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In arid and semi-arid savannas, species diversity is strongly influenced by structural diversity, which in these systems is characteristically formed by woody vegetation. Shrub encroachment, associated with overgrazing by domestic livestock, changes the structural diversity and hence affects biodiversity. Many investigations have been carried out with focus on the structure building trees, but little is known about the importance of shrubs. Here, we present a spatially explicit and individual-based population model for analysing the influence of shrub encroachment on the occurrence of yellow mongooses (Cynictis penicillata) in the Southern Kalahari, South Africa. This analysis is based on field investigations in Southern Africa. The results of the modelling study are in line with the results of a field study, in which the same unimodal relationship between shrub cover and yellow mongoose abundance was found. The model could explain this relationship by the need of shrubs as protective structures on the one hand, and the need of foraging habitat in the grass matrix on the other hand. To evaluate the factors influencing the population dynamics at different levels of shrub encroachment we carried out an extensive sensitivity analysis. Finally, we determined a range of existence of the yellow mongoose for various shrub covers. Model results indicate a lower and an upper limit of critical shrub densities at 1% and 38%, respectively. These limits indicate the range in shrub cover allowing the persistence of the yellow mongoose in the Southern Kalahari.