Species Richness and the Temporal Stability of Biomass ... et al 183.pdfSpecies Richness and the Temporal Stability of Biomass Production: A New Analysis of Recent Biodiversity Experiments

vol. 183, no. 1 the american naturalist january 2014

Species Richness and the Temporal Stability of

Biomass Production: A New Analysis of

Recent Biodiversity Experiments

Kevin Gross,1,* Bradley J. Cardinale,2 Jeremy W. Fox,3 Andrew Gonzalez,4 Michel Loreau,5

H. Wayne Polley,6 Peter B. Reich,7 and Jasper van Ruijven8

1. Biomathematics Program, North Carolina State University, Raleigh, North Carolina 27695; 2. School of Natural Resources andEnvironment, University of Michigan, Ann Arbor, Michigan 48109; 3. Department of Biological Sciences, University of Calgary,Calgary, Alberta T2N 1N4, Canada; 4. Department of Biology, McGill University, Montreal, Quebec H3A 1B1, Canada; 5. Centre forBiodiversity Theory and Modelling, Experimental Ecology Station, CNRS, 09200 Moulis, France; 6. Grassland, Soil and Water ResearchLaboratory, Agricultural Research Service, US Department of Agriculture, Temple, Texas 76502; 7. Department of Forest Resources,University of Minnesota, St. Paul, Minnesota 55108; and Hawkesbury Institute for the Environment, University of Western Sydney,Penrith, New South Wales 2753, Australia; 8. Nature Conservation and Plant Ecology group, Wageningen University, 6700 AAWageningen, the Netherlands

Submitted January 16, 2013; Accepted July 23, 2013; Electronically published November 12, 2013

Online enhancement: appendixes. Dryad data: http://dx.doi.org/10.5061/dryad.787rm.

abstract: The relationship between biological diversity and eco-logical stability has fascinated ecologists for decades. Determiningthe generality of this relationship, and discovering the mechanismsthat underlie it, are vitally important for ecosystem management.Here, we investigate how species richness affects the temporal stabilityof biomass production by reanalyzing 27 recent biodiversity exper-iments conducted with primary producers. We find that, in grass-lands, increasing species richness stabilizes whole-community bio-mass but destabilizes the dynamics of constituent populations.Community biomass is stabilized because species richness impactsmean biomass more strongly than its variance. In algal communities,species richness has a minimal effect on community stability becauserichness affects the mean and variance of biomass nearly equally.Using a new measure of synchrony among species, we find that forboth grasslands and algae, temporal correlations in species biomassare lower when species are grown together in polyculture than whengrown alone in monoculture. These results suggest that interspecificinteractions tend to stabilize community biomass in diverse com-munities. Contrary to prevailing theory, we found no evidence thatspecies’ responses to environmental variation in monoculture pre-dicted the strength of diversity’s stabilizing effect. Together, theseresults deepen our understanding of when and why increasing speciesrichness stabilizes community biomass.

Keywords: biodiversity, competition, species richness, primary pro-ductivity, stability.

* Corresponding author; e-mail: [email protected].

Am. Nat. 2014. Vol. 183, pp. 1–12. � 2013 by The University of Chicago.

0003-0147/2014/18301-54406$15.00. All rights reserved.

DOI: 10.1086/673915

Introduction

Are ecosystems that are biologically more diverse also morestable? If so, why? And if not, why not? These questionshave fascinated ecologists for generations, both because ofthe fundamental scientific challenges that they pose andtheir deep implications for ecosystem management, wheresustainability and reduced risk are often primary goals.Today, the specter of rapid biodiversity loss from ecosys-tems adds urgency to the effort to understand and toarticulate the relationship between biological diversity andthe different components of ecological stability (Hooperet al. 2005; Ives and Carpenter 2007; Cardinale et al. 2012).

The history of the diversity-stability debate is long andhas been reviewed in depth elsewhere (McCann 2000; Grif-fin et al. 2009); we summarize this history only brieflyhere. Early attempts to determine how biodiversity impactsecological stability relied mostly on verbal arguments andanecdote. This work suggested that more complex eco-logical communities with a greater number of species andtrophic linkages tend to be more stable in the face ofenvironmental perturbations (MacArthur 1955; Elton1958; Hutchinson 1959; Margalef 1969). Although con-clusions from these early studies initially gained broadacceptance because of their intuitive appeal, those con-clusions were subsequently challenged both on thegrounds that supporting experimental data were sparse(McNaughton 1977) and by mathematical models thatdemonstrated that more complex communities were lesslikely to exhibit stable equilibrium dynamics (May 1974).

