Understanding the spatial distribution of organisms throughout an environment is an important topic in population ecology. We briefly review ecological questions underpinning certain mathematical work that has been done in this area, before presenting a few examples of spatially structured population models. As a first example, we consider a model of two species aggregation and clustering in two-dimensional domains in the presence of heterogeneity, and demonstrate novel aggregation mechanisms in this setting. We next consider a second example consisting of a predator-prey-subsidy model in a spatially continuous domain where the spatial distribution of the subsidy influences the stability and spatial structure of steady states of the system. Finally, we discuss ongoing work on extending such results to network-structured domains, and discuss how and when the presence of a subsidy can stabilize predator-prey dynamics."
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Compaction is a primary process in the evolution of a sedimentary basin. Various 1D models exist to model a basin compacting due to overburden load. We explore a multi-dimensional model for a basin undergoing mechanical and chemical compaction. We discuss some properties of our model. Some test cases in the presence of geological features are considered, with appropriate numerical techniques presented.