Towards the Integration of Niche and Network Theories

14 Pages·2017·0.55 MB·English

by  Oscar Godoy

Published in "Trends in Ecology & Evolution 33 (4): 287–300, 2018"
which should be cited to refer to this work.
Towards the Integration of Niche and

Network Theories

Oscar Godoy,1,*,@ Ignasi Bartomeus,2 Rudolf P. Rohr,3 and Serguei Saavedra4

The quest for understanding how species interactions modulate diversity has Highlights

progressedbytheoreticalandempiricaladvancesfollowingnicheandnetwork We propose to integrate niche and

theories. Yet, niche studies have been limited to describe coexistence within network theories into a single

framework.
tropiclevelsdespiteincorporatinginformationaboutmulti-trophicinteractions.

Network approaches could address this limitation, but they have ignored the Thisintegrationispossiblethroughthe
h structure of species intera ctions w ithin trophic le vels . Her e we call for the stron g parallelis m s of co ncepts a nd
methodologiesofboththeories.
c integrationofnicheandnetworktheoriestoreachnewfrontiersofknowledge

exploring how interactions within and across trophic levels promote species Feasibilityandstabilityconditionsare
. the key c once pts that can allow the
o coexistence. This integration is possible due to the strong parallelisms in the
integration.
historical development, ecological concepts, and associated mathematical
r
toolsofboththeories.Weprovideaguidelinetointegratethisframeworkwith How species interactions across
e troph iclevelsfu lfillfeasibilitya ndstabi-
observational and experimental studies.
lityconditionsisyettobediscovered.
r
.
c Niche Theory Meets Network Theory

Onecentralaiminecologyisunderstandinghowspeciesinteractionsmodulatebiodiversity.At
o
theoriginofthisinterestisDarwin’slegacy;hereasonedthatspeciescoexistenceislesslikely

d amongcloselyrelatedspeciesastheytendtocompeteforsimilarresourcesforsurvivingand

reproducing[1].Giventhisreasoning,ecologistsbuilttheconceptoftheniche(seeGlossary)to
/
assess the degree of resource overlap among species [2,3], and early work explored the
/

: consequencesofcompetitionforasingle-resourcenichedimension[4,5].However,research-

p ers soon recognized that a species’ niche is composed of multiple dimensions [6,7]. For

instance,plantscompetedirectlyandindirectlyforabioticresourcessuchaswater,nutrients,
t
t and light [8–10], as well as for biotic resources in the form of mutualistic interactions (e.g.,

h pollinators,disperses,andmycorrhizae)[11–14].Inadditiontoresourcecompetition,parallel

workhasshownthatantagonistinteractionswithinatrophiclevel(i.e.,intraguildpredation)
1InstitutodeRecursosNaturalesy
[15]aswellasthosecomingfromothertrophiclevels(e.g.,predation,herbivory,andparasit-
ism) are also pa rtofa species ’nich e[16– 19].Mo reover ,posi tiveinteract ionssuch asfa cilitation AAvg.roRbeioinloagMíae drcee Sdeesvil1la0 ,(IER-N4A1S08-C0SIC)

canbeasimportantascompetitiveinteractionsforstructuringecologicalcommunities[20,21]. Sevilla,Spain
2Estació nBioló gicadeDoñana(EBD-
Tphroisc ebsosdtyh aonf okrnigoiwnalelldygteh ohuagsh tr.evealed that species coexistence is a much more complex 4C1S0IC92) CSael vleil leAam,́eSrpicao in Ve spucio 26, E-
3Depa rtmentof Biology–Ecologyand

cPraitriaclalell ptoro dgeresscsribbinyg rtehvee amliunlgtidgimeneenrsaiolnparli nncaiptuleres ooff stpheeciceos’n nseicqhuee, necceosloogfistms uhlatipvele osbptaeicnieeds ECFrvhiobelomuutiirnog n,d,uS U wMnitiuvzseéerrsleai tn1yd 0o, fC FHri-b1o7u0r0g
interac tions for spe cies coex istence. For exam ple , the concept of ap pa rent com petition 4Departm entofCiviland

EnvironmentalEngineering,MIT,77
[22,23]hasbeenparticularlykeytounderstandingtheroleofindirectmulti-trophicinteractions
incoex isten ceby describing how c ompetitionwith ina guild o fspecie sismodulate dbyshared CMaamssbarcidhgues,eMttsA ,AUv.S, A02139
en emies(e.g., pre datorsand path ogens).This conce p trece nt lysetth ep athtoreco gn izethat @Twitter:@E co_G odoy

competitionforresourcesandpredationcanbeofequalimportanceforlimitingorpromoting
*Correspondence:
diversitywithinaguildofprimaryproducersorconsumers(e.g.,plantsorherbivores)[24,25].
[email protected] (O. Godoy).
1
Glossary
Equilibriumpoint:afixedstateat

whichspeciesabundancesare

constantovertime.

