A Contribution to the Theory of Competing Predators

Abstract

This paper concerns the growth of 2 predator species competing exploitatively for the same prey population. The prey population grows logistically in the absence of predation, and the predators feed on the prey with a saturating functional response to prey density. Specifically, we assume that Michaelis—Menten kinetics or the Holling "disc" model describe how feeding rates and birth rates change with increasing prey density. We focus on the question of which predator species will survive and which will not, given the growth parameters of the prey and the functional response parameters of the 2 predators. Which predator wins or loses depends critically on the relative magnitude of the prey carrying capacity, K, and the λ parameters of the 2 predators. °i represents the prey density at which the ith predator "breaks even" (equal birth and death rates). This prey density is defined by the product of the predator's half—saturation (Michaelis—Menten) constant times the ratio of the predator's death rate to its intrinsic rate of increase. Coexistence is also possible for a wide range of parameters, but only as a periodic solution. A primary conclusion is that coexistence is possible only if the predator with the smaller half—saturation constant also has the smaller birth—rate—to—death—rate ratio. This necessary constraint is the mechanistic equivalent to requiring that 1 predator be an "r—strategist" and the other be a "K—strategist." This condition is insufficient to guarantee coexistence, however. If the prey carrying capacity, K, is "too small" the K—strategist wins, and if K is "too large," the r—strategist wins. The bounded region of intermediate K values permitting coexistence is defined by the functional response parameters of the 2 predator species. The greater the disparity between the half—saturation constants of the 2 predators, the larger the region of K permitting coexistence.