The condition a — V0/K< 0.192 means that the consumption function c (x) saturates at a biomass x for which biomass growth g (x) has not yet reached its maximum. In this case, the two functions intersect (Figure 2A). This general model behavior holds for modifications of g (x) and c (x) as long as the growth function is a convex, arch-shaped function of biomass with a single maximum and the consumption function is a saturation function of biomass which may include a residual ungrazable biomass. Noy-Meir suggested that herbivore saturation should occur at most grass-grazer systems and that dual stability should be a common phenomenon in grazing systems. However, if herbivores would be less efficient, the grazing system would show only a single stable equilibrium.
Originally, the Noy-Meir model described the biomass dynamics within a single grazing season (long enough to ensure equilibrium) where grazing is a homogeneous process with constant stocking rate in space and continuous in time. However, in real grazing systems these assumptions may not apply and additional factors that influence biomass dynamics may overpower and destroy the mathematical phenomenon of dual stability. In the following we will critically review the most important modifications of the Noy-Meir model.
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