The authors study a nonlinear, discrete time, integro-difference equation as a model of population dynamics in which population growth and dispersal phases are separated in time. The model is assumed to have a dispersal kernel of compact support since the authors are particularly interested in patch fragmentation and boundary effects. Mathematically, they study the existence, uniqueness and stability of equilibrium solutions and relate their results to conclusions concerning how population “persistence” (i.e., survivability in an equilibrium sense) depends on spatial scales of dispersal distances and habitat sizes.
A bifurcation result is proved for a general model equation using the classical theory of integral operators. Selected examples are further studied using computer explorations. They conclude that “when organisms tend to disperse only a short distance, population persistence is dominated by local conditions in high quality patches, but when dispersal distance is relatively large, poor quality habitat exerts a greater influence”.