Modeling Of Population Dynamics In Spatially Continuous And Heterogeneous Environments Using Partial Differential Equations

This thesis provides an expansion of existing reaction diffusion population ecology models into patchy landscapes with greater spatial heterogeneity. The Sturm-Loiville eigenvalue problem for a heterogeneous 3 patch landscape is solved implicitly and the population growth rate and migration dynamics on such a landscape are thoroughly discussed. In addition a system of interface equations is found whose greatest solution is the dominant eigenvalue of an N-patch landscape. The results of this model agree well with previously published results and show the mathematical equivalence of two published approaches for incorporating organism behavior at habitat interfaces. Increased modeling capabilities in heterogeneous environments may benefit the biological relevance of this model type to many organisms, but preference in applications and discussion is given to soil organisms due to their central role in terrestrial ecosystems and the great degree of spatial heterogeneity in soils. Soil environments motivate the discussion of a greater number of spatial habitat arrangements than previously considered as well as a different parameter correlations such as correlations of movement rate and mortality reflecting ecological mechanisms in coarse soil environments. This thesis lays the foundation for parameter dependence analysis and the application of a diverse array of established mathematical ecological methods to spatially heterogeneous patchy landscapes