How to summarize estimates of ancestral divergence times.

The use of molecular sequence data has increased interest in trying to date evolutionary events, with researchers wanting both an estimate of the divergence time and a confidence interval for that estimate. However, two methodological issues have recently been raised with respect to precision of the estimates: (i) the time of the ancestral event is over-estimated; and (ii) the confidence interval is asymmetrical. I argue that if the estimates of divergence time are considered to be samples from a lognormal probability distribution, then this would explain both of these problems. This implies that divergence times should be presented using geometric means rather than arithmetic means, both for estimates and for their confidence intervals. I present analyses based on both computer simulations and empirical data to show that this approach is effective for both single-gene and multiple-gene data sets. Treating divergence time as a lognormal variable thus provides a simple unifying framework for dealing with many of the problems associated with the estimation of divergence (and possibly coalescence) times. Use of this approach (based on geometric means) can, unfortunately, lead to very different biological conclusions compared to the currently used calculation methods (based on arithmetic means).