedpathogens).

Analternativetoexperimentsisthe useofobservationaldata(e.g.,[63,64]).Observational approachesarejustifiedwhenorganismsdifferintheirlife-span,orwhentheirmanipulationis notfeasible for technical or conservation issues. Thetraditional limitation of observational studiesisthatthestructureofspeciesinteractionsbetweentrophiclevelsisofteneasierto describe,atleastatthespecieslevel,thanthestructureofspeciesinteractionswithintrophic levels.Thislimitationcanbesolvedbyusingmathematicalmodelsfedwithspatiallyexplicit and/or temporal series data. These methodologies allow inferring species demographic parameters and species interactionsfrom changes inspecies fitness due to both natural variationsinthecommunitydensityandspeciesrelative abundances[65,66].Forexample, recent work [64] combined statistical models for survival, growth, and recruitment with individual-basedmodelstodescribetemporalpatternsinplantspeciesco-occurrences.These model-generated population abundances were then integrated into projection models to estimatethestructureofcompetitiveinteractionswithinplantspecies.

Regardlessoftheapproachselected,westresstheurgencyoflinkingtheoryandempirical work. We are at the dawn of understanding whether species characteristics, commonly reportedinthenicheandnetworkliterature,aremorestronglyrelatedtodifferencesinspecies demographyortothestrengthandsignofspeciesinteractions[50,67,68].Moreover,weare notawareofasinglestudythathasattemptedtoempiricallyestimateinaquantitativewaythe matrixofspeciesinteractionswithinandbetweentrophiclevelssimultaneously.Webelievethat taking such an approach is crucial for answering an outstanding research question that emerges with the integration of both theories, namely,how species interactions between trophiclevelsdrivenicheandfitnessregionswithintrophiclevelsandviceversa.Therefore,this isthetopicofournextsection.

HowDoSpeciesInteractionsBetweenTrophicLevelsDriveNicheand FitnessDifferencesWithin TrophicLevels?

Bycouplingrecentconceptualadvancesofnicheandnetworktheory,wearereadytounderstand howthespeciesdifferencesthatdeterminecoexistencewithintrophiclevels(nicheandfitness differences)feedbackwith thestructureofspeciesinteractionsthatdeterminecoexistence betweentrophiclevelsandviceversa.Toillustratetheseideas,letusconsideramutualisticplant– pollinatorsystem(seegraphicalexampleinFigure2).Whatwehavelearnedfrompriorworkisthat differencesinfeedingbehavior,bodymass,orinsectphenologycancontributetotheniche differencesthattendtostabilizecoexistencebetweenplants(seeTable1)[69,70].However, pollinatorsalsocontributetothefitnessdifferencespromotingplantcompetitivedominance.For instance,changesintheabundanceofpollinatorscan,inturn,modifythecompetitivehierarchyof aplantguildbyincreasingthenumberandthequalityofseedsproducedbypollinator-dependent

Box3.AnExampleofHowToIntegrateNicheandNetworkTheorieswithExperimentaland

ObservationalData

Ourapproachtoevaluatehowbetween-trophicinteractionsdrivenicheandfitnessdifferenceswithintrophiclevelsand

viceversainvolvesthreesteps.

Step1:Departfromarelativelysimplesystemofequations.Hereitiscomposedoftwoannualpopulationmodels

describingchangesinpopulationsizewithtimeinplants(seeds,Pi,t+1)andpollinators(eggs,Ai,t+1).Bothmodelsare

mirrorimagesincludinganequalnumberofparameterswiththesamebiologicalmeaning,

Pi;tþ1¼Pi;t ð1giÞsiþ ligið1þ X kgikAk;tÞ 1þX_jaijgjPj;t 0 @ 1 A Ai;tþ1¼Ai;t ð1eiÞtiþ nieið1þ X kdikPk;tÞ 1þX_juijejAj;t 0 @ 1 A ; 8 > > > > > > < > > > > > > : [I]

whereeachmodelisthesummationoftwocomponents.Thefirstcomponentdescribesthepossibilityofastorage

effectprocess,andthesecondcomponentdescribespercapitafecundity.Specifically,thissecondcomponent

describeshowmutualismsenhancethespeciesintrinsicabilitytoproduceoffspring,reducedbythecompetitive

effectsexertedbyotherspecieswithinthesameguild.

