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 ecological distribution of growth surplus 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 environmental 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. 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.