Abstract

Luckinbill (1973) demonstrated in a laboratory that populations of Paramecium Aurelia as a prey and Didinium Nasitum as a predator could maintain sustained oscillatory behaviour. Harrison (1995) modelled this data for testing predator-prey models. He used different kinds of functional responses, including responses with the predator mutual interference, ratio-dependency, Leslie and sigmoid types. He also used a delay in the predator numerical response for one model. Harrison successfully demonstrated the general features of the experiment including the sustained oscillations.

We have extended Harrison's model with the inclusion of spatial dependence through diffusion. The prupose of this paper is to show the role of the time delay inclusion in the numerical response of the predator for this spatial dependent model with various functional and numerical response terms.

We have observed that while diffusion accelerates the process of growth or extinction of a population, the time delay modifies the process of growth or extinction of the population and the properties of the cyclic steady state.