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Ecology, 85(3), 2004, pp. 847–857 q 2004 by the Ecological Society of America HOW DO DIFFERENT MEASURES OF FUNCTIONAL DIVERSITY PERFORM? OWEN L. PETCHEY,1,3 ANDY HECTOR,2,4 2 AND KEVIN J. GASTON1 1Department of Animal and Plant Sciences, University of Sheffield, Western Bank, Sheffield, S10 2TN, UK Natural Environment Research Council Centre for Population Biology, Imperial College London, Silwood Park Campus, Ascot, Berkshire, SL5 7PY, UK Abstract. Biodiversity can influence ecosystem functioning through changes in the amount of resource use complementary among species. Functional diversity is a measure of biodiversity that aims to quantify resource use complementarity and thereby explain and predict ecosystem functioning. The primary goal of this article is to compare the explanatory power of four measures of functional diversity: species richness, functional group richness, functional attribute diversity, and FD. The secondary goal is to showcase the novel methods required for calculating functional attribute diversity and FD. We find that species richness and functional group richness explain the least variation in aboveground biomass production within and across grassland biodiversity manipulations at six European locations; functional attribute diversity and FD explain greater variation. Reasons for differences in explanatory power are discussed, such as the relatively greater amount of information and fewer assumptions included in functional attribute diversity and FD. We explore the opportunities and limitations of the particular methods we used to calculate functional attribute diversity and FD. These mainly concern how best to select the information used to calculate them. Key words: biodiversity; biomass production; complementarity; ecosystem; functional groups; resource use differentiation; species richness. INTRODUCTION Interest in whether biodiversity determines ecosystem functioning (Schulze and Mooney 1993) spawned experimental studies specifically designed to answer that question (reviewed in Tilman 1999, Kinzig et al. 2001, Loreau et al. 2001, 2002). Whether these demonstrated functional consequences of biodiversity depended on factors such as trophic complexity (Raffaelli et al. 2002), temporal scale (Petchey et al. 2002), and spatial scale (Wardle et al. 1997, Loreau 2000), to name but a few (Hughes and Petchey 2001). Recently, attention has turned to why biodiversity matters (when it does): what are the functionally significant components of biodiversity (Dı́az and Cabido 2001, Hooper et al. 2002)? This attention is currently (Naeem and Wright 2003) focused on the concept of functional diversity, which Tilman (2001) defined as ‘‘those components of biodiversity that influence how an ecosystem operates or functions.’’ Theory predicts that increased functional diversity will increase ecosystem functioning due to greater resource use complementarity (Hooper 1998, Petchey 2003) among the species in a local community, all else being equal (Trenbath 1974, Harper 1977, Tilman et al. 1997b, Loreau 1998). Manuscript received 7 April 2003; revised 22 July 2003; accepted 25 July 2003. Corresponding Editor: M. Loreau. 3 E-mail: [email protected] 4 Present address: Institute of Environmental Sciences, University of Zurich, Winterthurerstrasse 190, CH-8057 Zurich, Switzerland. Such theory is closely related to niche models, where separation in niche space allows coexistence through lack of competition for similar resources (e.g., MacArthur and Levins 1967). For example, species that exhibit a large diversity of above and below ground architectures should coexist, capture light, and forage resources more completely and efficiently than a community containing species all with similar architectures (Berendse 1983, Naeem et al. 1994). Hence, an accurate measure of functional diversity could help explain and predict changes in ecosystem functioning that might result from extinctions (Petchey and Gaston 2002 a), for example. Yet the explanatory power of different measures of functional diversity remains largely unexplored. Experimental manipulations of biodiversity provide one method for assessing different measures of functional diversity by comparing how well they explain variation in ecosystem functioning. These experiments typically manipulate one or both of species richness and functional group richness (e.g., Tilman et al. 1997a, Hector et al. 1999). Species richness typically has low explanatory power perhaps because it ignores similarities or differences in the functional traits of species (Root 1967, Hooper et al. 2002). Indeed, when used as a measure of functional diversity, species richness implicitly assumes that all species are equally different (addition of any species to a community will increase functional diversity by one unit) and that the contribution of each species to functional diversity is independent of species richness. 