Normative assembly rule reveals fairness in microbial communities.

Understanding and predicting how communities assemble is a paramount challenge in ecology. Here we address these questions normatively by comparing the observed species abundance distribution to a game-theoretically fair distribution based on each species' Shapley value. By analyzing in total 56 distinct community outcomes, we assess how fairly biomass is distributed in microbial communities displaying both competitive and cooperative interactions in different growth conditions. We find examples of fair communities that closely follow their Shapley value across all environments as well as counterexamples where the true abundances deviate from the species' objective contribution to community biomass. Next, we develop a fair assembly rule based on the recursive definition of Shapley value and show that also unfair community compositions are consistent with the principles of fair assembly after the lower-level competitive outcomes are known. Our results give unique empirical insights into the distributive function of ecological dynamics and lay down the theoretical foundations of what might become a normative community assembly theory.