Benjamin Redelings Duke University Current estimates of diversifying positive selection rely on first having an accurate multiple sequence alignment. Simulation studies have shown that under biologically plausible conditions, relying on a single estimate of the alignment from commonly used alignment software can lead to unacceptably high false positive rates in detecting diversifying positive selection. We present a novel statistical method that eliminates excess false positives resulting from alignment error by jointly estimating the degree of positive selection and the alignment under an evolutionary model. Our model treats both substitutions and insertions/deletions as sequence changes on a tree, and allows site-heterogeneity in the substitution process. We conduct inference starting from unaligned sequence data by integrating over all alignments. This approach naturally accounts for ambiguous alignments without requiring ambiguously aligned sites to be identified and removed prior to analysis. We take a Bayesian approach and conduct inference using MCMC to integrate over all alignments on a fixed evolutionary tree topology. We introduce a Bayesian version of the branch-site test and assess the evidence for positive selection using Bayes factors. We compare two models of differing dimensionality using a simple alternative to reversible-jump methods. We then show using simulated data that jointly estimating the alignment and the presence of positive selection solves the problem with excessive false positives from erroneous alignments, and has nearly the same power to detect positive selection as when the true alignment is known. We also show that samples taken from the posterior alignment distribution using the software BAli-Phy have substantially lower alignment error compared to MUSCLE, MAFFT, PRANK, and FSA alignments.