Compositional Lotka-Volterra describes microbial dynamics in the simplex

Dynamic changes in microbial communities play an important role in human health and disease. Specifically, deciphering how microbial species in a community interact with each other and their environment can elucidate mechanisms of disease, a problem typically investigated using tools from community ecology. Yet, such methods require measurements of absolute densities, whereas typical datasets only provide estimates of relative abundances. Here, we systematically investigate models of microbial dynamics in the simplex of relative abundances. We derive a new nonlinear dynamical system for microbial dynamics, termed “compositional” Lotka-Volterra (cLV), unifying approaches using generalized Lotka-Volterra (gLV) equations from community ecology and compositional data analysis. On three real datasets, we demonstrate that cLV recapitulates interactions between relative abundances implied by gLV. Moreover, we show that cLV is as accurate as gLV in forecasting microbial trajectories in terms of relative abundances. We further compare cLV to two other models of relative abundance dynamics motivated by common assumptions in the literature—a linear model in a log-ratio transformed space, and a linear model in the space of relative abundances—and provide evidence that cLV more accurately describes community trajectories over time. Finally, we investigate when information about direct effects can be recovered from relative data that naively provide information about only indirect effects. Our results suggest that strong effects may be recoverable from relative data, but more subtle effects are challenging to identify.Author summary: Dynamic changes in microbial communities play an important role in human health and disease. Specifically, deciphering how microbial species in a community interact with each other and their environment can elucidate mechanisms of disease, a problem typically investigated using tools from community ecology. Yet, such methods require measurements of absolute densities, whereas typical only provide estimates of relative abundances. We investigate methods for describing microbial dynamics in terms of relative abundances using approaches from machine learning and dynamical systems. Across three real datasets, we show that relative abundances are sufficient to describe compositional dynamics. Additionally, we show that models trained on relative abundances alone predict future compositions as well models trained on absolute abundances. Finally, we provide criteria for when direct effects, which typically can only be learned from absolute abundances, are recoverable for relative data. As a proof of concept, we recapitulate a previously proposed interaction network for C. difficile colonization.