Mathematical theory for plant-herbivore systems
The model incorporates effects of the feature of vegetation loosely termed ''plant quality'', which conveys how a given part of the vegetation might be ''rated'' by a herbivore. After having shown that the frequency distribution of plant quality satisfies a conservation equation, qualitative aspects of the system are discussed in the following three situations: (1) mobile herbivores interacting with all plants; (2) sessile herbivores feeding exclusively on single plants; (3) intermediate situations in which mobility is moderate to low. It is shown that depending on the plant quality response and the herbivore response, it is possible to obtain stable equilibria and stable periodic oscillations. In the former case, the populations tend to lose their heterogeneity; in the latter case, oscillations are accompanied by alternate narrowing and broadening of the distribution. A discussion is given on the model compared with other theoretical work. Empirical approaches are also outlined.
scientific article; zbMATH DE number 3961409