{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,14]],"date-time":"2026-01-14T16:22:21Z","timestamp":1768407741384,"version":"3.49.0"},"update-to":[{"DOI":"10.1371\/journal.pcbi.1013691","type":"new_version","label":"New version","source":"publisher","updated":{"date-parts":[[2025,11,18]],"date-time":"2025-11-18T00:00:00Z","timestamp":1763424000000}}],"reference-count":31,"publisher":"Public Library of Science (PLoS)","issue":"11","license":[{"start":{"date-parts":[[2025,11,7]],"date-time":"2025-11-07T00:00:00Z","timestamp":1762473600000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["EF-2125142"],"award-info":[{"award-number":["EF-2125142"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000062","name":"National Institute of Diabetes and Digestive and Kidney Diseases","doi-asserted-by":"publisher","award":["R01DK142026"],"award-info":[{"award-number":["R01DK142026"]}],"id":[{"id":"10.13039\/100000062","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["www.ploscompbiol.org"],"crossmark-restriction":false},"short-container-title":["PLoS Comput Biol"],"abstract":"<jats:p>\n                    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,\n                    <jats:italic>Stylonychia pustula<\/jats:italic>\n                    -\n                    <jats:italic>P. caudatum<\/jats:italic>\n                    mixed 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.\n                  <\/jats:p>","DOI":"10.1371\/journal.pcbi.1013691","type":"journal-article","created":{"date-parts":[[2025,11,7]],"date-time":"2025-11-07T18:45:11Z","timestamp":1762541111000},"page":"e1013691","update-policy":"https:\/\/doi.org\/10.1371\/journal.pcbi.corrections_policy","source":"Crossref","is-referenced-by-count":1,"title":["Quantifying microbial interactions based on compositional data using an iterative approach for solving generalized Lotka-Volterra equations"],"prefix":"10.1371","volume":"21","author":[{"given":"Yue","family":"Huang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tianqi","family":"Tang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5889-5201","authenticated-orcid":true,"given":"Xiaowu","family":"Dai","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8552-043X","authenticated-orcid":true,"given":"Fengzhu","family":"Sun","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"340","published-online":{"date-parts":[[2025,11,7]]},"reference":[{"issue":"6261","key":"pcbi.1013691.ref001","doi-asserted-by":"crossref","first-page":"663","DOI":"10.1126\/science.aad2602","article-title":"The ecology of the microbiome: Networks, competition, and stability","volume":"350","author":"KZ Coyte","year":"2015","journal-title":"Science"},{"issue":"8","key":"pcbi.1013691.ref002","doi-asserted-by":"crossref","first-page":"538","DOI":"10.1038\/nrmicro2832","article-title":"Microbial interactions: from networks to models","volume":"10","author":"K Faust","year":"2012","journal-title":"Nat Rev Microbiol"},{"issue":"12","key":"pcbi.1013691.ref003","doi-asserted-by":"crossref","first-page":"6511","DOI":"10.1128\/IAI.68.12.6511-6518.2000","article-title":"Host-pathogen interactions: basic concepts of microbial commensalism, colonization, infection, and disease","volume":"68","author":"A Casadevall","year":"2000","journal-title":"Infect Immun"},{"key":"pcbi.1013691.ref004","volume-title":"Elements of physical biology","author":"AJ Lotka","year":"1925"},{"issue":"1","key":"pcbi.1013691.ref005","doi-asserted-by":"crossref","first-page":"121","DOI":"10.1186\/s13059-016-0980-6","article-title":"MDSINE: Microbial Dynamical Systems INference Engine for microbiome time-series analyses","volume":"17","author":"V Bucci","year":"2016","journal-title":"Genome Biol"},{"key":"pcbi.1013691.ref006","doi-asserted-by":"crossref","DOI":"10.3389\/fsysb.2022.1021897","article-title":"Methods of quantifying interactions among populations using Lotka-Volterra models","volume":"2","author":"JD Davis","year":"2022","journal-title":"Front