Dynamicalstability:thepropertyof

anecologicalsystemtoreturntoan

originalequilibriumpointafterapulse

perturbation.
Intrinsicgrowthrate:therateat

whichapopulationincreasesinsize

intheabsenceofdensity-dependent

regulation.
Feasibility:thepropertyofan

ecologicalsystemtoholdan

equilibriumpointwithpositive

abundancesinallitsconstituent

species.
Feasibilitydomain:therangeof
h
conditions(e.g.,demographic
Figure1.ResearchDomainsofNicheandNetworkTheories.Nichetheory(leftside)hasbeensuccessfulin parameters )com patiblewithall
c incorpo rati ngtheeffec tofdirecta nd indirect intera ctionswith inandbetw eentr ophicle vels (deno ted bybla ckarrows) on specieshavi ngpositive abun dance.
o. dchoaevnteetrr amnsoitnt,i ntahgdis ds trpaeesscks ieehdsa schobo eewxe insthtaeednsdcere ed wsirseitec hdtin ba ayn dsn ienin tgwdleior ertkrcotrp ethsroeicpa lhre civche i(lnr (itgliegh rhtatsc gitdi roeen)e.snW mrheoicledta uthnlaegtleae r)c e[o7a e,o1xf6iss,t2teu2 nd,c2ye4i s]a.b cHirgoogws eser vt( rgeorrpe, ehnniicc r heleecv tseatlnusgd. liBee)sy, Faonuetepindupbtu aot cfo kaf: astnhyose tt ehpmeror cissey srsos teu bmteyd fwo brhmaiccihnk g tahase
r network stud iesh ave notc onsidered the structur eofinter action swith intro phic leve ls (nou nb roken linesp resent).By loo p.

e tinrotepghriactlienvge nlsicahned athnedi rnreotlweo(ferke dthbeaocrkiess) iwnem coadnu lsattainrtg csopnescidieesricnoge exxisptelicnictley .aNnodt esitmhautltaarnroeowussalyr espdeocuibelse -inhteearadcetdio,ninsd aiccartoinsgs Fanitdnepsrosd: uthcee sopffescpireins ga.bility to mature
r ttrhoep ehxicis lteevneclse , oref s spueccht ivfeeelyd .backs. Unb ro ken and br oken ar rows indicate whe ther the int erac tion is within or between FCihtne sessosn d(i2f0fe0 r0e)n[4c8e]s,:a avcecraogrdeinfigtn teoss
.
differencesbetweenspeciesarean
c
equalizingmechanismofspecies
However,theseadvancestogetherwithnichestudiesarelimitedintheirapproach,astheirgoal
o coexistencethatreducecompetitive
is to understand the role of species interactions in shaping species coexistence within one
imbalancebetweencompetitors.In
d sin gl etrophiclev el[2 6].T he restofth especiesw ith inacom munityth atdonotbe longto the theabsenc eofnich edifferences,

focaltrophiclevelisconsideredtobealwayspresentandstatic.Thiscriticallimitationofniche determinethesuperiorcompetitorin
/ studi es clash es w it h the increa sin g interest of ecolo gist s in di senta ngling the mec ha nisms a commun ity.
/ Multi-trophicnetwork:anetwork
maintainingspeciescoexistenceinmorethanonetrophiclevel(seeFigure1foraschematic
: representing patterns of multiple
p representation).Indeed,partofthismotivationisduetohavingmulti-trophicinformationreadily interactiontypesbetweenspecies,

available [27,28], but the fundamental question is how to extend niche theory to study the includingcompetition,mutualistic,or

t antagonisticrelationships.Also
effects of species interactions on determining diversity across multiple trophic levels
t knownasmultiplexnetworks.
h simultaneously. Niche: the environm entalconditions

andresourcesaspeciesrequiresfor

To address this limitation, we call for the integration of niche theory with network theory. livingandreproducing.

Nichedifferences:accordingto
Network theory has already partially addressed the challenge of how to consider the roleof
Chesson(2000)[48],niche
speciesinteractionsinshapingspeciescoexistenceacrossseveraltrophiclevels[29,30],butit difference sarea stab ilizing

has missed theinformation withintrophiclevels thatnichetheory incorporates.Inparticular, mechanismofspeciescoexistence
netw ork stu dies have focus ed on the asso ciation of t he stru cture o f species inte rac tions with tboy ecxacueseindgi n intetr rassppeeccifiificc c coommppeetittiitoionn.
community dynamics in mutualistic (e.g., plant–pollinator and plant–disperser) [31–35] and
antagonistic systems( e.g .,host–para site,p rey–predator,a ndpl ant–herbivore)[34 ,36–38] Yet, cPoenrt rcibauptiitoan gtorotwhethp oraptuela: ttiohen relative

becausenetworkstudiesemphasizespeciesinteractionsbetweentrophiclevels,theyconsider increasesinsizeperindividual.
Species dy nam ics: changesin
that species within the same trophic level do not directly interact, or they all interact with the species’ populationo verspac eand
same strength[33,35].
time.

Trophiclevel:aleveloforganization

Because niche studies lack the ability to describe species coexistence for more than one withinthefoodchainofan
ecosy stem ,the organ ism sofwhich
trophic level, and network studies ignore the structure of species interactions within trophic
obtainresourcesinasimilarway.
levels(Figure1),itissurprisingthatboththeorieshavenotspokenfluentlytoeachotherdespite

2
their complementarities; doing so can provide new research avenues and understanding of

howspeciesdiversityismaintained.Ouraimhereistoshowadirectintegrationofboththeories

as they share strong similitudes in their theoretical motivations, ecological concepts, and

mathematicaltools.Thispathofmutualunderstandingpavestheroadtocombinetheoretical

conceptsandassociatedtoolboxesfromboththeoriesintoacommonmethodologicalframe-

work. We believe the emerging framework is particularly useful for investigating species

coexistenceinmulti-trophicnetworks,whichincludecompetitive,mutualistic,andantago-

nisticinteractionssimultaneously.Additionally,weprovidearoadmapthataccommodatesthis

newframework toexperimental andobservationalstudies.

