ABSTRACT
A. L. Koch’s numerical work suggested coexistence for quite a large range of values of the parameter space. Some interest in the study of predator-prey systems is the possibility of the coexistence of some number of distinct predatory species in competition for a food source consisting of some smaller number of species of prey. In studies related to the observation of plankton populations, MacArthur and F. M. Stewart and B. R. Levin suggested that under appropriate circumstances coexistence could occur. MacArthur expressed this possibility in terms of one species more suited to growing at low resource levels coexisting competitively with another species better adapted for growing at higher resource densities. Levin showed that can never possess an asymptotically stable critical point nor a stable periodic orbit within Ck, n, and R. McGehee and R. A. Armstrong showed that in fact any system for which the specific predator growth rates are affine must fail to persist.
