Homogenization of a directed periodic dispersal model for animal foraging
Prof. Brian Yurk (Hope College, Holland)
Monday 14th September, 2015 14:00-15:00 Maths 325
The movement patterns of foraging animals can have important ecological consequences, including determining dispersal shadows of the seeds of their food plants. In this talk, I will present a movement model that is motivated by data collected on birds foraging in the cloud forest of Monteverde, Costa Rica. The model, an advection diffusion equation sharing characteristics of simple home range models, describes directed movement towards the centers of foraging patches that are distributed in space. Intuitively, the model can be connected to a simple random walk model at large observational spatial scales, suggesting that the average large scale behavior should resemble diffusion. Assuming periodic (with respect to space) advection velocity (i.e., periodically distributed foraging patches), I will demonstrate how the method of homogenization can be used to confirm this hypothesis, while developing a formula for the diffusion coefficient at the observational scale that is based on fast scale movement characteristics. Additionally, the fast scale variability is recoverable. Finally, I will discus the extension of the movement model to an advection reaction diffusion model of biological invasion. Using a related homogenization result, we are able to predict invasion speeds for small foraging patches and low to moderate advection speeds that compare favorably with numerical simulations.