A model for the evolutionary dynamics of cross-feeding polymorphisms in microorganisms

Understanding mechanisms of evolutionary diversification is central to evolutionary biology. Microbes constitute promising model systems for observing processes of diversification directly in the laboratory. One of the main existing paradigms for microbial diversification is the evolution of cross-feeding polymorphisms, in which a strain specializing on a primary resource coexists with a cross-feeding strain that specializes on a waste product resulting from consumption of the primary resource. Here I propose a theoretical model for the evolutionary dynamics through which cross-feeding polymorphisms can gradually emerge from a single ancestral strain. The model is based on the framework of adaptive dynamics, which has proved to be very useful for studying adaptive processes of divergence under sympatric conditions. In particular, the phenomenon of evolutionary branching serves as a general paradigm for diversification. I show that evolutionary branching naturally occurs in evolutionary models of cross-feeding if (1) there is a trade-off between uptake efficiencies on the primary and secondary resources, and (2) this trade-off has positive curvature. The model also suggests that the evolution of cross-feeding should be more likely in chemostat cultures than in serial batch cultures, which conforms with empirical observations. Overall, the model provides a theoretical metaphor for the evolution of cross-feeding polymorphisms.