Population Growth in Space and Time: Spatial Logistic Equations

How great an effect does self-generated spatial structure have on logistic population growth? Results are described from an individual-based model (IBM) with spatially localized dispersal and competition, and from a deterministic approximation to the IBM describing the dynamics of the first and second spatial moments. The dynamical system incorporates a novel closure that gives a close approximation to the IBM in the presence of strong spatial structure. Population growth given by the spatial logistic model can differ greatly from that of the nonspatial logistic equation. Numerical simulations show that populations may grow more slowly or more rapidly than would be expected from the nonspatial model, and may reach their maximum rate of increase at densities other than half of the carrying capacity. Populations can achieve asymptotic densities substantially greater than or less than the carrying capacity of the nonspatial logistic model, and can even tend towards extinction. These properties of the spatial logistic model are caused by local dispersal and competition that affect spatial structure, which in turn affects population growth. Accounting for these local spatial processes brings the theory of single-species population growth a step closer to the growth of real spatially structured populations.