Introduction

A class of spatially explicit models, the grid-based simulation models, has proved valuable for dealing with problems on large temporal scales, and where complex interactions depend on coincidences in time and space (Menaut et al., 1990; Wiegand et al., 1995; Thiéry et al., 1995; Jeltsch et al., 1996, 1997a; Wiegand and Milton, 1996). Most of the grid-based models applied to vegetation dynamics in semiarid systems represent an advanced form of cellular automata models (Wolfram, 1986). These models typically subdivide a modelled area by a grid of spatial subunits, socalled ‘cells’. Each cell is characterized by its location and by one or more discrete ecological states which may change in the course of time due to the influence of (1) neighbouring cells, (2) the previous state of the cell itself and (3) of such external factors as climate, disturbance or management actions. The size of these spatial subunits is determined by the initial question to be addressed by the model, and is usually based on typical biological scales of the modelled system, for example the size of individual plants, characteristic distances for seed dispersal or typical ranges of plant interactions (Jeltsch and Wissel, 1994; Wiegand et al., 1995; Jeltsch et al., 1996, 1997a).

Grid-based models such as those of Wiegand et al. (1995) and Wiegand and Milton (1996) focus on the processes and mechanisms that drive community dynamics at the level of individual plants. Although there are usually few long-term field data available on the dynamics of arid plant communities, such rainfall-dependent lifehistory attributes as growth, seed production, germination, recruitment and mortality factors, and seed dispersal and interactions between individual species, are relatively easy to observe on shorter timescales.