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2 The American Naturalist

This collision of seemingly contradictory results forcedresearchers to think more deeply about the cause of thesecontradictions. Some emphasized that “biological diver-sity” (or complexity) and “ecological stability” were bothexpansive concepts that encompassed a range of defini-tions and that loose and imprecise usage of these termsobscured important distinctions among their differentmeanings (Pimm 1984). Indeed, recent mathematical the-ory has shown how distinct yet interrelated associationsbetween the many facets of diversity and stability can giverise to a multitude of different relationships (Ives andCarpenter 2007). Others have stressed that the impact ofspecies diversity on stability may vary between levels ofecological organization (Tilman 1996, 1999). For example,research focused on the relationship between terrestrialplant species richness and temporal variation in biomassproduction has led to a growing consensus that increasingspecies richness stabilizes the biomass of whole commu-nities (Cottingham et al. 2001; Hector et al. 2010; Camp-bell et al. 2011). However, the impact of species richnesson population-level stability is ambiguous. While theoryand some empirical work suggests that increasing speciesrichness should destabilize population-level biomass (Iveset al. 1999; Tilman 1999), others have found the reverseto be true (e.g., Steiner et al. 2005; Vogt et al. 2006), andone recent synthesis found sufficient variation amongstudies to defy generalization (Jiang and Pu 2009).

Despite progress, our understanding of diversity-sta-bility relationships remains hampered by an inability todecipher underlying mechanisms (Cardinale et al. 2012;de Mazancourt et al. 2013). For example, compensatorydynamics, whereby increases (decreases) in the density ofone species are offset by decreases (increases) in the densityof another species are generally thought to provide a prox-imate explanation for species richness’s stabilizing effecton community biomass (Gonzalez and Loreau [2009] pro-vide a review, but see Houlahan et al. 2007 for a dissentingview). However, the ultimate mechanism driving thesecompensatory dynamics has yet to be resolved. One pro-posed mechanism is interspecific competition, in whichfluctuations in the densities of one species lead directly tocountervailing fluctuations in the densities of competingspecies (Tilman et al. 1998; Lehman and Tilman 2000).Others have argued that diversity stabilizes communitiesby introducing species that respond differently to varyingenvironmental conditions (Doak et al. 1998; Ives et al.2000; Loreau and de Mazancourt 2013), leading to theprediction that diversity’s stabilizing effect should bestrongest when communities consist of species that re-spond independently to changing environments. So far,discussion about mechanisms has been primarily theoret-ical, as empirical support for one or multiple mechanisms

has been elusive (but see de Mazancourt et al. 2013 for arecent exception).

Here, we reanalyze data from 27 recent biodiversity ver-sus ecosystem function (BEF) experiments to ask how di-versity impacts the temporal stability of population andcommunity-level biomass production in competitive com-munities. BEF experiments consist of replicated commu-nities (alternatively described as species assemblages ormixtures) constructed by randomly selecting member spe-cies from an experimental species pool, most often usingeasily manipulated species groups such as herbaceousplants, algae, or microbes (Loreau et al. 2002). As this fieldof research has matured, some experiments have been runlong enough to quantify how differences in species richnessimpact temporal variation among primary producers (e.g.,Tilman 1996; Tilman et al. 2006; Hector et al. 2010; Reichet al. 2012).

Our analysis of these experiments is motivated by sev-eral questions that have yet to be resolved by any exper-iments individually or by data syntheses conducted to date.First, how can the effect of species richness on whole-community biomass production be “unpacked” into di-versity’s simultaneous effects on the mean and varianceof productivity? Second, do these 27 experiments showthat species richness has any consistent, repeatable impacton population-level stability? Third, do species interactionscontribute to the compensatory dynamics that stabilizewhole-community biomass? And fourth, is diversity’s ef-fect on community-level stability strongest when speciesresponses to environmental fluctuations are most dissim-ilar? The analysis of these latter two questions is enabledby the development of a new metric for quantifying thecorrelation among a group of species across different levelsof species richness.

The remainder of this article is structured unconven-tionally. First, the data sets and general strategy for theanalysis are described. Then, four separate analyses arepresented. Because the analyses build upon one anotherprogressively, methods and results are presented togetherfor each individual analysis before progressing to the next.A discussion concludes.

Data

To select data for this study, we began with data compiledfor Cardinale et al. (2013). In brief, those data were chosenusing the following steps (full details of the selection pro-cedure and data are available in Cardinale et al. 2013).First, a list of BEF experiments was compiled from severalrecent meta-analyses (Jiang and Pu 2009; Campbell et al.2011; Cardinale et al. 2011). From that list, we identifiedall studies that: (a) experimentally manipulated speciesrichness of primary producers, (b) included single-species



New Analysis of Ecosystem Stability 3

Table 1: Included studies and key characteristics

Study and representative citationNo. of

experiments System Response variableMax. species

richness

No. oftime

points

Fox 2004 5 Freshwater microalgae Algal wet mass 7 3Gonzalez and Descamps-Julien 2004 3 Freshwater microalgae Algal biovolume 6 32Weis et al. 2007 2 Freshwater microalgae Algal wet mass 3 9Zhang and Zhang 2006 1 Freshwater microalgae Algal wet mass 5 3Flombaum and Sala 2008a 1 Terrestrial plants Percent cover 6 3Hector et al. 2010b 6 Terrestrial plants Aboveground dry mass 8–16 3Isbell et al. 2009 1 Terrestrial plants Aboveground dry mass 8 10Reich et al. 2006 4 Terrestrial plants Aboveground dry mass 16 11Tilman et al. 1996c 1 Terrestrial plants Percent cover 24 7Tilman et al. 2006 1 Terrestrial plants Aboveground dry mass 16 8van Ruijven and Berendse 2005 1 Terrestrial plants Aboveground dry mass 8 4Weigelt et al. 2010c 1 Terrestrial plants Aboveground dry mass 60 6

a Species-level data not available in mixtures.b Data from Greece and Switzerland not included. Not all species planted in monoculture for Germany, Ireland, and Silwood.c Not all species planted in monoculture.

