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Abstract
Bayesian inference is now a leading technique for reconstructing phylogenetic trees
from aligned sequence data. In this short note, we formally show that the maximum
posterior tree topology provides a statistically consistent estimate of a fully-resolved
evolutionary tree under a wide variety of conditions. This includes the inference
of gene trees from aligned sequence data across the entire parameter range of branch
lengths, and under general conditions on priors in models where the usual `identifiability'
conditions hold. We extend this to the inference of species trees from sequence data,
where the gene trees constitute `nuisance parameters', as in the program *BEAST. This
note also addresses earlier concerns raised in the literature questioning the extent
to which statistical consistency for Bayesian methods might hold in general.