3 Continuous-Space Models for Population Dynamics

This chapter provides an overview of models for ecological dynamics in continuous space, while focusing on spatial rather than landscape ecology. In particular, it explores spatial moment equations, a relatively new framework for analyzing spatial dynamics in terms of mean population densities and spatial covariances. The chapter also gives a sample derivation of a set of spatial moment equations; summarizes various applications of moment equations for single-species and community dynamics; contrasts the strengths and weaknesses of the approach with other frameworks such as PDEs and IPSs; and discusses future directions and potential of spatial moment equations. Although this chapter concentrates on the effects of endogenous rather than exogenous variability, it also describes some strategies for incorporating both kinds of heterogeneities and bridging the gap between spatial and landscape ecology. Spatial moment equations are a powerful tool for this task; other advantages include preservation of the spatial and stochastic character of ecological systems; analytical tractability; and simple connections to field data on individual dispersal and performance and to well-established spatial statistical measures.