Quantifying microbial interactions based on compositional data using an iterative approach for solving generalized Lotka-Volterra equations

Understanding microbial interactions is fundamental for exploring population dynamics, particularly in microbial communities where interactions affect stability and host health. Generalized Lotka-Volterra (gLV) models have been widely used to investigate system dynamics but depend on absolute abundance data, which are often unavailable in microbiome studies. To address this limitation, we introduce an iterative Lotka-Volterra (iLV) model, a novel framework tailored for compositional data that leverages relative abundances and iterative refinements for parameter estimation. The iLV model features two key innovations: an adaptation of the gLV framework to compositional constraints and an iterative optimization strategy combining linear approximations with nonlinear refinements to enhance parameter estimation accuracy. Using simulations and real-world datasets, we demonstrate that iLV surpasses existing methodologies, such as the compositional LV (cLV) and the generalized LV (gLV) model, in recovering interaction coefficients and predicting species trajectories under varying noise levels and temporal resolutions. Applications to the lynx-hare predator-prey, Stylonychia pustula-P. caudatum mixed culture, and cheese microbial systems revealed consistency between predicted and observed relative abundances showcasing its accuracy and robustness. In summary, the iLV model bridges theoretical gLV models and practical compositional data analysis, offering a robust framework to infer microbial interactions and predict community dynamics using relative abundance data, with significant potential for advancing microbial research.Author summary: Microbes and animals often live in communities where species interact in complex ways. Understanding these interactions is essential for predicting population dynamics and how ecosystems respond to environmental changes. A widely used mathematical tool for modeling these interactions is the generalized Lotka-Volterra model. However, it requires information on absolute population sizes, which is rarely available in microbiome studies. We developed the iterative Lotka-Volterra (iLV) model to overcome this challenge. iLV adapts the classical framework to work directly with relative abundance data—the kind most often collected in microbiome studies. Through an iterative optimization process, iLV improves the accuracy of inferred species interactions and population trajectories. We validated our approach using simulated data, along with real-world systems including the snowshoe hare–Canadian lynx system, a microbial co-culture experiment, and a cheese microbial community. In each case, iLV provided more accurate results than existing methods. Our work offers a practical framework for studying species interactions using relative abundance data.