Event Type:

Mathematical Biology Seminar

Date/Time:

Wednesday, October 12, 2011 - 09:00 to 10:00

Location:

STAG 222

Guest Speaker:

Grant Thompson

Institution:

Alaska Fisheries Science Center, National Marine Fisheries Service and Department of Fisheries and Wildlife

Abstract:

Most theoretical work on the dynamics of interacting species in a biological community has been based on systems of differential equations, with the state variables representing the individual species. In particular, systems of equations involving first- and second-order terms, due to early papers by Lotka (1920, 1925) and Volterra (1926), have been the model of choice for the vast majority of such work. The original justification for this functional form was its similarity to the law of mass action in chemistry. However, this functional form has properties that are difficult to justify biologically; moreover, it does not admit a closed-form solution for the system’s time trajectory. By replacing first-order terms with square root terms and second-order terms with first-order terms, a model is obtained that appears to be more biologically reasonable. Furthermore, because the resulting model is a simple transform of a linear model, the system’s time trajectory is available in closed form. Possibilities for stochastic generalizations of the “square root model” will be considered in this talk.