Price Equations for Understanding the Response of Ecosystem Function to Community Change

The relationship between biodiversity and ecosystem function (BEF) remains unclear in many natural ecosystems, partially for lack of theoretical and analytical tools that match common characteristics of observational community data. The ecological Price equation promises to meet this need by organizing many different species-level changes into a few ecologically meaningful categories that sum to total ecosystem function change. Current versions of the ecological Price equation focus on species richness and presence-absence. However, abundance and relative abundance are better estimated in samples and are likely showing a stronger response to global change. Here, we present a novel, abundance-based version of the ecological Price equation in both discrete and continuous forms and explain the similarities and differences between this method and a related, previously developed richness-based method. We also present new empirical techniques for applying the Price equation to ecological data. Our two demonstration analyses reveal how additive effects of increasing abundance on total function are modified by concurrent selection effects due to shifts in species' composition as well as intraspecific change in species' per capita function. The ecological Price equations derived here complement existing approaches and together offer BEF researchers analytical tools and a unifying framework for studying BEF in observational community data.