Proportional stochastic generalized Lotka-Volterra model with an application to learning microbial community structures

作者全名："Xu, Libai; Kong, Dehan; Wang, Lidan; Gu, Hong; Kenney, Toby; Xu, Ximing"

作者地址："[Kong, Dehan] Soochow Univ, Sch Math Sci, 1 Shizi St, Suzhou 215006, Jiangsu, Peoples R China; [Wang, Lidan] Univ Toronto, Dept Stat Sci, 155 Coll St, Toronto, ON M5T 1P8, Canada; [Gu, Hong; Kenney, Toby] Nankai Univ, Sch Stat & Data Sci, 94 Weijin Rd, Tianjin 300071, Peoples R China; [Gu, Hong; Kenney, Toby] Dalhousie Univ, Dept Math & Stat, 6316 Coburg Rd, Halifax, NS B3H 4R2, Canada; [Xu, Ximing] Chongqing Med Univ, Big Data Ctr Childrens Med Care, Natl Clin Res Ctr Child Hlth & Disorders, Childrens Hosp,Minist Educ,Key Lab Child Dev & Dis, Chongqing 400014, Peoples R China"

通信作者："Xu, XM (通讯作者)，Chongqing Med Univ, Big Data Ctr Childrens Med Care, Natl Clin Res Ctr Child Hlth & Disorders, Childrens Hosp,Minist Educ,Key Lab Child Dev & Dis, Chongqing 400014, Peoples R China."

来源：APPLIED MATHEMATICS AND COMPUTATION

ESI学科分类：MATHEMATICS

WOS号：WOS:000948683800001

JCR分区：Q1

影响因子：3.5

年份：2023

卷号：448

期号：　

开始页：　

结束页：　

文献类型：Article

关键词：Interaction network; Maximum likelihood; Relative abundance; Stochastic differential equation

摘要："Inferring microbial community structure based on temporal metagenomics data is an im-portant goal in microbiome studies. The deterministic generalized Lotka-Volterra (GLV) dif-ferential equations have been commonly used to model the dynamics of microbial taxa. However, these approaches fail to take random environmental fluctuations into account and usually ignore the compositional nature of relative abundance data, which may deteri-orate the estimates. In this article, we consider the microbial dynamics in terms of relative abundances by introducing a reference taxon, and propose a new proportional stochas-tic GLV (pSGLV) differential equation model, where the random perturbations of Brownian motion in this model can naturally account for the external environmental effects on the microbial community. We establish conditions and show some mathematical properties of the solutions including general existence and uniqueness, stochastic ultimate bounded-ness, stochastic permanence, the existence of stationary distribution, and ergodicity prop-erty. We further develop approximate maximum likelihood estimators (AMLEs) based on discrete observations and systematically investigate the consistency and asymptotic nor-mality of the proposed estimators. At last, numerical simulations support our theoretical findings and our method is demonstrated through an application to the well-known ""mov-ing picture"" temporal microbial dataset.(c) 2023 Elsevier Inc. All rights reserved."

基金机构：Natural Sciences and Engineering Research Council of Canada; Chongqing Innovation Program for Returned Overseas Chinese Scholars [ex2021112]

基金资助正文："This work was supported in part by the Natural Sciences and Engineering Research Council of Canada , and Chongqing Innovation Program for Returned Overseas Chinese Scholars (ex2021112) ."