Are Nonuniform Clade Priors Important in Bayesian Phylogenetic Analysis? A Response to Brandley et al

The use and design of prior distributions that reflect prior ignorance have long been controversial in statistics. The use of any prior distribution marks the difference between Bayesian and frequentist schools of thought. Disagreements regarding the design of prior distributions to reflect ignorance, and the interpretation of posterior distributions derived from such priors, have resulted in conflicting Bayesian philosophies. In a recent study, Pickett and Randle (2005) examined uniform prior distribution on tree topologies, which has been commonly used as a reflection of prior ignorance. We demonstrated that if all trees are considered to be equally probable a priori, all clades cannot be (except when n taxa <4). In a combined analysis of 17 empirical studies, nonuniform clade priors were correlated with Bayesian clade support. However, resampling supports (bootstrap and jackknife values) were also correlated with clade priors in these empirical studies. Using contrived data, we demonstrated that the correlation between resampling support and nonuniform clade priors is due to character conflict. When data sets lacked conflict, correlation disappeared, which follows from well-known properties of the bootstrap and jackknife (Farris, 1996). On the other hand, Bayesian clade support was correlated with nonuniform clade priors, even when there was no character conflict. Brandley et al. have called these findings into question, and although we consider their arguments flawed in several ways, they have posed a provocative question; are unequal clade priors problematic in Bayesian analysis? We address their concerns with our work, and conclude with a consideration of whether the question they pose has been answered.