Model description of dynamics of disturbance and recovery of natural landscapes

We consider the dynamic simulation model of landscapes proposed by Turner et al. (1993). In this model a 'landscape', represented by a square grid of 100×100 cells, is exposed to disturbances of a fixed size at random locations at specified time intervals. The affected area recovers through a series of seral stages and achieves a mature stage unless it is affected again by successive disturbances. Two non-dimensional parameters, determining the dynamics of the model, are T, the ratio of the disturbance interval to the time of recovery and S, the ratio of the size of the disturbance to the size of the landscape. The main outcomes of analysis are the means and standard deviations of the areas occupied by different seral stages. We show that these characteristics of the system can be calculated analytically. This facilitates the understanding of the results of the computer experiments, the analysis of the asymptotic behaviour of the system (for example when the disturbances become increasingly small but very frequent, T,S1) and of more complex regimes of external disturbances, e.g., of the combined effects on a landscape from several types of disturbances with different spatial and time scales.[PUBLICATION ABSTRACT]