Auburn University Chapter of SIAM

Speaker: Jerome Goddard II, Department of Mathematics,
Auburn University at Montgomery

Title: To Harvest or Not to Harvest? How Much Is the Question.

Abstract:  In May 2003, USA Today published an article that emphasized the importance of imposing proper control on the level of worldwide harvesting of several large fish species, such as Bluefin tuna. Over-harvesting of our animal populations can have severe consequences, ultimately leading to extinction. Study of population models that incorporate diffusion and constant yield harvesting (in which the harvesting level is independent of the population itself) have become popular as a means to explore better ways to manage and preserve our precious resources. In this talk, we review some interesting population models with and without spatial effects. In particular, we will consider several growth functions including logistic and Allee effect. Priority in our discussion will be given to the effects of constant yield harvesting on the structure of positive steady states to our model. Finally, we consider a population that satisfies a certain nonlinear boundary condition, arising from negative density dependent emigration, and its
effect on the model's steady states.