The more the merrier : Multi-species experiments in ecology

The more the merrier: Multi-species experiments in ecology

Mark van Kleunen

, Wayne Dawson

, Oliver Bossdorf

, Markus Fischer

aEcology,DepartmentofBiology,UniversityofKonstanz,Universitätsstrasse10,KonstanzD-78457,Germany

bPlantEvolutionaryEcology,InstituteofEvolution&Ecology,UniversityofTübingen,AufderMorgenstelle1, D-72076Tübingen,Germany

cInstituteforPlantSciences,UniversityofBern,Altenbergrain21,Bern,CH-3013,Switzerland

dSenckenbergGesellschaftfürNaturforschung,BiodiversityandClimateResearchCentreBIK-F, Senckenberganlage25,60325Frankfurt,Germany

MarkvanKleunen WayneDawson OliverBossdorf MarkusFischer

Abstract

Amajorobjectiveinecologyistofindgeneralpatterns,andtoestablishtherulesandunderlyingmechanismsthatgenerate thosepatterns.Nevertheless, most of ourcurrent insightsinecology are based oncasestudiesof a singleor fewspecies, whereasmulti-speciesexperimentalstudiesremainrare.Weunderlinethepowerofthemulti-speciesexperimentalapproach for addressinggeneralecological questions,e.g.on speciesenvironmentalresponses oron patternsof among-andwithin- speciesvariation.Wepresentsimulationsthatshowthattheaccuracyofestimatesofbetween-groupdifferencesisincreasedby maximizingthenumberofspeciesratherthanthenumberofpopulationsorindividualsperspecies.Thus,themorespeciesa multi-speciesexperimentincludes,themorepowerfulitis.Inaddition,wediscusssomeinevitablemethodologicalchallenges ofmulti-speciesexperiments.Whileweacknowledgethevalueofsingle-orfew-speciesexperiments,westronglyadvocatethe useofmulti-speciesexperimentsforaddressingecologicalquestionsatamoregenerallevel.

Zusammenfassung

EinesderwichtigstenZieleinderÖkologieistes,allgemeineMusterzuerkennenunddieMechanismenzuverstehen,die solchenMusternzugrundeliegen.NichtsdestotrotzbasierendiemeistenneuerenErkenntnisseinderÖkologieaufUntersuchun- geneinzelneroderwenigerArten,währendexperimentelleStudienmitvielenArtennachwievorseltensind.Wirunterstreichen dieBedeutungvonMehrartenexperimentenfürdieBeantwortunggrundlegenderökologischerFragen,z.B.zurReaktionvon ArtenaufUmweltwandel,oderzuMusternzwischen-undinnerartlicherVariation.WirpräsentierenSimulationsergebnisse,die

∗Correspondingauthor.Tel.:+497531882997;fax:+497531883430.

E-mailaddress:mark.vankleunen@uni-konstanz.de(M.vanKleunen).

Konstanzer Online-Publikations-System (KOPS) URL: http://nbn-resolving.de/urn:nbn:de:bsz:352-259676

zeigen,dassSchätzungengenerellerUnterschiedezwischenArtengruppenvorallemdurcheineMaximierungderArtenzahl verbessertwerden,währendÄnderungeninderAnzahlvonPopulationenoderIndividuenkaumEinflusshaben.JemehrArten einMehrartenexperimentumfasst,destoaussagekräftigerundstatistischbelastbareristes.Wirdiskutiereneinigemethodische HerausforderungenbeiMehrartenexperimenten.ObwohlwirdenWertökologischerFallstudienmiteinzelnenoderwenigen Artenanerkennen,empfehlenwirausdrücklichdenEinsatzvonMehrartenexperimentenzurallgemeingültigenBeantwortung wichtigerökologischerFragen.

Keywords: Ecologicalexperiments;Generalism;Meta-analysis;Multiplespecies;Precision;Realism;Simulations

The precision-generalism-realism trade-off

Manyinsightsinecologyareinitiallybasedoncasestudies restrictedtosingleorfewspecies,or tosinglepopulations or genotypes. However,amajorobjective inecology isto findgeneralpatterns,andtoestablishrulesandmechanisms generatingthem.Manyecologistsgeneralize theresultsof casestudies,despitethefactthatthesestudiesmightnotbe representativeforthemajorityofspeciesandconditions.As aconsequence,manyofourcurrentinsightsinecologymight notbeasgeneralastheyclaimtobe.

