Microorganisms often live in symbiotic relationship with their environment and they play a central role in many biological processes. They form a complex system of interacting species. Within the gut micro-biota these interaction patterns have been shown to be involved in obesity, diabetes and mental disease. Understanding the mechanisms that govern this ecosystem is therefore an important scientific challenge. Recently, the acquisition of large samples of microbiota data through metabarcoding or metagenomics has become easier. Until now correlation-based network analysis and graphical modelling have been used to identify the putative interaction networks formed by the species of microorganisms, but these methods do not take into account all features of microbiota data. Indeed, correlation-based network cannot distinguish between direct and indirect correlations and simple graphical models cannot include covariates as environmental factors that shape the microbiota abundance. Furthermore, the compositional nature of the microbiota data is often ignored or existing normalizations are often based on log-transformations, which is somewhat arbitrary and therefore affects the results in unknown ways. We have developed a novel method, called MAGMA, for detecting interactions between microbiota that takes into account the noisy structure of the microbiota data, involving an excess of zero counts, overdispersion, compositionality and possible covariate inclusion. The method is based on Copula Gaus-sian graphical models whereby we model the marginals with zero-inflated negative binomial generalized linear models. The inference is based on an efficient median imputation procedure combined with the graphical lasso. We show that our method beats all existing methods in recovering microbial association networks in an extensive simulation study. Moreover, the analysis of two 16S microbial data studies with our method reveals interesting new biology. MAGMA is implemented as an R-package and is freely available at https://gitlab.com/arcgl/rmagma , which also includes the scripts used to prepare the material in this paper.