Comparing bootstrap and posterior probability values in the four-taxon case

Assessment of the reliability of a given phylogenetic hypothesis is an important step in phylogenetic analysis. Historically, the nonparametric bootstrap procedure has been the most frequently used method for assessing the support for specific phylogenetic relationships. The recent employment of Bayesian methods for phylogenetic inference problems has resulted in clade support being expressed in terms of posterior probabilities. We used simulated data and the four-taxon case to explore the relationship between nonparametric bootstrap values (as inferred by maximum likelihood) and posterior probabilities (as inferred by Bayesian analysis). The results suggest a complex association between the two measures. Three general regions of tree space can be identified: (1) the neutral zone, where differences between mean bootstrap and mean posterior probability values are not significant, (2) near the two-branch corner, and (3) deep in the two-branch corner. In the last two regions, significant differences occur between mean bootstrap and mean posterior probability values. Whether bootstrap or posterior probability values are higher depends on the data in support of alternative topologies. Examination of star topologies revealed that both bootstrap and posterior probability values differ significantly from theoretical expectations; in particular, there are more posterior probability values in the range 0.85-1 than expected by theory. Therefore, our results corroborate the findings of others that posterior probability values are excessively high. Our results also suggest that extrapolations from single topology branch-length studies are unlikely to provide any general conclusions regarding the relationship between bootstrap and posterior probability values.