A simulation study of a time lag population model

Abstract

The lack of terms representing time lags is a widely recognized weakness of the Volterra-Gause formulations of population growth and interaction. A number of analytical attempts to include time lag terms have been made in the past, but they have provided relatively little ecological insight. In this paper the Volterra-Gause equations for a predator and two competing prey are modified to include a number of time lags, and studied by simulation. The modifications include lags in the response to intra- and inter-specific competition and food supply, and terms that represent the “hunger” of the predator population. Predation is made size-selective as a function of hunger, and refuges are provided for the prey. Adding these factors greatly increases the variety of behavior exhibited by the model. Refuges for some minimum number of prey are required to assure persistence of the system. If the system persists its behavior ranges from damped to undamped oscillations of varying amplitude. Time lags in response of the predator to changes in prey abundance, the physiological food requirements of the predator, and the heterogeneity of the environment (as measured by prey refuges) all affect the form of the oscillations. The time lag terms can reverse the outcome of competition in some cases. In this model selective predation stabilizes otherwise unstable competitive relations. Certain results of laboratory predator-prey studies are difficult to explain in terms of the standard Volterra-Gause formalism. It is suggested that some of these features can be explained in terms of time lags in various population responses.