A Compound Poisson Process for Relaxing the Molecular Clock

TLDR

The molecular clock hypothesis remains a key tool in evolutionary biology, yet it does not fully explain observed DNA sequence variation. This study introduces a parametric model that relaxes the molecular clock by allowing substitution rates to vary across lineages through a compound Poisson process. Rate‑change events are placed on a phylogenetic tree via a Poisson process, with each event scaling the current rate by a gamma‑distributed factor, and the model’s parameters are estimated using Bayesian inference with a Metropolis‑Hastings‑Green MCMC algorithm employing 11 move types. Applied to a complete mtDNA dataset from 23 mammals, the model demonstrates advantages over previous approaches by being parametric and not restricting rate changes to speciation events, making it useful for estimating divergence times when rates vary across lineages.

Abstract

Abstract The molecular clock hypothesis remains an important conceptual and analytical tool in evolutionary biology despite the repeated observation that the clock hypothesis does not perfectly explain observed DNA sequence variation. We introduce a parametric model that relaxes the molecular clock by allowing rates to vary across lineages according to a compound Poisson process. Events of substitution rate change are placed onto a phylogenetic tree according to a Poisson process. When an event of substitution rate change occurs, the current rate of substitution is modified by a gamma-distributed random variable. Parameters of the model can be estimated using Bayesian inference. We use Markov chain Monte Carlo integration to evaluate the posterior probability distribution because the posterior probability involves high dimensional integrals and summations. Specifically, we use the Metropolis-Hastings-Green algorithm with 11 different move types to evaluate the posterior distribution. We demonstrate the method by analyzing a complete mtDNA sequence data set from 23 mammals. The model presented here has several potential advantages over other models that have been proposed to relax the clock because it is parametric and does not assume that rates change only at speciation events. This model should prove useful for estimating divergence times when substitution rates vary across lineages.