Mathematical modelling in ecology - A resource-based approach

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In my research I use a resource-based approach to study population dynamics.  In an attempt to better understand the structure of communities, and in particular, what factors promote or limit the diversity of natural ecosystems, I develop and analyze  mathematical models of  species interactions that make predictions that can be  tested in the laboratory. The goal is  to reconcile what were commonly   believed general principles, e.g., the  "Principle of Competitive Exclusion," that basically states that at most n species persist if competing for n niches (e.g., resources), with conflicting experimental observations e.g., the "Paradox of the Plankton," and hence  suggest new or modified principles. Whereas predation is generally considered to be one of the factors responsible for the diversity in natural ecosystems,  competition is usually thought of as limiting diversity.  However, in my research, I have found diverse examples of models that predict "Competitor-Mediated Coexistence" is possible, i.e. more species persist in the presence of a certain competitor than would persist if that competitor is eliminated. Whenever possible I try to do global analyses. Bifurcation theory helps one to determine the full spectrum of behaviour for all appropriate parameter ranges and initial states. It also identifies which key parameters need to be measured and how accurately, since only changes in their magnitude result in changes in the dynamics. Computer simulations are used to elucidate complicated dynamics, to test conjectures and to reveal properties of the models that are useful in developing analytic proofs. Symbolic computation is used for complicated calculations. Specialized software for obtaining bifurcation diagrams is especially useful when the attracting invariant sets are complicated and there are multiple attractors. The analyses often lead to interesting abstract mathematical problems in dynamical systems, ordinary, impulsive, integro- and functional differential equations, the qualitative theory of differential equations including bifurcation and stability theory.