A damage spreading transition in a stochastic host–pathogen system

Abstract

One of the leading proposals for solving the biodiversity problem is the Janzen–Connell hypothesis, suggesting that the abundance of a species is limited by a host-specific exploiter. Motivated by this model, here we analyze a spatially explicit host–pathogen system, looking for coexistence conditions under stochastic dynamics. Above the standard extinction transition associated with the failure of the pathogen to invade, we report another, damage spreading transition, marking the point where macroscopic clusters of host individuals disappear. Beyond its practical significance, this transition is apparently a generic landmark along the axis of decreasing stochasticity, if the deterministic dynamics support cycles or quasicycles.