Forest spatial dynamics with gap expansion: Total gap area and gap size distribution

Recent studies on forest dynamics in diverse forested ecosystems suggest that forest stands are disturbed more frequently if they are next to existing gaps, and that gaps once formed tend to expand their area in subsequent years. We examine total gap area and the size distribution of gaps at equilibrium in a lattice-structured forest model. Each site undergoes transition between two states (gaps and non-gaps), and the disturbance rate (transition from non-gap to gap) increases with the number of gap sites in the neighborhood. Dynamics based on a mean-field approximation (i.e. neglecting of spatial structure) failed to predict total gap area and the gap size distribution in the equilibrium forest. Pair approximation, which considers a closed dynamical system of average and local gap density (the conditional gap density among neighbors of a randomly chosen gap site), can predict the total gap area, the correlation between neighbors, and the gap size distribution fairly accurately. If the recruitment rate increases in proportion to non-gap area in the forest, the model may show bistability. We analyse data on forest spatial dynamics in the light of the model. We conclude that gap size distribution can often be described using two statistics (global and local gap densities) and that these in turn can be predicted by the dynamics of gap formation, gap expansion, regeneration, and gap closure.