Ecologicalstudiesareinevitablyconstrainedbya3-way trade-offinvolvingprecision,generalismandrealism(Fig.1;

Levins, 1966; Guisan & Zimmermann, 2000). Although methodologicaladvancesandlargelogisticeffortsmaypartly relievethisconstraint,westillhavetodecideforeachexper- imentwhetherwewantverypreciseresultsbyfocusingona singlespecies,moregeneralresultsbyusinglargenumbers of species (and many different environments), toconduct the experiment under the most realistic conditions (i.e. in thefield)oracompromise.Thereisaneedforalltypesof studiesfillingdifferentsectorsoftheprecision-generalism- realismtrade-offtriangle(Fig.1).However, thesearchfor generalpatterns,rulesandmechanismswouldprogressmuch morerapidlyifmulti-speciesexperiments(Fig.2)wouldbe used morefrequently.Here, wediscuss the typesofques- tions thatrequire amulti-speciesapproach,the numberof speciesrequiredinsuchexperiments,andsomemethodologi- calissues.Althoughwemainlyuseplantexamples,thepoints wemakeareequallyrelevantforstudiesofothertaxonomic groups.

Questions requiring a multi-species approach

Theconclusionsdrawnfromastudyareonlyvalidforthe statisticalpopulationfromwhichthestudyobjectsweresam- pled.Thisimpliesthatif,forexample,wewanttoknowhow CentralEuropeanspecieswillrespondtoclimatewarming, weshouldgrowarandomsampleofthesespecies–insteadof justourfavoritestudyspecies–underambientandelevated temperatures.Thus,questionsongeneralspeciesresponses requiremulti-speciesexperiments.

Asspeciesvary tremendouslyinsuccess,habitatprefer- encesandothercharacteristics,majorquestions inecology ask whether thisvariation mapsonto particular groups of speciesorhowitcorrelateswithotherspeciescharacteristics.

One example is the question of what differentiates inva- sivespeciesfromnon-invasivespecies.Furthermore,asthere isalso variation among populationsand genotypeswithin species, many other major questions in ecology address whetherparticularpatternsofwithin-speciesdifferencesare consistentacrossspecies.Atypicalexampleherewouldbe thequestion of whatdifferentiates populations inthe cen- ter of the range from those at the margins. Multi-species experimentscanthereforeprovidemoregeneralanswersto questionsconcerningbothwithin-andamong-speciesvaria- tion.

Fig.1. Thetrade-offbetweenprecision,generalismand realism whichconstrainsthedesignofecologicalstudies.Thedefinitions ofprecision,generalismandrealismarerelativeratherthanabso- lute,andcanbecontextdependent.However,ifprecisionofspecies estimatesisdeterminedbythenumberofpopulations,generalism bythenumberofspeciesandrealismbywhethertheexperiment wasdoneunderartificialorfieldconditions,theencirclednumbers intheplotcouldcorrespondtothefollowingtypesofstudies:(1)one species,onepopulation,fieldsite;(2)onespecies,50populations, growthroom;(3)50species,onepopulationeach,growthroom;(4) 25species,onepopulationeach,commongarden;(5)25species, 10populationseach,growthroom;(6)10species,10populations each,commongarden.

Fig. 2. An example of a multi-species greenhouse experiment, whereherbicidetoleranceofmultiplered-listedandcommonarable weedswasassessed(DavidGudnason,&MarkvanKleunen,unpub- lishedstudy).

Studiesbasedonmulti-speciesdatabaseshaveincreased inthelastcoupleofdecades (Pyˇsek&Richardson,2007), most likely due to the increased availability and accessi- bilityof traitdatabases(Kattgeetal., 2011).Multi-species experiments are also not new. Already in the 1960s and 1970s, Grime and his colleagues conducted large multi- speciesexperiments(e.g.Grime,1965;Grime&Hunt,1975) totestwhetherspecificecologicaltraitsyndromesexistacross manydifferentplantspecies.Nevertheless,mostexperiments addressingquestionsonwithin-speciesvariationcontinueto bedonewithsinglespecies,andmostexperimentsaddressing questionson among-speciesvariationuse twospecies.For example,amongthe117studiesincludedinameta-analysis ontraitsassociated withinvasiveness,89(76%) compared onlyoneinvasiveandonenon-invasivespecies(Fig.3;van

Fig.3. Histogramofthenumberofinvasiveplantspeciesusedin experimentsthattestedfortraitdifferencesbetweeninvasiveand non-invasiveplantspecies.