monocultures, (c) measured biomass production for atleast 3 time points, and (d) retained individual data forall experimental units (as opposed to treatment means).Additionally, we included both the Jena experiment, forwhich full data have only recently been made available(Weigelt et al. 2010), and more recent data updates fromtwo ongoing experiments (Isbell et al. 2009; Reich et al.2012).

Altogether, we analyzed data from 27 independent ex-periments associated with 12 separate studies (table 1; ad-ditional information in app. A; apps. A–E available online).We counted an experiment as a group of replicate com-munities subjected to identical manipulations and in-tended to be compared directly to one another, and a studyas an experiment or set of experiments reported in thesame article or sequence of related articles. For example,the European BioDEPTH project represents several in-dependent manipulations of plant species richness per-formed in different countries, yet these independent ex-periments were often reported together as a single study(e.g., Hector et al. 2010). Our data included 16 terrestrialgrassland experiments (from eight studies) and 11 labo-ratory microcosm experiments with freshwater microalgae(from four studies). Although these experiments representonly a small fraction of BEF experiments conducted todate, they are the only ones we found that met all thecriteria necessary for inclusion in this study.

The measured response variable in grassland experi-ments was typically aboveground dry biomass per unit area(or, alternatively, percent ground cover), while the re-sponse variable in algal experiments was algal wet massor biovolume per unit volume. Throughout, we refer tothe response variable as “biomass” to simplify presenta-

tion. Maximum species richness ranged from 6 to 60 spe-cies (median p 15) for grassland experiments, and from3 to 7 species (median p 6) for algal microcosms. When-ever possible, the biomass of unintended, routinely weededspecies was removed from whole-community biomassmeasurements before analysis.

Although we strove to select experiments with similardesigns, differences among these 27 experiments are nu-merous and go beyond simple taxonomic distinctions. Sev-eral of these differences are noteworthy. First, grasslandexperiments generally exhibited a marked seasonality, andbiomass production was typically measured once near theconclusion of each growing season. Grassland experimentsalso focused primarily on perennial plants whose averagegeneration time exceeded the annual sampling interval. Incontrast, algal experiments performed in laboratory mi-crocosms typically exhibited more continuous (i.e., non-seasonal) population dynamics, and experiments oftenspanned a dozen or more generations of the included taxa.Second, experiments differed in the extent to which com-munities were characterized by initial transient dynamicsas they progressed from their inoculation densities to theirsteady state biomass and community composition. Insome algal microcosms (e.g., Fox 2004; Weis et al. 2007),simultaneous exponential growth of all species was thepredominant initial dynamic, while in others (e.g., Gon-zalez and Descamps-Julien 2004; Zhang and Zhang 2006)sampling began only after exponential growth had waned.In grassland experiments, exponential population growthacross multiple growing seasons was rare because of highinitial seeding densities; however, community structure inmixtures typically evolved through time as these experi-ments matured (e.g., Reich et al. 2012). Third, in 8 of 11




algal experiments, growing conditions were tightly con-trolled and abiotic heterogeneity was minimized (e.g., Fox2004), while in the other three experiments, environmentalheterogeneity (e.g., fluctuating temperatures) was intro-duced as part of the experimental design (e.g., Gonzalezand Descamps-Julien 2004). In contrast, in terrestrialgrasslands, substantial effort was often made to minimizespatial heterogeneity across plots, although some year-to-year variation in abiotic conditions like temperature orprecipitation was inevitable. Finally, terrestrial experimentstypically included more species than their aquatic coun-terparts (table 1). While the data sets from all 27 exper-iments were subjected to identical analyses for consistency,the design differences mentioned above must be borne inmind when comparing the results for terrestrial versusaquatic ecosystems. However, the juxtaposition of the twosystems will also hint at new hypotheses about the rolesof the mechanisms driving diversity-stability relationships.

Analyses

Metrics and Terminology

We focused specifically on the relationship between speciesrichness and the variation and covariation in the biomassof individual species populations or entire communities(summed biomass of species) through time. Species rich-ness was measured as the number of species initially seededor inoculated in an experimental unit. Stability of biomasswas measured using the coefficient of variation (CV), de-fined as the ratio of the standard deviation to the mean.The CV is a widely used measure for stability (e.g., May1974; Tilman 1996; Doak et al. 1998) because it providesa standardized measure of variation that is comparableacross ecosystems. Increases in CV correspond to decreasesin stability, and vice versa. When increasing species rich-ness was associated with decreasing (increasing) CV, wereferred to this as a positive (negative) effect of richnesson stability.