Step2:Estimatesspeciesvitalrates.Estimatepercapitagrowthrateintheabsenceofspeciesinteraction[plants(l),

pollinators(n)],isbestdescribedastheinterceptofthestatisticalmodelsbuiltforStep3(seebelow).Additionalefforts

areneededtoestimateratesofseedgermination(g)orlarvasurvival(e),andthestorageeffectasthesurvivalofthe

species’lifestagesthatdonotproduceoffspringwithinayear[e.g.,soilseedbankinplants(s)andnonreproductive

adultmortalityinsomepollinators(t)].

Step3:Estimatespeciesinteractionmatrix.Toestimatespeciesintra-andinterspecificcompetitiveinteractionswithin

trophiclevels[plants(a),pollinators(u)],thebestapproachistofitaseriesofstatisticalmodelsdescribingforeach

speciesitspercapita growthrateasa functionofcompetitor’srelativeabundance. Formutualisticinteractions

[pollinator’seffectonplants(g),plants’effectonpollinators(d)],dothesamebutdescribespecies’percapitagrowth

rateasafunctionofthemutualisticrelativeabundances(FigureI).

FigureI.Competitive relationshipbetween species includingitself areexpectedto takea negative

exponentialform[59,66],whereasmutualisticrelationshipareexpectedtobefunctionallysaturatingbest

describedbynon-inflictedcurves[100]. Withthisinformationispossibletothenbuildthebmatrix

summarizingspeciesinteractionsacrosstrophiclevels.

plants.Differentiatingbetweenthesealternativesiscrucialbecauseifpollinatorsprimarilydrive nichedifferencesoverfitnessdifferencesbetweenplantcompetitors,thenwecanexpectamore diverseplantcommunity(e.g.,[11,70]).Acompletelydifferentoutcomewouldoccurifpollinators primarilydrivefitnessdifferencesamongplants.Inthatcase,adominantplantspeciesfavoredby pollinatorscandominatethecommunity.

Similarly,consideringpollinatorsbeyondbeingaresourceforplantsimpliesthatwehaveto assesssimultaneouslytheirpopulationdynamics.Forinstance,plantcharacteristicssuchas floralmorphologyorplantphenologicaltimingcancontributetothedifferentpollinator require-ments(i.e.,nichedifferences)thatstabilizetheircoexistence.Butsomeplantspeciescanalso contributetothedominanceofafewpollinators(i.e.,fitnessdifferences)ifthosecanparticularly benefitfromthem,asoccurswithpollinatorspecialists.Allinall,thiscouldleadustorethink whether mutualistic interactions between trophic levels always increase the likelihood of speciescoexistence. Traditionally,mutualismshave been considered apositiveinteraction thatenhancecoexistencebecausetheindividualsinvolvedobtainacertainbenefitthatcanbe translatedtotheirpopulationgrowthrates(butsee[16]inageneralcontext).However,towhat extentthesebeneficialeffectsbetweenparticularspeciesacrosstrophiclevelscanreducethe likelihoodofspeciescoexistenceintheentiresystem(i.e.,withinandamongtrophiclevels)is notknownyet(Figure2).

Notethatweneedtouseageometricalratherthananalgebraicapproachtostudyfitnessand nichedifferencesformorethantwospecies(seeFigureIinBox2).Thisapproachinformsus whetherspeciescoexistence ispossible whenthe fitness differencesbetween speciesfall withinthefeasibilitydomain(Figure2).Moreover,thisapproachallowsustoquantifyhow environmentalvariationmodulatestheextentofthefeasibilitydomainandthedifferencesin fitnessbetweenspecies.Estimatingtheseenvironmentallydependentrelationshipsis impor-tant as they determine how strongly an ecological community can be perturbed without pushingspecies towards extinction.As a ruleof thumb, the closerthe fitness differences totheedgeofthefeasibilitydomain,thelowertheabilityofthecommunitytofaceperturbations (Figure2)[71].Itisalsoimportanttonotethatthisapproachcanbeappliedtoothernetwork types,suchas food webs,parasitoidwebs [24,72],andmulti-trophic networkscombining antagonisticandmutualisticinteractions[56,73].

