The Karoo model

One early example of this approach is a model developed in the mid-1990s by T. Wiegand, S.J. Milton, and colleagues describing the community dynamics of a shrub community in the semiarid Karoo, South Africa (Figure 4). The model is based on detailed life-history data for the five dominant species and on monthly long-term rainfall data for this region. Growth, death, seed production, germination, and seedling establishment of individual shrubs are modeled over long timescales in monthly time-steps under the influence of the stochastic and unpredictable rainfall. Observed spatial relationships, for example, on establishment, are used as rules (Figure 4b), instead of attempting to model them on a detailed mechanistic basis. This is an important feature of this model type, making models simple but structurally realistic.

The model shows that the dynamics of the ungrazed shrub community are typified by episodic and discontinuous changes in species composition with intervening quasi-stable phases lasting some decades (Figures 5a and 5b). The reason for this episodic behavior is that rainfall allows for recruitment only in a few years (Figure 5b) and sufficient space must be available to create low-competition sites for recruitment. Reduced seed production due to sheep grazing reduces the potential of palatable species to recruit and causes substantial changes in species composition toward unpalatable species (Figure 5b). Once a long-lived cohort of unpalatable shrubs is established, low-competition sites become rare and palatable species cannot respond to favorable rain sequences with recruitment, even if grazing pressure is relaxed. Therefore, rehabilitation after overgrazing may last several decades until cohorts ofunpalatable shrubs die.

The rule-based approach is quite flexible and can also be extended to situations where different life forms occur at different scales. Examples are a model developed by F. Jeltsch and colleagues on the Savanna dynamics and bush encroachment in the semiarid Kalahari. In this model, space is represented as a grid of cells 5 m x 5 m in size. Each cell contains information on the life-form classes locally present (trees, shrubs, perennial gasses and herbs, annuals). In an annual time step, the spatial vegetation changes in response to rainfall, interactions among vegetation in different cells, and to grazing and fire. In a series of analyses, the model was used to investigate the coexistence of woody and grassy plants, and to study scenarios of increased shrub encroachment (at the expense of grassy vegetation) due to grazing.

In the 2000s F. D. Richardson and colleagues analyzed a detailed model that simulated a semiarid shrubland

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Figure 4 Grid- and rule- and individual-based simulation model, exemplified by the Karoo model. Here the main influence of grazing is modeled as reduced seed production as sheep feed on the flowers of palatable species. (a) Process chart for the fate of individual shrubs; (b) Influence of space on the fate of individual plants. The different colors indicate different species.

pastoral system of a Namaqualand communal rangeland in South Africa, including sheep and goat grazing. They found complex dynamics, for example, one single model run displayed equilibrium, disequilibrium, and threshold behavior.

Process-based models

Process-based ecosystem models (see Ecosystem Ecology) which describe plant growth, soil water, or carbon fluxes have a long tradition, especially in grassland modeling. However, their utility has been often hampered by the inability to provide a spatial distribution of the complete set of required model parameters and initial conditions. The availability of remote-sensing data may probably close this gap. The utility of this approach was demonstrated in a study by Y. Nouvellon in the 2000s who coupled a grassland ecosystem model for semiarid perennial grasslands in southeastern Arizona (USA) with Landsat imagery data for a 10-year simulation of carbon and water budgets.

Landscape-scale models

The individual-based approach described above in the Karoo model is well suited for modeling a small plot of

Figure 5 Karoo model. Output of a simulation using long-term rainfall from the study site. (a) A 200-year simulation without grazing showing episodic and event-driven behavior but coexistence of the five dominant species. (b) Same rainfall sequence as in (a), but reduced seed production of palatable species (blue and red). The palatable species go extinct because seed limitation produces failure to respond to favorable events (arrows). However, because of long life-span, substantial changes in species composition become only apparent several decades after initiation of grazing. (c) Snapshot of a 10 m x 10 m representative area of the simulation plot in good condition. The colours in (a), (b), and (c) represent the different species.

Figure 5 Karoo model. Output of a simulation using long-term rainfall from the study site. (a) A 200-year simulation without grazing showing episodic and event-driven behavior but coexistence of the five dominant species. (b) Same rainfall sequence as in (a), but reduced seed production of palatable species (blue and red). The palatable species go extinct because seed limitation produces failure to respond to favorable events (arrows). However, because of long life-span, substantial changes in species composition become only apparent several decades after initiation of grazing. (c) Snapshot of a 10 m x 10 m representative area of the simulation plot in good condition. The colours in (a), (b), and (c) represent the different species.

vegetation. This is sufficient if the aim is to identify the basic dynamic behavior and the driving demographic events in the system. However, a number of applied questions related to grazing require consideration of the landscape scale to accommodate environmental heterogeneity and paddocks, ranch, or even larger scales.

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