Our MAMS alumnus, Nicholas W. Barendrect, and MAMS Professor Peter Thomas recently published the paper “Heteroclinic cycling and extinction in May–Leonard models with demographic stochasticity” in the Journal of Mathematical Biology.
The paper can be accessed here.
Nick had this to say about his experience at CWRU, the MAMS department, and working with his advisor on this paper:
Because of the training I received during my time as an Applied Math undergrad at Case, I had a solid mathematical background that allowed me to start research the moment I entered my PhD program. As a result, I have developed a strong research career studying behavioral decision-making and mathematical neuroscience. Currently, I am preparing to complete and defend my dissertation, and am looking for a post-doctoral research position that allows me to continue modeling decision-making. My long-term goal is to end up back in academia, where I can both mentor new students in mathematical biology and perform research that addresses fundamental questions in cognition and behavior.
This project started out as my senior capstone project while I was an undergrad at Case, and has evolved while I have been a PhD student in CU Boulder’s Applied Math department. In this paper, we address a fundamental question in mathematical modeling: how should one add noise to a model to make it more applicable to real-world physical systems, and what are the consequences of this modeling decision? We focused on classical models from theoretical ecology, such as Lotka-Volterra and its extensions, and mathematical neuroscience, that often neglect the fact that environments (such as an ecosystem or a region of the brain) are made up of a discrete number of interacting individuals that are organized into populations. This discreteness gives rise to a type of noise called demographic stochasticity, and in the paper, we explore how different stochastic representations of the same classical model give rise to different behaviors, such as population extinctions and rock-paper-scissors-type cycles in population sizes.