Motivation: Identification of complex relationships among members of microbial communities is key to understand and control the microbiota. Co-exclusion is arguably one of the most important patterns reflecting microorganisms' intolerance to each other's presence. Knowing these relations opens an opportunity to manipulate microbiotas, personalize anti-microbial and probiotic treatments as well as guide microbiota transplantation. The co-exclusion pattern however, cannot be appropriately described by a linear function nor its strength be estimated using covariance or (negative) Pearson and Spearman correlation coefficients. This manuscript proposes a way to quantify the strength and evaluate the statistical significance of co-exclusion patterns between two, three or more variables describing a microbiota and allows one to extend analysis beyond microorganism abundance by including other microbiome associated measurements such as, pH, temperature etc., as well as estimate the expected numbers of false positive co-exclusion patterns in a co-exclusion network. Results: The implemented computational pipeline (CoEx) tested against 2,380 microbial profiles (samples) from The Human Microbiome Project resulted in body-site specific pairwise co-exclusion patterns. Availability: C++ source code for calculation of the score and p-value for 2, 3, and 4 dimensional co-exclusion patterns as well as source code and executable files for the CoEx pipeline are available at https://scsb.utmb.edu/labgroups/fofanov/co-exclusion_in_microbial_communities.asp Contact: lealbayr@utmb.edu Supplementary information: Supplementary data are available at biorxiv online.