BUGS In The Analysis Of Biodiversity Experiments: Species .

BUGS in the Analysis of Biodiversity Experiments:Species Richness and Composition Are of SimilarImportance for Grassland ProductivityAndy Hector1*, Thomas Bell2, Yann Hautier1, Forest Isbell3, Marc Kéry1,6, Peter B. Reich4, Jasper vanRuijven5, Bernhard Schmid11 Institute of Evolutionary Biology and Environmental Studies, University of Zurich, Zurich, Switzerland, 2 Department of Zoology, University of Oxford, Oxford, UnitedKingdom, 3 Department of Biology, McGill University, Montreal, Quebec, Canada, 4 Department of Forest Resources, University of Minnesota, St. Paul, Minnesota, UnitedStates of America, 5 Nature Conservation and Plant Ecology group, Wageningen University and Research Centre, Wageningen, the Netherlands, 6 Center for PopulationAnalysis, Swiss Ornithological Institute, Sempach, SwitzerlandAbstractThe idea that species diversity can influence ecosystem functioning has been controversial and its importance relative tocompositional effects hotly debated. Unfortunately, assessing the relative importance of different explanatory variables incomplex linear models is not simple. In this paper we assess the relative importance of species richness and speciescomposition in a multilevel model analysis of net aboveground biomass production in grassland biodiversity experimentsby estimating variance components for all explanatory variables. We compare the variance components using a recentlyintroduced graphical Bayesian ANOVA. We show that while the use of test statistics and the R2 gives contradictoryassessments, the variance components analysis reveals that species richness and composition are of roughly similarimportance for primary productivity in grassland biodiversity experiments.Citation: Hector A, Bell T, Hautier Y, Isbell F, Kéry M, et al. (2011) BUGS in the Analysis of Biodiversity Experiments: Species Richness and Composition Are ofSimilar Importance for Grassland Productivity. PLoS ONE 6(3): e17434. doi:10.1371/journal.pone.0017434Editor: Tamara Romanuk, Dalhousie University, CanadaReceived July 14, 2010; Accepted February 3, 2011; Published March 2, 2011Copyright: ! 2011 Hector et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permitsunrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.Funding: This project was financed by the Swiss SystemsX.ch initiative, grant IPP-2008/23 (to Bernhard Schmid, Jasmin Joshi and Prasenjit Saha). The funders hadno role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.Competing Interests: The authors have declared that no competing interests exist.* E-mail: andrew.hector@uzh.chIntroductioncompare a typical least squares mixed model ANOVA (‘‘mixedmodel ANOVA’’) with a maximum likelihood mixed-effects model(‘‘mixed-effects model’’) that treats some variables as fixed andsome as random [7,8] and a hierarchical or multilevel model(‘‘multilevel model’’) that calculates variance components for allvariables [9]. Because mixed-effects models treat some variables asfixed and some as random comparing the relative importance ofvariables from these two different classes can be difficult, as weexplain below. In contrast, multilevel models that calculatevariance components for all variables (presented here as agraphical ANOVA table) allow for easier assessment of theirrelative importance [9,10]. Using this recently suggested approach, we analyse data on aboveground annual net primaryproduction (ANPP) from grassland biodiversity experiments andshow that species richness and species composition are of similarimportance for this ecosystem process.Biodiversity experiments have typically been analyzed withinthe classical least squares linear model framework that includesregression and analysis of variance (ANOVA) as special cases[11,12,13,14]. Table 2 presents a typical analysis of data onaboveground biomass production from some of the majorgrassland biodiversity experiments. In ANOVA tables of this type,larger F values, with their accompanying lower P values, are oftentaken as evidence for greater importance of one explanatoryvariable relative to another. As we describe in the results in greaterdetail, species richness has an F value of 68.3 and speciesConcern over the ongoing loss of biodiversity has promptedecologists to investigate the consequences for ecosystem processes[1,2]. This biodiversity and ecosystem functioning research hasbeen one of the most hotly discussed topics in ecology since the mid1990s. Much of the research within this area has used biodiversityfunctioning experiments (biodiversity experiments for short) thatassemble communities of differing diversity and monitor theresponse of different ecosystem processes (other approaches includediversity removal experiments and observational comparativesurveys). Many of these biodiversity experiments feature replicatedmanipulations of more than one aspect of biodiversity raising theissue of how best to compare their relative importance. Oneparticular area of debate has been over the importance of speciesrichness – numbers of species - relative to other aspects ofbiodiversity, particularly composition – types of species [3,4,5,6].The terminology in this area can be confusing; to be clear, here weuse composition to mean all the different combinations (mixturesand monocultures) of species used in a biodiversity experiment (thatis, in our analysis composition is a factor with a level for eachdifferent combination of species). We do not examine speciesidentity effects, by which we mean the (binary) presence or absenceof each species across a range of mixtures.In this paper we extend existing analyses of data from grasslandbiodiversity experiments (Table 1) to derive new insights. WePLoS ONE www.plosone.org1March 2011 Volume 6 Issue 3 e17434