We quantified the relationship between species richnessand the mean, standard deviation, and CV of biomassproduction using linear regression slopes on a log-logscale. We log transformed predictor values (species rich-ness) because species richness levels were often moreevenly spaced on a log scale, and thus log transformationreduces the leverage of the most species-rich treatments.We log transformed response variables to ensure that pre-dicted values of all quantities would be positive. Lack-of-fit testing indicated that linear regressions on log-log scalesprovided adequate fits in the large majority of cases (resultsin app. B). Helpfully, log CV can be rewritten as the dif-ference between log SD and the log of the mean, whichallows the effect of richness on stability to be separated

into the effects of richness on average biomass and onunscaled variance (see below).

We also measured the correlation among the biomassesof several species in a group as they fluctuated throughtime. Depending on the analysis, this group was eitherspecies grown separately in monoculture or together inpolyculture. A single quantity that measures the overallsynchrony among fluctuations of more than two popu-lations has proven elusive (Loreau and de Mazancourt,2008; Gonzalez and Loreau 2009). For example, the av-erage correlation among n variables can be no less than

(Willis 1959), and thus the average correlation�1/(n � 1)is poorly suited for comparing groups with differing num-bers of species. Others (e.g., Lehman et al. 2000; Mikkelsonet al. 2011) have used the sum of the covariances betweenall pairs of species to measure how species interactionsimpact synchrony. While summed covariance may be use-ful for comparing the same group of species under dif-ferent conditions, it also depends on the number of speciesand the scale of measurement and thus is difficult to com-pare across ecosystems. More recently, Loreau and de Ma-zancourt (2008) proposed a scale-free metric J that variesbetween 0 when species fluctuations are maximally asyn-chronous (and hence the total biomass is constant) and 1when species are perfectly synchronized. Loreau and deMazancourt’s J can also be interpreted as the square ofthe ratio between the community-wide CV and theweighted CVs of constituent species (Thibaut and Con-nolly 2013). While Loreau and de Mazancourt’s J is easyto calculate and intuitive, it suffers from the limitationthat independently fluctuating species will generate dif-ferent values of J depending on the number of speciesand the individual species’ variances. Consequently, thismetric is less useful for our purposes because it does notprovide a benchmark that can be used to assess how speciesinteractions influence synchrony in population dynamics.

We developed a new measure of overall synchronyamong species that overcomes this limitation. This metric,which we denote h, is the average across species of thecorrelation between the biomass of each species and thetotal biomass of all other species in the group. In notation,if Yi is the biomass of species i in a group of n species, h

is written as

h p (1/n) corr Y , Y . (1)� ( � )i ji j(i

This calculation provides an overall measure of synchronyamong species biomasses that has appealing properties(proofs in app. C). First, similarly to Loreau and de Ma-zancourt’s J, h ranges from its minimum value of �1when species are maximally asynchronized (and total bio-mass is constant) to a maximum of �1 when species are




Figure 1: A graphical summary of the effects of species richness on mean, SD, and stability of biomass. The horizontal axis shows , theb̂m

least squares regression slope of log(mean biomass) versus log(species richness). The vertical axis shows , the least squares regressionb̂j

slope of log(SD of biomass) versus log(species richness). Because , the distance that points fall from the 45� (dashed) line isˆ ˆ ˆb p b � bCV j m

proportional to , the least squares regression slope of log(CV of biomass yield) versus log(species richness). Points below the 45� lineb̂CV

indicate a stabilizing effect of species richness ( ), and points above the 45� line indicate a destabilizing effect of species richnessb̂ ! 0CV

( ). The perpendicular distance from the 45� line to each data point equals .ˆ ˆ �b 1 0 b / 2CV CV

perfectly synchronized. Second, h is centered at 0 whenspecies fluctuate independently, thus providing a usefulreference point that enables comparisons to be madeacross organisms, experiments, or study systems. AppendixD provides a simulation study that verifies that h reliablymeasures the overall synhcrony among a group of com-peting species.

Calculated metrics for all analyses are available in theDryad Digital Repository, http://dx.doi.org/10.5061/dryad.787rm (Gross and Cardinale 2013).

Analysis 1: Unpacking Species Richness’s Impact onCommunity Stability into Its Effects on the Mean

and Variance of Community Biomass

Methods. We first quantified the association between spe-cies richness and the mean, SD, and CV of communitybiomass for each experiment. To do so, we calculated themean, SD, and CV for each experimental unit (e.g., replicate

community, plot, jar, etc.) in each experiment and regressedthe log of each response versus log(species richness). Denotethe estimated slopes from each of these linear regressionsas , , and , respectively. Conveniently,ˆ ˆ ˆ ˆb b b b pm j CV CV

, and thus, the impact of species richness on com-ˆ ˆb � bj m

munity-level stability ( ) can be separated into the im-b̂CV

pacts of species richness on the mean and variance ofbiomass (see app. E for an illustration with data). In ad-dition, we plotted versus to graphically summarizeˆ ˆb bj m

diversity’s stabilizing effect on community biomass (fig.1). In this plot, experiments in which species richness sta-bilizes community biomass ( ) generate points thatb̂ ! 0CV

fall below a 45� line (where ), while experimentsb̂ p 0CV

in which richness destabilizes community biomass gen-erate points above a 45� line. Moreover, points furtheraway from the 45� line indicate a stronger effect of speciesrichness on community stability.

