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

TL;DR

This paper introduces Steady State Reduction (SSR), a novel method to simplify complex high-dimensional generalized Lotka-Volterra models of microbiomes into manageable 2D systems, aiding understanding of microbial state transitions.

Contribution

The paper presents SSR, a new reduction technique for high-dimensional gLV models, enabling analysis of microbiome dynamics and treatment effects in a simplified framework.

Findings

SSR effectively reduces complex gLV models to 2D systems.

Application of SSR reveals insights into microbiome state transitions.

SSR helps evaluate fecal microbiota transplantation outcomes.

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.