An equation of state unifies diversity, productivity, abundance and biomass

Combining metabolic and maximum entropy theories of ecology, the authors derive an equation of state capable of capturing the relationships between multiple ecological variables across varied spatial scales and habitats. To advance understanding of biodiversity and ecosystem function, ecologists seek widely applicable relationships among species diversity and other ecosystem characteristics such as species productivity, biomass, and abundance. These metrics vary widely across ecosystems and no relationship among any combination of them that is valid across habitats, taxa, and spatial scales, has heretofore been found. Here we derive such a relationship, an equation of state, among species richness, energy flow, biomass, and abundance by combining results from the Maximum Entropy Theory of Ecology and the Metabolic Theory of Ecology. It accurately captures the relationship among these state variables in 42 data sets, including vegetation and arthropod communities, that span a wide variety of spatial scales and habitats. The success of our ecological equation of state opens opportunities for estimating difficult-to-measure state variables from measurements of others, adds support for two current theories in ecology, and is a step toward unification in ecology.

Automated summary

By combining the Maximum Entropy Theory of Ecology and the Metabolic Theory of Ecology, the authors have derived an equation of state that accurately captures the relationships among various ecological variables in 42 datasets, spanning different spatial scales and habitats, providing opportunities for estimating difficult-to-measure state variables and supporting current ecological theories.