Morning Plenary Lecture
How small is too small? Modeling the effects of habitat fragmentation via reaction diffusion equations
Assistant Professor of Mathematics
Department of Mathematics
Auburn University Montgomery
Abstract: Habitat fragmentation occurs when an organism�s preferred habitat is divided or broken into smaller fragments (called patches) and can be caused by natural events, such as geological processes, or human activity, such as land conversion. Habitat fragmentation is often cited as a contributor to animal species becoming threatened or endangered. Two important aspects of habitat fragmentation are the size of fragmented patches of preferred habitat and the inferior habitat surrounding the patches, called the matrix. Ecological field studies have indicated that an organism�s survival in a patch is often linked to both the size of the patch and the quality of its surrounding matrix. In this talk, we will focus on modeling the effects of habitat fragmentation via the reaction diffusion framework. The reaction diffusion framework has been extensively employed in population dynamics providing important biological insight into the patch-level consequences of various assumptions made on individual behavior in ecological systems. Such models have seen enormous success both in their empirical validation with actual spatio-temporal distribution data and their ability to yield general conclusions about an eco-system based on the analytical results of these theoretical models. First, we will introduce the reaction diffusion framework and a specific reaction diffusion model with logistic growth and Robin boundary condition (which will model the negative effects of the patch matrix). Second, we will use mathematics to explore the dynamics of the model via the well-known quadrature method and ultimately obtain a causal relationship between the size of the patch and the quality of the matrix versus the maximum population density sustainable by that patch. This important example regarding habitat fragmentation will hopefully serve to illustrate the usefulness of mathematical models in helping to understand complex biological relationships.
Biosketch: Jerome Goddard II is an assistant professor of mathematics at Auburn University at Montgomery (AUM) in Alabama. He received his Ph. D. in Mathematical Sciences from Mississippi State University (MSU) in 2011 under the supervision of Prof. Ratnasingham Shivaji, W. L. Giles Distinguished Professor Emeritus (MSU) & H. Barton Excellence Professor & Head, Department of Mathematics & Statistics (UNCG). His research focuses on the study of nonnegative solutions of partial differential equations arising from reaction diffusion equations used to model population dynamics and combustion theory. Goddard is particularly interested in the study of such models with nonlinear boundary conditions. He has been awarded the AUM School of Sciences Junior Faculty Award, along with various teaching awards at both AUM and MSU. Goddard is passionate about preparing the next generation of mathematician researchers and continually mentors students in undergraduate research projects. He is married and enjoys outdoor hobbies such as hiking, camping, and backpacking.