ThedataarefromvanKleunenetal.(2010).

Kleunen,Weber,&Fischer,2010).Moreover,manyofthese studiesincludedonlyonepopulationorgenotypeperspecies.

Eachofthetwo-speciesstudiesalonecannotrevealwhatgen- erallydifferentiatesinvasivefromnon-invasivespecies.This questioncanonlybeaddressedifeachcomparatorgroupis representedbymultiplespecies.

Meta-analysisis apowerfulstatistical tooltosynthesize the results of a largenumber of studies(Hedges &Olkin 1985;Rosenberg,Adams,&Gurevitch,2000).Meta-analysis hascontributedtomoregeneralinsightsregardingforexam- pledifferencesbetweensmallandlargepopulations(Leimu, Mutikainen,Koricheva,&Fischer,2006)andtraitdifferences betweeninvasiveandnon-invasivespecies(Dawson,Rohr, van Kleunen, & Fischer,2012; van Kleunenet al., 2010).

The studiesincluded inameta-analysishaveusually been conductedunderdifferentconditionsandfordifferentdura- tions, and mighthave used different criteria for assigning speciestocomparatorgroups.Although thisvariationcon- tributestothegeneralityoftheresults,itcouldalsoobscure the patterns that we are interestedin. Theselimitations of meta-analysiscanbeavoidedbydoingexperimentsinwhich multiplespecies aregrownsimultaneouslyunderthesame conditions.

How many species does an experiment need?

One challenge of multi-speciesexperimentsis that they quickly reach logistical limits. As a consequence, multi- species experimentsusuallyhavetokeepthe totalnumber ofexperimentalunitswithinlimitsbyreducingthenumber of replicatesperspecies(i.e.byreducingtheprecisionper species;Fig.1).Frequently,suchmulti-speciesexperiments therefore include plant materialof onlyoneor fewpopu- lationsper species(e.g.vanKleunen&Johnson,2007)or genotypesper species(e.g.Burns&Winn, 2006).Avalid criticism isthat each speciesmight bepoorly represented.

However,the objectiveofmulti-speciesexperimentsisnot togethighlyaccuratevaluesforeachspeciesbuttogetrep- resentative values for the comparator groupsto whichthe speciesbelong.

Thus,animportantquestionishowtodistributethesamp- ling effort amongandwithin species.Forexample, if one can include no more than 600 experimental units, should onetaketwospecieseachwith300replicatesor200species eachwiththreereplicates?Ananswertothisquestioncanbe derived frompoweranalysis.Thepowerofastudycanbe increasedbyincreasingthenumberofsamplesperspecies, while keepingthenumberof speciesconstant.However,if onedoublesthenumberof samplesperspecies– andthus doublesthetotalsamplesize–theeffectivesamplesizewill belessthandoubled.Thisisbecausetheobservationswithin a species are correlated (i.e. there is a positive intraclass correlation; Zuur, Ieno, Walker, Saveliev, & Smith 2009).

Forexample,ifonehasfivespecies,eachwith20samples (N=100),andanintraclasscorrelationof0.5(thisisthecase

whenthestandarddeviationofthespeciesequalstheresid- ualstandarddeviation),theresultingeffectivesamplesizeis 10(Zuuretal.,2009).Ifonehasonlyonespecies,theintr- aclasscorrelationisone,andtheresultingeffectivesample size isone. The latter caseispseudoreplication (Hurlbert, 1984),atleastatthegrouplevel.Therefore,increasingthe numberofspecieswillalwaysmoreeffectivelyincreasesta- tistical power than increasing the number of samples per species.

When there are more thantwo levels of sampling,e.g.

species,populationsandindividuals,calculatingtheeffective samplesizeisnotstraightforward.Toillustratehowsamp- lingeffortacrossthesethreedifferentlevelsmightaffectthe accuracyoftheestimatesof differencesbetweencompara- tor groups, we carried out simulations (see Appendix A).

