Movement at and of patch boundaries
As organisms move across a landscape, they encounter habitats of di˙erent quality (patches). At patch boundaries, they have various movement options, such as stay in the current patch or leave it. In the first part of my talk, I will present a population-level model for this boundary behaviour in the form of a reaction-diffusion equation, derived from a stochastic movement model at the individual level. With this model, I will study the evolution of dispersal and habitat preference and formulate an optimal movement strategy. Some organisms, known as ecosystem engineers, are able to modify their physical environment in their favour. Their engineering activity can move the boundary of a patch and expand their suitable habitat in space. In the second part of my talk, I will expand the model from the first part and include an additional equation to represent the movement of the boundary. I will analyze traveling wave solutions of the resulting free boundary problem and give results in terms of the speed of range expansion of the species.