The ratio of single to co‐colonization is key to complexity in interacting systems with multiple strains

Abstract

Abstract The high number and diversity of microbial strains circulating in host populations have motivated extensive research on the mechanisms that maintain biodiversity. However, much of this work focuses on strain‐specific and cross‐immunity interactions. Another less explored mode of pairwise interaction is via altered susceptibilities to co‐colonization in hosts already colonized by one strain. Diversity in such interaction coefficients enables strains to create dynamically their niches for growth and persistence, and “engineer” their common environment. How such a network of interactions with others mediates collective coexistence remains puzzling analytically and computationally difficult to simulate. Furthermore, the gradients modulating stability‐complexity regimes in such multi‐player endemic systems remain poorly understood. In a recent study (Madec & Gjini, Bulletin of Mathematical Biology, 82), we obtained an analytic representation for N‐type coexistence in an SIS epidemiological model with co‐colonization. We mapped multi‐strain dynamics to a replicator equation using timescale separation. Here, we examine what drives coexistence regimes in such co‐colonization system. We find the ratio of single to co‐colonization, µ, critically determines the type of equilibrium and number of coexisting strains, and encodes a trade‐off between overall transmission intensity R0 and mean interaction coefficient in strain space, k. Preserving a given coexistence regime, under fixed trait variation, requires balancing between higher mean competition in favorable environments, and higher cooperation in harsher environments, and is consistent with the stress gradient hypothesis. Multi‐strain coexistence tends to steady‐state attractors for small µ, whereas as µ increases, dynamics tend to more complex attractors. Following strain frequencies, evolutionary dynamics in the system also display contrasting patterns with µ, interpolating between multi‐stable and fluctuating selection for cooperation and mean invasion fitness, in the two extremes. This co‐colonization framework could be applied more generally, to study invariant principles in collective coexistence, and to quantify how critical shifts in community dynamics get potentiated by mean‐field and environmental gradients.

Keywords

• co‐colonization
• complexity
• cooperation‐competition
• evolution
• multi‐species dynamics
• single‐to‐coinfection ratio