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The branch-site model is a widely popular approach that accommodates for the lineage- and the site-specific heterogeneity of natural selection regimes among coding sequences. This model relies on prior knowledge of the (foreground) lineage(s) evolving under positive selection at some sites. Unfortunately, such prior information is not always available in practice. A more recent technique (Guindon S, Rodrigo A, Dyer K, Huelsenbeck J. 2004. Modeling the site-specific variation of selection patterns along lineages.Proc Natl Acad Sci USA101:12957–12962) alleviates this issue by explicitly modeling the variability of selection patterns using a stochastic process. However, the performance of this approach for deciding whether a set of homologous sequences evolved under positive selection at some point has not been assessed yet. This study compares the sensitivity and specificity of tests for positive selection derived from both the standard and the stochastic approaches using extensive simulations. We show that the two methods have low proportions of type I errors, that is, they tend to be conservative when testing the null hypothesis of no positive selection if sequences truly evolve under neutral or negative selection regimes. Also, the standard approach is more powerful than the stochastic one when the prior knowledge on foreground lineages is correct. When this prior is incorrect, however, the stochastic approach outperforms the standard model in a broad range of conditions. Additional comparisons also suggest that the stochastic branch-site method compares favorably with the recently proposed mixed-effects model of evolution of Murrell et al. (Murrell B, Wertheim JO, Moola S, Weighill T, Scheffler K, Pond SLK. 2012. Detecting individual sites subject to episodic diversifying selection.PLoS Genet. 8:e1002764). Altogether, our results show that the standard branch-site model is well suited to confirmatory analyses, whereas the stochastic approach should be preferred over the standard or the mixed-effects ones for exploratory studies.