A semi-Markovian model for predator-prey interactions.

In the study of population dynamics, the predator-prey system is recognized as a vitally important aspect in natural population control. On aspect of predator-prey interactions is studied in this paper. The attack cycle of a predator is assumed to consist of four different activities, namely, search, pursuit, handle and eat, and digestion. A semi-Markovian model is proposed to obtain the number of prey devoured by a predator during the activity of a day. The advantages of a new semi-Markovian model to the queueing model developed by Curry and DeMichele (1977) is demonstrated, as the results from the semi-Markovian model are closer to Holling's (1966) experimental data than their results, which were based entirely on Poisson assumptions.