PARENT SESSION
Oral Session 11: Predator - Prey Ecology I: Modeling.
Presiding: L Prugh
Monday, August 2, 8:00 AM to 11:30 AM, Meeting Room C 124.

A novel interpretation of the ratio-dependent and Lotka-Volterra predator-prey models.

Takimoto, Gaku^*,1, ¹ Yale University, New Haven, CT, USA

ABSTRACT- About a decade ago, an intense debate arose as to whether the ratio-dependent or the classical Lotka-Volterra models are the better basic formulation of predator-prey interactions, and has not been fully settled. One of the most significant predictions from the ratio-dependent models is that enrichment causes the increases of both prey and predator abundance. This prediction matches empirical patterns better than that from the Lotka-Volterra models forecasting the increase of only predator abundance, apparently supporting the appropriateness of the ratio-dependent models. It has been argued that the common difference in temporal scales between the foraging and reproduction processes of predators justifies the ratio-dependent formulation. However, there has been no formal derivation of the ratio-dependent models from such temporal-scale difference. In this paper, I develop discrete-time predator-prey models that explicitly incorporate the temporal-scale difference. Two models are explored: one describing the dynamics of prey and predator abundance at the onset of predator's reproduction intervals, and the other describing the dynamics of the average abundance of the intervals. The first model predicts the positive responses to enrichment of both prey and predators as the ratio-dependent models do, whereas the second model predicts the positive response of only predators as the Lotka-Volterra models do. Moreover, the numerical responses of predators to prey abundance in the first model depend on both prey and predators as in the ratio-dependent models, whereas those in the second model depend on only prey abundance as in the Lotka-Volterra models. These results suggest that the ratio-dependent models can be interpreted as describing the continuous-time dynamics of the initial abundance of predator's reproduction intervals, and that the Lotka-Volterra models as describing the continuous-time dynamics of the average abundance. Furthermore, this interpretation indicates that, as far as enrichment responses are measured empirically with respect to average abundance, the temporal-scale difference between predator's foraging and reproduction cannot explain the positive responses of both prey and predators, and other explanations such as prey heterogeneity should be invoked.

Key words: ratio-dependent functional responses, enrichment, the Lotka-Volterra predator-prey model, time scales