A study of a stage-structured model of two competing species

Abstract

The purpose of this dissertation is to develop and study a competition model which, being capable of a wide range of population dynamics, will exhibit phenomena in multi-species interactions not seen in simpler models. We consider a structured, non-linear model of two competing species, each having three life stages. This model is based on a single-species model that has been used to demonstrate many interesting effects in population dynamics and, in particular, has been highly successful in describing and predicting the dynamics of insect populations in controlled laboratory experiments, A thorough examination of equilibria provides necessary and sufficient conditions for stability of axis equilibria, which corresponds to the extinction of one species. Applying the concept of persistence to the model, we obtain sufficient conditions under which the model is persistent with respect to the extinction states, implying indefinite coexistence of both species. Finally, we give specific examples in which the model contradicts classical (equilibrium) competition theory by showing non-equilibrium coexistence in the presence of unstable positive equilibria, stable axis equilibria, and high levels of inter-specific competition.