Using the Price Equation to partition the effects of biodiversity loss on ecosystem function

Species loss can impact ecosystem functioning, but no general framework for analyzing these impacts exists. Here I derive a general partitioning of the effects of species loss on any ecosystem function comprising the summed contributions of individual species (e.g., primary productivity). The approach partitions the difference in ecosystem function between two sites (a "pre-loss" site, and a "post-loss" site comprising a strict subset of the species at the pre-loss site) into additive components attributable to different effects. The approach does not assume a particular experimental design or require monoculture data, making it more general than previous approaches. Using the Price Equation from evolutionary biology, I show that three distinct effects cause ecosystem function to vary between sites: the "species richness effect" (SRE; random loss of species richness), the "species composition effect" (SCE; nonrandom loss of high- or low-functioning species), and the "context dependence effect" (CDE; post-loss changes in the functioning of the remaining species). The SRE reduces ecosystem function without altering mean function per species. The SCE is analogous to natural selection in evolution. Nonrandom loss of, for example, high-functioning species will reduce mean function per species, and thus total function, just as selection against large individuals in an evolving population reduces mean body size in the next generation. The CDE is analogous to imperfect transmission in evolution. For instance, any factor (e.g., an environmental change) causing offspring to attain smaller body sizes than their parents (imperfect transmission) will reduce the mean body size in the next generation. Analogously, any factor causing the species remaining at the post-loss site to make smaller functional contributions than at the pre-loss site will reduce mean function per species, and thus total function. I use published data to illustrate how this new partition generalizes previous approaches, facilitates comparative analyses, and generates new empirical insights. In particular, the SCE often is less important than other effects.