Dynamics of a contact process with ontogeny

Abstract

We propose a simple model of how sessile organisms grow, disperse, and die. Our model extends the contact process to include a spatially explicit representation of organismal growth in addition to the familiar terms denoting reproduction and mortality. We develop a size-structured mean field theory which predicts an oscillatory phase as a consequence of excess reproduction. Monte Carlo simulations of a spatial implementation show instead a transition from a dilute to a ring-like phase. The ring-like phase arises as a consequence of the competition for limited space among juvenile and mature organisms, i.e., the ecological cost of reproduction. We also calculate the phase transition between life and death in the spatial model and find that it is in the same universality class as directed percolation. Finally, we analyze the onset of the ring-like phase via a spatial autocorrelation and comment on the model's applicability to problems in the study of ecosystem structure and dynamics.