Briefly,wecreatedmanyreplicatedatasetsoftwocompara- torgroupsofspeciesthathaveanaveragetraitdifferenceof 50units.The valuesof thesampledspeciesineachgroup, thevaluesofthesampledpopulationswithinspecies,andthe valuesof the sampledindividualswithin populationswere drawnatrandomfromspecifiednormaldistributions.Inour simulations,wevariedthenumberofspeciespergroup,the numberofpopulationsperspeciesandthenumberofsam- plesperpopulation,withtherestrictionthatthetotalnumber of samples remained at600 (i.e. 300 samples per group).

For each simulated data set, we used linear mixed mod- elstoestimatebetween-groupdifferences.Wesimulatedsix scenariosthatdifferedinthetotalvariationamongspecies withingroups(SDspecies)andtherelativeamountsofvariation amongpopulationswithinspecies(SDpopulations)andamong individualswithinpopulations(SDindividuals;Supplementary Fig.1).

When we increased the variation amongspecies within groupsbydoublingthevalueofSDspeciesfrom10to20,the overallaccuracyoftheestimateswashalved(i.e.thestandard deviation of the estimated group difference was doubled;

Fig.4).However, the valueof SDspecies didnot affectthe shapeoftherelationshipbetweenaccuracyandthenumbers of species per groupandpopulations perspecies (Fig. 4).

Irrespectiveofwhetherwithin-speciesvariationwaslarger, equalto,orsmallerthanamong-speciesvariation,theaccu- racyof theestimatesincreasedwiththe numberof species pergroup.However,theincreaseinaccuracysloweddown athigherspeciesnumbers.

Intheunrealisticscenariowherevariationamongpopula- tionswaslargerthanvariationamongspeciesandvariation within populationswas largerthanvariation amongpopu- lations,theaccuracyofthebetween-groupestimatesfurther increasedwiththenumberofpopulationsperspecies(Fig.4).

However,inthemostrealisticscenariowherevariationwithin specieswassmallerthanvariationamongspecies,accuracy was hardly affected by whether one or multiple popula- tions per species were included, given a certain overall numberof replicates per species(Fig.4).Our simulations thus confirm that the number of species should be maxi- mizedover the number of replicates per species, andthat

the number of populations per species is then not very critical.

Thenumberofspeciesthatweshouldincludeinanexper- imenttohaveenoughstatisticalpowerfordetectingagroup differencedependsonmanyfactors.Thesimulationsthatwe didcanbe used tofind outhow many speciesone should include,givenacertainsetofparametervalues.InSupple- mentaryFig.2,weplottedtheproportionofsimulationsthat revealedasignificant group difference(at p<0.05)versus thenumberofspeciespergroupfordifferentparameterval- ues. In the most realistic scenario where variation within speciesissmallerthanvariationamongspecies,thenumber of species pergroup required tohave95% of the simula- tionsrevealasignificantgroupdifferenceincreasedwiththe variationamongspecies.Itwasc.threewhenSDspecies=10, c.eightwhenSDspecies=20,c.12whenSDspecies=30,and c.30when SDspecies=50.Thismeansthatthereisnogen- eral rule of thumb for the number of species that should beincluded inamulti-speciesexperiment.Whenplanning amulti-speciesexperiment,werecommendrunningsimula- tionsfordifferentparametervaluestogetanideaofhowmany speciesshouldbeused(seeAppendicesB–Dforexamplesof Rsyntax).

Accounting for phylogenetic non-independence of species

Oneimportantissuetoconsiderwhenconductingmulti- speciesstudiesisthatspecieshavesharedevolutionaryhis- toriesofvaryingdegrees(Felsenstein,1985).Consequently, closelyrelatedspeciesarenotindependentdatapoints,ina similarwayassampleswithinaspeciesarenotindependent datapoints.Althoughpartofthetraitvariationthatiscorre- latedwithphylogenymaybeecologicallyrelevant(Westoby, Leishman,&Lord,1995),itisfrequentlydesirabletoaccount forphylogeneticnon-independenceofspecies.Forexample, if one compares common and rare plant species, and the commonspeciesallareAsteraceaeandtherareonesallare Orchidaceae,commonnesswouldbehighlyconfoundedwith phylogeny.Ontheotherhand,phylogeneticanalysismight revealconsistentdifferenceswithincladesofcloselyrelated organisms that would otherwise be obscured by the large variationamongclades.So,itisimportanttoincludeabroad rangeoffamilies,aswellasgrowthforms,ineachcomparator group.