We also averaged , , and within terrestrial andˆ ˆ ˆb b bm j CV

algal data sets. Statistical inference for these averages is






grassland communities

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algal microcosms

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Slope of log(biomass) vs log(richness)

Slo

pe o

f log

(SD

) vs

log(

richn

ess)

Figure 2: Effects of species richness on mean, SD, and coefficient of variation (CV) of community biomass for terrestrial (A) and algalmicrocosm (B) experiments. In A, filled symbols correspond to experiments with ≥4 time points, and open symbols show experiments with3 time points.

complicated by the fact that the statistical uncertainty ineach estimate differs among experiments (because differ-ent experiments may have different levels of replication,etc.). To account for this heterogeneity, we used a two-stage bootstrap resampling process that captured variationboth within and among experiments. In the first stage,experiments were resampled with replacement. In the sec-ond stage, for each selected experiment, values of , ,ˆ ˆb bm j

and were resampled from their estimated samplingb̂CV

distribution. Statistical inference was based on 10,000 suchbootstrap samples.

Results. Increasing species richness stabilized communitybiomass in terrestrial grasslands but not in algal micro-cosms (fig. 2). In grassland experiments, increasing speciesrichness increased mean biomass production in all 16 stud-ies (average over terrestrial experiments , boot-ˆ p 0.308bm

strap SE , two-tailed bootstrap ; cf.(BSE) p 0.035 P ! .001Cardinale et al. 2007). In 12 of 16 experiments, increasingspecies richness also increased variance, although the sta-tistical significance of the average effect was marginal( , , ). Because increasingˆ p 0.124 BSE p 0.061 P p .051bj

species richness had a larger effect on mean biomass thanits variance, increasing species richness had a positive effecton community stability ( , ,ˆ p �0.185 BSE p 0.043bCV

).P ! .001In algal microcosms, however, increasing species rich-

ness increased both mean biomass ( ,ˆ p 0.668 BSE pbm

, ) and variance ( , ,ˆ0.179 P ! .001 p 0.572 BSE p 0.228bj

) at comparable rates. Thus, no association be-P p .010

tween species richness and community stability was found( , , ).ˆ p �0.096 BSE p 0.076 P p .21bCV

Analysis 2: How Does Species Richness ImpactPopulation-Level Stability?

Methods. Although theory has suggested that increasingspecies richness should destabilize the dynamics of indi-vidual populations (Tilman 1999), empirical evidence forthis pattern has so far been equivocal (e.g., Cottinghamet al. 2001; Steiner et al. 2005; Vogt et al. 2006; Jiang andPu 2009; Campbell et al. 2011). We looked for an impactof species richness on species-level stability by first cal-culating the CV of each individual species biomass in eachmonoculture or mixture in which that species occurred.We then averaged these population-level CVs across allspecies in an experimental unit, using species average bio-masses as weights. (Weighted averaging was used becausevery rare species—especially those near a detection thresh-old—tended to have large CVs that were likely artifacts ofmeasurement error.) Average population-level CVs werethen regressed against species richness for each experi-ment, again using logs of both variables. The slope of thisregression quantified the effect of species richness on pop-ulation-level stability for a single experiment. Statisticalinferences for average slopes across experiments werebased on a bootstrap similar to analysis 1. This analysisexcluded one terrestrial experiment for which species-leveldata were not available (table 1).





community−level β^CV

popu

latio

n−le

vel β^ C

V

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algal microcosms

community−level β^CV

B−0.4 −0.2 0.0 0.2 0.4

−0.4

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0.0

0.2

0.4

popu

latio

n−le

vel β^ C

V

Figure 3: A comparison of the effects of species richness on population-level coefficient of variation (CV) versus community-level CV forterrestrial (A) and algal microcosm (B) experiments. Along both axes, indicates a positive effect of species richness on stability, andb̂ ! 0CV

indicates a negative effect of species richness on stability. The dashed line is a line of equality. In A, filled symbols correspond tob̂ 1 0CV

experiments with ≥4 time points, and open symbols show experiments with 3 time points.

Results. Increasing species richness destabilized individualpopulations in 21 of 26 experiments (fig. 3). Differencesbetween terrestrial and aquatic studies were again clear. Inall 15 grassland studies, increasing species richness in-creased population-level CV, with an average regressionslope of �0.161 ( , ). Among the nineBSE p 0.028 P ! .001terrestrial experiments with at least 4 years of data, theeffects of species richness on community and population-level stability were strikingly consistent (filled points, fig.3A; note that six of these nine experiments came fromCedar Creek, MN). In contrast, there was no consistenteffect of species richness on population-level stability inalgal microcosms (average regression slope of �0.011;

, ).BSE p 0.72 P p .87

Analysis 3: How Do Species Interactions AffectCorrelations among Species?

