The Structural Stability of a Three-Species Food Chain Model

Abstract

A three-species food-chain model which was previously shown to exhibit chaotic dynamics was revisited. By exploring the sensitivity of that result this study found that complex behaviour depended on the functional form chosen to model the interaction between the two highest species in the food chain. Two separate scenarios were explored: the gradual addition of refugia modeling the escape from predation at low prey densities; and the gradual addition of predator interference modeling territorial behaviour. The addition of even a small amount of refugia provided a stabilizing influence as the chaotic dynamics collapsed to stable limit cycles. The results of adding interference to the model were more complex. Although the numerical simulations indicated that a low level of interference provided a stabilizing influence, the analytical results suggest that complex dynamics are possible for a range of parameter values that are biologically relevant. The sensitivity of the stability profile to functional changes in the model suggests two important ecological motivations for structural stability analysis. First, in ecological systems, environmental fluctuations cause continuous changes in the functional relationships between and within species, resulting in potential changes in the complexity of the dynamics over time. Second, slight changes in ecological structure may cause significant bifurcations; however, most ecological data are inadequate to distinguish such phenomena.