Seminar on numerical methods - Shankara Narayana Rao, Bheemaiah V (WPI) - Salisbury Labs 406
Title: On a spatiotemporal population dynamics model and its applications to fishery science
Abstract: Structured population models (SPM) have been used to model density, age and mass of individuals over time. Traditional ecological models do not introduce a separate partial differential equation for mass; rather they model the population as being subdivided into classes parameterized by mass and then number density is written as a function of spatial location, time and mass. In this talk, a new approach of modeling mass as dependent variable will be discussed. The resultant model yields a coupled reaction-diffusion and hyperbolic partial differential equations. To show the applicability of the model, I will discuss the following issues from fishery science: (1) how the mobility of species affects the yield with multiple fishing zones and network of marine protected areas (MPAs), (2) the efficacy of MPAs under multiple fishing zones, and (3) how mass dependent mortality influences density and mass of a population. This is a joint work with Dr. Jay R. Walton (Department of Mathematics) and Dr. Masami Fujiwara (Department of Wildlife and Fisheries), Texas A&M University.