The temporal dynamics of interacting consumer and resource populations is one of the most thoroughly studied problems of theoretical population biology (see Prey-Predator Models); however, making these models spatially explicit may alter their behavior substantially. One revealing example was given in a study of A. Basset, D. DeAngelis, and J. Diffendorfer published in 1997. They studied classical herbivore dynamics similar to eqns  and , but implemented it on a spatially explicit grid. The vegetation dynamics within each grid cell was described by logistic growth, but the grazers could move across the landscape of patchily distributed grass resources to neighboring cells. The grazer had less than perfect information concerning the grass biomass in other patches leaving a cell out if the expected intake became too low. The herbivore consumption rate was modeled using the functional responses C(V) ~ Vn/(V0 + Vn) which yields for n = 1 the Holling type II response (herbivore saturation and efficient grazer at low biomass), and for n = 2 a Holling type III response (less-efficient grazer, biomass protected at low densities).
Basset and co-authors selected parameter values based on the behavior of the nonspatial model. With efficient grazers (n = 1), herbivore-vegetation dynamics was unstable, producing propagating oscillations, while less-efficient grazers (n = 2 or n = 3) stabilized the system. Simulations of the corresponding spatially explicit system indicated a reversal ofthe relationship between functional response and stability. The underlying mechanism of this finding is that an efficient grazer completely exploits the patch before leaving it. However, because the grazer has no global knowledge on the distribution of grass biomass on the entire landscape, there are always patches that escape from grazing for a period of time that is long enough to recover. This is one hypothesis explaining the long-term stability of natural grazing systems where huge herds of wild herbivores once roamed over the prairies of the US or the savannas of Africa. The question of large-scale herd movement is also of importance in grazing systems where substantial temporal variation in food resources occurs over time. In this case, local food scarceness can be compensated by movement of large herds to take advantage of ephemeral spatial distribution of food resources. Species of high conservation interest with herd movements are, for example, Thomson's gazelles living on the Serengeti Plains, East Africa, Saiga antelopes in Kalmykia, Mongolian gazelles, or reindeer in the Taymyr in the Russian Arctic.
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