Answeringthisquestionusingempiricalapproachesinvolvesthreesteps(Box3).First,weneed aframeworkfordescribingspeciespopulationdynamicsasafunctionofspeciesdemographic parametersandspeciesinteractionswithin andbetweentrophiclevels. Forexample,for a plant–pollinatorsystem,thisframeworkcanbeasystemoftwoannualpopulationmodels(one foreachtrophiclevel)thatcanincludeastorageeffectcomponentifdesired(Box3).Second,in ordertoparameterizethemodels,weneedinformationonspeciesdemography.Forspecies, demographicparameterssuchas percapitagrowthrateintheabsence ofcompetition, germination rate, or larval survival, can be inferred relatively easily from experimental or observationaldata[43,57,64,66].Third,weneedtoestimatethematrixbthatsummarizes speciesinteractionsacrosstrophiclevels.

Thisthirdstepisbyfarthemostchallengingaspectasthenumberofparametersthatneedto beestimatedgrowsexponentiallywiththenumberofspeciesinthecommunity.Inprinciple, theseestimatescanbeobtainedfromstatisticalmodelsfittingempiricalorobservationaldata

[27,59,74].Forintra-andinterspecificcompetitivecoefficientswithinplantsandwithin polli-nators,theseparameterscanbeobtainedbydescribinghowspeciespercapitagrowthrates dependoneachcompetitor’srelativeabundance[50,59](seeFigureIinBox3).Forthecaseof

mutualisticeffectsofplantsonpollinatorsandviceversa,theprocedureissimilartotheone previouslydescribed,butthistimepercapitagrowthratesshouldbedescribedasafunctionof therelativeabundanceofeachmutualisticspecies.In thelikelycasethat thisoptionisnot feasible, onepossibility isto group species byfunctionalgroups, and estimateinteraction coefficients(atthatresolution)viachangesinpopulationsizeofbothtrophiclevelsthroughtime

[75].Whilethefunctionalgroupapproachassumesuniformityofresponseswithinfunctional groups,itmightbearequirementwhenscalinguptohigherdimensions.Anotherpossibilityis tousenoveltechniquesthatcombineecological,phylogenetic,andgeographicinformationto predictforbiddenlinksanddefinearealizedratherthanapotentialmatrixofspeciesinteractions forlargecommunities[76].Thislatterpossibilityinfersthestrengthofspeciesinteraction(e.g., competition, mutualism, etc.) without the necessity of measuring fitness directly. In sum, obtaining information for estimating the matrix b is challenging, but there are techniques availabletosolvethatlimitation[75–77].

Thisthree-stepapproachcan alsobecombinedwithvariation inspecies’functionaltraits, phylogenetic relatedness,orintraspecificvariation to test amyriad ofecologicalquestions regardingthe functionaland phylogenetic assemblyof communities (e.g. limiting similarity hypothesis,Darwin’snaturalizationhypothesis)[4,78].Moreover,measuringemergent prop-ertiesofthecommunity,suchasbiomassorfoodproduction,wouldallowlinkingthe mecha-nisms of biodiversity maintenance to ecosystem functioning (e.g. biodiversity insurance hypothesis, biodiversity-complementarity hypothesis) [79,80]. For instance, experimental assemblagesvaryingplantandflowermorphologyandpollinators’bodysizecanallowtesting theroleofspeciestraitsinprovidinghigherfoodproductionyields[81]bytheeffectsofplant andanimaltraitsonnicheandfitnessdifferences(see[82]fordetails).

ConcludingRemarks

Theintegrationofnicheandnetworktheoriesprovidesanaturalpathwaytoobtainadeeper understandingoftheroleofspeciesinteractionsinmodulatingspeciescoexistence.Here,we show that this integration isstraightforward thanks to the strong parallelism of ecological concepts,complementaryapproaches,andassociatedmathematicaltoolsfoundacrossthese tworesearchareas.Theemergentpropertyofthisintegrationistheconsiderationthatdiversity withinecologicalcommunitiesismaintainedwhenspeciesinteractionscreateacoexistence spacethataccommodatesthedifferencesinfitnessbetweenspecies.Importantly,wehave provided a methodological framework readily available to investigate howthe strength of mutualistic,antagonistic,andcompetitiveinteractionsacrosstrophiclevelspromotespecies coexistenceinmulti-trophicnetworksandvariableenvironments.Thekeylimitationweface nowistheempiricalparameterizationoftheinteractionmatrix,whichsummarizesthestructure of species interactions across trophic levels. It should be no surprise that applying the integrationofnicheandnetworktheorytoexperimentalandobservationalapproachescan bechallenging,butwehaveprovidedaguidelinetoaccomplishthisaim.Whilethisisnotan easytask,thebenefitscanbeunlimited.

