Model of populations are one of the oldest examples of the interaction between mathematics and biology. Today, mathematical ecology and population biology represents the confluence of two great traditions, one originating with the work of Lotka and Volterra in their study of population dynamics, and a second developed by Haldane, Fisher, and Wright to study the mechanisms of inheritance. In terms of mathematical methodology, those who work in the Lotka-Volterra tradition rely on the theory of dynamical systems whereas much of the mathematical achievements on inheritance came from those well versed in probability theory.
In recent
times, these interactions have called upon a broader team of experts in order
to continue to keep pace with the vast array of genetic information from the
laboratory and behavioral information from the field. This has led to the
need to develop stochastic models of population dynamics or genetic evolution
and to recruit mathematicians and physicist familiar with these methods. Here
our work has focused on two major themes: arthropod populations and human
evolution and epidemiology.