The use of fossil evidence to calibrate divergence time estimation has a long
history. More recently Bayesian MCMC has become the dominant method of
divergence time estimation and fossil evidence has been re-interpreted as the
specification of prior distributions on the divergence times of calibration
nodes. These so-called "soft calibrations" have become widely used but the
statistical properties of calibrated tree priors in a Bayesian setting has not
been carefully investigated. Here we clarify that calibration densities, such
as those defined in BEAST 1.5, do not represent the marginal prior distribution
of the calibration node. We illustrate this with a number of analytical results
on small trees. We also describe an alternative construction for a calibrated
Yule prior on trees that allows direct specification of the marginal prior
distribution of the calibrated divergence time, with or without the restriction
of monophyly. This method requires the computation of the Yule prior
conditional on the height of the divergence being calibrated. Unfortunately, a
practical solution for multiple calibrations remains elusive. Our results
suggest that direct estimation of the prior induced by specifying multiple
calibration densities should be a prerequisite of any divergence time dating
analysis