One way to account a priori for phylogenetic non- independenceistoselectthespeciesinsuchawaythatonehas taxonomicgroupsofspecies,eachwithrepresentativesofall comparatorgroups(e.g.Agrawaletal.,2005;Huber,Fijan,

&During,1998;vanKleunen,Schlaepfer,Glättli,&Fischer, 2011).Theanalysisof suchdatashouldthenincludetaxo- nomicgroupasarandomfactorinthestatisticalmodel.Totest howgroupingofspeciesaccordingtotaxonomyaffectsthe relationshipbetweenaccuracyoftheestimatedgroupdiffer- ences,we simulatedpaired speciesdata(seeAppendixA).

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Fig. 4. Rcsults of simulations te:stinghow the Standard dcviation of thc estimntcd diffcrencc betwecn groups of spccie~ dcpends on the nurnber of ~pccics and.thcnumbcr ofpopulutions per companu.or group. The truc bctween-groujl difference was setcqual to 50. The six. diagrams show the different seenarios of standard de.vial:ions nmong species within groups (SD,J"'<I«), and thc relative standard devinfions among population.s wilhin specics {SDpopui>Uom) and among indiv.idua.ls witbin populations (SD;ruJivldllllli). Euchstandarddeviation of the estimated group diffcrence is basecl on I 0,000 simulntions. Thc R syntax: is included in Appendix B. F .. ach co.lored line connecls points where tJw number of samples per population wus cqual. Foreach simulation, tbe totul m1mbcr of smnples was the sarne (6(K) in total; 300 pcr group). Thus, whcn onc n1ovcs ihm1 thc left to the rig)!t aloug cach line, thc oumber of spedcs increnscs while the number of popuhttions per species decreuses.

The results (Appendix A: Fig. 3) Wl't-e very similar to the resulls or the Simulations of unpaired data (Fig. 4).

A disadvantage of using taxonomic pairs or groups of species is that the pool of possible. study species is rcstricted to lhose with a rclaied partncr species in tbe othcr cmnpamtor group, :Moreover, if' on' includes equal numbers of spccics per taxonomic group in the experiment, taxonomic groups with many species will be underrepre-

entcd. An alternative approach is to consider alt species, and to ac:count for phylogenetic relatedness of U1e species a posteriori. H has hecome relativdy easy to build phy- logen..:tic trees nsing onlinc databases (e.g. Phylommjc, http://phyJodivet~ity.net/phylomutic/; Wcbb & Donoghue, 2005) or published super trees (e.g. the DaPhnE super tree forCentrat Europcan plants; Durka & Michalski, 201 2).

Phy[ogenetit· infmmation caH be included in the anal- yscs in different ways. Th two most frequcntly uscd approaches are the generalized-least- ·quares approach.

wirich also includes phylogenetic independent contrasts, and phylogenctic-eigcnveclor regression (Freckleton, Cooper, &

Jelz, 20 ll ). The gencralized-lcasl-squares approach has an cvolutionary hasis,. and is implemented by using a phy- logenetic variance-covariance mntrix (Grafen, 1989). The phylogenetic-eigenvector tegression has no evo[utionary

basis, and is irnplemented by flrsl doing a principal- coordinatc analysis on a phylogcnciic distance matrix, and subscquent inclusion of those principal coordinalcs that explain a significant amount of lrail variution in lhc modds (Dawson, 15urslem, & Hulme, 2009; Desdevises, Legendte, Azouzi, & .Mmand, 2003; K ilster, Kiihn, Hruelheide, & K lntz, 2008). Thc laUer method has thc advantagetimt it can also he used relntively ensily in gencralized linear (rnixed} models.

