On the growth of locally interacting plants: differential equations for the dynamics of spatial moments

Ecologists are faced with the challenge of how to scale up from the activities of individual plants and animals to the macroscopic dynamics of populations and communities. It is especially difficult to do this in communities of plants where the fate of individuals depends on their immediate neighbors rather than an average over a larger region. This has meant that algorithmic, agent-based models are typically used to understand their dynamics, although certain macroscopic models have been developed for neighbor-dependent, birth-death processes. Here we present a macroscopic model that, for the first time, incorporates explicit, gradual, neighbor-dependent plant growth, as a third fundamental process of plant communities. The model is derived from a stochastic, agent-based model, and describes the dynamics of the first and second spatial moments of a multispecies, spatially structured plant community with neighbor-dependent growth, births, and deaths. A simple example shows that strong neighborhood space-filling during tree growth in an even-aged stand of Scots pine is well captured by the spatial-moment model. The space-filling has a spatial signature consistent with that observed in several field studies of forests. Small neighborhoods of interaction, nonuniform spacing of trees, and asymmetric competition all contribute to the buildup of a wide range of tree sizes with some large dominant individuals and many smaller ones.