Biodiversity-ecosystem function (BEF) theory has focused on mechanisms like species interactions that are infeasible to study in diverse natural communities. Assuming that species' function contributions are additive allows a feasible approach: using the Price equation from evolutionary biology to define a small, complete set of mathematical possibilities for ecosystem function change. Previous work defined three processes: change in species richness, change in species function, and differential loss of high functioning species. Here we derive a more general form of the ecological Price equation identical to Price's original equation used for evolutionary trait changes, but indexing species in communities rather than individuals in populations. It states that all changes in average function are a result of interspecific changes in relative abundance or intraspecific changes in per-capita function. To analyze changes in total function, a term is added for changes in total community size. From this general form we develop three novel applications of the ecological Price equation that expand the range of BEF questions that can be addressed in diverse natural communities. We discuss strategies for applying Price equations in observational studies, and present a demonstration analysis of previously published data on changes in stream invertebrate biomass across a pollution gradient.
Results/Conclusions
Our three novel applications arise from the Price equation's high level of abstraction. First, the Price equation uses arbitrary measures of species' quantities. We therefore choose to describe changes in ecosystem function in terms of changes in species abundances, which aligns with our understanding of local community change and is more robust to sampling error than previously developed richness-based partitions. Second, we depart from previous derivations by assiging the same species the same index number across all sites. This uniquely allows us to analyze change across non-nested communities, and to treat species absence as continuous with abundance loss. Alternatively, our approach can be combined with previous work to separate effects of species loss and gain. Finally, the Price equation uses arbitrary descriptions of change; these are typically discrete (ie, communities before and after disturbance) but derivatives of continuous functions are equally valid. We use the continuous ecological Price equation to show that 78% of stream insect biomass was lost along a pollution gradient due to abundance decline, and a further 18% to intraspecific body size decline. Our three innovations provide unique approaches to a key BEF question: how abundance, composition and per-capita function affect ecosystem function across global change gradients.