However, tbe method has been criticized, particuJarly because the few signi!lcant principle coordinutes cannol accounl for all phylogenctic clfects (Frcckleton ~l al., 201 J; Roblf2001). These phylogenetically informcd analyses arc relativdy Straightforward to apply whcn one has one single valuc per species (i.e. when cach tip of the phylogenetic ITee has one value). In experimental studics, howcver, we usually have rcplit·ation, and thus havc. multiple vaJues per species. A pragmati<; solution is to usc averag' values pcr sp(.~cics (e.g.

Fischer. Burkart, Pasqualetto, & van Kleunl!n. 2010). To accounl for the variation nround the spcdes twentges, one could i nclude thc inverse of the variance per spccies as u weighling in thc analysis. An alternative solution is to inscrt multiple very shorl hranches per specics. eadt branch cor- responding to a replicatc (also see Chrobock et al., 2013;

Dawson, .Robret al., 2012; Felsenstein, 2008). This method

is,however,notwellestablishedyet,anditsappropriateness androbustnessneedsmoreverificationbystatisticians.

Getting the study material and cultivating the species

Thechoiceofstudyspeciesinmulti-speciesexperimentsis oftenconstrainedbytheavailabilityofspecies.Thismightbe particularlyrestrictiveifoneisworkingwithanimals.How- ever, withplants it is alsonot always easy toobtain seed or plantmaterialfor all speciesthat onewantstoinclude.

The restricted availability of species also means that it is impossibletoincludeatrulyrandomsampleofspecies,and thislimitationshouldbeconsideredwhengeneralizingthe results.Ifonecannotcollecttheseedsbyoneself,seedsof many species can be boughtfrom commercialseed com- panies (e.g. Chrobock, Kempel, Fischer, & van Kleunen, 2011;Kempel,Schädler,Chrobock,Fischer,&vanKleunen, 2011).Furthermore, most botanicalgardens provide seeds fromtheircollectionsforscientificpurposes.Adisadvantage of usingseeds fromcommercialseedsuppliersandbotan- icalgardensis thatonehasnocontrol overhow theseeds are collected, and that frequently the originalsources are unknown.

Onceonehastheseedsofthedifferentplantspecies,they may differ in germination requirements (Chrobock et al., 2011).Analogously insomegroups of animals,eggs may differinhatchingrequirements.Inmoststudies,onewould like to treat the seeds or eggs of all species the same to avoidthatthedifferencesthatarelaterobservedreflectdif- ferencesingermination or hatching conditions ratherthan truedifferencesamongspecies.Moreover,wewouldlikethe seedlingsorhatchlingstoemergeatapproximatelythesame time.Therefore,itisadvisabletodopilotexperimentswith seedsoreggsbeforestartingthemainexperiment.

Speciesdifferingrowthoptima,andasaconsequencethey donot occur inarandomsample of environmentsbut are usuallyassociatedwithoneoralimitednumberofhabitats.

Becauseof thisspecies-environment covariationinnature, theconclusionsofourexperimentsmightdependontheenvi- ronmentsfromwhichwesampledthestudyspecies,aswellas ontheenvironmentsinwhichwegrewthem.Despitediffer- encesingrowthoptima,ifwewanttocomparethespecies, we needtogrowthemunderthe sameenvironmentalcon- ditions. Ifweare interestedinthedifferentgrowthoptima themselves,wewillhavetogroweachspeciesundermulti- pleenvironmentalconditions.Forexample,Dawson,Fischer, andvanKleunen(2012)askedwhethercommonnativeand invasivealienherbsinSwitzerlandarebettercapableoftak- ing advantage of high nutrientlevels thanrare native and non-invasivealienspeciesbygrowingatotalof41species underbothnutrient-poorandnutrient-richconditions.Ifonly onesetofenvironmentalconditionsispossible,oneshould choosethoseinwhichallor moststudyspecies cangrow.

However,onehastobecarefulwheninterpretingtheresults,

astheymaybe validonlyforthesespecificenvironmental conditions.

