Modeling the dynamics of interacting populations with differential equations has a long history in ecology that can be traced back to Lotka and Volterra. While such models can easily run out of hand with over-parameterization as the number of species increases, the approach continues to provide insights into the rich behaviors of populations that can potentially arise under different assumptions on fundamental ecological processes such as birth, death, competition, and predation.
With collaborator and former mentor Dr. Gregor Fussmann, I examined the effect of Holling Type II function response (i.e., intake rate saturates with increasing resource level) on the coexistence of two consumers competing for the same resource. The project first started in Summer 2007 as part of SURA (Science Undergraduate Research Award) at McGill University, and was resumed and further extended in 2012. We found that while coexistence requires differentiation in the level of nonlinearity between the functional response of the two consumers, severe levels of nonlinearity lead to more stringent requirement for a consumer to successfully sustain itself and thus may actually prevent coexistence.
This work is published in Journal of Theoretical Biology (DOI: 10.1016/j.jtbi.2013.05.025).