Approximate Conditional Independence of Separated Subtrees and Phylogenetic Inference

• Activity Number: 639
• Type: Topic Contributed
• Date/Time: Thursday, August 8, 2013 : 8:30 AM to 10:20 AM
• Sponsor: Biometrics Section
• Author(s): Bret Larget*+
• Companies: Univ of Wisconsin-Madison
• Keywords: phylogenetics ; Bayesian inference ; likelihood calculation ; trees ; importance sampling

Abstract

Bayesian methods to reconstruct evolutionary trees from aligned DNA sequence data from different species depend on Markov chain Monte Carlo sampling of phylogenetic trees from a posterior distribution. The probabilities of tree topologies are typically estimated with the simple relative frequencies of the trees in the sample. We present a new method for estimating the posterior distribution on the space of trees from samples based on the approximation of conditional independence between subtrees given their separation by an edge in the tree. This approximation procedure effectively spreads the estimated posterior distribution from the sampled trees to the larger set of trees that contain clades (sets of species in subtrees) that have been sampled, even if the full tree is not part of the sample. The approximation is shown to be accurate for many data sets and is theoretically justified. We also explore a consequence of this result that may lead to substantial increases in computational efficiency for sampling trees from posterior distributions.