CIRCLES AND SPIRALS - POPULATION PERSISTENCE IN A SPATIALLY EXPLICIT PREDATOR-PREY MODEL

The primary aim of the work reported in this paper is to elucidate the relationship between discrete and continuous deterministic representa tions of spatial population processes. Our experimental vehicle is a s patially explicit version of the Rosenzweig-McArthur model with immobi le prey and a diffusively dispersing predator. We find that careful fo rmulation of the discrete representation leads to essentially complete behavioral concordance between the two representations. We examine th e invasions that follow localized introduction of predators into such a system and show that the biological realism of the model predictions can be greatly enhanced by preventing in situ regrowth of predator po pulations from densities that should be interpreted as representing lo cal extinction. We exploit the close concordance of behavior between c ontinuous and discrete representations by using the discrete version t o perform a wide range of numerical experiments on one-dimensional and two-dimensional systems, while turning to the continous version to pr ovide approximate analytic results for the natural time and space scal es of the predicted population patterns. We conclude by discussing the implications of our findings for the experimental and theoretical stu dy of spatial population dynamics.