Accurate estimations of evolutionary times in the context of strong CpG hypermutability.

We consider the substitution model T92+CpG of DNA sequence evolution which takes into account the hypermutability of CpG dinucleotides, an effect that can be especially observed in vertebrate genomes. We provide an exact method to simulate the evolution of finite DNA sequences under this model and numerical procedures to infer evolutionary times in two cases: between an ancestral and a present sequence and between two homologous sequences. We show on simulated data that our new numerical method yields very accurate estimations of divergence times. In a context of strong CpG hypermutability, it clearly outperforms the classical estimation procedure that is solely based on the model T92 without CpG influence. Supplementary Material is available at www.liebertonline.com/cmb .

Priors for the Bayesian star paradox.

We show that the Bayesian star paradox, first proved mathematically by Steel and Matsen for a specific class of prior distributions, occurs in a wider context including less regular, possibly discontinuous, prior distributions.

Phylogenetic distances for neighbour dependent substitution processes.

We consider models of nucleotidic substitution processes where the rate of substitution at a given site depends on the state of the neighbours of the site. We first estimate the time elapsed between an ancestral sequence at stationarity and a present sequence. Second, assuming that two sequences are issued from a common ancestral sequence at stationarity, we estimate the time since divergence. In the simplest non-trivial case of a Jukes-Cantor model with CpG influence, we provide and justify mathematically consistent estimators in these two settings. We also provide asymptotic confidence intervals, valid for nucleotidic sequences of finite length, and we compute explicit formulas for the estimators and for their confidence intervals. In the general case of an RN model with YpR influence, we extend these results under a proviso, namely that the equation defining the estimator has a unique solution.