This paper presents an annual multidisciplinary, non-spatial model which formalizes the relationships linking the dynamics of shrubs, herbs, soil, livestock and farmers' behaviour with possible exogenous drivers of degradation, such as weather and prices. The model does not represent a pasture–livestock system but a shrub–soil one and is applied to a rangeland in Lagadas County (Northern Greece). A sensitivity analysis of the model is also presented. It shows that livestock, in general, and factors increasing farmers' profits, in particular, are currently helping to combat shrub invasion in Lagadas while having low impacts on erosion rates. Copyright © 2012 John Wiley & Sons, Ltd.