Cross-feeding is not necessarily evolutionarily stable

Cross-feeding is widely observed in microbial communities. Intuitively, cross-feeding provides mutual benefits: one species exports metabolic waste which can be taken up and utilized by another species. However, it remains unclear whether mutually beneficial cross-feeding is evolutionarily stable in the face of mutations, invasion by other species, and the cost of transporting metabolites. To address this question, we constructed a minimum metabolic model of cross-feeding, with trade-offs in enzyme allocation and reversible energy-producing reactions. The population dynamics of this system in a chemostat reveal that cross-feeding is evolutionarily unstable. Instead, we find stable coexistence between a species that exports an intermediate and a species that consumes the same nutrient but processes the intermediate. We show why cross-feeding is unstable for this system, and generalize our results for the coexistence of different consumption strategies to multi-step reactions. Further, we identify a scaling relation for the population ratios of coexisting species at large nutrient supply. In summary, our model reveals that cross-feeding is not necessarily evolutionarily stable, and identifies a mechanism for coexistence based on species polluting their own metabolic environment.