From Lotka–Volterra to Arditi–Ginzburg: 90 Years of Evolving Trophic Functions
Yu. V. Tyutyunov, Lyudmila I. Titova
Abstract
The trophic function, often called a “functional response,” determines qualitative properties in models of predator–prey dynamics. Many of the theoretical and empirical studies have demonstrated the problem of choosing and fitting a trophic function to experimental data. Notably the publication by Arditi and Ginzburg (1989) has stimulated a lively debate in scientific literature regarding the application of trophic functions. The authors highlighted contradictions between the observed dynamics of natural ecosystems and the qualitative properties of predator–prey models using Holling-type trophic functions. They suggested revising the theoretical models by means of the trophic functions that depend on the ratio of prey to predator abundances. By comparing this and other proposed trophic functions, we demonstrate that the Arditi–Ginzburg function offers the simplest way of accounting for mutual interference in predator–prey models. This trophic function effectively resolves contradictions between theoretical models and natural systems, including the paradox of enrichment, paradox of biological control, and the paradoxical enrichment response mediated by trophic cascades. We review the debate regarding the Arditi–Ginzburg model and present recent results obtained with continuous and individual-based models of animal foraging behaviour in predator–prey systems, which explain predator interference as an emerging property.