David LeBauer points me to this article in PLoS One by Andy Hector, Thomas Bell, Yann Hautier, Forest Isbell, Marc Kéry, Peter Reich, Jasper van Ruijven, and Bernhard Schmid. Here’s the abstract:
The idea that species diversity can influence ecosystem functioning has been controversial and its importance relative to compositional effects hotly debated. Unfortunately, assessing the relative importance of different explanatory variables in complex linear models is not simple. In this paper we assess the relative importance of species richness and species composition in a multilevel model analysis of net aboveground biomass production in grassland biodiversity experiments by estimating variance components for all explanatory variables. We compare the variance components using a recently introduced graphical Bayesian ANOVA [emphasis added]. We show that while the use of test statistics and the R2 gives contradictory assessments, the variance components analysis reveals that species richness and composition are of roughly similar importance for primary productivity in grassland biodiversity experiments.
That “recently introduced graphical Bayesian ANOVA” is from my 2005 paper, “Analysis of variance: why it is more important than ever.” That is just soooo cool.
Small world! Andy Hector is a good friend, but I hadn’t been aware of this paper until just now. He’s a sharp and thoughtful guy, always on the lookout for useful new analytical methods.
In a comment of the paper (http://www.plosone.org/attachments/pone.0017434_Hector_2011_PLoSone_Comment1_15Dec2011.pdf) we further explored how to compare the relative importance of species richness and species composition when treated as a fixed and random effect respectively in the maximum likelihood mixed-effects implementation of the same model. Our results are broadly in line with those of the Bayesian ANOVA but this new approach favors somewhat greater importance of species richness relative to composition. We show how this interpretation is specific to the full range of species richness included in the data-set and how the calculations can be easily modified to produce new estimates for subsets of the diversity gradient or for individual studies.