Steady State Reduction of generalized Lotka-Volterra systems in the microbiome

Abstract

The generalized Lotka-Volterra (gLV) equations, a classic model from theoretical ecology, describe the population dynamics of a set of interacting species. As the number of species in these systems grow in number, their dynamics become increasingly complex and intractable. We introduce Steady State Reduction (SSR), a method that reduces a gLV system of many ecological species into two-dimensional (2D) subsystems that each obey 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 fecal microbiota transplantation, a promising clinical treatment for dysbiosis, can revert a diseased microbial state to health.