Complex dynamics in coevolution models with ratio-dependent functional response

TL;DR

This paper investigates complex predator-prey dynamics in coevolution models incorporating ratio-dependent functional responses, revealing robust 1/f noise, power-law species lifetime distributions, and the effects of adaptive foraging on biodiversity.

Contribution

It introduces a detailed analysis of coevolution models with ratio-dependent responses, deriving analytical fixed points and exploring their dynamic behaviors through simulations.

Findings

Robust 1/f noise observed in species diversity and population sizes

Power-law distributions for species lifetimes and stasis periods

Adaptive foraging promotes coexistence and creates distinct biodiversity phases

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 [W.M. Getz, J. Theor. Biol. 108, 623 (1984)]. 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.