EMBED: a low dimensional reconstruction of gut microbiome dynamics based on ecological normal modes*

The gut microbiome is a significant driver of host health and disease. Longitudinal studies of the microbiome have unraveled the complex dynamics of these ecosystems, and quantitative frameworks are now being developed to better understand their organizing principles. Dimensionality reduction offers unique insights into gut bacterial dynamics by leveraging collective abundance fluctuations of multiple bacteria driven by similar underlying ecological factors. However, methods providing lower-dimensional representations of gut microbial dynamics both at the community and individual taxa level are currently missing. To that end, we develop EMBED: Essential Microbiome Dynamics; a matrix factorization method that embeds longitudinal microbiome abundance data onto a series of lower dimensional Boltzmann Distributions. EMBED learns from the data ecological normal modes (ECNs). ECNs represent the unique set of orthogonal dynamical trajectories capturing the collective behavior of a community akin to “normal modes” in soft matter physics. We show that a small number of ECNs accurately describe gut microbiome dynamics across data sets that encompass dietary changes and antibiotic-related perturbations. Importantly, we find that ECNs often reflect specific ecological behaviors, providing natural templates along which the dynamics of individual bacteria may be partitioned. EMBED also offers insight about subject-specific and universal dynamical processes in the microbiome. Collectively, our results highlight the utility of EMBED to understanding the dynamics of the gut microbiome and provide a framework to study the dynamics of other sequencing-based data as well.