A simulation model for a shrub ecosystem in the semiarid Karoo, South Africa

Ecology, Oct, 1995 by Thorsten Wiegand, Suzanne J. Milton, Christian Wissel

Key words: automata; event-driven system; individual-based simulation model; Karoo; nonequilibrium; semiarid ecosystem; spatial and temporal dynamics.

INTRODUCTION

Semiarid ecosystems are believed to be sensitive to climatic change and such forms of landuse as heavy grazing, ploughing, and strip mining (UNESCO 1980, Barrow 1991). Degradation and desertification in semiarid rangeland may be rapid, but recovery is slow because plant growth is rain limited and denudation reduces rainfall effectivity (Milton et al. 1994). The dominant species of semiarid plant ecosystems often have life-spans up to decades, so that changes in vegetation composition may take longer than human life-spans. Databases for assessing vegetation trends seldom exceed a few years. Because of the mismatch between time scales for observation and vegetation change (Scholes 1990), little is known about the dynamics of semiarid ecosystems over long temporal scales. Although models could address the problem of temporal and spatial dynamics. few have been attempted for semiarid ecosystems (Walker 1993).

Rangeland ecosystem models

The early model of rangeland dynamics, which still forms the basis of much current management, is a simple application of Clementsian theory of ecological succession (Clements 1916). This model assumes continuous and reversible transitions along a single, monotonic gradient between an overgrazed subclimax and an undisturbed climax state of vegetation and assumes that grazing and interannual variation in rainfall cause vegetation to change in the same way. Over the past decades this range succession model has been criticized because of its inability to deal with vegetation changes. especially in the arid and semiarid zones (Smith 1988, Walker 1988, Westoby et al. 1989, Friedel 1991). Instead of continuous and reversible transitions semiarid ecosystems typically show abrupt. discontinuous and irreversible transitions between discrete states. Walker 1993) pointed out, that "changes in the species composition of rangelands are commonly episodic, occurring in response to rare and extreme events, or more commonly, particular sequences of events such as a very dry year followed by a very wet year . . . In between such events, production will vary from year to year in response to variation in rainfall, but the composition of the rangeland remains essentially the same, and changes little in response to management . . . The reason for this episodic behaviour is that both successful reproduction, i.e.. establishment, and mortality in plants depend on particular conditions." He concluded that event-driven systems must be event managed and that being able to recognize the significant events is a key to successful rangeland management.

To deal with the complicated dynamics of semiarid and arid ecosystems, some range scientists (Smith 1988, Westoby et al. 1989, Milton and Hoffman 1994) suggested that these ecosystems could be described in terms of discrete states and interstate transitions. Transitions could be triggered by natural events (rainfall, drought, hail, fire) or by management actions (removal of herbivores, altered intensity or timing of herbivory, addition of fertilizer, burning). Such "state-and-transition" models are valuable tools for describing the structure of the ecosystem, but they provide little information applicable to forecasting and prediction. Some event-orientated grazing strategies make use of state-and-transition models and include information on the attributes of the most important species of the ecosystem (Hodgkinson 1992) and their response to grazing. However, additional models that improve the user's understanding of ecosystem dynamics over a long temporal scale are needed to identify significant events that drive semiarid ecosystems.

The "gap dynamics approach" to modelling plant community dynamics focuses on resource space associated with individual plants and simulates establishment, growth, and death of individuals on a small isolated plot through time (Coffin and Lauenroth 1990). This approach has been used for analyzing temporal and spatial pattern in semiarid grassland and temperate and tropical forests (Coffin and Lauenroth 1990, Belsky and Canham 1994, Shugart 1984). The model presented by Coffin and Lauenroth (1990) incorporates effects of small-scale disturbances and stochastic environmental factors, but does not consider spatially explicit processes and interactions between plots.

"Dynamic automata" models, recently developed by Jeltsch and Wissel (1993a, 1994), are appropriate for systems characterized by distinct spatial pattern and spatial interactions. They extended the method of cellular automata (Wolfram 1986) by including autonomous dynamics of a local cell so as to model the temporal and spatial dynamics of forests on a large spatial scale. Fundamental to dynamic automata models is the division of space into small subunits (Wissel 1991, 1992, Wissel and Jeltsch 1993), the cells. Each cell can exist in a variety of states, chosen depending on the aim of the model and the knowledge available for defining possible states. The states change over time according to predefined rules formulated from empirical and anecdotal knowledge. In contrast to cellular automata models, where the state of any one cell in the next time step depends only on its present state and on the state of some of its neighboring cells (Molofsky 1994), dynamic automata models assume autonomous dynamics of local cells that can be influenced by the states of neighboring cells and by such external factors as rainfall, disturbances, or management actions. The size of cells and the length of the time steps are chosen in accordance with the aim of the model and the question being investigated.