SFU: Applied Math Seminar - Eric Jones

Abstract: The generalized Lotka-Volterra (gLV) equations describe the population dynamics of a set of interacting species, and are a classic model in theoretical ecology. As the number of species in these systems grow in number, their dynamics become increasingly complex and difficult to examine analytically. We introduce steady-state reduction (SSR), a method that approximates a bistable gLV system with many ecological species by a two-dimensional (2D) subsystem that obeys gLV dynamics and whose basis vectors are steady states of the high-dimensional model. We apply this method to an experimentally derived model of the gut microbiome in order to observe the transition between “healthy” and “diseased” microbial states. Specifically, we use SSR to investigate how the efficacy of microbial therapies like fecal microbiota transplantation (FMT) depends on ecological dynamics. Lastly, we examine how FMT efficacy depends on noise in the approximate 2D system.