Compositional Lotka-Volterra describes microbial dynamics in the simplex

Abstract

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.

Formation, characterization and modeling of emergent synthetic microbial communities

“…The genome-scale, mechanistic modeling provided by the FBA approach is presently insufficient to account for a large fraction of intracellular networks or assess dynamic, population level changes that likely lead to community structuring [72] . Integration with population-level dynamic models, such Lotka-Volterra (LV) [86] , [87] , [88] , or r/K selection strategies [89] may help to describe the temporal progress of species abundances and community formation processes. Dynamic FBA, which simulates the dynamics of community growth and substrate consumption in time-dependent processes, can also extend current FBA approaches to temporal changes [90] , [91] , [92] .…”

Network analysis methods for studying microbial communities: A mini review

“…While classical Lotka-Volterra models are used to predict predator–prey (competition) interaction between two species, the generalized Lotka–Volterra (gLV) [73] , [74] uses a logistic model to simulate the growth of microbes and to infer whether an interaction of two species is competitive, amensalistic or predator–prey [75] . However, since gLV-based models estimate dynamics with respect to absolute abundance, a new nonlinear dynamical system called compositionally aware Lotka-Volterra method (cLV) [76] was developed. cLV predicts microbial dynamics in-terms of ratio of relative abundance between taxa.…”

“…cLV predicts microbial dynamics in-terms of ratio of relative abundance between taxa. Joseph TA et al [76] compared the performance of cLV against gLV using simulated and real datasets and showed that cLV forecasts microbial interactions more accurately compared to gLV.…”

A Dirichlet Autoregressive Model for the Analysis of Microbiota Time‐Series Data

“…Many proposals for microbiota data longitudinal analyses use count-based strategies (see, for instance, Section 3.5 in [4] and the references therein). However, more recent approaches suggest considering compositional vectors of relative abundances [5][6][7]. e reason is that microbiota data are generated through DNA sequencing and they are constrained by an arbitrary constant sum.…”