PARTIAL-DIFFERENTIAL EQUATIONS IN ECOLOGY - SPATIAL INTERACTIONS AND POPULATION-DYNAMICS

Most of the fundamental elements of ecology, ranging from individual b ehavior to species abundance, diversity, and population dynamics, exhi bit spatial variation. Partial differential equation models provide a means of melding organism movement with population processes and have been used extensively to elucidate the effects of spatial variation on populations. While there has been an explosion of theoretical advance s in partial differential equation models in the past two decades, thi s work has been generally neglected in mathematical ecology textbooks. Our goal in this paper is to make this literature accessible to exper imental ecologists. Partial differential equations are used to model a variety of ecological phenomena; here we discuss dispersal, ecologica l invasions, critical patch size, dispersal-mediated coexistence, and diffusion-driven spatial patterning. These models emphasize that simpl e organism movement can produce striking large-scale patterns in homog eneous environments, and that in heterogeneous environments, movement of multiple species can change the outcome of competition or predation .