Conceptual Parallelisms Between Niche and Network Theories

Obtaining a common theoretical framework from the integration of both niche and network

theoriesisstraightforwardasthesestudieshavestartedfromsimilarconceptualconstructs,

andafterdecadesofresearchhaveindependentlyconvergedonequivalentconclusionsabout

h theconditionsleadingtospeciescoexistence.Toreachthemaximumaudience,weverbally

detailthishistoricalconvergenceandexplainherewhyboththeoriesspeakthesamelanguage
c despi te u sing diffe rent technica l ter ms. We als o aim to present a rigo rous mat hematical

. explanationofthisconceptualparallelism.Thisispossiblebecauseboththeoriesusesimilar

o population dynamics models to build ecological theory rooted in the Lotka-Volterra form

[4,24,25,35,38–41](Box1).WeareawarethatthedirectapplicationofLotka-Volterramodels
r
todescribenaturalsystemsmightbelimitedassumingspecieslinearresponses,anddonot
e
takeintoaccountmeta-communitydynamics.Partoftheselimitationswillbesolvedlaterwhen

r wepresentmoremechanisticmodelsthatcaptureadditionalnonlinearspeciesresponsesin

. order to explain how to apply this emerging framework to experimental and observational
c appro xim ations [ 42,43 ].

o
Aswepreviouslymentioned,thenicheconceptwasafundamentalconstructtounderstand
d
patternsofspeciesdistributionandco-occurrencewithinatrophiclevelbasedonhowspecies

interact with the habitat they experience (Grinnellian niche), how they modify the habitat
/

/ (Eltonian niche)and howinteract withotherspeciesinthecommunity (Hutchinsonianniche)

: [44].Underclassicnichetheory,theonlyconditionmodulatingspeciescoexistencewasthe
p
amount of niche overlap between species [4,45], which ecologists assumed to arise, for

t instance, from differences in phenology, bill size, shade tolerance, or feeding preferences.

t The rationale was that the smaller the niche overlap, the larger the chances of species
h coex istence [7 ,46,4 7].

However,subsequentwork[25,41,48]showedthatnichedifferencesalonearenotenough

to determine species coexistence. Under recent advances of niche theory (also known as

‘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

dynamics occur when species do not differ in their niches but have equivalent fitness [49].

The estimation of nichedifferences usingcoexistence theory techniques remains phenome-

nological(i.e.,thesourceofvariationisunknown),andrecentstudiesare,forinstance,mapping

how speciesfunctionaltrait differencesrelateto nichedifferences[50].

Conversely,speciescanalsodifferintheirfitness.Fitnessdifferencesarerelatedtospecies’

abilitytocaptureandtransformresourcesintooffspring,whichisgenerallyacombinationof

demographicparameters(e.g.,fecundity,survival,andrecruitment)andthespecies’sensitivity

3
Box1.ConceptualParallelismbetweenConditionsLeadingSpeciesCoexistenceforNicheand

NetworkTheory

Forapairofspeciesincompetition,thecoexistenceconditionsaccordingtonichetheoryaredefinedby:
r ffiffiffiffiffiffiffiffi ffiffiffiffiffiffi r ffiffiffiffiffiffiffiffiffiffiffiffiffiffi rffiffi ffiffiffiffiffiffiffiffiffiffiffiffi
a11a22 > r1 a22a21 > a12a21 [I]
a12a21 r2 a11a12 a11a22
ð1(cid:2)Niche differenceÞ(cid:2)1 Fitness difference 1(cid:2)Niche difference
wherer >0correspondstotheintrinsicgrowthrate(demographicparameter)ofspecies1,anda >0represents
1 12
thecompetitivepercapitaeffectofspecies2onthepercapitagrowthrateofspecies1.Thisequationstatesthatthe
fitne ssdifferenc e(i.e .,ther atiobe tw eenintri ns icg row thr atesmo dulated byw h atiskno wn asth ecompe titivere spo nse

ratio)ofthetwospecieshastofallbetweenalowerandanupperbound,computedfromthenichedifference(i.e.,range
ofva lue sd efine dbythe rat io bet weenint er -and intra sp ecificc ompeti tion).Note that the seine qualitiesc anb ealso
sim ply wr itten as a 11/ a21 > r1/ r2> a12/a 22. M oreov er, such ineq ualities have a lso to ass ume th at the niche diffe ren ce is
smallerthanone,i.e.,

a12a21< a11a22 [II]
whichguaranteesthattheequilibriumpointisdynamicallystable(thesystemreturnstoitsoriginalequilibriumpointafter

