Complex dynamics in coevolution models with ratio-dependent functional response

Abstract

We explore the complex dynamical behavior of two simple predator–prey models of biological coevolution that on the ecological level account for interspecific and intraspecific competition, as well as adaptive foraging behavior. The underlying individual-based population dynamics are based on a ratio-dependent functional response [Getz, W.M., 1984. Population dynamics: a per capita resource approach. J. Theor. Biol. 108, 623–643]. Analytical results for fixed-point population sizes in some simple communities are derived and discussed. In long kinetic Monte Carlo simulations we find quite robust, approximate 1 / f noise in species diversity and population sizes, as well as power-law distributions for the lifetimes of individual species and the durations of periods of relative evolutionary stasis. Adaptive foraging enhances coexistence of species and produces a metastable low-diversity phase and a stable high-diversity phase.