The microbial interactions within the human microbiome are complex and temporally dynamic, but few methods are available to model this system within a longitudinal network framework. Based on general longitudinal 16S rRNA sequence data, we propose a stationary Gaussian graphical model (SGGM) for microbial interaction networks (MIN) which can accommodate the possible correlations between the high-dimensional observations. For SGGM, an EM-type algorithm is devised to compute the $L_1$-penalized maximum likelihood estimate of MIN which employs the classic graphical LASSO algorithm as the building block and can therefore be implemented easily. Simulation studies show that the proposed algorithms can significantly outperform the conventional algorithms when the correlations between measurements grow large. The algorithms are then applied to a real 16S rRNA gene sequence data set for gut microbiome. With the estimated MIN in hand, module-preserving permutation test is proposed to test the independence of the MIN and the corresponding phylogenetic tree. The results demonstrate strong evidence of an association between the MIN and the phylogenetic tree which indicates that the genetically related taxa tend to have more/stronger interactions. The proposed algorithms are implemented in R package {\it lglasso} at \url{https://CRAN.R-project.org/package=lglasso}.

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