apulseperturbation)inaLotka-Volterracompetitionmodeloftheform:
8
h ><ddNt1¼ N1ðr1(cid:2) a11N1(cid:2) a12N2Þ [III]
c >:ddNt2¼ N2ðr2(cid:2) a21N1(cid:2) a22N2Þ
.
ro csNwpo2her*er ce>riesfi pc0No)c 1n[a3ads5n ed,t5ot N2h a–e2n5cg 4oelo,qr9bru9eais]ll.ipb sBortiauynb mdcil io ttopyn )ottrhbinaeyst athc,ba atuvlhlienneddg i anfinneectaqresau isbaopllfie tesy cpb ioefiefccc iEaecuqsos um1ea pataineolldtn its i2IopI, ne orcesnisetlyrpso e gnhcrgaateivvnreetst lyhp .tao hNnseoi itnitdvetyee tn rhasaapbmteu ticnchiadefilca insncetcaoqebmusil apit(liyei.te ite(i.ti,sni o Ninnfa1. Ec*N tq>,o u itn0aet ittaohhnnaad ttI
e feasibilit yisa nec essary conditio nf orspec iespersisten ceinaLotk a-Volterr amo del[54].

r
Letusexplainhowdynamicalstabilityandfeasibilityconditionsariseinmulti-trophicsystemsbytakingasanexamplea
. two -tro phicle velsy stemdesc ribingth em utualistic interactions betw e enasetofpl ants(P)a nd aseto fp oll inators(A ).
c Notethatsim ilarc onclusi onsareobt aine dbyconsid eringantag onistinter ac tion s sucha sa prey –p red ato rsystem.T his

mutualisticsystemcanbedescribedbythefollowingsetofdynamicalequations:
o 8 !
d >>>><ddPti¼ Pi r iðPÞ(cid:2)XaðijPÞPjþXgiðjPÞAj
/ >>>>:ddAti¼ Ai r ðiAÞ(cid:2)Xj aðijAÞAjþXj gðijAÞPj! [IV]
/ j j
p: wmhueturea ltishteic vmaroiadbelelsc oPrireasnpdo Aniddetonothtee tvhaelu aebsudnedsacnrcibei nogf pinlatrnint saicndg raonwimthalr astpeesc(ire)s, iw, ritehsinp-egcutiivldelcyo. mThpee ptitaioranm(aete>rs0 o),f athnids
thebenefit receive dviamutua list icin teracti onsbetwee ntrophi clevels (g > 0i). Alltheseinte ractionstre ngitjhs ca n,in
t turn ,beem bedded ina two-by-tw oblockmat rix; ij
t (cid:3) (cid:4)
h b ¼ (cid:2)agðPðAÞÞ (cid:2)agðAðPÞÞ [V]
Theconditionsforfeasibilitydependonboththespeciesinteractionsdefinedbybandthedemographicparametersof

speciesr(analogoustoEquationIabove)[71].Notethattheconditionsfordynamicalstabilityaremorecomplex[40].
Indeed, s everalmean in gfulnotion s ofsta bility have been de finedineco log y,suchas Volterra -dis sipativ e,D-stab ility,

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

matrixb.Sign-stabilityhasthepropertyofgrantingglobalstabilityonlyonthedescriptionofwhoeatswhomandnoton

thestrengthofthetrophicinteractions.Volterra-dissipativeimpliestheglobalstabilityofafeasibleequilibrium,whileD-

stabilitygrantsonlylocalstability.Finally,localstabilityinvolvesalsotheequilibriumdensitiesandthereforetheintrinsic
growth rates.T her elatio nsamon gthese notio nsofst ability(an dm ore )arewellre presented by Logofet’s flow er[53].

to reduce these demographic parameters in the presence of neighbors [25,43,49]. Fitness

differencesinessencedeterminethesuperiorcompetitorwithinaspeciespairintheabsenceof

niche differences. It has been well recognized that coexistence is the result of a balance

betweentherelativestrengthofnicheversusfitnessdifferences.Thatis,twospecieswillstably

coexistwhentheirnichedifferencesovercometheirfitnessdifferences[48,49](seeTable1for

examplesofbothspeciesdifferencesacrossawiderangeoforganisms).Thisconditionhas

4
Table1.ExamplesofNicheandFitnessDifferencesforDifferentOrganismsandTrophicLevelsa

Trophiclevel Evidencesofnicheandfitnessdifferences Refs

Niche Fitness

Plant–plant Spatialsegregation,phenology,orplantmorphology Speciesabilitytodrawdowncommonlimitingresources [4,8,48]
differen cesreducen icheoverlap . determin essp eci esfitn ess.

Plant–insect Fragmentedevidencessuggestthatdifferencesin Herbivorousinsectsandtheirnetworkofhyperparasitoids [11,70,83]
pollinatorsc anstabilize plantco exist ence. cansignifica ntlyaffe ctp lantfi tness.

Plant–vertebrate Interactiveeffectsbetweenabioticstress,tolerancetoherbivory,andherbivorebodysizedetermineplantabundances [84,85]

andrichness.

Plant–fungi Fungalpathogensmediatecoexistencethroughtrade-offs Lowspecificityoffungalpathogensdetermineslocal [19,86]

betweencompetitiveabilityandresistancetopathogens abundanceofplantspeciesinatropicalforest.

andthroughpathogenspecialization.

