Introduction

The relationship between the dynamics of animal populations and the variability of their environment is a central concern of applied and theoretical ecology, if only due to the long-standing debate over the roles of density-dependent and density-independent factors in determining animal abundance (e.g. Sæther 1997). There is a gradation between predictable environments and those that are highly variable that is quite apart from the gradation between cold or wet environments and those that are hot or dry. Much of southern and central Australia is characterized by extreme climatic variability. The coefficient of variation in summer rainfall, for example, can be close to unity. In these environments, models of wildlife population dynamics have emphasized the numerical response (Solomon 1949) to variable resources, rather than density-dependent processes. This is the approach that was taken by Caughley (1987a) and subsequently used by others to analyse the population dynamics of both native and introduced herbivores in Australia (Cairns & Grigg 1993; Caley 1993; Choquenot 1998; Pech & Hood 1998; Pech et al. 1999; Brown & Singleton 1999; Cairns et al. 2000). In each case the authors proposed a numerical response of the herbivore to either rainfall or pasture biomass. Pech & Hood (1998) used a similar form of the numerical response for the interaction of red fox populations with their prey.

The change in the numbers of a predator in response to the density of its prey was termed the ‘numerical’ response by Solomon (1949).