The Exact Distribution of Divergence Times

The recent work of Haubold and Wiehe (Mol. Biol. Evol. 18:1157–1160, 2001) considered statistical inference of the divergence time. However, there appears to be a fundamental flaw in the paper since it treated the divergence time as a random variable and not as a parameter. In this note, we derive a valid statistical inference for the divergence time. We derive an estimator for the divergence time as well as explicit expressions for its the probability density function, cumulative distribution function and the means. We also provide a 5-line computer program for computing the associated confidence intervals. We expect that the results presented could be useful for statistical modeling of divergence times.