847 848 OWEN L. PETCHEY ET AL. Ecology, Vol. 85, No. 3 PLATE 1. The BIODEPTH biodiversity manipulation experiment at Silwood Park, near London UK, after three years showing plots with different plant diversity, composition, and productivity. The plot in the center foreground is a monoculture of Hypochaeris radicata. Photograph by Andy Hector. Functional group richness (FGR) also has limitations. It relies on an arbitrary decision about the level at which interspecific differences among species are functionally significant (Simberloff and Dayan 1991, Vitousek and Hooper 1993). It assumes that species within groups are functionally identical, that is, species within groups are entirely redundant (Lawton and Brown 1993). It also assumes that all pairs of species drawn from different functional groups are equally different. In other words, adding a species from a novel functional group to a community adds unity to functional group richness, regardless of the identity of group(s) that are present and the identity of the novel group. The explanatory power of two recently developed measures of functional diversity has never been measured in a biodiversity experiment. These are functional attribute diversity (Walker et al. 1999) (hereafter FAD) and FD (Petchey and Gaston 2002b). Both of these measures have the traits of species as their foundation and estimate some component of the dispersion of species in trait space. For FAD this dispersion is estimated as the sum of the distances between species in trait space (Walker et al. 1999) and need not be limited to plant assemblages. For FD, dispersion is estimated as the total branch length of the functional dendrogram that results from clustering the species in trait space (Petchey and Gaston 2002b). The implications of this difference are covered in the Discussion section of this paper. They both require an assumption about how to measure distance (e.g., Euclidean or Manhattan) and FD requires an assumption about how to cluster species (e.g., unweighted pair group method using arithmetic averages or minimum variance clustering) (see Pielou 1984). Previous analyses show that the qualitative behavior of FAD and FD are not sensitive to a range of distance measures and cluster methods (Petchey and Gaston 2002b). Several properties of these two measures predict that they will explain greater variance in ecosystem func- tioning than either species richness or FGR. Unlike FGR, FAD and FD require no arbitrary decision about the functional significance of interspecific differences among species (because they do not assign species to groups) (Walker et al. 1999, Petchey and Gaston 2002b). They include the large functional differences that might delineate groups and the small functional differences that groups ignore. Consequently, both can be continuous measures of functional diversity, whereas species richness and FGR are discrete; this could enhance their explanatory power if natural interspecific variation is continuous (Hooper et al. 2002). We used data from the BIODEPTH project (Hector et al. 1999) to compare the performance of these four measures of functional diversity: species richness, functional group diversity, FAD, and FD. We also discuss the novel methods used to calculate FAD and FD. MATERIALS AND METHODS The BIODEPTH project manipulated plant species and functional group richness at eight European sites (Plate 1); the methods are described in detail elsewhere (Hector et al. 1999). Here we consider only aboveground plant biomass production (g/m2) at six of these sites in the second year as the ecosystem process of interest. We used the same classification of species into three functional groups (legumes, grasses, herbaceous) as in the original study (Hector et al. 1999). We performed four separate analyses of the BIODEPTH project: (1) an analysis of all polycultures across all sites simultaneously; (2) an analysis of all polycultures at each separate site; (3) an analysis of all four-species mixtures across all sites, and (4) an analysis of all two-species mixtures across all sites. We performed analyses A and B for consistency with previously published analyses (Hector et al. 1999). We performed analyses C and D to assess the explanatory power of functional diversity in the absence of the interpretive difficulties caused by variation in species richness among communities (Aarssen 1997, March 2004 EXPLAINING ECOSYSTEM FUNCTIONING 849 TABLE 1. The candidate traits that were used to calculate FD (Petchey and Gaston 2002b) and FAD (functional attribute diversity). Source of traits Unpublished measurements BIODEPTH monoculture measurements Additional Trait number Trait 1 2 3 4 specific leaf area leaf area leaf thickness dry matter content 5 canopy structure 6 canopy height 7 lateral spread† 8 seed mass continuous measure; mm2/mg continuous measure; mm2 continuous measure; mm continuous measure; percentage of saturated mass categorical measure; leaves all basal or plant prostrate, semi-rosette (stems leafy but largest leaves at base), leafy