Phylogenetic distances for neighbour dependent substitution processes

TL;DR

This paper develops methods to accurately estimate evolutionary divergence times under complex nucleotide substitution models that depend on neighboring sites, providing explicit formulas and confidence intervals.

Contribution

It introduces exact estimators and confidence intervals for divergence times in neighbor-dependent substitution models, including explicit formulas for the Jukes-Cantor with CpG influence.

Findings

Exact estimators for divergence times are derived.

Confidence intervals are provided for finite sequence lengths.

Explicit formulas are given for the Jukes-Cantor model with CpG influence.

Abstract

We consider models of nucleotidic substitution processes where the rate of substitution at a given site depends on the state of its neighbours. For a wide class of such nonreversible models, we show how to compute consistent, mathematically exact, estimators of the time elapsed between aligned sequences, for an ancestral sequence and a present one, and also for two present sequences. In both cases, we provide asymptotic confidence intervals, valid for nucleotidic sequences of finite length. We compute explicit formulas for the estimators and for their confidence intervals in the simplest nontrivial case, the Jukes-Cantor model with CpG influence.