Insect–insect Plantspecies,stemsize,andlocationwithinstem Searchingability,femalefecundity,andresource [87,88]
deter minenich ediff erenc esw ithinag uildof herbivorous degradatio nandp reemp tiondeterm inefi tnessdifferences

h insects. among parasitoids, phytophagous insects, and
arachnids.
c Insect–plant Wildbeesspecializeintheirfloralrewardincludingnectar, Foragingratesandfoodstoragedeterminefitness [11,89]

pollen,pollenresins,volatiles,lipids,andwaxes. differences(i.e.,droneproduction,wintersurvival)among
.
geneticallydiversehoney-beecolonies.
o
Insect–vertebrate Tickhabitatdiffersgreatlyamongspeciesfromrodent Thetiminganddurationofaquaticinsectemergenceis [90,91]

r burrowstocavesandbirdnests. regulatedbytemporalvariationinsalmondensity.

e Vertebrate–vertebrate Differencesinbillshapeandbodysizestabilize IntraguildpredationoflargecarnivoresonAfricanwild [92,93]

coexistencebetweenbirdsbytheuseofdifferent dogsreducestheirpopulationsize.
r resources.
.
Vertebrate–plant Strongoverlapofdietaryrequirementsbetweenwildand [94,95]
c
domesticherbivores.

o Insect–vertebrate Vertebratesdifferinthenumberandspecificityoftheir Ticksreduceoffspringandincreasemortalityinawide [90,96]

parasiticinsects. varietyofanimalsincludingbirds,lizards,andmammals.
d
Trematode–mollusk Spatialheterogeneitystabilizescoexistenceofaguildof Competition-colonizationtrade-offsdeterminetrematode [72]
/ saltma rshtrematode s. fitness.

/ Alga–alga Nicheandfitness:Phylogeneticrelatednessdoesnotpredictcompetitiveoutcomesbetweenfreshwateralgae. [58]
:
p Bacteria–vertebrate SpecificimmunityofStreptococcuspneumoniae Acquiredimmunitytononcapsularantigensdetermines [97]
serotype sstabilize s coexistence. serotype fitness.

t Protist–bacteria Nicheandfitness:Differencesinmouthsizeofbacterivorousprotistspeciesreducescompetitiveexclusion. [46]
t
h aSomeexamplesexplicitlyseparatethestudyofthespecies’nichefromthespecies’fitness,whileinotherexamplesresearchershaveonlystudiedonecomponent,or
bothn icheandfi tnessdiff erencesh ave been co nsi deredtog ether .Not eth atforma nytroph iclev els ,infor mationof nicheandfit ness differ encesis asy mmetric,the se
differ ences are better knownforo netr ophic levelthanf ortheoth er(e. g.,p lan ts–fun giorin sects–v ertebrate).

alsobeenreinterpretedasthelargerthenichedifferencebetweentwospecies,thelargerthe

combinationoftheirfitnessdifferencescompatiblewiththeircoexistence[49,51](Box1).This

reinterpretation is critical as it provides the main bridge of common understanding between

nicheand networktheories, explaininghow speciescoexistenceis possible.

Networkresearchonspeciescoexistencestartedbystudyingthestabilizingmechanismsfor

entirecommunities[5],ratherthanfocusingonpairwiseinteractions.Thisstabilitywasdefined

in a dynamical rather than a static way. Dynamical stability is the property of a system to

returntoanoriginalequilibriumpoint(ifitexists)afterapulseperturbation(e.g.,achangein

speciesabundances)comingfromdemographicstochasticity,whichincludesmigrationand

random changes in birth and death processes. Early network studies showed that this

dynamical stability depends on species interactions (analogous to niche differences) within

5
andbetweentrophiclevelcompartments(containedinbmatrix,Box1).Importantly,anumber

ofinterestingquestionsemergedfromtheseconcepts,suchaswhethertheobservedstructure

oflargemulti-trophicsystemsnecessarilyleadstomoredynamicallystablecommunities[5].

However,extensiveresearchshowedthatdynamicalstabilityalone(asnichedifferencesalone)

isnotenoughtoguaranteestablecoexistenceofallspeciesinacommunity.Thismeansthatit

canbepossibletohaveadynamicallystablecommunitywheretheequilibriumpointwillalways

lead to one or more species with zero abundance (Ni*=0), even if reintroduced into the

community [35,52,53]. In other words, the system is dynamically stable but contains only a

subset ofspecies fromtheoriginalpool.

As it has happened with the historical development of niche theory, subsequent work on

networktheoryhasshownthatitisalsonecessarytoaccountforthespecies’fitnessinorderto

evaluatetheconditionofwhetherspeciescanattainpositiveabundancesatequilibrium[54].

