Biodiversity and ecosystem function: making sense of numerous species interactions in multi-species communities

Understanding the biodiversity and ecosystem function relationship can be challenging in species-rich ecosystems. Traditionally, species richness has been relied on heavily to explain changes in ecosystem function across diversity gradients. Diversity-Interactions models can test how ecosystem function is affected by species identity, species interactions, and evenness, in addition to richness. However, in a species-rich system, there may be too many species interactions to allow estimation of each coefficient, and if all interaction coefficients are estimable, they may be devoid of any sensible biological meaning. Parsimonious descriptions using constraints among interaction coefficients have been developed but important variability may still remain unexplained. Here, we extend Diversity-Interactions models to describe the effects of diversity on ecosystem function using a combination of fixed coefficients and random effects. Our approach provides improved standard errors for testing fixed coefficients and incorporates lack-of-fit tests for diversity effects. We illustrate our methods using data from a grassland and a microbial experiment. Our framework considerably reduces the complexities associated with understanding how species interactions contribute to ecosystem function in species-rich ecosystems.