Acknowledgements

Commentsfromthreeanonymousreviewersgreatlyimprovethequalityofthispaper,whichistheresultofacollaborative

projectfundedbytheSpanishMinistryofEconomyandCompetitiveness(LINCX,CGL2014-61590-EXP).OGacknowledges

postdoctoralfinancialsupportprovidedbytheSpanishMinistryofEconomyandCompetitiveness(JCI-2012-12061)andby

theEuropeanUnionHorizon2020researchandinnovationprogramundertheMarieSklodowska-CuriegrantagreementNo

661118-BioFUNC.SS alsoacknowledges support fromMIT Research CommitteeFundsand theMitsuiChair.Wefinallythank

Phylopic.comandMelissaBroussardforprovidingsilhouetteimagesofplantsandpollinators.

SupplementalInformation

Supplementalinformationassociatedwiththisarticlecanbefound,intheonlineversion,athttps://doi.org/10.1016/j.tree.

2018.01.007.

References

1. Darwin,C.(1859)TheOriginoftheSpecies,ModernLibrary 2. Grinnell, J.(1917) Theniche-relationships of theCalifornia

Thrasher.Auk34,427–433

3. Elton,C.(1946)Competitionandthestructureofecological communities.J.Anim.Ecol.15,54–68

4. Macarthur,R.andLevins,R.(1967)Thelimitingsimilarity, con-vergence,anddivergenceofcoexistingspecies.Am.Nat.101, 377–385

5. May,R.M.andMacArthur,R.H.(1972)Nicheoverlapasa functionof environmentalvariability.Proc.Natl.Acad.Sci. U.S.A.69,1109–1113

6. Hutchinson,G.E.(1961)Theparadoxoftheplankton.Am.Nat. 95,137–145

7. Abrams,P.(1983)Thetheoryoflimitingsimilarity.Annu.Rev. Ecol.Syst.14,359–376

8. Tilman,D.(1982)ResourceCompetitionandCommunity Struc-ture,PrincetonUniversityPress

9. McKane,R.B.etal.(2002)Resource-basednichesprovidea basisforplantspeciesdiversityanddominanceinarctictundra. Nature415,68–71

10. Hautier,Y.etal.(2009)Competitionforlightcauses plant biodiversitylossaftereutrophication.Science324,636–638 11. Pauw,A.(2013)Canpollinationnichesfacilitateplant

coexis-tence?TrendsEcol.Evol.28,30–37

12. Bennett,J.A.etal.(2017)Plant-soilfeedbacksandmycorrhizal typeinfluencetemperateforestpopulationdynamics.Science 355,181–184

13. Runquist,R.B.andStanton,M.L.(2013)Asymmetricand fre-quencydependentpollinatormediatedinteractionsmayin flu-encecompetitivedisplacementintwovernalpoolplants.Ecol. Lett.16,183–190

14. Howe,H.F.andEstabrook,G.F.(1977)Onintraspecific com-petitionforaviandispersersintropicaltrees.Am.Nat.111, 817–832

15. Polis,G.A.etal.(1989)Theecologyandevolutionofintraguild predation:potentialcompetitorsthateateachother.Annu.Rev. Ecol.Syst.20,297–330

16. Abrams,P.A.etal.(1998)Apparentcompetitionorapparent mutualism?Sharedpredationwhenpopulationscycle.Ecology 79,201–212

17. Pacala,S.andCrawley,M.(1992)Herbivoresandplant diver-sity.Am.Nat.140,243–260

18. Parker,I.M.etal.(2015)Phylogeneticstructureandhost abun-dancedrivedisease pressurein communities.Nature520, 542–544

19. Gilbert,G.S.andWebb,C.O.(2007)Phylogeneticsignalinplant pathogen–hostrange.Proc.Natl.Acad.Sci.U.S.A.104, 4979–4983

20. Bertness,M.D.andCallaway,R.(1994)Positiveinteractionsin communities.TrendsEcol.Evol.9,191–193

21. Callaway,R.M.(1995)Positiveinteractionsamongplants.Bot. Rev.61,306–349

22. Holt,R.D.(1977)Predation,apparentcompetition,andthe structureofpreycommunities.Theor.Popul.Biol.12,197–229 23. Holt,R.D.(1984)Spatialheterogeneity,indirectinteractions,and

thecoexistenceofpreyspecies.Am.Nat.124,377–406 24. Chesson,P.andKuang,J.J.(2008)Theinteractionbetween

predationandcompetition.Nature456,235–238

25. Chesson,P.(2013)Speciescompetitionandpredation.In Ency-clopediaofSustainabilityScienceandTechnology(Leemans, R.,ed.),pp.223–256,Springer

