Abstract
Dating the divergence in a phylogenetic tree is a fundamental step in evolutionary analysis. Some extensions and improvements of the penalised likelihood method originally presented by Sander-son are introduced. The improvements are the introduction of alternative models, including one with non-correlated rates of molecular substitution (" relaxed " model), a completely reworked fitting algorithm that considers the high-dimensionality of the optimisation problem, and the development of a new information criterion for model selection in the presence of a penalised term. It is also shown that the strict clock model is a special case of the present approach. An extensive simulation study was conducted to assess the statistical performance of these improvements. Overall, the different estimators studied here appeared as unbiased though their variance varied depending on the fitted and the simulated models and on the number of calibration points. The strict clock model gave good estimates of branch lengths even in the presence of heterogeneous substitution rates. The correlated model gave the best estimates of substitution rates whatever the model used to simulate the data. These results, which are certainly the first from an extensive simulation study of a molecular dating method, call for more comparison with alternative methods, as well as further work on the developments introduced here.