On the impossibility of uniform priors on clades.
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Algorithms↗
Biomedical subjects
Kurt M Pickett
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Strange bayes indeed: uniform topological priors imply non-uniform clade priors.
While Bayesian analysis has become common in phylogenetics, the effects of topological prior probabilities on tree inference have not been investigated. In Bayesian analyses, the prior probability of topologies is almost always considered equal for all possible trees, and clade support is calculated from the majority rule consensus of the approximated posterior distribution of topologies. These uniform priors on tree topologies imply non-uniform prior probabilities of clades, which are dependent on the number of taxa in a clade as well as the number of taxa in the analysis. As such, uniform topological priors do not model ignorance with respect to clades. Here, we demonstrate that Bayesian clade support, bootstrap support, and jackknife support from 17 empirical studies are significantly and positively correlated with non-uniform clade priors resulting from uniform topological priors. Further, we demonstrate that this effect disappears for bootstrap and jackknife when data sets are free from character conflict, but remains pronounced for Bayesian clade supports, regardless of tree shape. Finally, we propose the use of a Bayes factor to account for the fact that uniform topological priors do not model ignorance with respect to clade probability.
Bayes Theorem↗
How meaningful are Bayesian support values?
In this study, we used an empirical example based on 100 mitochondrial genomes from higher teleost fishes to compare the accuracy of parsimony-based jackknife values with Bayesian support values. Phylogenetic analyses of 366 partitions, using differential taxon and character sampling from the entire data matrix of 100 taxa and 7,990 characters, were performed for both phylogenetic methods. The tree topology and branch-support values from each partition were compared with the tree inferred from all taxa and characters. Using this approach, we quantified the accuracy of the branch-support values assigned by the jackknife and Bayesian methods, with respect to each of 15 basal clades. In comparing the jackknife and Bayesian methods, we found that (1) both measures of support differ significantly from an ideal support index; (2) the jackknife underestimated support values; (3) the Bayesian method consistently overestimated support; (4) the magnitude by which Bayesian values overestimate support exceeds the magnitude by which the jackknife underestimates support; and (5) both methods performed poorly when taxon sampling was increased and character sampling was not increases. These results indicate that (1) the higher Bayesian support values are inappropriate (in magnitude), and (2) Bayesian support values should not be interpreted as probabilities that clades are correctly resolved. We advocate the continued use of the relatively conservative bootstrap and jackknife approaches to estimating branch support rather than the more extreme overestimates provided by the Markov Chain Monte Carlo-based Bayesian methods.
Animals↗