26. Chase,J.M.etal.(2002)Theinteractionbetweenpredation and competition: a review and synthesis. Ecol. Lett. 5, 302–315

27. Deraison,H.etal.(2015)Functionaltraitdiversityacrosstrophic levelsdeterminesherbivoreimpactonplantcommunity bio-mass.Ecol.Lett.18,1346–1355

28. Soliveres,S.etal.(2016)Biodiversityatmultipletrophiclevelsis neededforecosystemmultifunctionality.Nature536,456 29. Bascompte,J.andSolé,R.V.(1995)Rethinkingcomplexity:

modellingspatiotemporaldynamicsinecology.TrendsEcol. Evol.10,361–366

30. Harfoot,M.B.etal.(2014)Emergentglobalpatternsof ecosys-temstructureandfunctionfromamechanisticgeneral ecosys-temmodel.PLoSBiol.12,e1001841

31. Jordano,P.etal.(2003)Invariantpropertiesincoevolutionary networksofplant–animalinteractions.Ecol.Lett.6,69–81 32. Bascompte,J.andJordano,P.(2007)Plant-animalmutualistic

networks:thearchitectureofbiodiversity.Annu.Rev.Ecol.Evol. Syst.38,567–593

33. Bastolla,U.etal.(2009)Thearchitectureofmutualisticnetworks minimizescompetitionandincreasesbiodiversity.Nature458, 1018–1020

34. Pocock,M.J.etal.(2012)Therobustnessandrestorationofa networkofecologicalnetworks.Science335,973–977 35. Rohr,R.P.etal.(2014)Onthestructuralstabilityofmutualistic

systems.Science345,1253497

36. Lafferty,K.D.etal.(2008)Parasitesinfoodwebs:theultimate missinglinks.Ecol.Lett.11,533–546

37. Allesina,S.andPascual,M.(2008)Networkstructure,predator– preymodules,andstabilityinlargefoodwebs.Theor.Ecol.1, 55–64

38. May,R.M.andLeonard,W.J.(1975) Nonlinearaspectsof competitionbetweenthreespecies.SIAMJ.Appl.Math.29, 243–253

39. Chase,J.M.andLeibold,M.A.(2003)EcologicalNiches:Linking ClassicalandContemporaryApproaches,UniversityofChicago Press

40. Case, T.J. (1999) Illustrated guide to theoretical ecology. Ecology80, 2848–2848

41. Chesson,P.(1990)MacArthur’sconsumer-resourcemodel. Theor.Popul.Biol.37,26–38

42. Kuang,J.J.andChesson,P.(2009)Coexistenceofannual plants:generalistseedpredationweakensthestorageeffect. Ecology90,170–182

43. Godoy,O.andLevine,J.M.(2014)Phenologyeffectson inva-sionsuccess:insightsfromcouplingfieldexperimentsto coex-istencetheory.Ecology95,726–736

44. Hutchinson,G.E.(1957)Concludingremarks.ColdSpringHarb. Symp.Quant.Biol.22,415–427

45. Diamond,J.M.(1975)Assemblyofspeciescommunities.In EcologyandEvolutionofCommunities(Cody,M.andDiamond, J.M.,eds),pp.342–444,BelknapPress,HarvardUniversity 46. Violle,C.etal.(2011)Phylogeneticlimitingsimilarityand

com-petitiveexclusion.Ecol.Lett.14,782–787

47. Pacala,S.W.andTilman,D.(1994)Limitingsimilarityin mecha-nisticandspatialmodelsofplantcompetitioninheterogeneous environments.Am.Nat.143,222–257

48. Chesson,P.(2000)Mechanismsofmaintenanceofspecies diversity.Annu.Rev.Ecol.Syst.31,343–366

49. Adler,P.B.etal.(2007)Anicheforneutrality.Ecol.Lett.10, 95–104

50. Kraft,N.J.B.etal.(2015)Plantfunctionaltraitsandthe multidi-mensionalnatureofspeciescoexistence.Proc.Natl.Acad.Sci. U.S.A.112,797–802

