A Pair-Approximation Model for Spatial Patterns in Tree Populations with Asymmetrical Resource Competition

A pair-approximation model for the spatial dynamics of a height-structured tree population is defined on a regular lattice where each site can be in 1 of 3 states: empty (gap site), occupied by an immature tree, and occupied by a mature tree. The nonlinearities are associated with resource competition effects of mature trees on immature ones (asymmetric competition) affecting the mortality of the latter but not their growth. The survival--extinction transition of the forest is expressed; the early dynamics of colonization are described in terms of local densities. Predictions of the pair-approximation model are compared with results from numerical simulations of cellular automata.