Mathematical models for ecological processes in rivers and fragmented habitats

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The main objective of my research program is to mechanistically understand and explain patterns of  populations and communities in spatially heterogeneous environments through development and analysis of mathematical models and through data-model fitting. Understanding the composition of communities, the origin of species, and the maintenance of diversity is of major importance in conservation biology and ecosystem management. Environmental heterogeneity in space and time plays a crucial role in all the above questions. Through several (nonlinear) feedback mechanisms (competition, dispersal, adaptation...), it determines viability of populations,  the extend and boundary of species' ranges, and their phenotypic structure. I concentrate on stream ecosystems where unidirectional flow and pool-riffle structure create several forms of heterogeneity. The mathematical models studied are spatially explicit and either discrete or continuous in time. The analysis reveals conditions for persistence, existence and speed of traveling waves, stability of steady states and possibilities of pattern formation.