Abstract
A fundamental question in ecology is the generation and maintenance of biodiversity. Classical approaches consider multi-species communities with Lotka-Volterra ODE models where inter- vs. intra-species interactions are key. Typically in high-dimensional systems, analysis is hard and model reduction is needed. Here, we describe and study a new system of multi-type interactions that arise in co-colonization, and develop a useful model reduction framework based on slow-fast dynamics under quasi-neutrality. We show that in a multi-type, Susceptible-Infected-Susceptible (SIS) system with co-colonization, neutral coexistence dynamics between N closely related strains occurs on a fast timescale, based on mean trait values, whereas the non-neutral selective forces act on a slow timescale, driven by the variance and asymmetries of the co-colonization interaction matrix. The explicit N equations for relative type frequencies on the slow manifold enable efficient computation of complex multi-strain dynamics, and provide analytical insight into high-dimensional community ecology, with potential applications to other multi-body systems.