Network studies called this condition feasibility, which also depends on the species inter-

h actionscontainedinthematrix(b)andthespecies’demographicparameters(r)[35,52,55](Box

1).Importantly,theserecentadvanceshaveshownthatthestructureofspeciesinteractions
c be tweentrophi clevel scanm odulateth eran geofc omb inat ionsofde mo graphic parameters

. leadingtofeasiblesystems[35,55].Therefore,inlinewithnichetheory,networkstudiesalso

o found that species coexistence within communities depends on how the demography of

speciesmatch theconstraints imposedby speciesinteractions.
r
e
This historical convergence shows the existence of a common theoretical framework for

r understanding how species interactions modulate diversity, which has two key ingredients:

. (i)species’demographyand(ii)thestructureofspeciesinteractions.Thisstructureiscontained
c in the b m atrix describ ed i n Box 1. The t ak e-home message of this framewo rk is that a

o communityofspeciescancoexistwhenbothingredientsarecombinedinthefollowingway:

d Box2.EmergingPropertiesoftheIntegrationofNicheandNetworkTheory

/ For multi-trophic dynamical systems of the general form dNi/dt = Nifi(N), an n (cid:3) n block matrix emerges for describing
speciesinteractionacrossntrophiclevels:
/ 2 3
p: b ¼6664ga2...11 ga1...22 }(cid:4)(cid:4) (cid:4)(cid:4) (cid:4)(cid:4) gg...12nn7775; [I]
t gn1 gn2 (cid:4) (cid:4) (cid:4) an
t
where the diagonal blocks (a) correspond to the within-trophic level (i) interactions (i.e., competition, intraguild
h i
predation,facilitation)andtheotherblocks(g)representthebetween-trophiclevelinteractions(effectoftrophiclevel
ij
joniintheformofmutualismorantagonisminteractions).Asbisablockmatrix,eachelementofthematrixrepresentsa

submatrix of species interaction. For instance, a1is a matrix describing all species interaction within the trophic level 1,
and g12is another matrix describing all interactive effects of species from the trophic level 2 on species from the trophic
level1.

dSetamboleg rcaopehxiics tpeanrcaem oeft earlls s rpiescaiteissfi e(Ns i*t o>g e0t)h aecr rboossth t rtohpe hsicta lbeivliteyls a dnedp feenadsisb iolitny wcohnedthiteior ntsh is[5 i3n,t5e4ra,7c1tio]. nT hmearetr ixa rbe dainffde rtehnet
classesofdynamicalstability.Forinstance,localstabilityisthepropertyofthesystemtoreturntotheequilibriumpointaftera

smallpulseperturbation(changesinspeciesabundances),whereasglobalstabilityisconcernedwithexternalperturbations
ofanygiven magnitudec onvergin gtothesa meequilibriumpoint.Ea chcla ssdem an dsspecific prop ertiesto befulfilledby

theinteractionmatrixbincombinationwiththespeciesdemographicparametersr[53,71],andwhichclassofstability
i
shouldbestudieddependsonboththeresearchquestionandknowledgeaboutthesystem.Thefeasibilityofamulti-trophic

systemcorrespondstotheconditionsallowingallspeciestohavepositiveabundances,whichalsodependsonboththe
interact ionmatrixb an dth edemogra phicpa ram etersr [3 5,52– 54,71]. Thefigurebe lowillu stra testhec ond itions of
i
feasibilityinathree-speciessystem.Thegreenareaonthesphererepresentstherangeofdemographicparametersleading

tofeasibilitygiventheinteractionstrengthsmatrix.Tosomeextent,FigureIoftheextensionofmoderncoexistencetheoryto
mu ltispecies coex iste nce;theb orderofth egree na reais themultispec ie s ana logousof th efitness andniched ifferenc e

inequality(seeEquationIinBox1)thatappliestospeciespairsonly.

6
h
c
.
o
r
e
r
.
c
o
d
/ FigureI.IllustrationoftheFeasibilityDomainforaMulti-TrophicSystem.Thefigureshowsthenormalized

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

: pollinatorsandoneplant)cantheoreticallyhavetobecompatiblewithallspecieshavingpositiveabundances.This
p normalized feas ibility doma in(g reenspheric altrian gle )is constrained byth ei ntra-and intersp ecificint eractionmatrix (b).

The columns of the interaction matrix (e.g. [b11, b12, b13]) give the boundaries of the feasibility domain (three blue lines).
t Thelargerthisvolumeis,thelargerthesetofdemographicvaluescompatiblewithfeasibility,andthelargerthelikelihood

t ofspeciescoexistenceacrosstrophiclevels[55,71].

h
speciesinteractionsdefinethecoexistencespace(i.e.thefeasibilityregion)andspeciescoexist

whenthecombinationoftheirdemographicparameters(i.e.fitness)fallswithinthisspace(Box

2andFigure2).Onecrucialadvantageofthisframeworkisthatitisnotlimitedtoanyparticular

typeofmulti-trophicinteractions,andcanbethereforeaccommodatedtobothmutualisticand

antagonistic interactions, such as a plant–pollinator or a predator–prey community. Another

keyimportantadvantageisthatthisframeworkisnotlimitedtotwo trophiclevels.Itcanbe

extended to multi-trophic structures, where three or more trophic levels are considered

simultaneously.Indeed,thesemulti-trophicstructuresaresimplythecombinationofcompeti-

tive/facilitativeinteractionswithintrophiclevels, aswellasantagonisticandmutualisticinter-

actionsbetween trophiclevels [56](Box2).

