Nearest-neighbor interactions, habitat fragmentation, and the persistence of host-pathogen systems.

Spatial interactions are known to promote stability and persistence in enemy-victim interactions if instability and extinction occur in well-mixed settings. We investigate the effect of spatial interactions in the opposite case, where populations can persist in well-mixed systems. A stochastic agent-based model of host-pathogen dynamics is considered that describes nearest-neighbor interactions in an undivided habitat. Contrary to previous notions, we find that in this setting, spatial interactions in fact promote extinction. The reason is that, in contrast to the mass-action system, the outcome of the nearest-neighbor model is governed by dynamics in small "local neighborhoods." This is an abstraction that describes interactions in a minimal grid consisting of an individual plus its nearest neighbors. The small size of this characteristic scale accounts for the higher extinction probabilities. Hence, nearest-neighbor interactions in a continuous habitat lead to outcomes reminiscent of a fragmented habitat, which is underlined further with a metapopulation model that explicitly assumes habitat fragmentation. Beyond host-pathogen dynamics, axiomatic modeling shows that our results hold for generic enemy-victim interactions under specified assumptions. These results are used to interpret a set of published experiments that provide a first step toward model testing and are discussed in the context of the literature.