Confidence intervals in molecular dating by maximum likelihood

Molecular dating has been widely used to infer the times of past evolutionary events using molecular sequences. This paper describes three bootstrap methods to infer confidence intervals under a penalized likelihood framework. The basic idea is to use data pseudoreplicates to infer uncertainty in the branch lengths of a phylogeny reconstructed with molecular sequences. The three specific bootstrap methods are nonparametric (direct tree bootstrapping), semiparametric (rate smoothing), and parametric (Poisson simulation). Our extensive simulation study showed that the three methods perform generally well under a simple strict clock model of molecular evolution; however, the results were less positive with data simulated using an uncorrelated or a correlated relaxed clock model. Several factors impacted, possibly in interaction, the performance of the confidence intervals. Increasing the number of calibration points had a positive effect, as well as increasing the sequence length or the number of sequences although both latter effects depended on the model of evolution. A case study is presented with a molecular phylogeny of the Felidae (Mammalia: Carnivora). A comparison was made with a Bayesian analysis: the results were very close in terms of confidence intervals and there was no marked tendency for an approach to produce younger or older bounds compared to the other.