A dynamical system for neighborhoods in plant communities

How should plant ecologists scale up from the fine-scale events affecting individual plants in small neighborhoods to the coarse-scale dynamics of plant communities? We give here a dynamical system, derived from an individual-based model, that captures the main effects of spatial structure. The individual-based model describes a multispecies plant community, living in a spatial domain, containing plants that (1) reproduce and die with rates that depend on other individuals in a specified neighborhood, and (2) move through seed dispersal and clonal growth. Over the course of time, substantial spatial structure can build up in such a community due to local interactions and dispersal. The dynamical system describes how the structure of local neighborhoods changes over time, using the first and second spatial moments of the individual-based model. We show, by means of an example of two competing species, that the dynamical system gives a close approximation to the behavior of the underlying individual- based model, and that the changes in local spatial structure as time progresses have fundamental effects on the dynamics.
KEYWORDS: Community dynamics; Competition; Competitive exclusion; Dispersal; Dynamical systems; Individual-based models; Moment dynamics; Plant's-eye view; Reproduction; Seed dispersal; Spatial ecology; Stochastic processes.

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