Methods. If, in grasslands, increasing species richness sta-bilizes community biomass but destabilizes the popula-tions in those communities, then on the whole correlationsamong species biomasses must decline as species richnessincreases. Here, we investigated this phenomenon by com-paring the synchrony among species in the most species-rich mixtures to the synchrony of those same species grownalone in monoculture. Specifically, for every replicate ofthe most species-rich mixtures, we used h (eq. [1]) tomeasure the synchrony among species in that replicatemixture. We then used h to measure the synchrony ofthose same species grown in monoculture (after averaging

across replicate monocultures of the same species at eachtime point when necessary). Each of these two quantitieswas then averaged across all replicates of the most species-rich mixtures in an experiment. Comparison of the averagevalues of h across experiments reveals how interspecificinteractions impact temporal correlations among com-peting species.

This analysis was only possible for the 10 grassland ex-periments and 11 algal microcosms in which population-level data were available in mixtures and for which allspecies in the experiment were grown in monoculture.Statistical inference for averages across experiments wasbased on a bootstrap similar to analyses 1 and 2, exceptthat here the second stage of the bootstrap entailed re-sampling replicates of the most species-rich mixtures.

Results. Species synchrony in the most species-richmixtures was lower than the synchrony among the samespecies grown in monoculture in 20 of 21 experiments (fig.4; two-tailed sign test ). This suggests that inter-P ! .001specific interactions reduce correlations among species bio-masses. In the most species-rich mixtures, the average valueof h was small in grasslands (average across

, , ) and mod-experiments p �0.10 BSE p 0.09 n p 10erate in algal microcosms (average across experiments p

, , ). The average value of h was�0.34 BSE p 0.08 n p 11larger among species in monoculture (average across grass-land , ; in algalexperiments p �0.50 BSE p 0.09

, ). Reduced correlationsmicrocosms p �0.54 BSE p 0.07among species were particularly marked in the seven ter-




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Species synchrony (η) in monoculture

Spe

cies

syn

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ny (η

) in

poly

cultu

re

Figure 4: Synchrony among species in the most species-rich mixtures versus synchrony among the same species grown alone in monoculturefor terrestrial (A) and algal microcosm (B) studies. Species synchrony is measured using h from equation (1). The dashed line is a line ofequality. In A, filled symbols correspond to experiments with ≥4 time points, and open symbols show experiments with 3 time points.

restrial experiments with at least 4 years of data. In theseexperiments, the average value of h in polycultures was�0.00 ( ), compared to �0.37 ( ) inBSE p 0.02 BSE p 0.08monocultures. These results show that interspecific inter-actions generate compensatory dynamics among species.

Analysis 4: Do Species Responses to EnvironmentalFluctuations Predict the Strength of Diversity’s

Effect on Community Stability?

Methods. Some theory predicts that the effect of speciesrichness on community stability will be strongest whenspecies respond independently to environmental fluctua-tions and weakest when species responses to environmen-tal fluctuations are strongly positively correlated (Ives etal. 2000). To examine this prediction, we compared speciescorrelations in monoculture to the strength of diversity’seffect on community stability. Correlations of speciesabundance in monoculture are, at best, an indirect mea-sure of the (dis)similarity of species responses to environ-mental fluctuations. However, direct measures of speciesresponses to the environment were not available for moststudies, and model simulation suggests that the synchronyof species abundances when grown alone indicates howsimilarly species respond to environmental variation (app.D). Thus, we quantified the synchrony among species inmonoculture by calculating h for the monocultures of allspecies in an experiment (again after averaging across rep-licate monocultures of the same species when necessary).We compared this measure to community-level , ourb̂CV

measure of the stabilizing effect of species richness oncommunity biomass from analysis 1.

For the eight algal experiments in which growing con-ditions were held constant, the correlations among speciesin monoculture probably have little to do with how sim-ilarly those species would respond to changing environ-ments in nature. Even so, to remain consistent with ouranalysis of the terrestrial data, we subjected all algal ex-periments with suitable data to the same analysis, althoughcare was taken not to overinterpret our results. This anal-ysis excluded five terrestrial studies for which not all spe-cies were planted in monoculture.

Results. In both grassland (rank ,correlation p �0.05two-tailed asymptotic t-test , ) and algalP p .88 n p 11(rank , two-tailed asymptotic t-testcorrelation p �0.09

, ) experiments, there was no associationP p .80 n p 11between species synchrony in monoculture and commu-nity-level (fig. 5). Thus, the effect of species richnessb̂CV

on community stability was not predicted by species cor-relations in monoculture. This result suggests that inde-pendent responses of species to a fluctuating environmentdid not contribute to increased stability of communitybiomass in these experiments.