categorical measure: ,100 mm, 100–200 mm, 300–500 mm, 600–1000 mm, 1–3 m categorical measure: therophytes, ,100 mm, 100–250 mm, 250–1000 mm, .1 m continuous measure; log(mass [in mg]) 9 biomass† continuous measure; g/m2 10 11 vegetation cover† canopy height continuous measure; % continuous measure; cm 12 legume or not† binary measure Details Notes: Trait numbers are used in the text for brevity. Daggers (†) indicate the four traits that were used in a separate bootstrap analysis. Huston 1997). Sample sizes were not large enough to warrant analyses within any other levels of species richness. Each analysis comprised the same four steps. (A) A matrix of candidate traits was compiled (candidate traits sensu the candidate function groups of Vitousek and Hooper [1993]). (B) Each possible combination of candidate traits was used to calculate a candidate measure of FAD and FD of each experimental plot in the analysis. (C) The amount of variance in ecosystem functioning explained by each candidate measure of FAD and FD was recorded. (D) The analysis was bootstrapped to test statistical significance of relationships between ecosystem functioning and FAD or FD. Candidate traits.—Eight traits collected from various sources (J. P. Grime, J. Hodgson, K. Thompson, P. Wilson, and R. Ceriani, unpublished data), three measurements from the BIODEPTH monoculture plots, and a legume/non-legume trait were the candidate traits used to calculate FAD and FD (Table 1). The first eight traits, such as leaf thickness, were typically measured from individual plants. BIODEPTH monoculture measurements were the ecosystem-level properties that were also measured in species mixtures (measurements that contained missing values were not included as candidate traits). Monoculture measurements from all Northern European BIODEPTH sites were pooled and where there was more than one monoculture of a species, the mean across plots and sites was calculated. We were only able to compile traits for the species used in the six most-northern BIODEPTH sites, consequently the Greek and Portuguese sites were excluded from all analyses. These two sites show nonsignificant and significant relationships between species richness and biomass production, respectively, so excluding them should not bias conclusions in a particular direction. Calculating FAD and FD.—Each of the 212 possible combinations of the 12 candidate traits was used to calculate candidate measures of FAD and FD of all plots across the experiment. The rationale for this is as follows. An assumption of any measure of functional diversity is that the traits/criteria used to calculate it are functionally important; that is, they inform about interspecific differences in resource use differentiation. We were unsure of which candidate traits met this criterion. Rather than make a more or less subjective decision about the functional importance of each trait, we calculated a separate candidate measure of FAD and FD for each possible combination of candidate traits. This equates to weighting the candidate traits by zero or one, in all possible combinations. Using zero/one weights (and no fractional weights) was a pragmatic solution to reducing the number of trait combinations to manageable levels (4096). There would have been 531 441 possible combinations of trait weightings if we had used 0, 0.5, and 1 as weights, and the analyses would have taken months of computer time. As mentioned, both FAD and FD require an assumption about the measure used to quantify distance in trait space and the algorithm used to cluster species. We used Euclidean distance and the unweighted pair-group method using arithmetic averages (UPGMA) clustering method and standardized all candidate traits to have a mean of zero and variance of one. Estimating the explanatory power of FAD and FD.— The amount of variance in aboveground biomass production explained by each separate candidate measure of FAD or FD was estimated as the R2 of the appropriate 850 OWEN L. PETCHEY ET AL. Ecology, Vol. 85, No. 3 FIG. 1. Relationships between aboveground biomass production and (a) log2(species richness), (b) FGR (functional group richness), (c) FAD (functional attribute diversity), and (d) FD (Petchey and Gaston 2002b) across the six analysed BIODEPTH sites. Lines show the fitted relationships of analysis of covariance (which included the interaction term between diversity and site). statistical model. For analyses A, C, and D, this was analysis of covariance (ANCOVA) with FAD or FD as a continuous explanatory variable and European location as a categorical explanatory variable. For analysis B, the model was linear regression. The explanatory powers of models with log2(initial species richness, S) and functional group richness (the number of grasses, legume and herb functional groups represented) as continuous explanatory variables were also estimated. Estimating statistical significance by bootstrap.