High-throughput sequencing technologies allow easy characterization of the human microbiome, but the statistical methods to analyze microbiome data are still in their infancy. Differential abundance methods aim at detecting associations between the abundances of bacterial species and subject grouping factors. The results of such methods are important to identify the microbiome as a prognostic or diagnostic biomarker or to demonstrate efficacy of prodrug or antibiotic drugs. Because of a lack of benchmarking studies in the microbiome field, no consensus exists on the performance of the statistical methods. We have compared a large number of popular methods through extensive parametric and nonparametric simulation as well as real data shuffling algorithms. The results are consistent over the different approaches and all point to an alarming excess of false discoveries. This raises great doubts about the reliability of discoveries in past studies and imperils reproducibility of microbiome experiments. To further improve method benchmarking, we introduce a new simulation tool that allows to generate correlated count data following any univariate count distribution; the correlation structure may be inferred from real data. Most simulation studies discard the correlation between species, but our results indicate that this correlation can negatively affect the performance of statistical methods.