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Abstract Time-calibrated phylogenetic trees are a tremendously powerful tool for studying evolutionary, ecological, and epidemiological phenomena. Such trees are predominantly inferred in a Bayesian framework, with the phylogeny itself treated as a parameter with a prior distribution (a “tree prior”). However, we show that the tree “parameter” consists, in part, of data, in the form of taxon samples. Treating the tree as a parameter fails to account for these data and compromises our ability to compare among models using standard techniques (e.g., marginal likelihoods estimated using path-sampling and stepping-stone sampling algorithms). Since accuracy of the inferred phylogeny strongly depends on how well the tree prior approximates the true diversification process that gave rise to the tree, the inability to accurately compare competing tree priors has broad implications for applications based on time-calibrated trees. We outline potential remedies to this problem, and provide guidance for researchers interested in assessing the fit of tree models. [Bayes factors; Bayesian model comparison; birth-death models; divergence-time estimation; lineage diversification]