Syst Biol"},{"key":"pcbi.1013691.ref007","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1016\/j.destud.2018.11.001","article-title":"System evolution prediction and manipulation using a Lotka\u2013Volterra ecosystem model","volume":"60","author":"G Zhang","year":"2019","journal-title":"Design Studies"},{"issue":"12","key":"pcbi.1013691.ref008","doi-asserted-by":"crossref","DOI":"10.1371\/journal.pcbi.1003388","article-title":"Ecological modeling from time-series inference: insight into dynamics and stability of intestinal microbiota","volume":"9","author":"RR Stein","year":"2013","journal-title":"PLoS Comput Biol"},{"key":"pcbi.1013691.ref009","doi-asserted-by":"crossref","first-page":"572487","DOI":"10.3389\/fmicb.2020.572487","article-title":"Modeling Competitive Mixtures With the Lotka-Volterra Framework for More Complex Fitness Assessment Between Strains","volume":"11","author":"A Dimas Martins","year":"2020","journal-title":"Front Microbiol"},{"key":"pcbi.1013691.ref010","doi-asserted-by":"crossref","first-page":"2224","DOI":"10.3389\/fmicb.2017.02224","article-title":"Microbiome Datasets Are Compositional: And This Is Not Optional","volume":"8","author":"GB Gloor","year":"2017","journal-title":"Front Microbiol"},{"issue":"5","key":"pcbi.1013691.ref011","doi-asserted-by":"crossref","first-page":"330","DOI":"10.1016\/j.annepidem.2016.03.002","article-title":"Compositional data analysis of the microbiome: fundamentals, tools, and challenges","volume":"26","author":"MCB Tsilimigras","year":"2016","journal-title":"Ann Epidemiol"},{"issue":"7","key":"pcbi.1013691.ref012","doi-asserted-by":"crossref","first-page":"201378","DOI":"10.1098\/rsos.201378","article-title":"Structural identifiability of the generalized Lotka-Volterra model for microbiome studies","volume":"8","author":"CH Remien","year":"2021","journal-title":"R Soc Open Sci"},{"issue":"5","key":"pcbi.1013691.ref013","doi-asserted-by":"crossref","DOI":"10.1371\/journal.pcbi.1007917","article-title":"Compositional Lotka-Volterra describes microbial dynamics in the simplex","volume":"16","author":"TA Joseph","year":"2020","journal-title":"PLoS Comput Biol"},{"issue":"2","key":"pcbi.1013691.ref014","doi-asserted-by":"crossref","first-page":"215","DOI":"10.2307\/1358","article-title":"The Ten-Year Cycle in Numbers of the Lynx in Canada","volume":"11","author":"C Elton","year":"1942","journal-title":"The Journal of Animal Ecology"},{"issue":"1","key":"pcbi.1013691.ref015","doi-asserted-by":"crossref","first-page":"172","DOI":"10.1128\/AEM.01338-07","article-title":"Microbial interactions within a cheese microbial community","volume":"74","author":"J Mounier","year":"2008","journal-title":"Appl Environ Microbiol"},{"key":"pcbi.1013691.ref016","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9781139173179","volume-title":"Evolutionary games and population dynamics","author":"J Hofbauer","year":"1998"},{"key":"pcbi.1013691.ref017","volume-title":"Stability and complexity in model ecosystems","author":"RM May","year":"2001"},{"key":"pcbi.1013691.ref018","author":"DA MacLulich","year":"1937","journal-title":"Fluctuations in the Numbers of the Varying Hare (Lepus Americanus). University of Toronto Press"},{"issue":"2036","key":"pcbi.1013691.ref019","doi-asserted-by":"crossref","first-page":"16","DOI":"10.1126\/science.79.2036.16.b","article-title":"Experimental Analysis of Vito Volterra\u2019s Mathematical Theory of the Struggle for Existence","volume":"79","author":"GF Gause","year":"1934","journal-title":"Science"},{"issue":"23","key":"pcbi.1013691.ref020","doi-asserted-by":"crossref","first-page":"13275","DOI":"10.1002\/ece3.6926","article-title":"gauseR: Simple methods for fitting Lotka-Volterra models describing Gause\u2019s \u201cStruggle for Existence\u201d","volume":"10","author":"LK M\u00fchlbauer","year":"2020","journal-title":"Ecol Evol"},{"issue":"3","key":"pcbi.1013691.ref021","doi-asserted-by":"crossref","first-page":"261","DOI":"10.1038\/s41592-019-0686-2","article-title":"SciPy 