51. Leibold,M.A.andMcPeek,M.A.(2006)Coexistenceofthe nicheandneutralperspectivesincommunityecology.Ecology 87,1399–1410

52. Roberts,A.(1974)Thestabilityofafeasiblerandomecosystem. Nature251,607–608

53. Logofet,D.O.(2005)Stronger-than-Lyapunovnotionsofmatrix stability,orhowflowershelpsolveproblemsinmathematical ecology.LinearAlgebraAppl.398,75–100

54. Hofbauer,J.andSigmund,K.(1998)EvolutionaryGamesand PopulationDynamics,CambridgeUniversityPress 55. Saavedra,S.etal.(2016)Seasonalspeciesinteractions

mini-mizetheimpactofspeciesturnoveronthelikelihoodof com-munitypersistence.Ecology97,865–873

56. Kéfi,S.etal.(2016)Howstructuredistheentangledbank?The surprisinglysimpleorganizationofmultiplexecologicalnetworks leadstoincreasedpersistenceandresilience.PLoSBiol.14, e1002527

57. Levine,J.M.andHilleRisLambers,J.(2009)Theimportanceof nichesforthemaintenanceofspeciesdiversity.Nature461, 254–257

58. Narwani,A.etal.(2013)Experimentalevidencethatevolutionary relatednessdoesnotaffecttheecologicalmechanismsof coex-istenceinfreshwatergreenalgae.Ecol.Lett.16,1373–1381 59. Godoy,O.etal.(2017)Intransitivityisinfrequentandfailsto

promoteannualplantcoexistencewithoutpairwiseniche differ-ences.Ecology98,1193–1200

60. Germain,R.M.etal.(2016)Speciescoexistence: macroevolu-tionaryrelationshipsandthecontingencyofhistorical interac-tions.Proc.R.Soc.B283,20160047

61. Hart,S.P.etal.(2016)Howvariationbetweenindividualsaffects speciescoexistence.Ecol.Lett.19,825–838

62. Turcotte,M.M.andLevine,J.M.(2016)Phenotypicplasticity andspeciescoexistence.TrendsEcol.Evol.31,803–813 63. Siepielski,A.M.etal.(2011)Signatureofecologicalpartitioning

inthemaintenanceofdamselflydiversity.J.Anim.Ecol.80, 1163–1173

64. Chu,C.andAdler,P.B.(2015)Largenichedifferencesemerge attherecruitmentstagetostabilizegrasslandcoexistence.Ecol. Monogr.85,373–392

65. Ives,A.etal.(2003)Estimatingcommunitystabilityand ecologi-cal interactions fromtime series data.Ecol. Monogr.73, 301–330

66. Kunstler,G.etal.(2016)Plantfunctionaltraitshaveglobally consistenteffectsoncompetition.Nature529,204–207 67. Angert,A.L.etal.(2009)Functionaltradeoffsdeterminespecies

coexistenceviathestorageeffect.Proc.Natl.Acad.Sci.U.S.A. 106,11641–11645

68. Coux,C.etal.(2016)Linkingspeciesfunctionalrolestotheir networkroles.Ecol.Lett.19,762–770

69. Buchmann,S.L.(1987)Theecologyofoilflowersandtheirbees. Annu.Rev.Ecol.Syst.18,343–369

70. Benadi,G.etal.(2014)Specializationandphenological syn-chronyofplant–pollinatorinteractionsalonganaltitudinal gradi-ent.J.Anim.Ecol.83,639–650

71. Saavedra,S.etal.(2017)Astructuralapproachfor understand-ingmultispeciescoexistence.Ecol.Monogr.87,470–486 72. Mordecai,E.A.etal.(2016)Theroleofcompetition–colonization

tradeoffsandspatialheterogeneityinpromotingtrematode coexistence.Ecology97,1484–1496

73. Pilosof,S.etal.(2017)Themultilayernatureofecological net-works.Nat.Ecol.Evol.1,0101

74. Fründ,J.etal.(2013)Beediversityeffectsonpollinationdepend onfunctionalcomplementarityandnicheshifts.Ecology94, 2042–2054

75. Tack,A.J.etal.(2011)Canwepredictindirectinteractionsfrom quantitativefoodwebs?–anexperimentalapproach.J.Anim. Ecol.80,108–118

