Habitat fragmentation breaks continuous habitat into smaller patches separated by a less suitable “matrix.” For many species, persistence depends not only on births and deaths within a patch, but also on movement across patch boundaries and that movement can change when a patch becomes crowded. In this talk I’ll introduce a mathematical framework for fragmentation using reaction diffusion models. The reaction term describes local population growth, while diffusion captures movement that resembles random walk-like movement. We’ll begin by introducing diffusion (how a concentration spreads in space) and then translate the same idea into animal dispersal across a landscape.

A key modeling choice is how individuals behave at habitat edges. We’ll discuss emigration (leaving a patch) and density-dependent emigration, where departure rates increase with local density. These assumptions lead to “rules at the boundary” (boundary conditions) that represent how animals cross edges which is an ingredient that strongly influences persistence predictions.

We’ll end with a conservation-focused application to Northern Bobwhite quail: estimating a biologically meaningful minimum patch size needed for persistence. Using movement and demographic rates reported in field studies (and simple fitted components when needed), we’ll see how mathematics can test common rule-of-thumb recommendations and identify which movement assumptions matter most.

Bio

Jerome Goddard II is a Professor of Mathematics at Auburn University Montgomery. His research focuses on partial differential equations and reaction diffusion models in mathematical biology, with applications to spatial ecology and habitat fragmentation. He earned his Ph.D. in Mathematical Sciences from Mississippi State University and has been supported by multiple collaborative National Science Foundation grants. Goddard has served as Alabama State Director for the Mathematical Association of America (Southeastern Section) and as President of the Alabama Association of College Teachers of Mathematics. In his spare time, he enjoys spending time with his wife and two kids on outdoor adventures including camping, hiking, and fishing.

Moderator

Shalmali Bandyopadhyay