Mathematical modelling of insect oviposition behaviour

Abstract

This thesis is concerned with various aspects of insect oviposition behaviour. In the first chapter published mathematical models developed to understand optimal insect oviposition behaviour are reviewed. In these models it is assumed that selection favours females that maximize their offspring's total reproductive success. In the second chapter a different approach to the optimization problem is presented. It is shown that the quantity that is maximized in the models that were discussed in the review is not well defined. It is suggested that instead the total expected resource gain that can be acquired by a female's offspring should be used as a fitness measure. The main reason for this is that if fitness is defined as the ability to pass genes on to all future generations, maximizing the fitness measure used in the existing models would not completely resolve the recursive nature of this definition. The third chapter investigates the effects of density-dependent fecundity on population size. It is assumed that females lay only one single clutch and that the size of the clutch is directly related to the female's fecundity. An iterative model is derived to calculate variation in population size. An analysis of the model and subsequent simulation predict that low levels of competition among larvae is likely to cause chaotic behaviour and overpopulation of the environment whereas high competition is likely to have a. stabilizing effect on population size. A fourth chapter briefly summarizes an experiment conducted on Pieris brassi-cae to measure variation in egg size and to estimate larval surviral rates.