Abstract
In the study of population dynamics, the predator-prey system is recognized as a vitally important aspect in natural population control. Some aspects concerning the predator-prey interactions are studied in this dissertation. Since the emphasis is more on the stochastic nature of the models, the distinction between deterministic and stochastic models is exemplified by means of an ecological example. The relative advantages of stochastic models over the deterministic models are also demonstrated. Assuming the attack cycle of the predator consists of four different activities (namely, search, pursuit, handle and eat, and digestion), a semi-Markovian model is developed to find the number of prey devoured by a predator during the activity of a day. To test the adequacy of the semi-Markovian model, a lognormal distribution is assumed for all the sojourn times and the model is tested using the modified x² goodness-of-fit tests. Optimization equations are developed for the predator to maximize the caloric content in its diet and the role of time and energy in food preference is explained. Some of the models developed in this dissertation are compared with the models found in the literature.
Rao, Chennupati Raghavendra (1976). Mathematical models for predator-prey interactions. Texas A&M University. Texas A&M University. Libraries. Available electronically from
https : / /hdl .handle .net /1969 .1 /DISSERTATIONS -474979.