Reinterpreting space, time lags, and functional responses in ecological models.

Natural enemy-victim interactions are of major applied importance and of fundamental interest to ecologists. A key question is what stabilizes these interactions, allowing the long-term coexistence of the two species. Three main theoretical explanations have been proposed: behavioral responses, time-dependent factors such as delayed density dependence, and spatial heterogeneity. Here, using the powerful moment-closure technique, we show a fundamental equivalence between these three elements. Limited movement by organisms is a ubiquitous feature of ecological systems, allowing spatial structure to develop; we show that the effects of this can be naturally described in terms of time lags or within-generation functional responses.