1. We consider the movement of carabid beetles in a fragmented woodland landscape. Landscape ecology has lacked a formal framework for the analysis of dynamics of this kind, and stochastic spatial simulations have generally been needed to gain insight.
2. We first define an individual-based stochastic model for movement in a heterogeneous landscape. From this a deterministic approximation is derived which describes the build-up in association of the beetles with their environment; the deterministic model makes use of a second-order spatial moment. It is shown that the results of the deterministic approximation match closely those of the underlying stochastic process. On this basis we suggest that the dynamical system provides a formal framework for the dynamics of animal movements in ecological landscapes.
3. The results show that the beetles, starting from an initial random layout, rapidly become associated with the woodlands and, by the time 100 days have elapsed, the association is close to its asymptotic state. The strength of the association depends very much on the spatial auto-covariance function of the environment.
4. A number of extensions are suggested, including landscapes comprising multiple habitats of different degrees of suitability, landscapes that change through human activity, birth and death processes of single species, and interactions between species. The method of moments provides a flexible basis for future work in this area.