Poster M6 - Machine Learning Reveals Hidden Simplicity in Microbial Community Dynamics

Introduction: Microbial communities can harbor up to thousands of species actively interacting with one another, making their assemblage and dynamics difficult to predict. Despite this diversity, focus is often cast upon a subset of the microbiota, e.g., invading pathogens, engineered probiotics, plasmid carrying microbes, and certain metabolic traits. These focal populations engage in complex interactions with the background microbiota, making it hard to disentangle their dynamics without knowledge of the diverse background population it co-resides with. Formulation of effective models with minimum degrees of freedom (DoF) but accurate predictive power will not only advance our understanding of the ecological principles governing the focal species, but also facilitate prediction and rational engineering of the focal populations when limited information of the microbiome is available.
By using autoencoder neural networks to compress the focal population dynamics into different latent spaces, we systematically quantified the DoF of focal microbial populations. We found a linear correlation between the DoF and the focal population size, suggesting the feasibility of simple models in predicting focal microbial dynamics. We further show low-dimensional generalized Lotka-Volterra models can be formulated to effectively describe the focal dynamics. Our results manifest the low-dimensional nature of focal microbial dynamics, providing key insights into the prediction and engineering of focal microbial species in complex communities.

Materials and

Methods: Different dynamical models simulating complex microbial communies have been used to generate the microbial population time series. Longitudinal microbiome datasets have been collected from literatures. For a N-member microbial community, we designated the random choice of the first n members as the focal population, while taking the rest (N-n) members as the background community. We focus the downstream analysis on the dynamics of the n focal members.
Variational Autoencoder neural networks (VAEs) are constructed and trained to compress the focal microbial dynamics in numerical simulations and microbiome datasets. By changing the size of the latent space, we can create individual VAEs that compress and reconstruct the time series of the focal population abundance. We hypothesize that reconstruction should fail when the latent space dimensionality falls below a threshold, which defines the DoF of the focal population.

Results, Conclusions, and Discussions: Results
VAEs with different latent dimensions are trained to compress the focal populations with size of 2, 3, 5, 8, and 10 members. For each case, the reconstruction quality is assessed by the mean squared error (MSE) of between the ground truth data and reconstructed trajectories. Consistent with our hypothesis, the MSE decreases with increasing embedding dimension, and saturates above a critical dimension. We found the critical dimensionalities of the latent space scale linearly with the size of the focal population, and are significantly smaller than the community size. This linear correlation has been repeatedly observed in simulations of communities 1) in well-mixed environment, 2) forming patches, 3) with constant species dispersal, and 4) horizontally transferring plasmids within microbial communities, and in experimental data of 1) soil, 2) lake water, and 3) gut microbiomes.
Through nonlinear optimization of a low-dimensional dynamical model, we further manifested the feasibility of implementing effective models to describe the focal population dynamics.
Discussion
Past studies have delineated simple metrics responsible for the prediction of the fate or dynamics of specific microbes. Coarse-grained models have also been formulated to describe focal population dynamics while ignoring the others, in the context of pathogen infection, and community assembly. The empirical evidence suggest the feasibility of coarse-graining microbial communities when only a subset of its members are of interest.
In this work we systematically assessed the DoF in focal microbial populations. By leveraging Variational Autoencoder, we demonstrated the low-dimensional nature of focal population dynamics, where DoF of O(n) is required to describe the n focal members within a complex microbiota. Our work highlights the simplicity in microbial community dynamics, providing a baseline reference for the formulation of effective focal population models which could be used for precision engineering of microbiome composition and function landscapes.

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