Resilience of a stochastic generalized Lotka-Volterra model for microbiome studies 

Abstract

Microbial communities are constantly challenged by environmental stochasticity, rendering time series data obtained from these communities inherently noisy. Traditional mathematical models, such as the first-order multivariate autoregressive (MAR) model and the deterministic generalized Lotka-Volterra model, are no longer suitable for predicting the stability of a microbiome from its time series data, as they fail to capture volatility in the environment. To accurately measure microbiome stability, it is imperative to incorporate stochasticity into existing mathematical models in microbiome research. In this paper, we introduce a stochastic generalized Lotka-Volterra (SgLV) system that characterizes the temporal dynamics of a microbial community. To study this system, we developed a comprehensive theoretical framework for calculating four resilience measures based on the SgLV model. These resilience metrics effectively capture short- and long-term behaviors of resilience of the microbiome. To illustrate the practical application of our approach, we demonstrate the procedure for calculating the four resilience measures using simulated microbial abundance data sets. The procedural simplicity enhances its utility as a valuable tool for application in various microbial and ecological communities.

Keywords: stochastic gLV, resilience measures, instantaneous return rate, average return rate, convergence rate, asymptotic resilience

JEL Classification: C32, C61, C62, C63