{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,14]],"date-time":"2026-05-14T19:39:04Z","timestamp":1778787544847,"version":"3.51.4"},"reference-count":46,"publisher":"Frontiers Media SA","license":[{"start":{"date-parts":[[2024,6,3]],"date-time":"2024-06-03T00:00:00Z","timestamp":1717372800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["frontiersin.org"],"crossmark-restriction":true},"short-container-title":["Front. Microbiomes"],"abstract":"<jats:sec><jats:title>Introduction<\/jats:title><jats:p>The microbial interactions within the human microbiome are complex, and few methods are available to identify these interactions within a longitudinal microbial abundance framework. Existing methods typically impose restrictive constraints, such as requiring long sequences and equal spacing, on the data format which in many cases are violated.<\/jats:p><\/jats:sec><jats:sec><jats:title>Methods<\/jats:title><jats:p>To identify microbial interaction networks (MINs) with general longitudinal data settings, we propose a stationary Gaussian graphical model (SGGM) based on 16S rRNA gene sequencing data. In the SGGM, data can be arbitrarily spaced, and there are no restrictions on the length of data sequences from a single subject. Based on the SGGM, EM -type algorithms are devised to compute the <jats:italic>L<\/jats:italic>1-penalized maximum likelihood estimate of MINs. The algorithms employ the classical graphical LASSO algorithm as the building block and can be implemented efficiently. <\/jats:p><\/jats:sec><jats:sec><jats:title>Results<\/jats:title><jats:p>Extensive simulation studies show that the proposed algorithms can significantly outperform the conventional algorithms if the correlations among the longitudinal data are reasonably high. When the assumptions in the SGGM areviolated, e.g., zero inflation or data from heterogeneous microbial communities, the proposed algorithms still demonstrate robustness and perform better than the other existing algorithms. The algorithms are applied to a 16S rRNA gene sequencing data set from patients with cystic fibrosis. The results demonstrate strong evidence of an association between the MINs and the phylogenetic tree, indicating that the genetically related taxa tend to have more\/stronger interactions. These results strengthen the existing findings in literature. <\/jats:p><\/jats:sec><jats:sec><jats:title>Discussion<\/jats:title><jats:p>The proposed algorithms can potentially be used to explore the network structure in genome, metabolome etc. as well.<\/jats:p><\/jats:sec>","DOI":"10.3389\/frmbi.2024.1366948","type":"journal-article","created":{"date-parts":[[2024,6,3]],"date-time":"2024-06-03T04:29:53Z","timestamp":1717388993000},"update-policy":"https:\/\/doi.org\/10.3389\/crossmark-policy","source":"Crossref","is-referenced-by-count":1,"title":["Identifying stationary microbial interaction networks based on irregularly spaced longitudinal 16S rRNA gene sequencing data"],"prefix":"10.3389","volume":"3","author":[{"given":"Jie","family":"Zhou","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jiang","family":"Gui","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Weston D.","family":"Viles","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Haobin","family":"Chen","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Siting","family":"Li","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Juliette C.","family":"Madan","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Modupe O.","family":"Coker","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Anne G.","family":"Hoen","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1965","published-online":{"date-parts":[[2024,6,3]]},"reference":[{"key":"B1","doi-asserted-by":"publisher","first-page":"174","DOI":"10.1038\/nature09944","article-title":"Enterotypes of the human gut microbiome","volume":"473","author":"Arumugam","year":"2011","journal-title":"Nature"},{"key":"B2","doi-asserted-by":"publisher","first-page":"271","DOI":"10.1093\/biomet\/asy011","article-title":"Robust estimation of high-dimensional covariance and precision matrices","volume":"105","author":"Avella-Medina","year":"2018","journal-title":"Biometrika"},{"key":"B3","doi-asserted-by":"publisher","first-page":"2189","DOI":"10.1109\/TSP.2004.831032","article-title":"Learning graphical models for stationary time series","volume":"52","author":"Bach","year":"2004","journal-title":"IEEE Trans. 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