—To estimate statistical significance of FAD and FD we bootstrapped each analysis (Manly 1997). This tested whether high amounts of variance explained by either FAD or FD resulted from chance or not; a parametric test was not appropriate because multiple candidate explanatory variables were tested in step 3. We first randomized the trait matrix: values were randomized among species and within traits. That is, trait values were not allowed to swap between traits. We then calculated the maximum explanatory power of FAD (or FD) given the randomised trait matrix. Repeating this 1000 times produced a bootstrapped distribution of maximum explanatory powers for each measure of FAD and FD against which the observed maximum explanatory power could be compared for statistical significance. In addition, we repeated each analysis while including only four traits in the analyses to see if the number of candidate traits affected the bootstrapped significance level (Table 1). The four traits EXPLAINING ECOSYSTEM FUNCTIONING March 2004 851 TABLE 2. The explanatory power (R2) in analysis B of linear relationships between biomass production and log2(species richness, [S]), FGR (functional group richness), both log2(S) and FGR fitted simultaneously, FD (Petchey and Gaston 2002b), and FAD (functional attribute diversity) across the n plots at each site. FGR Log2(S ) 1 FGR FAD FD FD last FAD last NS 0.34*** 0.34** 0.35 0.79 Legume P , 0.001 P , 0.001 0.05 NS 0.22* 0.22* 0.16 0.67 Legume P , 0.001 P 5 0.45 50 0.02 NS 20.01 0.03 NS Legume P 5 0.13 P 5 0.99 34 Monoculture biomass Vegetation cover Lateral spread P , 0.001 P 5 0.40 P , 0.001 P 5 0.99 P , 0.05 P 5 0.32 Site n Log2(S ) Bayreuth, Germany Lupsingen, Switzerland Riverstick, Ireland Röbäcksdalen, Sweden Sheffield, England Silwood, England 30 ,0.01 28 Trait ,0.01 NS 0.02 0.19* 0.10 NS 0.19* 0.2 0.43 NS 30 0.49*** 0.40*** 0.50*** 0.39 0.70 NS 32 0.03 0.06 0.06 0.05 0.11 NS NS NS NS NS Notes: Standard parametric P values are denoted as follows: NS, P . 0.05; *P , 0.05; **P , 0.01; ***P , 0.001; or the exact value. Bold type indicates that the relationship between FD and biomass production was significant when the observed R2 was compared with a bootstrapped distribution of R2. The last two rows show the standard parametric significance levels when FD or FAD is fit after species richness and FGR. used were those that maximized explanatory power in analysis B (see Tables 1 and 2). RESULTS Analysis A: all polycultures, all sites The overall R2 values of the analysis of covariance with log2(species richness), FGR, FAD, or FD as the continuous explanatory variable were respectively 0.33, 0.40, 0.40, and 0.55 (Fig. 1). Each explanatory variable was significantly associated with aboveground biomass production, whether probabilities were calculated by F tests in the case of log2(species richness) and FGR or by bootstrapping in the case of FAD and FD. The maximum explanatory power of both FAD and FD was attained by including only one trait in the matrix, the legume/non-legume trait. Two other combinations of traits produced significant explanatory power of FD (Fig. 2), both of which included the legume/ non-legume trait and one other trait (either trait 5 or 10; see Table 1). The vast majority (99.6%) of all possible trait combinations resulted in a measure of FD with greater explanatory power (though not necessarily significant explanatory power) than FAD (when comparing FAD and FD models with the same traits; Fig. 2). Including only four candidate traits (instead of 12) lowered the critical R2 value for FAD and FD, which resulted in no change in the significance of the most powerful trait combination at a 5 0.05 (Fig. 2). The number of significant trait combinations increased to seven for FAD (including traits 3, 4, 5, 6, 8, and 12) and 13 for FD (including traits 1, 2, 3, 4, 5, 7, 8, 10, 11, and 12), all of which included the legume/nonlegume trait. The next most common trait was vegetation cover and was present in only six of the 20 combinations. Analysis B: all polycultures, each site separately At each site, the explanatory variable with greatest power was FD; the relative explanatory powers of other variables varied across sites (Table 2). Within any one site, the maximum explanatory power of FD and FAD was always attained by including a single trait, though the identity of this trait differed between sites (Table 2). The explanatory power was only significant by bootstrap test at two sites, Germany and Switzerland, where the only trait included was legume/non-legume. This supports the results of analysis A, where the effect of FAD and FD varies across sites (Fig. 1c and d). In Germany, only one of the 4096 different trait combinations resulted in a measure of FD and FAD with significant bootstrapped explanatory power. In Switzerland, four trait combinations resulted in a measure of FD with significant explanatory power and all of these included the legume/non-legume trait (the other traits were 5, 9, and 10). Similarly, the two significant combinations of traits for FAD both included