An official website of the United States government
Abstract Our recent work on linear and affine dynamical systems has laid out a general framework for inferring the parameters of a differential equation model from a discrete set of data points collected from a system being modeled. It introduced a new class of inverse problems where qualitative information about the parameters and the associated dynamics of the system is determined for regions of the data space, rather than just for isolated experiments. Rigorous mathematical results have justified this approach and have identified common features that arise for certain classes of integrable models. In this work we present a thorough numerical investigation that shows that several of these core features extend to a paradigmatic linear-in-parameters model, the Lotka–Volterra (LV) system, which we consider in the conservative case as well as under the addition of terms that perturb the system away from this regime. A central construct for this analysis is a concise representation of parameter and dynamical features in the data space that we call the P n -diagram, which is particularly useful for visualization of the qualitative dependence of the system dynamics on data for low-dimensional (small n ) systems. Our work also exposes some new properties related to non-uniqueness that arise for these LV systems, with non-uniqueness manifesting as a multi-layered structure in the associated P 2 -diagrams.
more »
« less
This content will become publicly available on November 7, 2026
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. caudatummixed 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.
more »
« less
- Award ID(s):
- 2125142
- PAR ID:
- 10654602
- Editor(s):
- Zhu, Shanfeng
- Publisher / Repository:
- PLOS
- Date Published:
- Journal Name:
- PLOS Computational Biology
- Volume:
- 21
- Issue:
- 11
- ISSN:
- 1553-7358
- Page Range / eLocation ID:
- e1013691
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
Feedbacks between evolution and ecology are ubiquitous, with ecological interactions determining which mutants are successful, and these mutants in turn modifying community structure. We study the evolutionary dynamics of several ecological models with overlapping niches, including consumer resource and Lotka-Volterra models. Evolution is assumed slow, with ecological dynamics producing a stable community (with some strains going permanently extinct) between successive introductions of an invader or mutant. When new strains are slowly added to the community, either from an external pool or by large-effect mutations of exant strains, an initial evolutionary transient gives way to a diverse eco-evolutionary steady state. In this “Red Queen” phase of continual evolution, the biodiversity continues to turn over without the invasion probability of new variants getting smaller. For resource-mediated interactions, the Red Queen phase obtains for any amount of asymmetry in the interactions between strains, and is robust to “general fitness” differences in the intrinsic growth rates of strains. Via a dynamical mean-field theory framework valid for high-dimensional phenotype space, we analytically characterize the Red Queen eco-evolutionary steady state in a particular limit of model parameters. Scaling arguments enable a more general understanding of the steady state and evolutionary transients toward it. This work therefore establishes simple models of continual evolution in an ecological context host-pathogen arms races and points to the generality of Red Queen evolution. However, we also find other eco-evolutionary phases in simple models: For generalized Lotka-Volterra models with near-symmetric interactions an “oligarch” phase emerges in which the evolutionary dynamics continually slow down and a substantial fraction of the community's abundance condenses into a handful of slowly turning-over strains.more » « less
-
ABSTRACT Microbial communities are complex ecological systems of organisms that evolve in time, with new variants created, while others disappear. Understanding how species interact within communities can help us shed light into the mechanisms that drive ecosystem processes. We studied systems with serial propagation, where the community is kept alive by taking a subsample at regular intervals and replating it in fresh medium. The data that are usually collected consist of the % of the population for each of the species, at several time points. In order to utilize this type of data, we formulated a system of equations (based on the generalized Lotka–Volterra model) and derived conditions of species noninteraction. This was possible to achieve by reformulating the problem as a problem of finding feasibility domains, which can be solved by a number of efficient algorithms. This methodology provides a cost‐effective way to investigate interactions in microbial communities.more » « less
-
We apply a perturbative Doi-Peliti field-theoretical analysis to the stochastic spatially extended symmetric Rock-paper-Scissors (RPS) and May-Leonard (ML) models, in which three species compete cyclically. Compared to the two-species Lotka-Volterra predator-prey (LV) model, according to numerical simulations, these cyclical models appear to be less affected by intrinsic stochastic fluctuations. Indeed, we demonstrate that the qualitative features of the ML model are insensitive to intrinsic reaction noise. In contrast, and although not yet observed in numerical simulations, we find that the RPS model acquires significant fluctuation-induced renormalizations in the perturbative regime, similar to the LV model. We also study the formation of spatio-temporal structures in the framework of stability analysis and provide a clearcut explanation for the absence of spatial patterns in the RPS system, whereas the spontaneous emergence of spatio-temporal structures features prominently in the LV and the ML models.more » « less
-
ABSTRACT MotivationStrain-level microbiome profiling has revealed key insights into microbial community composition and strain dynamics. However, accurate strain-level analysis remains challenging due to limited linkage information, ambiguous read mapping, and complicating factors such as genome similarity, sequencing depth, and community complexity. These challenges are especially pronounced for short-read metagenomic data when estimating the relative abundances of multiple strains, a task critical for genotype-phenotype association studies. ResultsTo address this gap, we present Strainify, which enables accurate strain-level abundance estimation from short-read metagenomes with as little as 1% genome coverage. Specifically, Strainify combines (1) identification of informative variants via core genome alignment, (2) filtering of confounding variants via a window-based test, and (3) maximum likelihood estimation of strain abundances. A Shannon entropy-weighted version of the model further improves robustness in noisy, low-coverage settings by downweighting sites with low information content. Across simulated communities of varying complexity, Strainify consistently outperformed existing approaches. On mock community sequencing data, Strainify’s estimates aligned more closely with reference abundances. When applied to a longitudinal gut microbiome dataset, Strainify successfully recapitulated the reported temporal dynamics ofBacteroides ovatusstrain groups, demonstrating its ability to recover biologically meaningful patterns from real-world metagenomes. Together, these results establish Strainify as a robust and versatile solution for accurate strain-level abundance estimation in short-read, low-coverage microbiome studies. AvailabilityThe Strainify code and results are available at:https://github.com/treangenlab/Strainifymore » « less
