The Stability and the Intrinsic Growth Rates of Prey and Predator Populations

Abstract

Models of prey—predator systems incorporating the intrinsic population growth rates of each species were analyzed mathematically and were also simulated. The behavior of the two basic models led to a hypothesis: either a stable prey population possesses strong self—limitation, e.g., territoriality, or the growth rate of the prey species is less than that of its predator. Intrinsic population growth rates calculated for eight species of prey and of their important predators showed that the prey had higher rates than their predators in two cases, in both of which the prey species are known to be self—limited. The prey and predator have approximately equal rates in the snowshoe hare and lynx, known to be cyclic. Five species of ungulates, lacking intraspecific population controls, had lower growth rates than their predators. Incorporation of two habitats, one with good and a second with poor cover for the prey, changed a limit cycle to a stable focus; this fits some observations of snowshoe hares. The properties with the greatest effect on stability shown by these models are prey self—limitation and predator searching time.