1.0: fundamental algorithms for scientific computing in Python","volume":"17","author":"P Virtanen","year":"2020","journal-title":"Nat Methods"},{"key":"pcbi.1013691.ref022","doi-asserted-by":"crossref","DOI":"10.1137\/1.9780898719857","author":"AR Conn","year":"2000","journal-title":"Trust Region Methods. Society for Industrial and Applied Mathematics"},{"key":"pcbi.1013691.ref023","doi-asserted-by":"crossref","first-page":"105","DOI":"10.1007\/BFb0067700","article-title":"The Levenberg-Marquardt algorithm: Implementation and theory","author":"JJ Mor\u00e9","year":"1978","journal-title":"Lecture Notes in Mathematics. Springer Berlin Heidelberg"},{"issue":"1","key":"pcbi.1013691.ref024","doi-asserted-by":"crossref","first-page":"169","DOI":"10.1007\/s11081-020-09571-2","article-title":"Cluster Gauss\u2013Newton method","volume":"23","author":"Y Aoki","year":"2020","journal-title":"Optim Eng"},{"issue":"4","key":"pcbi.1013691.ref025","doi-asserted-by":"crossref","first-page":"1675","DOI":"10.1007\/s11075-023-01681-z","article-title":"Approximating sparse Hessian matrices using large-scale linear least squares","volume":"96","author":"JM Fowkes","year":"2023","journal-title":"Numer Algor"},{"issue":"1","key":"pcbi.1013691.ref026","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1145\/1322436.1322439","article-title":"Computing sparse Hessians with automatic differentiation","volume":"34","author":"A Walther","year":"2008","journal-title":"ACM Trans Math Softw"},{"issue":"1","key":"pcbi.1013691.ref027","doi-asserted-by":"crossref","first-page":"2423","DOI":"10.1038\/s41598-020-58769-y","article-title":"Model-based Comparisons of the Abundance Dynamics of Bacterial Communities in Two Lakes","volume":"10","author":"P Dam","year":"2020","journal-title":"Sci Rep"},{"issue":"3","key":"pcbi.1013691.ref028","doi-asserted-by":"crossref","first-page":"271","DOI":"10.1021\/j150111a004","article-title":"Contribution to the Theory of Periodic Reactions","volume":"14","author":"AJ Lotka","year":"1910","journal-title":"J Phys Chem"},{"key":"pcbi.1013691.ref029","volume-title":"Variazioni e fluttuazioni del numero d\u2019individui in specie animali conviventi","author":"V Volterra","year":"1926"},{"issue":"6","key":"pcbi.1013691.ref030","doi-asserted-by":"crossref","DOI":"10.15252\/msb.20178157","article-title":"Deciphering microbial interactions in synthetic human gut microbiome communities","volume":"14","author":"OS Venturelli","year":"2018","journal-title":"Mol Syst Biol"},{"key":"pcbi.1013691.ref031","doi-asserted-by":"crossref","DOI":"10.1007\/b98874","author":"J Nocedal","year":"1999","journal-title":"Numerical Optimization. Springer-Verlag"}],"updated-by":[{"DOI":"10.1371\/journal.pcbi.1013691","type":"new_version","label":"New version","source":"publisher","updated":{"date-parts":[[2025,11,18]],"date-time":"2025-11-18T00:00:00Z","timestamp":1763424000000}},{"DOI":"10.1371\/journal.pcbi.1013876","type":"correction","label":"Correction","source":"publisher","updated":{"date-parts":[[2026,1,6]],"date-time":"2026-01-06T00:00:00Z","timestamp":1767657600000}}],"container-title":["PLOS Computational Biology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dx.plos.org\/10.1371\/journal.pcbi.1013691","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,11,18]],"date-time":"2025-11-18T18:43:02Z","timestamp":1763491382000},"score":1,"resource":{"primary":{"URL":"https:\/\/dx.plos.org\/10.1371\/journal.pcbi.1013691"}},"subtitle":[],"editor":[{"given":"Shanfeng","family":"Zhu","sequence":"first","affiliation":[],"role":[{"role":"editor","vocabulary":"crossref"}]}],"short-title":[],"issued":{"date-parts":[[2025,11,7]]},"references-count":31,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2025,11,7]]}},"URL":"https:\/\/doi.org\/10.1371\/journal.pcbi.1013691","relation":{},"ISSN":["1553-7358"],"issn-type":[{"value":"1553-7358","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,11,7]]}}}