the legume/non-legume trait (the other trait was 10). The next most common trait occurred in a maximum of one of the four combinations for both FD and FAD. F tests indicated that FD explains variance that is not accounted for by log2(species richness) or FGR, more frequently (at five of six sites) than does FAD (one of six sites) (Table 2). Including only four candidate traits (instead of 12) sometimes decreased and sometimes increased the critical R2 value for FAD and FD (Fig. 3). In only two of 12 cases did the change in critical value cause a change in significance at a 5 0.05: FAD at Riverstick, Ireland included the legume/non-legume trait and FAD at Sheffield, England included the vegetation cover trait (Fig. 3c and e). In Switzerland, the number of significant trait combinations increased from four to eight for FD; all but one included the legume/non-legume trait and 852 OWEN L. PETCHEY ET AL. Ecology, Vol. 85, No. 3 the next most common trait was included only twice (other traits were 3, 4, 5, 9, 10, and 11). Otherwise, there were no changes in the numbers of significant trait combinations. Analysis C: four-species mixtures, all sites FIG. 2. A comparison of the explanatory power of FD (Petchey and Gaston 2002b) and FAD (functional attribute diversity) in analysis A. Each data point represents the explanatory power of a particular combination of traits. The solid line represents equal explanatory power of FD and FAD. The vertical dashed (dotted) line is the 95th percentile of the bootstrapped explanatory power for FD with 12 (four) candidate traits; the horizontal dashed and dotted lines are the same except for FAD. The overall R2 values of analysis of covariance with FAD or FD as the continuous explanatory variable were high (R2 5 0.62 and 0.68, respectively). They were not, however, statistically significant when compared to the bootstrapped analyses. That is, given the large number of tests (4096), the high explanatory power was relatively likely by chance alone. The explanatory power of FGR was lower, though significant, with an R2 of 0.32. Notably, FAD and FD have more similar explanatory power than in analyses A and B and changes in trait combinations have a similar effect on the explanatory power of both measures of functional diversity (Fig. 4a). The maximum explanatory power of both FAD and FD resulted from including the legume/nonlegume trait and three (FAD; traits 3, 4, and 10) or one (FD; trait 9) other trait(s). Including only four candidate traits (instead of 12) reduced the critical R2 value for FAD and FD (Fig. 4a). In both cases, this changed the statistical significance FIG. 3. A comparison of the explanatory power of FD (Petchey and Gaston 2002b) and FAD (functional attribute diversity) at each site (analysis B). All details are as for Fig. 2. The relative positions of the dotted and dashed lines differ between sites, indicating that changing the number of traits had different effects on the 95th percentile at different sites. EXPLAINING ECOSYSTEM FUNCTIONING March 2004 853 FIG. 4. A comparison of the explanatory power of FD (Petchey and Gaston 2002b) and FAD (functional attribute diversity) in (a) analysis C and (b) in analysis D. All details are as for Fig. 2. of the results so that both FAD and FD were significantly associated with biomass production as a result of including the legume/non-legume trait. Analysis D: two-species mixtures, all sites Again, no combinations of traits produced a measure of FAD or FD that explained greater variance in aboveground biomass production than expected by chance. Maximum R2 was 0.71 for both FAD and FD. The explanatory power of FGR was lower, though significant (P , 0.01), with an R2 of 0.48. Again, FAD and FD have more similar explanatory power than in analyses A and B and changes in trait combinations have a similar effect on the explanatory power of both measures of functional diversity (Fig. 4b). The maximum explanatory power of both FAD and FD resulted from including the legume/non-legume trait and no (FAD) or two (FD; traits 7 and 10) other traits. Including only four candidate traits (instead of 12) reduced the critical R2 value for FAD and FD (Fig. 4b). In both cases this changed the statistical significance of the results so that both FAD and FD were significantly associated with biomass production and both result from including the legume/non-legume trait. DISCUSSION These results suggest that species richness and functional group richness explain a relatively small proportion of local-scale variation in ecosystem functioning of experimental grassland plots. Other measures of functional diversity, such as functional attribute diversity (Walker et al. 1999), that incorporate trait information about species tend to explain greater variance. These findings are consistent with theoretical predictions that functional differences among species are the basis of biodiversity effects on ecosystem functioning (Tilman et al. 1997b, Loreau 1998). They also reinforce recent