In contrast, the Rel Time approach does not require specification of such priors, and produces relative node ages that can then be transformed into absolute dates by using calibration constraints for one or more nodes (Tamura et al. Rel Time performs well for estimating divergence times in analyses of many large empirical data sets (Mello et al. The above equations (19–27) establish RRF of the Rel Time approach for a tree containing four taxa and one outgroup.As previously mentioned, point estimates of node ages and lineage rates have variances because branch lengths have variances and because evolutionary rates are not equal among lineages (see Discussion).In both the original Rel Time approach (Tamura et al.2012) and the mathematical formulations above, we considered an arithmetic mean when averaging branch lengths to minimize evolutionary rate changes.This approach does not assume an equal rate, but is rather a natural way to calculate node depths by averaging branch lengths.We have now developed analytical formulas for an alternative RRF using the geometric mean that balances the rate changes between two descendant lineages.For example, if , as compared with the average rate.That is, the difference in rate between the ancestral and descendant lineages is always equal for sister lineages when using the geometric mean, which is not the case if the arithmetic mean is used.

2006), as well as a model that contains multiple distributions of rates (hybrid rates [HR]).Next, we consider a general case of a phylogeny with more than four ingroup taxa.In this case, Rel Time applies RRF with a bottom-up approach, starting from the tips (external branches) of the phylogeny and moving toward the root. Then, we use equations (34–39) to compute relative rates for all the lineages using these branch lengths.Rel Time estimates divergence times by relaxing the assumption of a strict molecular clock in a phylogeny.It shows excellent performance in estimating divergence times for both simulated and empirical molecular sequence data sets in which evolutionary rates varied extensively throughout the tree.