Genetic variation and the persistence of predator-prey interactions in the Nicholson-Bailey model

The unstable Nicholson-Bailey predator-prey model is extended by assuming that the predation efficiency depends on quantitative characters in both the prey and the predator. The genetics of these characters is assumed to be determined by many diploid loci with additive effects. It is shown that in contrast to the monomorphic model, predator-prey coexistence is possible in the genetically variable system, and that even if the interactions lead to extinction, the time to extinction is typically much larger than in the monomorphic model. Coexistence is mediated by a coevolutionary arms race involving oscillations of the character means in the prey and predator populations. Such an arms race can occur even if costs to increase (or decrease) the character value are introduced, and coexistence is possible if such costs are not too high. The results also hold if self-limitation of the prey is included in the model. In this case, both the basic and the genetic model show the paradox of enrichment, but whereas predator-prey coexistence is only possible for low prey carrying capacities in the monomorphic model, the populations can persist in the genetically variable system even for very high prey carrying capacities. The results suggest that genetic variability is a condition which promotes predator-prey coexistence, and which should generally be taken into consideration when studying the ecology of extinctions. (C) 1997 Academic Press Limited.