opinion that a better understanding of the determinants of local-scale ecosystem functioning may be developed by considering the diversity of trait values among species (Bengtsson 1998, Dı́az and Cabido 2001, Hooper et al. 2002, Schmid et al. 2002, Naeem and Wright 2003). In other words, a better understanding will result from considering information about the natural history and strategies of different species. The results also suggest that the effects of biodiversity on ecosystem functioning, albeit only the diversity of nitrogen fixing ability, depend on geographic location. Such context dependence is predicted by theory and demonstrated by varying environmental conditions at a single site (Cardinale et al. 2000, Jonsson et al. 2001, Fridley 2002). Such findings caution against using any single-site experiment, or single relationship between biodiversity and ecosystem functioning to predict regional-scale consequences of biodiversity loss. The remainder of this discussion addresses potential reasons for the differences in explanatory power among the four measures of functional diversity, notable features of the novel analyses used to calculate FAD and FD, and alternate explanations for the results. Reasons for differences in explanatory power The relative explanatory power of species richness and FGR varied, so that species richness was a more powerful explanatory variable at some sites, but not at others. This may result somewhat from the design of the BIODEPTH project experiments, where the species richness and FGR treatments were correlated, so that they share some explanatory power in common (Naeem 2002). Indeed, previous analyses of the BIODEPTH project experiments shows that the explanatory power of species richness and FGR overlaps strongly, and each explains a similar amount of variance in ecosystem functioning that the other does not (Hector 2002). Though we did not make exactly the same comparisons, deviation of our results from these previously published results are most likely a consequence of not including monocultures in our analyses. For example, Hector et 854 OWEN L. PETCHEY ET AL. al. (1999) found a significant effect of species richness at the German site, whereas we did not. Differences in explanatory power between FGR and FAD or FD could result from a variety of sources. First, FGR in this paper results from different information than FAD and FD. The division of species into functional groups in the BIODEPTH project was a qualitative exercise quite different to using quantitative traits to assign species to groups (e.g., Dı́az and Cabido 1997). Indeed, if we use the same information for FGR as for FD, whether species are legumes or not, both result in two values of biodiversity, low and high, and exactly the same explanatory power. Second, FGR makes the assumptions (mentioned in the introduction) that result from grouping species, whereas FAD and FD make no such assumptions. Our data provide little evidence regarding this explanation because a binary trait resulted in measures of FAD and FD with the greatest explanatory power. Many combinations of continuous traits did, however, produce greater (and significant) explanatory power than FGR, suggesting that grouping may reduce explanatory power by producing a distorted measure of continuous natural interspecific variation. Differences in explanatory power between FAD and FD can only be explained by differences between these measures, since exactly the same data and analyses were used for both. Fig. 1 illustrates that these two measures differ significantly: the binary legume/nonlegume trait results in only two values of FD but several values of FAD (Fig. 1). The two values of FD correspond to experimental plots that contained only nonlegumes and plots that contained legumes and nonlegumes, independent of how many species of each type were present. The several values of FAD result from whether a legume was present or not, and also how many legume and non-legume species were present. This difference can be explained by considering species as points in n-dimensional trait space. Here, FD is a measure of the volume of space occupied by these points. Adding a species that lies at exactly the same point as an existing species causes no increase in the total volume occupied. In contrast, FAD is a measure of the total distance between all pairs of points. Here, adding a new species that coincides exactly with an existing species adds all the new pair-wise distances. Consequently, FAD is a function of both trait differences among species and total number of species present, while FD is only a function of trait differences among species. When there is no variation in number of species (e.g., analyses C and D) there is much tighter correlation between FAD and FD within a site (mean R2 across sites 5 0.84 6 0.01 [mean 6 1 SD] for the most significant trait combination) than when variation in species richness is present (e.g., analyses A and B) (mean R2 across sites 5 0.50 6 0.19 [mean 6 1 SD] for the most significant trait combination). These pat- Ecology, Vol. 85, No. 3 terns support the verbal argument presented above, that variation in species richness per se (i.e., without and irrespective of functional differences) affects FAD, but not FD. Furthermore, the relatively horizontal spread of points in Figs. 2 and 3 indicates that the variance in explanatory power of FAD (across different combinations of traits) is affected less by the particular combination of traits used than is the explanatory power of FD. Presumably this occurs because the explanatory power of FAD is constrained by the effect of species richness on FAD, which remains relatively constant regardless of trait combinations. In contrast, the explanatory power of FD is only affected by the trait combination used. When effects of species richness on FAD are eliminated (e.g., in analyses C and D), the explanatory power of both measures changes similarly, again supporting the argument that species richness contributes to FAD, and that this results in the lower explanatory power for FAD. These results suggest that a measure of functional diversity that is not influenced by number of species per se will be a better predictor of ecosystem functioning than otherwise. Analyzing biodiversity-ecosystem functioning experiments using FAD and FD We are aware that our methods of relating FAD and FD with aboveground biomass production are previously untested. Consequently, we will highlight some of the more important considerations surrounding the approach. First, it is worth pointing out that our analyses are conceptually similar to more traditional analyses that assign species a priori to candidate functional groups and test whether ecosystem functioning increases with increases in FGR (Bengtsson 1998) and with the proposed iterative selection of important functional characteristics (Hooper et al. 2002). The difference here is that we test many possible functional difference schemes/traits within a single experiment. A critical property of both FAD and FD is that they must include the functionally important traits (Petchey and Gaston 2002b). This property focuses attention on the question of what these traits are. We took the approach of compiling a set of candidate traits and testing their explanatory power to find traits that when used to calculate FAD or FD explained significant variation in ecosystem functioning. This approach should be used with caution, however, because omission of important traits and inclusion of unimportant traits could influence the ecological interpretation of the results. For example, we cannot be sure that we included all, or indeed any of the functionally important traits in the candidate trait matrix. We did not have access to traits relating to belowground characteristics of plants, where much resource acquisition occurs. Furthermore, none of the candidate traits were collected with our use in mind. The eight unpublished traits (Table 1) were collected primarily to distinguish between species typical March 2004 EXPLAINING ECOSYSTEM FUNCTIONING of different stress and disturbance habitat types (Grime 2001) and the BIODEPTH monoculture traits were the measures of ecosystem functioning taken across the entire experiment. Any of these features of the candidate traits could explain why none were functionally important at four sites when analysed separately (analysis B; Table 2). Perhaps we did not include any of the traits that are functionally important at these sites. That is, FAD and FD are powerless if they are not supplied with functionally important traits. A direction for future research will be to collect trait information specifically for the purpose of explaining and predicting ecosystem functioning. Such candidate traits could be selected on the basis of independent information about the likelihood that they are important descriptors of resource use partitioning among species. Similarly, including unimportant traits can influence the interpretation of the results. The number of candidate traits used influences the likelihood of finding strong correlations between FAD (or FD) and ecosystem functioning by chance alone. This seems intuitive, since the number of possible trait combinations to search in each bootstrap iteration increases as the number of candidate traits increases. Reducing the number of candidate traits from 12 to four sometimes increased and sometimes decreased the bootstrapped significance value in analyses A and B in which there was variation in species richness. This idiosyncrasy could result because variation in species richness allows other processes to operate (such as sampling probability effects) with which FAD and FD derived from random traits will always correlate. The effect of this on bootstrapped significance may dominate over any effect of changing the number of candidate traits. In the absence of variation in species richness (analyses C and D), bootstrapped significance values always decreased to