Towards a mathematical understanding of colonization resistance

Abstract

Microbial community composition and dynamics are key to health and disease. Explaining the forces generating and shaping diversity in the microbial consortia making up our body’s defenses is a major aim of current research in microbiology. For this, tractable models are needed, that bridge the gap between observations of patterns and underlying mechanisms. While most microbial dynamics models are based on the Lotka-Volterra framework, we still do not have an analytic notion of colonization resistance, by which a microbial system’s fitness as a whole can be understood. Here, we propose a modeling framework where similar species interact with each other at the micro-scale through a co-colonization interaction network encompassing competition and cooperation. This model is based on a generic notion of shared resources between species, affords explicit mathematical results for frequency-dependent dynamics among N species, and offers a precise definition of colonization resistance, directly related to Fisher’s fundamental theorem. We contend this approach can be a powerful new tool to model, test and validate interaction networks in complex microbial consortia, and quantify their role in colonization resistance and system invasibility.