Swati Patel

One of the fundamental questions in ecology is how do population interactions influence their ability to coexist with one another. As ongoing empirical investigations uncover the nuances of population interactions, they open the way for more sophisticated models and the need for expanding mathematical methods to analyze them. Classical nonlinear differential equations that capture these interactions have played an important role in developing biological theories on coexistence. Recently, there has been empirical evidence that populations evolve in important traits that influence their interactions and this has implications for their dynamics.  In this talk, I will present a modeling framework for coupling classical ecological differential equations that capture population interactions with evolutionary dynamics that describe how traits change. I will then develop general results for persistence (a mathematical notion of coexistence) of this class of models and then apply them to specific models of three-species interactions.  This mathematical analysis highlights the role of evolution within populations in enabling coexistence amongst populations.