If we interpret the Noy-Meir model at the scale of a single season, grazing is not a continuous process, but involves discrete defoliation events which are followed by a variable period of regrowth. Thus, in grazed grassland, different patches will be in different states of recovery from previous defoliation events leading to a spatially heterogeneous grassland. Additionally, grazing is a stochastic process with uncertainty about the patch where animals take the next bites.
S. Schwinning and A. J. Parsons analyzed in the late 1990s the dual stability property in an extension of the Noy-Meir model describing grazing as a discrete and stochastic process at the bite scale. They found that dual stability was much less likely than previous models predicted and the potential effects of dual stability were minor because the productivities of the two stable equilibria were virtually indistinguishable in a field situation. In a second analysis, they assumed that patches with low biomass were more likely to be defoliated and found again a reduced tendency for dual stability. Instead, the system showed a tendency to generate bimodal frequency distributions (of biomass per patch) where two distinct patch populations are maintained side by side. This phenomenon has, for example, been observed repeatedly in cattle-grazed systems and is known as grazing lawns in rangelands. Further refinements of grazing models at the bite scale require a spatially explicit account of grazing within the framework of optimal foraging (see Optimal Foraging Theory).
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