Space and stochasticity in population dynamics

摘要: Organisms interact with each other mostly over local scales, so the density experienced by an individual is of greater importance than mean in a population. This simple observation poses tremendous challenge to theoretical ecology, and because nonlinear stochastic spatial models cannot be solved exactly, much effort has been spent seeking effective approximations. Several authors have observed that population systems behave like deterministic nonspatial if dispersal averages dynamics sufficiently large scale. We exploit this fact develop exact series expansion, which allows one derive approximations individual-based without resorting heuristic assumptions. Our approach makes it possible calculate corrections mean-field limit where interaction range large, provides insight into performance moment closure methods. With approach, we demonstrate how buildup spatiotemporal correlations slows down spread invasion, prolongs time lags associated extinction debt, leads locally oscillating but globally stable coexistence host parasite.