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 abundance1-4. 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

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... w, biomass and abundance by combining results from the Maximum Entropy Theory of Ecology5-7 and the Metabolic Theory of Ecology8,9. 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 predicting 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.