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

Tuan A. Phan; Benjamin J. Ridenhour; Christopher H. Remien; Tuan A. Phan; Benjamin J. Ridenhour; Christopher H. Remien

doi:10.3934/mbe.2025056

Mathematical Biosciences and Engineering

2025, Volume 22, Issue 6: 1517-1550. doi: 10.3934/mbe.2025056

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Research article

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

1.
Institute for Modeling Collaboration and Innovation, University of Idaho, Moscow, ID 83844, USA
2.
Department of Mathematics and Statistical Science, University of Idaho, Moscow, ID 83844, USA

Received: 10 October 2024 Revised: 04 March 2025 Accepted: 22 April 2025 Published: 14 May 2025

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 the 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 the short- and long-term behaviors of the 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 datasets. The procedural simplicity enhances its utility as a valuable tool for application in various microbial and ecological communities.
- stochastic gLV,
- resilience measures,
- instantaneous return rate,
- average return rate,
- convergence rate,
- asymptotic resilience
Citation: Tuan A. Phan, Benjamin J. Ridenhour, Christopher H. Remien. Resilience of a stochastic generalized Lotka–Volterra model for microbiome studies[J]. Mathematical Biosciences and Engineering, 2025, 22(6): 1517-1550. doi: 10.3934/mbe.2025056

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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 the 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 the short- and long-term behaviors of the 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 datasets. The procedural simplicity enhances its utility as a valuable tool for application in various microbial and ecological communities.

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