the extent that the ecological interpretation of the results changed. For example, the legume/non-legume trait was either interpreted as significant or not in analysis C depending on whether four or 12 candidate traits were used. Without variation in species richness, there is no possible correlation of FAD and FD derived from random traits with sampling probability effects, and changing the number of candidate traits consistently alters bootstrapped significance values. Another notable characteristic of these analyses is their correlational nature. So called ‘‘soft’’ traits could be selected because they are correlated with functionally important traits (so called ‘‘hard’’ traits), rather than because of any direct link with mechanisms determining ecosystem processes (Hodgson et al. 1999). This seems unlikely for the legume/non-legume trait that was selected as important by our analyses. Nevertheless and in general, inclusion of soft traits will reduce the ability of these analyses to identify the functionally important differences among species (hard traits). An alternate perspective is that soft traits may 855 still be useful for identifying important axes of differentiation if suites of traits (soft and hard) always go together (Hodgson et al. 1999). Each of these properties of the analyses highlights the importance of selecting candidate traits that are known or at least probable determinants of ecosystem functioning. Although we have shown that the analyses can identify a functionally important trait from a set of less important traits, more careful selection of candidate traits may have produced better performing measures of functional diversity. Alternate explanations of results and sources of error The results of experimental manipulations of biodiversity have attracted multiple explanations. For example, the contribution of resource use complementarity and the selection probability effect have both been implicated (Naeem et al. 1996, Hector et al. 1999, Emmerson et al. 2001, Cardinale et al. 2002). Our analyses of plots that vary in species richness (A and B) are open to similar alternate explanations. Here, both FAD and FD are correlated with variation in species richness, so that any of the hidden effects mentioned by Huston (1997) could operate. Our analyses C and D are immune to these effects, however, since there is no variation in species richness. These analyses showed a significant explanatory power of either FAD or FD with four candidate traits (see Discussion: Analyzing biodiversity-ecosystem functioning experiments using FAD and FD for discussion of this) so that there is some evidence of functional diversity effects in the absence of variation in species richness. Furthermore, the traits contributing were similar to those that contribute in analyses A and B, suggesting that these results were not due only to hidden treatments (Huston 1997). The candidate traits measured from the BIODEPTH monoculture plots (Table 1) were measured at several European locations. We calculated a regional average for each species across locations, and used this in the candidate trait matrix. This approach allowed us to analyze all sites simultaneously using FAD and FD. Trait values differed across Europe, due to changes in the local environment, such that perhaps use of local trait values (rather than regional averages) would result in more powerful measures of FAD and FD. This hypothesis remains to be tested. Concluding remarks A trade-off exists among different measures of biodiversity (Tilman and Lehman 2002). At one extreme are measures such as species richness that incorporate little or no information about individual species and are, therefore, relatively easy to obtain. Since they incorporate little information they may explain less and predict relatively poorly. At the other extreme are measures that incorporate more detailed information about OWEN L. PETCHEY ET AL. 856 individual species, such as PD (phylogenetic diversity [Faith 1992]), FAD and FD, and these are relatively harder to obtain (also see Clarke and Warwick 1998). Our results suggest that the additional biological information they contain allows for better explanation and possibly prediction. Some of the variance in ecosystem functioning cannot be accounted for by any of the functional diversity measures used here. For example, none of the discussed measures of functional diversity incorporate the abundances of species. That is, there is no functional equivalent of Shannon or Simpson’s diversity (though see Clarke and Warwick 1999). Other examples are given by facilitative interactions among species (Bertness and Hacker 1994) that impact ecosystem functioning (Cardinale et al. 2002) and ecosystem engineers (Jones et al. 1994); some aspects of each may be difficult to include in measures of functional diversity. Including aspects of trophic structure in measures of functional diversity could also be a great challenge. 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