Discussion

This study provides a deep analysis of longer-running bio-diversity versus ecosystem function experiments that helpsexplain why species richness affects the temporal stabilityof biomass in both individual populations and whole com-




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algal microcosms

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Species synchrony (η) in monoculture

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Figure 5: Strength of the effect of species richness on community stability, as measured by (CV p coefficient of variation) versus theb̂CV

similarity in species responses to environmental fluctuations, as measured by the synchrony of species grown in monoculture for terrestrial(A) and algal microcosm (B) studies. Species synchrony is measured using h from equation (1). In A, filled symbols correspond to experimentswith ≥4 time points, and open symbols show experiments with 3 time points. In B, plus signs show experiments in which environmentalconditions were intentionally varied, and times signs show experiments in which environmental conditions were held constant.

munities. We discuss results for grassland experimentsfirst, before turning to algal microcosms and comparisonsbetween systems. In grasslands, the results here add to theburgeoning evidence that increasing species richness tendsto stabilize community biomass (e.g., Tilman 1996; Cot-tingham et al. 2001; Jiang and Pu 2009; Campbell et al.2011; Cardinale et al. 2012). However, this analysis extendsour understanding in three important ways. First, theseresults show that the stabilizing effect of species richnesson community biomass arises because increasing speciesrichness increases mean biomass by a larger amount thanit increases variance, thus increasing stability (fig. 2A).Second, we find clear and consistent evidence that in-creasing species richness destabilizes individual popula-tions in grasslands (fig. 3A). As discussed above, previouswork has led to little agreement regarding diversity’s im-pact on population stability (e.g., Cottingham et al. 2001;Jiang and Pu 2009; Campbell et al. 2011). The pairing ofa stabilizing effect of species richness on community bio-mass with a destabilizing effect on individual populationsmatches theoretical predictions (Ives et al. 1999; Tilman1999).

Third, this analysis shows that interspecific competitiongenerates compensatory dynamics in grasslands and sug-gests that compensatory dynamics help stabilize com-munity biomass. This latter conclusion follows from threeseparate findings: (a) richness stabilizes community bio-mass, (b) species biomasses are less correlated when speciesare grown together in polyculture (fig. 4A), and (c) sim-

ilarity among species responses to environmental fluctu-ations when grown alone as monocultures does not predictthe strength of diversity’s stabilizing effect (fig. 5A). Thesefindings contradict some prior analyses that have beenunable to detect compensatory dynamics in mixtures withmore than two species (e.g., Houlahan et al. 2007). How-ever, early work relied heavily on metrics such as summedcovariances that are not well suited to quantifying syn-chrony in multispecies communities (Gonzalez and Loreau2009). New measures of species synchrony, such as h fromequation (1), provide a more reliable way to compare cor-relations across different species mixtures.

Algal systems show strikingly different stability prop-erties than terrestrial grasslands. Chiefly, increasing speciesrichness in aquatic microcosms leads to similar increasesin both the mean and variance of community biomass,resulting in a minimal effect on community stability. Spe-cies richness also does not have a consistent effect onpopulation-level stability. One qualitatively similar resultbetween grassland and algal systems is that correlationsamong species biomasses are lower when they are rearedin polyculture than when grown alone, although the effectis less dramatic with algae than in grasslands (fig. 4).

It is difficult to determine whether differences betweengrassland versus algal experiments are due to any funda-mental ecological properties of these taxa or the com-munities and ecosystems they collectively inhabit, or aresimply caused by inevitable design differences in terrestrialversus microcosm studies. There are, however, select bi-




ological differences among the dominant primary pro-ducers that hint at underlying ecological explanations.First, in algal studies, species that were more productivein monoculture were also less stable (rank correlation be-tween biomass and CV for monoculture species, averagedacross , , ). Inexperiments p �0.24 SE p 0.15 n p 10grasslands, the reverse was true—more productive specieswere more stable in monoculture (average rank

, , ). Second, algalcorrelation p �0.45 SE p 0.07 n p 16communities were more strongly dominated by speciesthat were more productive in monoculture (average rankcorrelation between abundance in the most species-richpolycultures versus abundance in monoculture for algal

, , ; for grasslandcommunities p �0.63 SE p 0.09 n p 11, , ). Thus,communities p �0.26 SE p 0.08 n p 10

aquatic communities tended to be dominated by low-sta-bility taxa to an extent not observed in grasslands.

With respect to why this may be so, it has also beensuggested that aquatic systems have a simplified physicalenvironment that may reduce the potential for comple-mentary resource use among algae relative to terrestrialplants (Schmidtke et al. 2010). If aquatic systems are, infact, more spatially homogeneous—either in nature, or justin these experiments—it could explain why more pro-ductive but less stable species come to dominate aquaticcommunities. Although the data currently available do notallow us to explore this possibility definitively, this sug-gestion does underscore how differences in species traitscould interact with environmental conditions to impactthe diversity-stability relationship.

