Stability of Cross-Feeding Polymorphisms in Microbial Communities

Cross-feeding, a relationship wherein one organism consumes metabolites excreted by another, is a ubiquitous feature of natural and clinically-relevant microbial communities and could be a key factor promoting diversity in extreme and/or nutrient-poor environments. However, it remains unclear how readily cross-feeding interactions form, and therefore our ability to predict their emergence is limited. In this paper we developed a mathematical model parameterized using data from the biochemistry and ecology of an E. coli cross-feeding laboratory system. The model accurately captures short-term dynamics of the two competitors that have been observed empirically and we use it to systematically explore the stability of cross-feeding interactions for a range of environmental conditions. We find that our simple system can display complex dynamics including multi-stable behavior separated by a critical point. Therefore whether cross-feeding interactions form depends on the complex interplay between density and frequency of the competitors as well as on the concentration of resources in the environment. Moreover, we find that subtly different environmental conditions can lead to dramatically different results regarding the establishment of cross-feeding, which could explain the apparently unpredictable between-population differences in experimental outcomes. We argue that mathematical models are essential tools for disentangling the complexities of cross-feeding interactions.Author Summary: Simple environments, even those used in laboratory experimental evolution, have proven vastly richer than originally thought, capable of generating and supporting genetic and phenotypic diversity. This was not foreseen by Gause’s seminal competitive exclusion theory, which predicted that simple single niche environments cannot support diversity. We now know that cross-feeding interactions can be a major driver of diversity maintenance in simple environments. Cross-feeding, a relationship wherein one organism consumes metabolites excreted by another, is a ubiquitous feature of natural and clinically-relevant microbial communities and even tumour cell populations. However, it remains unclear how readily such relationships form, and therefore our ability to predict their emergence is limited. Here we developed a mathematical model of cross-feeding and find that this system can display complex dynamics including multi-stable behaviour separated by a critical point. Therefore, the emergence of cross-feeding depends on complex interplay between density and frequency of competitors. Moreover we predict that small changes in environmental conditions can cause abrupt and irreversible shifts from cross-feeding permissive to cross-feeding prohibitive states. We argue that mathematical models are essential tools for disentangling the complexities of cross-feeding interactions.