Our next colloquium will be on Friday February 24 at 1:30pm in Bush Mathematical Sciences Building 357. Dr. Md Istiaq Hossain from The Pensylvania State University (Fayette) will speak on Understanding the predator-prey population dynamics though discrete-time mathematical modeling.
Abstract: The Deepwater Horizon (DWH) oil spill is considered to be the largest marine oil spill in the history of the Gulf of Mexico (GoM). The impacts of this may affect species interactions for an extended period of time as the effects of the spill go away and may also change as a result of species responding to the toxicity. In particular, long-term exposure to a toxicant may cause the rapid evolution of toxicant resistance in relatively short-lived species. This kind of scenario may happen when, for example, the lifespan of the prey population is considerably shorter than the predator population, such as sperm whales and their main food source giant squid. In the first part of this study, we consider the asymptotic stability of equilibria as well as the system persistence of an unstructured discrete-time predator-prey model when the prey population evolves to gain resistance to a toxicant. We show that, with the help of the evolution of toxicant resistance, both the predator and prey population may survive when, without the evolution, both go extinct. Next, we extend the population model to have juvenile and adult stage-structure in the predator population. We assume that only adult predator attacks and consumes the prey population. Our results are also accompanied by various numerical examples. We find that incorporating stage structure into the predator population can introduce rich dynamics (such as chaos) that do not occur when the predator is unstructured. Finally, this talk ends with some current and possible future directions for undergraduate research. (flyer in PDF form)
SFA | Department of Mathematics and Statistics 