Modeling Substitution Rate Evolution across Lineages and Relaxing the Molecular Clock

Abstract

Relaxing the molecular clock using models of how substitution rates change across lineages has become essential for addressing evolutionary problems. The diversity of rate evolution models and their implementations are substantial, and studies have demonstrated their impact on divergence time estimates can be as significant as that of calibration information. In this review, we trace the development of rate evolution models from the proposal of the molecular clock concept to the development of sophisticated Bayesian and non-Bayesian methods that handle rate variation in phylogenies. We discuss the various approaches to modeling rate evolution, provide a comprehensive list of available software, and examine the challenges and advancements of the prevalent Bayesian framework, contrasting them to faster non-Bayesian methods. Lastly, we offer insights into potential advancements in the field in the era of big data.

Keywords: model comparison; molecular clock history; molecular dating; rate heterogeneity; rate models; relaxed molecular clock.

Fig. 1.

The strict molecular clock (a) compared to models of rate evolution that assume discrete variation of substitution rates across branches: b) local clocks and c) discrete multirate clocks.

Fig. 2.

Models of rate evolution that assume continuous variation of substitution rates across branches: a) the autocorrelated lognormal relaxed clock and b) the uncorrelated lognormal relaxed clock. Autocorrelated rates were simulated following the method described by Thorne et al. (1998), resulting in a distribution of evolutionary rates shown as a mixture of lognormal distributions, which arises from the recursively iteration of the autocorrelated process. Uncorrelated rates were simulated by independently drawing from a lognormal distribution.

Fig. 3.

Diversity of current molecular dating software depicted according to their assumptions regarding the variation of rates along the phylogenetic tree. Asterisks indicate approaches that use a combination of rate evolution models. Methods marked in light gray indicate approaches that were originally developed with a focus on serially sampled/pathogen data. ME, mixed effects clock (Bletsa et al. 2019); FLC, flexible local clock (Fourment and Darling 2018); S-RLC, shrinkage-based random local clock (Fisher et al. 2023); RLC, random local clock (Drummond and Suchard 2010); AURC, additive uncorrelated relaxed clock (Didelot et al. 2021); WN, white-noise process (Lepage et al. 2007); MRC, mixed relaxed clock (Lartillot et al. 2016); CIR, Cox–Ingersoll–Ross process (Lepage et al. 2007); CPP, compound Poisson process (Huelsenbeck et al. 2000).