76. Morales-Castilla,I.etal.(2015)Inferringbioticinteractionsfrom proxies.TrendsEcol.Evol.30,347–356

77. Bartomeus,I.etal.(2016)Acommonframeworkforidentifying linkagerulesacrossdifferenttypesofinteractions.Funct.Ecol. 30,1894–1903

78. Duncan,R.P.andWilliams,P.A.(2002)Ecology:Darwin’s nat-uralizationhypothesischallenged.Nature417,608–609 79. Loreau,M.andHector,A.(2001)Partitioningselectionand

complementarityinbiodiversityexperiments.Nature412,72–76 80. Lawton,J.H.andBrown,V.K.(1994)Redundancyin ecosys-tems.InBiodiversityandEcosystemFunction(Schulze,E.-D. andMooney,H.A.,eds),pp.255–270,Springer

81. Garibaldi,L.A.etal.(2015)Traitmatchingofflowervisitorsand cropspredictsfruitsetbetterthantraitdiversity.J.Appl.Ecol. 52,1436–1444

82. Carroll,I.T.etal.(2011)Nicheandfitnessdifferencesrelatethe maintenanceofdiversitytoecosystemfunction.Ecology92, 1157–1165

83. Pashalidou,F.G.etal.(2015)Earlyherbivorealertmatters:plant mediatedeffectsofeggdepositiononhighertrophiclevels benefitplantfitness.Ecol.Lett.18,927–936

84. Rueda,M.etal.(2013)Contrastingimpactsofdifferent-sized herbivoresonspeciesrichnessofMediterraneanannual pas-turesdifferinginprimaryproductivity.Oecologia172,449–459 85. Louthan,A.M.etal.(2013)Climaticstressmediatestheimpacts ofherbivoryonplantpopulationstructureandcomponentsof individualfitness.J.Ecol.101,1074–1083

86. Bever,J.D.etal.(2015)Maintenanceofplantspeciesdiversity bypathogens.Annu.Rev.Ecol.Evol.Syst.46,305–325 87. Venner,S.etal.(2011)Coexistenceofinsectspeciescompeting

forapulsedresource:towardaunifiedtheoryofbiodiversityin fluctuatingenvironments.PLoSOne6,e18039

88. Reitz,S.R.andTrumble,J.T.(2002)Competitivedisplacement amonginsectsandarachnids.Annu.Rev.Entomol.47,435–465 89. Mattila,H.R.andSeeley,T.D.(2007)Geneticdiversityinhoney beecoloniesenhancesproductivityandfitness.Science317, 362–364

90. Jongejan,F.andUilenberg,G.(2004)Theglobalimportanceof ticks.Parasitology129,S3–S14

91. Moore,J.W.andSchindler,D.E.(2010)Spawningsalmonand thephenologyofemergenceinstreaminsects.Proc.R.Soc. Lond.BBiol.Sci.277,1695–1703

92. Abzhanov,A.etal.(2004)Bmp4andmorphologicalvariationof beaksinDarwin’sfinches.Science305,1462–1465 93. Creel,S.andCreel,N.M.(1996)LimitationofAfricanwilddogs

by competition with larger carnivores. Conserv. Biol. 10, 526–538

94. Voeten,M.M.andPrins,H.H.(1999)Resourcepartitioning betweensympatricwildanddomesticherbivoresinthe Taran-gireregionofTanzania.Oecologia120,287–294

95. Mishra,C.etal.(2004)Competitionbetweendomesticlivestock andwildbharalPseudoisnayaurintheIndianTransHimalaya.J. Appl.Ecol.41,344–354

96. Askew,R.R.(1971)ParasiticInsects,Heinmann

97. Cobey,S.andLipsitch,M.(2012)Nicheandneutraleffectsof acquiredimmunitypermitcoexistenceofpneumococcal sero-types.Science335,1376–1380

98. Cenci,S.etal.(2018)Estimatingtheeffectofthereorganization ofinteractionsontheadaptabilityofspeciestochanging envi-ronments.J.Theor.Biol.437,115–125

99. Svirezhev,I.U.andLogofet,D.O.(1978)TheStabilityof Biologi-calCommunities,MIRPublishers

100.Morris,W.F.etal.(2010)Benefitandcostcurvesfortypical pollinationmutualisms.Ecology91,1276–1285