Coupling the Integration of Niche and Network Theories With Experimental

and Observational Work

We acknowledge that one critical step to consider in full is that this integrative framework

dependsonhoweasilyresearcherscanadaptittotheirparticularsystems.Thebasictaskisto

7
Network Interac(cid:2)ons with environmental varia(cid:2)on in (cid:2)me and space
(A) (B) (C)

(D) (E) (F)

Feasibility domain
h
c
Fitness differences
.
o
Coexistence Coexistence Exclusion
r
e
r Figure2.EffectsofSpecies’IntrinsicPropertiesandNetworkStructureonSpeciesCoexistence
. ForaF igu re360au tho rpresenta tionofFig ure2,seeth efig urelegend athttps://d oi.o rg/10.101 6/j.tree.2018.01.007
c
Speciestraitssuchasbodysize,phenologicaltiming,orfeedingpreferencesinteractwithenvironmentalvariationsin
o spacean dtim etod ete rmine (i)ne tworkstructur eand(i i)s pecies’fi tness.Broke nlinesr epres entthestreng thofspeci es

interactionswithintrophiclevelsandunbrokenlinesrepresentthesameacrosstrophiclevels.Obtaininginformationon
d howsuchtr ait–env ironmen tinter actio nsmodifie dthe setwoele me ntsine cologic alcomm unitie sremains fundamenta lto

predicttheconsequencesofspeciesinteractionsforthemaintenanceofdiversity[98].Considerahypotheticalcaseofa
/ plant–p ollin atorsysteminw h ichenviro nmentalvar iati onm odifiesthese tw oelemen tsin threediffe re ntways(Pan elsA –C ).
/ Thesizeofthec irclesde n otesth erealizedspec ies’fitnes s,which arises asa combina tio nofs peciesin teract ionsand their
:
demographicparameters(plantsingreenandinsectsinblue).Additionally,wehavelearnedfromtheintegrationofniche
p
andnetworktheoriesthatthestructureofspeciesinteractionswithinandbetweentrophiclevelsrendersthefeasibility
dom ain(here represen tedi ntw odimensi on sforsim plicity;darkg rayare ain PanelsD– F).Note thate achnetw ork structure
t
givesadifferentsizeoffeasibilitydomain.Inprinciple,thelargerthefeasibilitydomain,themorelikelyspeciescoexistasit
t allows foralarg erc om bination offitness d ifferences (se eFfe asib ilitydoma incomp ared with Dan dE).Ho wever, it is
h
paramounttopointoutthatevenwithalargefeasibilitydomain,speciesmaynotcoexistifthepositionofthevector
containing spe cies’ fitne ss(re dline )falls o utside thefeasi bilitydom ain(i.e., fallsw ithi nthelig ht gra yarea)[7 1]. This isthe

caseofFwhereoneplantspeciesisexcluded.Conversely,thesystemcanbemaintaineddespiteshowingasmaller
feasib ilit yr egioni fthe vecto rofspec ies ’fitnessfal lswithinthef easi bilitydom ain (ca sesDandE ).Theref ore,theta k e-home

messageisthatcoexistenceoccurswhenspeciesinteractionscreateafeasibilitydomaincompatiblewiththeobserved
fitnessdif fer ence s.Recalltha tfitness differe ncesare measureda sthed ist ancebetw eenthe centerofth efeas ibili tydomain
andthe positionof theve ctor contai ningspecie sfit ness(redli ne ).Im portantly ,systems wi thlow fitn ess differenc esmay

facelargerperturbations.Forinstance,speciescancoexistincaseEbutcanbelessresistanttoperturbationscompared
with case D,giventhatth ep ositionof thevec toro fspecie s ’fitne ss is close to the exclusio nr egion.

obtaininformationofdemographicparametersaswellasspeciesinteractioncoefficientswithin

andbetweentrophiclevels.However,itisnotsoobvioushowthisinformationcanbeobtained

andrelatedtotheory.Wecanstartlearningfromtheabilityofrecentadvancesinnichetheoryto

couple theory withfieldandlabexperiments[42,57–60].

Thesestudiessuggestthatthemostrigorouswaytoproceedwouldbetoconductexperiments

inordertoparameterizeandvalidateasystemofequationscontainingamodelofpopulation

dynamicsforeachtrophiclevel.Technically,thisparameterizationiseasiertoobtainwhenthe

8
life-span between organisms is similar. In particular, population models describing species

dynamicswithanannuallifecycleseemamongthebestapproximationstochooseforseveral

reasons.Theydefinethenetworkstructureandspeciesfitnessintheexactsamewayasthe

originaldefinitionusingtheLotka-Volterraframework[25,43],yettheyarecomplexenoughto

includenonlinearmechanismsofspeciescoexistencesuchasthestorageeffect,andsaturat-

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., fungalseed pathogens).

