Estimating the probability of coexistence in cross-feeding communities. (7th November 2016) - Vessman, Björn; Gerlee, Philip; Lundh, Torbjörn
Abstract: The dynamics of many microbial ecosystems are driven by cross-feeding interactions, in which metabolites excreted by some species are metabolised further by others. The population dynamics of such ecosystems are governed by frequency-dependent selection, which allows for stable coexistence of two or more species. We have analysed a model of cross-feeding based on the replicator equation, with the aim of establishing criteria for coexistence in ecosystems containing three species, given the information of the three species' ability to coexist in their three separate pairs, i.e. the long term dynamics in the three two-species component systems. The triple-system is studied statistically and the probability of coexistence in the species triplet is computed for two models of species interactions. The interaction parameters are modelled either as stochastically independent or organised in a hierarchy where any derived metabolite carries less energy than previous nutrients in the metabolic chain. We differentiate between different modes of coexistence with respect to the pair-wise dynamics of the species, and find that the probability of coexistence is close to 1 2 for triplet systems with three pair-wise coexistent pairs and for the so-called intransitive systems. Systems with two and one pair-wise coexistent pairs are more likely to exist for random interaction parameters, but are on the other hand much less likely to exhibit triplet coexistence. Hence we conclude that certain species triplets are, from a statistical point of view, rare, but if allowed to interact are likely to coexist. This knowledge might be helpful when constructing synthetic microbial communities for industrial purposes. Abstract : Highlights: This manuscript investigates the likelihood of coexistent triplets of cross-feeding species, based on the species' pair-wise interactions. The analysis is based on qualitative information about the pair-wise interactions between the species. The analysis shows that three species that coexist pair-wise and intransitive triplets of species are likely to exhibit coexistence. This information could be valuable when synthetic microbial communities are to be constructed.