Jack Farrell

Abstract:

The mathematical modeling of population dynamics has provided researchers and ecologists with critical insights into the progression, control, and preservation of many species. Classically, these mathematical models are composed of systems of differential equations that abstractly categorize a species into distinct stages. However, these models have a significant shortcoming in that their stage-structured formulations are typically unable to account for the variability in reproductive potential across a population. As the misspecification of such a biological characteristic is known to affect predictions, there is a need to develop new modeling approaches that capture this information. So, we illustrate a new class of stage-structured models that capture the variability in the reproductive potential of a species, while maintaining the convenient ODE model formulations that are the preferred choice of ecological modelers and population dynamics researchers.