Grassland Productivity in Biodiversity ExperimentsTable 1. Summary of the relevant design details for the subsets of compatible data analysed from the grassland biodiversityexperiments that replicated both species richness and composition (ordered by increasing aboveground annual net biomassproduction, ANPP).Experimental ngen149.91,896543BIODEPTH 63BIODEPTH Greece232.41,2,4,8,18262522BIODEPTH 562BIODEPTH Switzerland500.81,2,4,8,32322642BIODEPTH Sheffield528.81,2,4,8,12262542BIODEPTH ODEPTH Ireland630.71,2,3,4,8,332702BIODEPTH Bayreuth681.61,2,4,8,16302602359 (308 crossed)29778TotalThe subsets of the species richness gradients used are given by ‘Diversity’ and the number of species compositions (monocultures or polycultures) in each experimentby ‘Compositions’. For comparability we used data from the earlier stages of each experiment (year 2 or 3). Numbers of compositions for each experiment ignoreduplication of species mixtures with other experiments but the row titled Total gives the number of compositions ignoring duplicates and discounting duplicates (inparentheses). The version of the variable with 308 levels was used in all analyses, resulting in partially crossed random effects for experimental sites and speciescomposition in the mixed-effects model.doi:10.1371/journal.pone.0017434.t001R2 is positively related to the range of continuous explanatoryvariables [9]. In other words, all else being equal, experiments witha wider range of species richness will have higher R2s.Variance components are a better quantity for comparing therelative importance of different explanatory variables [10,15,16].Each variance (mean square) in an ANOVA table is made up ofvariation from different sources - the variance components. Thereis one special case where the variance and the variance componentare equal, and that is for the residual mean square at the bottom ofthe ANOVA table. As we move up the ANOVA table the othermean squares are made up of this residual variance componentplus one or more additional (or added) variance components. Weillustrate this with regard to this example below but first detailseveral problems that must be overcome in order to get variancecomponents for all explanatory variables.Within the mixed-effects model framework, variance components are calculated only for random effects and not for fixedeffects. This is an issue of interpretation, not calculation[17,18,19]: the variance component for a random effect is thevariation estimated for the entire population of possible levels ofthe random effect (the so-called super population) whereas avariance component calculated for a fixed effect would reflect onlythe variation in the sample of levels used in that particular analysis(the so-called finite population) which may not extend toalternative versions of the design that use other levels of the fixedfactor. However, the calculation of variance components for fixedand random effects would be identical, despite this difference ininterpretation [18,19]. This lack of variance components for fixedeffects in mixed-effects models obviously means that they cannotbe used to compare the importance of fixed and random effects.There are no watertight definitions of fixed and random effects[9,20] but the basic idea can be illustrated by contrastingexperimental treatments with blocking variables [21]. Fixed effectsare easier to explain since least squares analysis mostly treatsvariables as fixed (indeed random effects were not distinguishedcomposition an F value of 1.3, which could be taken to imply that,on average, species richness was more important than speciescomposition. However, test statistics and P values are a poormeasure of relative importance of different explanatory variablessince predictors with higher F ratios (and lower P values) do notnecessarily correspond to effects with higher estimated magnitudes. The F value (variance ratio) for each explanatory variable iscalculated by dividing its mean square - the signal - by theappropriate error, or noise, term. In many complex ANOVAdesigns (e.g. split-plot, repeated measures), including those thatmanipulate both species richness and composition, there aremultiple treatment (signal) and error (noise) terms (as implied bythe naming of multilevel or hierarchical models) and differentexplanatory variables are compared to different error terms.Therefore, in multilevel models F and P values are not useful forcomparing the importance of explanatory variables that are testedagainst different error terms [9,10].An alternative measure of the relative importance of differentexplanatory variables is the increase (or decrease) in the multiple Rsquare (the proportion of the total sums of squares explained by agiven variable) of a model when an explanatory variable is added (orremoved). However, this also has limitations. First, conventionalmeasures of R2 may not be appropriate for mixed models [9].However, even if we ignore this problem the R2 may not be a goodindicator or relative importance of different explanatory variables. Forexample, as we will discuss later, in Table 2 species richness explains 9percent of the total sums of squares while species composition explains41 percent. Comparison of the R2 values could be taken to imply thatspecies composition is more important than species richness andtherefore leads to a conclusion opposite to that given by the F and Pvalues. However, this fails to take into account the large disparity inthe degrees of freedom (1 for species richness when it is treated as acontinuous predictor versus 294 for species composition).R2 also has limitations for comparing the importance of speciesrichness at different experimental sites since, all else being equal,PLoS ONE www.plosone.org2March 2011 Volume 6 Issue 3 e17434