  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.
