Mathematical modelling in population dynamics

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The focus of my research programme is on the development and analysis of mathematical models to study population dynamics. Instead of analyzing models of specific organisms, I try to determine robust classes of models that exhibit similar dynamics and to investigate what modifications result in significant changes to these 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 use a resource-based approach that results in mathematical models of species interactions that often make predictions that can be tested in the laboratory in such devices as chemostats or self cycling fermentors. I consider both this mechanistic, resource-based approach, as well as classical models that are often more general, and require fewer equations, but involve parameters that may not be as easily measured. Comparing the range of dynamics predicted by different models is important, to understand how sensitive model predictions are to the various modelling approaches. One goal is to reconcile commonly believed general principles with conflicting experimental observations, and hence suggest new or modified principles. Another goal is the development of measurable criteria that would enable scientists to predict which combination of microorganisms would be most effective and safest for use in such processes as water purification, biological waste decomposition, biological remediation, and the production of bio-fuels. Other potential applications include pest control on the one hand and the prevention of the extinction of endangered species on the other.