Vertically transmitted symbionts in structured host metapopulations

We develop a structured metapopulation model for vertically transmitted symbionts in natural host populations. We focus primarily on two questions: Are mutualism and high transmission probability prerequisites for the survival of symbionts in structured host metapopulations? What are the ecological conditions under which coexistence of infected and uninfected hosts is possible? We start with studying in depth the case of qualitatively identical patches and derive conditions for invasion and coexistence of uninfected and infected hosts. Our model predicts that, in a qualitatively uniform environment, coexistence is possible only if the symbionts increase the fitness of their host, so the mutualism is indeed needed for coexistence. We also prove that evolution selects for 100% infection frequency in the metapopulation. Then we generalize the model for different patch qualities and get conditions for invasion in a virgin environment.