Optimal transportation theory for species interaction networks

1. Observed biotic interactions between species, such as in pollination, predation, and competition, are determined by combinations of population densities, matching in functional traits and phenology among the organisms, and stochastic events (neutral effects). 2. We propose optimal transportation theory as a unified view for modeling species interaction networks with different intensities of interactions. We pose the coupling of two distributions as a constrained optimization problem, maximizing both the system's average utility and its global entropy, that is, randomness. Our model follows naturally from applying the MaxEnt principle to this problem setting. 3. This approach allows for simulating changes in species relative densities as well as to disentangle the impact of trait matching and neutral forces. 4. We provide a framework for estimating the pairwise species utilities from data. Experimentally, we show how to use this framework to perform trait matching and predict the coupling in pollination and host–parasite networks.