African Journal of Range and Forage Science

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Modelling the complex dynamics of vegetation, livestock and rainfall in a semiarid rangeland in South Africa

FD Richardson, MT Hoffman, L Gillson


Predicting the effect of different management strategies on range condition is a challenge for farmers in highly variable environments. A model that explains how the relations between rainfall, livestock and vegetation composition vary over time and interact is needed. Rangeland ecosystems have a hierarchical structure that can be described in terms of vegetation composition, stocking rate and rainfall at the ecosystem level, and the performance of individual animals and plants at the lower level. In this paper, we present mathematical models that incorporate ideas from complex systems theory to integrate several strands of rangeland theory in a hierarchical framework. Compared with observed data from South Africa, the model successfully predicted the relationship between rainfall, vegetation composition and animal numbers over 30 years. Extending model runs over 100 years suggested that initial starting conditions can have a major effect on rangeland dynamics (divergence), and that hysteresis is more likely during a series of low rainfall years. Our model suggests that applying an upper threshold to animal numbers may help to conserve the biodiversity and resilience of grazing systems, whilst maintaining farmers’ ability to respond to changing environmental conditions, a management option here termed controlled disequilibrium.

Keywords: catastrophe theory; complexity theory; disequilibrium; hysteresis; moving attractors

African Journal of Range & Forage Science 2010, 27(3): 125–142
AJOL African Journals Online