Herbivore regulation and irreversible vegetation change in semi-arid grazing systems

Models made to explain sudden and irreversible vegetation shifts in semi-arid grasslands typically assume that herbivore density is independent of the state of the vegetation, e.g., under the control of humans. We relax this assumption and investigate the mathematical implications of vegetation-regulated herbivore population dynamics. We show that irreversible vegetation change may also occur in systems where herbivore population dynamics are affected by changes in plant standing crop. Our analysis furthermore shows that irreversible vegetation change may occur for a larger set of soil and climatic conditions when herbivore numbers are independent of the vegetation, as compared to systems where vegetation density determines herbivore population size. Hence, our analysis suggests that irreversible vegetation change is less likely to occur in systems with natural herbivore population dynamics than in systems where humans control herbivore density.