An alternative to experiments is the use of observational data (e.g., [63,64]). Observational

h approachesarejustifiedwhenorganismsdifferintheirlife-span,orwhentheirmanipulationis

not feasible for technical or conservation issues. The traditional limitation of observational
c stud ies is th at t he structu re of species int eraction s bet ween trop hic levels is o ften easier to

. describe,atleastatthespecieslevel,thanthestructureofspeciesinteractionswithintrophic

o levels. This limitation can be solved by using mathematical models fed with spatially explicit

and/or temporal series data. These methodologies allow inferring species demographic
r
parameters and species interactions from changes in species fitness due to both natural
e
variations in the community density and species relative abundances [65,66]. For example,

r recent work [64] combined statistical models for survival, growth, and recruitment with

. individual-basedmodelstodescribetemporalpatternsinplantspeciesco-occurrences.These
c model-generated popula tio n abund ances w ere then in tegra ted into projection mod els to

o estimate the structureofcompetitive interactions withinplantspecies.

d
Regardless of the approach selected, we stress the urgency of linking theory and empirical

work. We are at the dawn of understanding whether species characteristics, commonly
/

/ reportedinthenicheandnetworkliterature,aremorestronglyrelatedtodifferencesinspecies

: demographyortothestrengthandsignofspeciesinteractions[50,67,68].Moreover,weare
p
notawareofasinglestudythathasattemptedtoempiricallyestimateinaquantitativewaythe

t matrixofspeciesinteractionswithinandbetweentrophiclevelssimultaneously.Webelievethat

t taking such an approach is crucial for answering an outstanding research question that
h emerg es wit h th e integrat ion of bot h th eories, nam ely , how specie s interac tions betw een

trophiclevelsdrivenicheandfitnessregionswithintrophiclevelsandviceversa.Therefore,this

isthe topic ofour nextsection.

How Do Species Interactions Between Trophic Levels Drive Niche and

Fitness Differences Within Trophic Levels?

Bycouplingrecentconceptualadvancesofnicheandnetworktheory,wearereadytounderstand

howthespeciesdifferencesthatdeterminecoexistencewithintrophiclevels(nicheandfitness

differences) feedback with the structure of species interactions that determine coexistence

betweentrophiclevelsandviceversa.Toillustratetheseideas,letusconsideramutualisticplant–

pollinatorsystem(seegraphicalexampleinFigure2).Whatwehavelearnedfrompriorworkisthat

differences in feeding behavior, body mass, or insect phenology can contribute to the niche

differences that tend tostabilizecoexistencebetweenplants (seeTable 1) [69,70]. However,

pollinatorsalsocontributetothefitnessdifferencespromotingplantcompetitivedominance.For

instance,changesintheabundanceofpollinatorscan,inturn,modifythecompetitivehierarchyof

aplantguildbyincreasingthenumberandthequalityofseedsproducedbypollinator-dependent

9
Box3.AnExampleofHowToIntegrateNicheandNetworkTheorieswithExperimentaland

ObservationalData

Ourapproachtoevaluatehowbetween-trophicinteractionsdrivenicheandfitnessdifferenceswithintrophiclevelsand

viceversainvolvesthreesteps.

Step1:Departfromarelativelysimplesystemofequations.Hereitiscomposedoftwoannualpopulationmodels

describing changes in population size with time in plants (seeds, Pi,t+1) and pollinators (eggs, Ai,t+1). Both models are
mirrorimagesincludinganequalnumberofparameterswiththesamebiologicalmeaning,
8 0 X 1
>>>>>><Pi;tþ1¼ Pi;t@0ð1 (cid:2) giÞsiþlig1ið þ1 þXXjaikjggjiPkAj;tk;tÞ1A; [I]
>>>>>>:Ai;tþ1¼ Ai;t@ð1 (cid:2) eiÞtiþnie1ið þ1 þXjuikjedjiAkPj;tk;tÞA
whereeachmodelisthesummationoftwocomponents.Thefirstcomponentdescribesthepossibilityofastorage
effect proce ss, an d the second com p onen t describes p er c apita fecundity. Specifically , th is second co m ponent

describeshowmutualismsenhancethespeciesintrinsicabilitytoproduceoffspring,reducedbythecompetitive

h effectsexertedbyotherspecieswithinthesameguild.

c Step2:Estimatesspeciesvitalrates.Estimatepercapitagrowthrateintheabsenceofspeciesinteraction[plants(l),

pollinators(n)],isbestdescribedastheinterceptofthestatisticalmodelsbuiltforStep3(seebelow).Additionalefforts
.
areneededtoestimateratesofseedgermination(g)orlarvasurvival(e),andthestorageeffectasthesurvivalofthe
o spe cies’life st agesthat dono tp rodu ceoffspring with in ayea r[e.g.,s oil seed ban kinplan ts(s) and no nreprod uc tive

adultmortalityinsomepollinators(t)].
r
e Step3:Estimatespeciesinteractionmatrix.Toestimatespeciesintra-andinterspecificcompetitiveinteractionswithin
troph ic levels[pla nts(a), pollinators (u)],the be stappro achisto fita serie sofstatistic almodelsd escribingfor each
r species its p er capit a g rowth rate as a fu nctio n of comp et ito r’s re lative ab undance. For mu tualistic inte rac tions
. [pollinat or’s effe ctonp lants(g) ,plan ts’ eff ectonpo llin ators(d)],dot hesam ebutdescrib esp ecies’perc apitagrowth
c rateasafu nction of themu tua listicrel ativea bu ndances(F igur eI).

o
d
/
/
:
p
t
t
h
Figure I. Competitive relationship between species including itself are expected to take a negative

exponentialform[59,66],whereasmutualisticrelationshipareexpectedtobefunctionallysaturatingbest
described b y no n-inflicte d curves [100]. Wit h this inform ati on is pos sib le to then buil d the b m atrix

summarizingspeciesinteractionsacrosstrophiclevels.

10