Microbial interaction networks can rewire in response to host and environmental factors, yet most existing methods for network estimation treat the covariance structure as static across samples. We propose TRECOR, a Bayesian covariance regression framework for inferring covariate-dependent microbial covariation networks from zero-inflated compositional count data. The method models microbiome counts through a latent multivariate normal distribution defined on the internal nodes of a phylogenetic tree, where both the mean and covariance of the latent variables depend on covariates. The covariance is decomposed into a sparse baseline component, representing a stable microbial covariation network, and a low-rank covariate-dependent perturbation that captures network rewiring. By exploiting the binomial factorization of the multinomial distribution under the logistic-tree-normal representation, the model achieves full conjugacy and posterior inference proceeds via an efficient Gibbs sampler. In simulations, TRECOR substantially outperforms covariance regression applied to transformed counts, demonstrating the importance of explicitly modeling the compositional sampling layer. Applied to gut microbiome data from 531 individuals across three countries, we find that age has the largest effect on microbial covariation, which is a pattern not revealed by mean-based analysis alone. The age-associated differential network is enriched for Enterobacteriaceae and related families, consistent with known developmental shifts in the gut microbiota, while country-associated differential networks implicate diet-related taxa.

翻译：摘要：微生物相互作用网络会因宿主和环境因素发生重构，然而现有的大多数网络估计方法将协方差结构视为跨样本静态不变。我们提出TRECOR——一种贝叶斯协方差回归框架，用于从零膨胀组成型计数数据推断协变量依赖的微生物共变网络。该方法通过定义在系统发育树内部节点上的潜在多元正态分布对微生物组计数建模，其中潜在变量的均值和协方差均依赖于协变量。协方差被分解为表征稳定微生物共变网络的稀疏基线成分，以及刻画网络重构的低秩协变量依赖扰动。通过利用逻辑树正态表示下多项分布的二项式分解，该模型实现完全共轭性，并通过高效吉布斯采样器进行后验推断。在模拟实验中，TRECOR显著优于对转换计数数据应用的协方差回归，凸显了显式建模组成型采样层的必要性。将该方法应用于来自三个国家531名个体的肠道微生物组数据，我们发现年龄对微生物共变的影响最大——这一模式无法通过基于均值的分析单独揭示。与年龄相关的差异网络富集了肠杆菌科及相关科属，这与已知的肠道微生物群发育变化一致，而与国家相关的差异网络则涉及饮食相关类群。