In grassland systems, the lack of an association betweenthe correlations among species densities in monoculturesand the strength of the richness-stability relationship ispuzzling (fig. 5A). To the extent that monocultures reflectspecies’ responses to the abiotic environment, this resultclashes with the theoretical prediction that the effect ofspecies richness on stability should be controlled by howsimilarly or dissimilarly species respond to environmentalfluctuations (e.g., Ives et al. 2000). There are several pos-sible reasons why data and theory do not align in this case.First, much of the theory relevant to diversity-stabilityrelationships pertains to stability across many generationsfor systems that have achieved their stochastic steady stateand are buffeted only by small perturbations (May 1974;Ives et al. 2000; Lehman and Tilman 2000; Loreau and deMazancourt 2013). However, even though some of thesegrassland experiments are among the longest-running eco-logical manipulations, most encompass only a few gen-erations of their constituent species, if they incorporatereproduction at all. In contrast, algal experiments oftenextend for a greater number of generations, albeit withfewer species. Second, this same theory assumes that spe-cies’ growth rates are determined by the separate and ad-

ditive effects of species interactions and environmentalfluctuations. However, this separation may be too sim-plistic, as species’ perceptions of, and responses to, theenvironment may be mediated by the presence of othernearby species in ways that extend beyond mere resourcecompetition (Loreau and de Mazancourt 2013). For ex-ample, in experimental communities of bryophytes, spe-cies richness reduces water stress during drought becausegreater architectural complexity in polycultures trapsmoisture and enhances microclimate humidity (Mulder etal. 2001). Finally, recent theoretical work has shown thatdiversity-stability relationships may be affected by strongovercompensatory density dependence (Fowler et al. 2012)and also by serial correlation in the environment (so-calledred noise; Fowler and Ruokolainen 2013). Both of thesephenomena may be more amenable to exploration in mi-crocosms that allow multigenerational dynamics and tightcontrol of environmental variables (e.g., Gonzalez andDescamps-Julien 2004). Each of these observations posesnew challenges for diversity-stability research and under-scores the value of conducting BEF research across a broadrange of taxa and ecological systems.

The disagreement between theory and these experi-ments suggested by analysis 4 also helps explain why theinterpretation of our findings differs from the conclusionsof a recent article by de Mazancourt et al. (2013). Thatstudy analyzed four of the grassland biodiversity experi-ments examined here (van Ruijven and Berendse 2005;Tilman et al. 2006; Isbell et al. 2009; Weigelt et al. 2010)and concluded that species richness “stabilized commu-nities mainly by increasing community biomass and re-ducing the strength of demographic stochasticity.” De-mographic stochasticity may indeed contribute tocommunity stability in these experiments (see below).However, de Mazancourt et al. (2013) based their analysison a theoretical framework (Ives et al. 2000; Loreau andde Mazancourt 2013) that does not allow species inter-actions to impact the variance of community biomass.Therefore, they did not look for, and did not find, animpact of species interactions on community stability, nordid they compare species synchrony in monoculture versuspolyculture. Certainly, the difference between our studyand de Mazancourt et al.’s highlights how different the-oretical foundations can suggest different analyses thatyield different interpretations of similar data. That said,the argument for our approach and interpretation is thatthe theory that guided de Mazancourt et al.’s analysis restson assumptions that may not apply to these BEF experi-ments, as suggested by analysis 4 above. Consequently, weneed a deeper (and likely more mechanistic) understand-ing of how and why species interactions impact com-munity biomass in these experiments before we can pred-icate their analysis on any single theoretical model.




Finally, in both terrestrial and algal systems, both de-mographic stochasticity and measurement error may havecontributed to decreased population-level stability and de-creased synchrony among species in polycultures. Bothdemographic stochasticity and measurement error intro-duce variation in the measured abundances of individualspecies that disproportionately affects small populations.Thus, if the average abundance of a species declines as itsnumber of competitors increases, then both demographicstochasticity and measurement error will inflate the CV ofindividual populations and will decrease the correlationsin measured species abundances as richness increases (deMazancourt et al. 2013). Of course, demographic sto-chasticity would impact natural populations in a similarway, albeit only in very small populations. Conversely,measurement error is an artifact that may exaggerate theeffects of species richness on population-level stability andinterspecific correlations in the analysis of BEF experi-ments such as these.

To sum up, contemporary BEF experiments in grass-lands show compelling evidence that increasing speciesrichness stabilizes community biomass while destabilizingthe dynamics of individual populations, at least at thetemporal, spatial, and taxonomic scales characteristic ofthose experiments. In contrast, increasing species richnessdoes not stabilize community biomass in algal micro-cosms, perhaps because experimental algal communitieswere more strongly dominated by highly productive butless stable species. In grasslands, compensatory dynamicsamong species promote community stability, regardless ofhow similarly or dissimilarly those species respond to theenvironment. Species interactions also moderately reducecorrelations among algal species, although the effect is notsufficient to stabilize total community biomass. While theextent to which these findings may pertain to other taxa,trophic levels or spatiotemporal scales remains an openquestion, they do provide a point of reference from whichour understanding may grow.

Acknowledgments

We thank T. Ives for helpful discussion, we thank K. Frit-schie for curating data, and we thank two reviewers forhelpful comments. This work was supported by NationalScience Foundation (NSF) grants DEB-0842101 to K.G.and NSF-1046121 to B.J.C. A.G. is supported by the Ca-nada Research Chair program, and M.L. acknowledgessupport by the TULIP Laboratory of Excellence (ANR-10-LABX-41).

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