Phylogenetic diversity and productivity: gauging interpretations from experiments that do not manipulate phylogenetic diversity

Ample evidence exists showing that measures of ecosystem function are related to the amount and kind of species diversity in a system (Tilman et al. 2001; Srivastava & Vellend 2005; Cardinale et al. 2011). These observations gave way to further investigations that sought to predict what kinds of assemblages should maximize function, and these investigations have focussed on measures of species’ niche, functional or trait similarities and differences (Petchey, Hector & Gaston 2004; Srivastava et al. 2012). One aspect of this movement has been to quantify these differences by patterns of evolutionary relatedness using phylogenetic trees, which can provide additional explanatory power over other diversity measures (Cadotte et al. 2009; Mouquet et al. 2012; Srivastava et al. 2012). A recent analysis by Venail et al. (2015a) provides a novel take on the relationship between biomass production and both species richness and phylogenetic diversity (PD). They analysed 16 grassland experiments that were designed to test the effect of species richness or evenness on biomass production and stability. Like previous analyses (Cadotte, Cardinale & Oakley 2008; Flynn et al. 2011), Venail et al. created a post hoc phylogeny and compared the explanatory power of PD to species richness. However, Venail et al. came to very different conclusions than other analyses, even though they had a substantial number of data sets in common. Specifically, they concluded that PD did not provide any additional explanatory power beyond that provided by species richness. While there are certainly reasons that PD may be a poor predictor of species interactions and ecosystem function (Gravel et al. 2011, 2012; Gerhold et al. 2015), aspects of the data and analysis by Venail et al. may have limited the ability to detect patterns. As noted previously (Cadotte, Cardinale & Oakley 2008), the studies analysed were not designed to test hypotheses about PD and vary greatly in their appropriateness for these analyses. Venial et al. analyse these data in ways that exacerbate the problems with these data. For example, in their ‘Type 1’ analysis, they examine PD–biomass correlations within richness levels for each study. Examining the distribution of PD values reveals that a number of these correlations lacked variation in PD, resulting in limited power to detect correlations. In this commentary, there are two main thrusts of my criticism. First, the data set provides clear evidence of PD value, after accounting for study differences in biomass production, and secondly, the data subsets used in their analyses may have biased the results. Venail et al. present a number of different analyses that use data subsets, but they never present statistical analyses of the entire data set. Further, some of their analyses appear to have included studies without accounting for biomass differences among studies (for example, their fig. 4). Considering Venail et al.s’ (2015b) data, the studies vary considerably in the average amount of biomass produced with the lowest average biomass for a study 14·41 g m−2 (standard deviation = 3·15) and the highest 662·58 g m−2 (SD = 251·03) (Fig. 1a). The effect of study differences is substantial. In simple linear models, neither PD nor richness significantly predicts biomass production (PD: F1,822 = 1·38, P = 0·241; richness: F1,822 = 0·59, P = 0·444) (see r code in Appendix S1, Supporting information, for all analyses). However, when I include a random effect for the study, allowing the intercepts to vary with study, which accounts for differences in average biomass produced among sites, the result is drastically different, with both PD and richness highly significant (PD: F1,808 = 84·66, P < 0·0001; richness: F1,808 = 60·39, P < 0·0001). Further, if we compare the AIC values for the four different models, PD from the mixed-effects model is by far the best single predictor of biomass (AICPD.mixed = 10 194·24 < AICrich.mixed = 10 216·49 < AICPD = 11 278·16 ≅ AICrich = 11 278·96). Similar results are obtained when slopes are also allowed to vary. Most critically, Venail et al. claim that PD is not important once richness is included in a model. Using the residuals from the richness mixed-effects model above, I examined the additional explanatory power of PD. PD does explain significant variation in these residuals (F1,822 = 4·09, P = 0·044) though the effect is not strong. However, the reverse – using richness to explain residuals from the PD mixed-effects model – was not significant (F1,822 = 0·0867, P = 0·768). Further, I use a mixed-effects multiple regression (the univariate version of Venail et al.'s SEM, since I am only looking at biomass production here) with richness and PD, the model is not an improvement on the model with PD only (AICPD.mixed = 10 194·24 < AICmulti.mixed = 10 195·76), and only the effect of PD is significant in this multiple regression (PD: P < 0·0001; richness: P = 0·489). Venail et al. use a structural equation model (SEM) to assess the relative contributions of PD and species richness to the average and standard deviation in biomass production and a measure of community stability. The SEM is a different approach than has been used elsewhere, where researchers typically ask whether PD or richness is a better explanatory variable, making comparisons difficult, as Venail et al. acknowledge. That said, SEMs are a valuable and potentially powerful statistical approach. For thoroughness, I evaluated an SEM performed on the entire data set by using the ‘sem’ function in the r package ‘lavaan’. However, instead of using the raw biomass estimates, which contain substantial among-study differences in biomass (Fig. 1a), I scaled biomass, within studies, thus forcing all studies to have equivalent means of 0 (Fig. 1b). I also scaled the standard deviation in biomass production as it also varied with study, but stability did not, and so was not scaled. In the SEM (χ2 = 3·65, P = 0·161; Fig. 2), PD is a significant predictor of scaled biomass (P = 0·002) and standard deviation (P = 0·002), while richness was marginally significant (P = 0·055 and P = 0·060, respectively), and like the Venail results, both biomass and SD predicted stability (P < 0·001 for both, and with SD being negatively related to stability). Venail et al. rightly point out that PD and richness are often strongly correlated and so comparing them in models can be tricky (and so we should have limited faith in the above SEM), and one approach would be to compare their explanatory power and simply choose the best one – as I prefer; as opposed to selecting non-random subsets of the data as Venail et al. did (see more below). One alternative is to use a phylogenetic measure that is uncorrelated with richness, such as MPD – though the variance in MPD is not independent of richness (see their fig. 1) and researchers