Abstract
The increasing quality and the reducing cost of high-throughput sequencing technologies for 16S rRNA gene profiling enable researchers to directly analyze microbe communities in natural environments. The direct interactions among microbial species of a given ecological system can help us understand the principles of community assembly and maintenance under various conditions. Compositionality and dimensionality of microbiome data are two main challenges for inferring the direct interaction network of microbes. In this article, we use the logistic normal distribution to model the background mechanism of microbiome data, which can appropriately deal with the compositional nature of the data. The direct interaction relationships are then modeled via the conditional dependence network under this logistic normal assumption. We then propose a novel penalized maximum likelihood method called gCoda to estimate the sparse structure of inverse covariance for latent normal variables to address the high dimensionality of the microbiome data. An effective Majorization-Minimization algorithm is proposed to solve the optimization problem in gCoda. Simulation studies show that gCoda outperforms existing methods (e.g., SPIEC-EASI) in edge recovery of inverse covariance for compositional data under a variety of scenarios. gCoda also performs better than SPIEC-EASI for inferring direct microbial interactions of mouse skin microbiome data.