Bayesian Markov chain Monte Carlo explores tree space slowly, in part because it frequently returns to the same tree topology. An alternative strategy would be to explore tree space systematically, and never return to the same topology. In this article, we present an efficient parallelized method to map out the high likelihood set of phylogenetic tree topologies via systematic search, which we show to be a good approximation of the high posterior set of tree topologies on the data sets analyzed. Here, “likelihood” of a topology refers to the tree likelihood for the corresponding tree with optimized branch lengths. We call this method “phylogenetic topographer” (PT). The PT strategy is very simple: starting in a number of local topology maxima (obtained by hillclimbing from random starting points), explore out using local topology rearrangements, only continuing through topologies that are better than some likelihood threshold below the best observed topology. We show that the normalized topology likelihoods are a useful proxy for the Bayesian posterior probability of those topologies. By using a nonblocking hash table keyed on unique representations of tree topologies, we avoid visiting topologies more than once across all concurrent threads exploring tree space. We demonstrate that PT can be used directly to approximate a Bayesian consensus tree topology. When combined with an accurate means of evaluating pertopology marginal likelihoods, PT gives an alternative procedure for obtaining Bayesian posterior distributions on phylogenetic tree topologies.
The Lowest Radial Distance (LoRaD) method is a modification of the recently introduced PartitionWeighted Kernel method for estimating the marginal likelihood of a model, a quantity important for Bayesian model selection. For analyses involving a fixed tree topology, LoRaD improves upon the Steppingstone or Thermodynamic Integration (Path Sampling) approaches now in common use in phylogenetics because it requires sampling only from the posterior distribution, avoiding the need to sample from a series of ad hoc power posterior distributions, and yet is more accurate than other fast methods such as the Generalized Harmonic Mean (GHM) method. We show that the method performs well in comparison to the Generalized Steppingstone method on an empirical fixedtopology example from molecular phylogenetics involving 180 parameters. The LoRaD method can also be used to obtain the marginal likelihood in the variabletopology case if at least one tree topology occurs with sufficient frequency in the posterior sample to allow accurate estimation of the marginal likelihood conditional on that topology. [Bayesian; marginal likelihood; phylogenetics.]
more » « less NSFPAR ID:
 10404989
 Publisher / Repository:
 Oxford University Press
 Date Published:
 Journal Name:
 Systematic Biology
 ISSN:
 10635157
 Format(s):
 Medium: X
 Sponsoring Org:
 National Science Foundation
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Abstract 
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