Root-mean-square error (RMSE) of both Pearson (A) and SparCC (B) inferred correlations, as a function of the density of the underlying correlation network, as given by the probability that any pair of components be strongly correlated

, and community diversity, as given by the Shannon entropy effective number of components

. SparCC errors are smaller than Pearson errors for all parameter values. For the maximal diversity plotted, 50 effective OTU, the inference error obtained using Pearson correlations is greatly decreased. Therefore, it is likely that Pearson correlations perform well on gene expression data, where the effective number of genes is typically in the hundreds or thousands. For each combination of density and diversity, multiple basis correlation networks were randomly generated, and corresponding data was sampled and used for correlation estimation. Dots labeled mid-vagina and gut indicate the average diversity observed in the mid-vagina and gut communities, and the density of their estimated correlation networks. Dots labeled 2D–I indicate the diversity and density used to generate the communities analyzed in .

## PubMed Commons