Simple testing procedures for the Holling type II model

Abstract

In this paper, we consider predator-prey data that can be viewed as solutions to a planar system of ordinary differential equations (ODE) observed with random error. The ODE system admits a limit cycle, while the random error is supposed to act additively in the log-scale. One of the oldest such systems is Holling's type II model. In spite of its simplicity, it is still very popular in data analyses, although more sophisticated models have been introduced in the literature. We propose a simple way of deciding whether a set of predator-prey pairs is indicative or not of a departure from this basic model by exploiting the geometric properties of the solution in the phase plane. To illustrate our method, we use simulated and real data.