Forest gap dynamics with partially synchronized disturbances and patch age distribution

Many mathematical or computer simulation models for forest gap dynamics assume an ensemble of independent patches. However, global or regional scaled fluctuation of weather would result in gap formation partially synchronized over distant patches. In addition, forest fire, land slide, and pest outbreak produce a spatially clumped disturbance. In this paper we study a simple mathematical model for forest gap dynamics in which gap formation in different patches tends to be synchronized. We trace the distribution of “age” of patches defined as the time since the latest disturbance by assuming that the age controls the biomass, productivity, species composition, etc., in the patch. Years of unfavorable climate come at random times, and in each of these years, a fraction of patches are disturbed. Then the states of distant patches that never interact with each other may become strongly correlated. If the biomass in a patch is a function of time since the latest disturbance, the degree of fluctuation in the total biomass in the forest may be much larger if gaps are formed more synchronously. Maximum likelihood estimate of the parameters from the age distribution of patches is given. We also analyzed the case in which disturbance events occur at a constant rate, and where each event resets all the patches within a circle centered at a randomly chosen location. This would produce a between-patch correlation that decreases with the distance.