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Populations of some native trees and shrubs have been declining in the arid rangelands of southern Australia due to grazing by herbivores, particularly sheep and rabbits. These reduced levels of regeneration are responsible for the gradual alteration of the composition and overall cover of vegetation. In the long term, this could result in a loss of palatable species considered valuable to the pastoral industry for animal production. Previous research has investigated the effect of sheep grazing on native arid land plant species in Australia, using Matrix Population Models (MPMs). The study was undertaken using a focus species, Myoporum platycarpum, which is a long lived tree species found in the chenopod shrublands of southern Australia. The results of the MPMs suggest that only with higher than average rainfall for extended periods will the M. platycarpum survive under grazing. In this paper, we describe the MPM model and its outcomes and also the alternative approach to the investigation of the effects of sheep grazing using a system dynamics approach. The motivation of the MPM study was based upon the need of arid rangeland graziers to assess alternative management practices in order to improve their ability to be both financially and environmentally sustainable. The system dynamics model again uses M. platycarpum as the focus species, it being assumed that the sustainability of the M. platycarpum population can be used as an indicator for the sustainability of the overall ecosystem. In the system dynamics model, existing and alternative land use practices are evaluated for three different scenarios in order to answer the following research questions: 1. 'What is the effect of alternative land use practices on the long term development of the ecosystems in the shrub land areas of southern Australia?' and 2. 'Which of these land use practices would be optimal to attain an ecologically and economically sustainable shrub land ecosystem in eastern South Australia?' The results of the system dynamics study show that the current land use practices are potentially unsustainable. It was found that three factors directly influence the population dynamics of the M. platycarpum population: presence of sheep, distance to water points, and rainfall. The system dynamics model was used to investigate three different grazing regimes: sheep enclosures, additional watering points, and a rotational grazing system, and found that rotationally grazing the sheep was by far the best alternative.

To investigate the effects of grazing, an MPM was developed to project the long term survival rate of a focus species, M. platycarpum, under grazing and non-grazing regimes. For simplicity, we assume that the sustainability of the M. platycarpum population can be used as an indicator for the sustainability of the overall ecosystem. The technique applied is an extension of the Leslie growth model ( Leslie, 1948), where the vital rates are linked to random rainfall events and deterministic grazing. The effect of grazing is incorporated into the model based upon data primarily collected from the TGB Osborn Koonamore Vegetation Reserve, 400 km north of Adelaide in South Australia within and without a long established sheep exclosure. The results suggest that only with higher than average rainfall for extended periods will the species of interest, M. platycarpum, survive under grazing, without adopting alternative management practices. The second study proposes alternative management practices. The results of the system dynamics study also shows that existing land use practices are potentially unsustainable. The grazing process causes steep drops in the population of M. platycarpum and in some cases even leads to the extinction of the population. It was found that three factors directly influence the population dynamics of the M. platycarpum population: presence of sheep; distance to water points; and rainfall. Three alternative land use practices were investigated and the effect of each alternative land use practice is compared to the non-grazing scenario. This paper describes the results obtained from both studies.