Comparing within-species differences across multiple species

Multi-species experiments are not only a powerful approach to address questions concerning among-species variation,butalsotoaddressquestionsregardingthegener- alityofpatternsofwithin-speciesvariation.Forexample,the evolutionofincreasedcompetitiveability(EICA)hypothesis postulatesthatareducedattackbynaturalenemiesafterintro- ductionofaspeciesintoanewrangemayallowittoevolve agreatergrowth–potentiallyresultinginagreatercompeti- tiveability–atthecostofplantdefences(Blossey&Nötzold, 1995).TheEICAhypothesishasoftenbeentestedbycom- paringattributesofnative-andintroduced-rangepopulations of single species (e.g. Bossdorf, Prati, Auge, & Schmid, 2004;Oduor,Lankau,Strauss,&Gómez,2011;vanKleunen

&Fischer 2008). General patterns havethen been sought afterwardsbysummarizingthesesingle-speciesexperiments usingavote-countingapproach(Bossdorfetal.,2005)orby statisticalmeta-analysis(Colautti,Maron,&Barrett,2009).

However, an alternative approach is conducting a multi- speciesexperiment,asBlumenthalandHufbauer(2007)did.

Theyusedonlyonenativeandoneintroducedpopulationper species,buttheyhad14speciesintotal,andgrewthemat threelevelsofcompetition.Thus,althoughtheirexperiment didnotprovidepreciseestimatesofnative-introduceddiffer- encesforeachindividualspecies,itprovidedamoregeneral pictureofdifferencesincompetitiveabilitybetweennative andintroducedpopulationsthanasingle-speciesexperiment with14 nativeand 14introduced populations would have done.Although multi-speciesexperiments havebeen used to address questions about within-species differences, the approachisstillveryunderutilized.

Toillustratethe advantageof usingmulti-speciesexper- iments for addressing the generality of within-species differences, we simulated again six scenarios of variation of the different samplinglevels. Aswe were interested in within-speciesdifferences,wedidnotvarytheamongspecies variation,butinsteadvaried thevariation inthedifference betweenthegroupsofpopulationswithineachspecies(see AppendixA).Oursimulationsconfirmthattheaccuracyof theestimatesofwithin-speciesdifferences(e.g.differences betweennativeandintroducedpopulations)increaseswith thenumberof species (Fig.5).Moreover,the accuracyof theseestimatesforagivennumberofspeciesincreasedwith thenumberofpopulationsperspecies(Fig.5).Thiseffectwas againsmallestunderthemostrealisticscenariowherewithin- group variation was smaller than among-group variation.

Thus,testingthegeneralityofhypothesesonwithin-species variation across multiple species will also become more powerfulifmorespecies,ratherthanmorepopulationsper species,areincluded.

depends on the number of species and the number of population& per comparator group within a species. The true between-group difference was set equal to 50. The six diagrams show the different scenarios of standard deviations of the difference between groups of population&

within species (SDgroops), and the relative standard deviations among populations within groups (SDpopulations) and among individuals within population& (SD;ndividuaJs)· Each standard deviation of the estimated group difference is based on 10,000 simulations. The R syntax is included in Appendix D. Each colored line connects points where the number of samples per population was equal. For each simulation, the total number of samples was the same (600 in total; 300 per group). Thus, when one moves from the left to the right along each line, the number of species increases while the number of population& per species decreases.

Final remarks and conclusions

The search for general patterns, rules and mechanisms in ecology requires multi-species experiments. Although we only discussed using multiple species, the same principles also apply to questions at other levels of biological orga- nization. For example, if one studies a particular species, and asks a question about among-population variation, one should maximize the number of populations over the num- ber of genotypes or individuals per population, whereas for questions about among-community or among-landscape variation, the numbers of communities or landscapes should be maximized. Ideally, if one wants to make the results of multi-species experiments even more general, they should be replicated at many different locations. More broadly, the power of an ecological study is increased by increasing replication at the critical level relevant for testing a specific hypothesis. In multi-species experiments this critical level is the number of species.

In conclusion, although ecologists are asking many questions concerning the cross-species generality of char- acteristics, multi-species experiments are still surprisingly rare. While we acknowledge the value of single- or few- species experiments in ecology, we strongly recommend the

use of multi-species experiments for addressing important ecological questions in a more robust and general way.

Acknowledgements

We thank Teja Tschamtke for the invitation to write this invited view, and two anonymous reviewers for valuable comments on a previous version of the manuscript. Rudolf Rohr provided useful advice for some of the simulations.

M v K acknowledges funding of the D FG (KL 1 866/3-1).

Appendix A. Supplementary data

Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/

j.baae.2013.l0.006.

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