Dr. William Cuello (Dept. of Mathematics, Rutgers Univ.) 

03/24/2022  3:10pm

Abstract: 

It has recently become more and more pertinent to study the fates of communities of species, especially with the presence of climate change and anthropological disturbances. In particular, it has become increasingly important to find a mathematical framework to analyze the long-term population dynamics of interacting species. Traditionally, ordinary differential equations have lended valuable insight into possible fine-scale dynamics that can occur between multiple species (e.g., predator-prey and mutualistic models). Yet, as the number of species, interactions, and complexity of those interactions grow within such models, the more challenging it is to find analytical solutions to them. Furthermore, these additions typically introduce more unknown variables (parameters) into the system; while one choice of parameters may lead to one set of qualitative solutions, another choice could lead to entirely different dynamics. The higher dimension this parameter space is, the more infeasible it is to theoretically or numerically explore the long-term behaviors of interacting species.

To show how we can overcome this hurdle, I will introduce a new mathematical framework, Widespread Ecological Networks and their Dynamical Signatures (WENDy). Here, we will take a step back from fine-scale dynamics. I will instead show how we can use WENDy to take a community and its interactions and translate them into a set of simple coarse-scale, population growth models. From these models, we output a library of all possible population dynamics within the community; each set of dynamics is generated by different relative orderings of variables that parameterize these models. In other words, by foregoing fine-scale details, we can explore all of parameter space at once and output all possible long-term dynamics of a community of species.

Joint work with Drs. Konstantin Mischaikow (Dept. of Mathematics; Rutgers), Marcio Gameiro (Dept. of Mathematics; Rutgers), and Juan Bonachela (Dept. of Ecology, Evolution, and Natural Resources; Rutgers).