Quantification of microbial covariations from 16S rRNA and metagenomic sequencing data is difficult due to their sparse nature. In this article, we propose using copula models with mixed zero-beta margins for the estimation of taxon–taxon covariations using data of normalized microbial relative abundances. Copulas allow for separate modeling of the dependence structure from the margins, marginal covariate adjustment, and uncertainty measurement.


Our method shows that a two-stage maximum-likelihood approach provides accurate estimation of model parameters. A corresponding two-stage likelihood ratio test for the dependence parameter is derived and is used for constructing covariation networks. Simulation studies show that the test is valid, robust, and more powerful than tests based upon Pearson’s and rank correlations. Furthermore, we demonstrate that our method can be used to build biologically meaningful microbial networks based on a dataset from the American Gut Project.

Availability and implementation

R package for implementation is available at

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