should be cognizant of this when they run analyses that implicitly assume constant variance. Venail et al. assess MPD using mixed-effects models and state that MPD does not add to the explanation of biomass beyond species richness. When I run mixed-effects models, MPD is a significant predictor (F1,822 = 8·97, P = 0·003, AIC = 10 265·81), but it is not a predictor of biomass as good as PD or richness (recall: AICPD.mixed = 10 194·24 < AICrich.mixed = 10 216·49). However, in contrast to their reported results, a mixed-effects model that includes both MPD and richness is a better model than either richness or MPD alone, with both terms significant (richness: P < 0·001; MPD: P = 0·002; AIC = 10 208·56, compared to 10 216·49 for richness alone). It is difficult to compare these results to Venail et al. since their methods are unclear about which data they used for this analysis, and they do not report degrees of freedom. My result is compatible with that reported by Dinnage et al. (2012), who analysed one of the data sets used by Venail et al. and showed that increases in richness mattered more when those increases were with distantly related species. Thus, these data again provide evidence that phylogenetic relationships are meaningful. One of the analyses Venail et al. use to support the main conclusion that PD does not add value beyond richness is an SEM (their fig. 4). Their SEM results are based on the analysis of a subset of five data sets. They remove 11 data sets in an attempt to reduce the correlation between PD and richness, which results in the exclusion of about 73% of their data. The strength of the correlation between PD and richness for the full data set is 0·899, and 0·720 for the reduced data set. Both of these correlations are highly significant (P < 0·001) and so the collinearity problem potentially remains (though the variance inflation factors are moderate to low for the complete and subset data; 5·19 and 2·08, respectively). Like the Venail analysis, the SEMs I ran using the 5-study subset indicate that richness is the most important predictor for both the unscaled and scaled biomass (though the explanatory power of richness is reduced with the scaled biomass). How do we reconcile these results with that from the entire data set (e.g. Fig. 2)? PD is superior to richness according to the analysis on the full data set (and if Venail et al. analysed patterns on the full data set, they did not say). We need to ask whether the explanatory power of PD vs. richness in the subset data is somehow different from the excluded studies. To do this, I compared the ∆AIC (AICPD – AICrich) from the 5-study data set analysed by Venail et al. to 1000 randomly selected 5-study subsets. The 5-study subset used by Venail et al. strongly favours richness over PD (from mixed-effects models; AICPD = 2959·304 vs. AICrich = 2950·962; and ∆AIC = 8·342). However, the distribution of ∆AIC values from the randomly created 5-study subsets is highly significantly negatively skewed (mean = −6·301, t = −19·228, P < 0·001; Fig. 3), and the Venail et al.s’ subset is significantly different than this distribution (one-tailed P = 0·045). Further, we might ask whether the studies with lower PD–richness correlations are more likely to show support for richness, but there is not a significant relationship between the PD–richness correlation and the ∆AIC within studies (F1,14 = 0·620; P = 0·444). Individually, the studies tend to support PD as the best model (6 of 16 studies with ∆AIC < −2 vs. three of 16 studies with ∆AIC > 2). There is one obvious outlier, which is the Isbell study (∆AIC = 10·87), which strongly supports richness and was included in the 5-study subset. This study (Isbell, Polley & Wilsey 2009) is a well-designed and robust experiment examining the effect of richness on productivity and stability. Their study was not designed to examine PD–biomass relationships, and they use nine grass species (Poaceae) and four forbs (across three families) in their experiment. It would be interesting to see how the phylogenetic balance of a species pool influences the relative explanatory power of PD and richness. Given these concerns about the 5-study subset, the resulting inferences that agree with neither the excluded studies nor the full data set should be interpreted cautiously. While Venail et al. take a thoughtful and novel approach to analysing PD–biomass relationships, there are concerns with the data and how they were analysed, and re-analyses weaken, or reverse, some of their conclusions. That the studies used in the analyses were not designed to test these hypotheses has important implications for the assumptions about independence of PD values and their distributions. These concerns were present for the original analysis (Cadotte, Cardinale & Oakley 2008) that Venail et al. compare their results to (and which Venail et al. acknowledge), and these types of concerns led to another published experiment that explicitly manipulated and replicated PD within richness levels and found that phylogeny provided unequivocal power to explain biomass production (Cadotte 2013). Venail et al. use a set of very conservative statistical approaches to deal with the richness–PD collinearity, which results in a loss of information. The alternative approach advocated here is to select the variable with the best explanatory power, which turns out to be PD. However, there are other reasons to measure richness only, including (i) researchers, students, naturalists and citizen scientists can easily measure it; (ii) it has a long history of being measured and studies can be compared directly; and (iii) richness is what the vast majority of restoration and conservation projects base success on – though papers increasingly argue that PD should be explicitly considered (Winter, Devictor & Schweiger 2013; Hipp et al. 2015). There are also arguments to choose PD, including (i) it better links with mechanisms based on species’ differences; (ii) it supplies the ability to predict which species should add most to biomass production; and (iii) it explicitly links models of evolutionary change to ecological patterns and processes. Phylogenetic diversity–ecosystem function research is a young and expanding area of enquiry, and there are many reasons to question basic assumptions and to improve statistical methods. Understanding if and how PD contributes to ecosystem function will require further experiments and analyses. Though the opinions expressed in this commentary are completely my own, I wish to thank the following people for their valuable feedback: Jonathan Davies, Dan Simberloff, Caroline Tucker, and four others who wish to remain anonymous. Please note: The publisher is not responsible for the content or functionality of any supporting information supplied by the authors. Any queries (other than missing content) should be directed to the corresponding author for the article.

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