Combining endogenous and exogenous spatial variability in analytical population models

Abstract

Analytically tractable models of dynamics in continuous space rarely incorporate both endogenous and exogenous spatial heterogeneity. We use spatial moment equations in combination with simulation models to analyze the combined effects of endogenous and exogenous variability on population viability in a simple single-population model where landscape heterogeneity and local population density both affect mortality rate. The equations partition the effects of heterogeneity into an effect of local crowding and an effect of habitat association caused by differential mortality. Exogenous heterogeneity in mortality rate increases population viability through habitat association and decreases it through increased crowding; the net effect of exogenous heterogeneity is generally to improve population viability. This result is contrary to some (but not all) conclusions in the literature, which usually focus on the effects of fragmentation rather than the benefits of refuges to short-dispersing individuals.