Developing a computational approach for moving-habitat models in two dimensions
Developing a computational approach for moving-habitat models in two dimensions
ABSTRACT:
Moving-habitat models describe a species’ dynamics over a climate-driven shifting habitat. They lend insight into the mechanisms promoting a species’ persistence in the face of climate change. In our approach, reaction-diffusion equations track the species’ density in time over the whole space. The suitable habitat, defined by a positive intrinsic growth rate, is bounded by a closed curve, called the interface, which shifts in time. Across the interface, there is a jump in density resulting from the consideration of habitat-dependent dispersal rates and habitat bias. Such a system motivates the development of a numerical method which can capture a jump in density across a moving interface. We introduce a mixed weak formulation for this system, where a dual variable acts as a Lagrange multiplier. For this problem, we construct a finite element method. We prove well-posedness for continuous and discrete cases. For the no-shift case, we derive a priori error estimates for the primal variable. In the case of a nonzero shift, validated solutions in the 1-dimensional system are available. With a 2-dimensional analogue, we validate our numerical solutions against the previously validated solutions for a wide set of parameter values. We look at a first application and discuss applications for further research.
BIO:
Jane Shaw MacDonald is a post-doctoral researcher at Oregon State University in the Mathematics Department. A driving motivation for her research is ecological phenomena, particularly, conservation issues and climate change. Her research program sits at the confluence of computational science, and mathematical ecology.