Modeling Microbial Interactions across Nutritional Environments using Maximum Entropy

Abstract

Microbial communities have exponential capacity for complexity. (In principle, among k species, each of (2∧k - 1) subsets (every pair, triplet, or larger group up to size k) could modulate the consortium's macroscopic dynamics.) Indeed, recent studies on synthetic communities have argued that high-dimensional (many-species) interactions dominate communal function. Here we explore a contrasting view. Despite the combinatorial potential for multiscale interactions, two features of microbial social life—localized diffusion of intercellular signals and prevalent evolutionary incentives for trophic specialization—provide some physical grounds for relatively low-dimensional behavior. We show how a commonly-used null model used to interpret consortial function can misidentify low-order dynamics as high-dimensional. As an alternative, we develop a mechanism-free model of microbial interactions based on the principle of maximum entropy. The model encodes the effects of potential species interactions via correlated random variables governed by a probability distribution informed by measurements. Our model is statistically-coherent, mathematically-flexible, and compatible with (though not limited to) plausible dynamics of bacterial growth. We test the model using data on microbial growth across carbon sources from a recent droplet microfluidics technology that enables wide sampling over the space of microbial compositions. Over hundreds of synthetic small-scale synthetic communities, our model better generalizes over carbon sources in capturing more nonlinear structure of interactions relative to a set of alternative models. The model's failures identify intriguing ecological behavior. These results highlight the potential predictability of some microbial ecosystems from limited measurements. These ideas also show a framework to identify genuinely emergent interactions in a statistically-principled fashion.