Relaxing the Molecular Clock to Different Degrees for Different Substitution Types

Abstract

Rates of molecular evolution can vary over time. Diverse statistical techniques for divergence time estimation have been developed to accommodate this variation. These typically require that all sequence (or codon) positions at a locus change independently of one another. They also generally assume that the rates of different types of nucleotide substitutions vary across a phylogeny in the same way. This permits divergence time estimation procedures to employ an instantaneous rate matrix with relative rates that do not differ among branches. However, previous studies have suggested that some substitution types (e.g., CpG to TpG changes in mammals) are more clock-like than others. As has been previously noted, this is biologically plausible given the mutational mechanism of CpG to TpG changes. Through stochastic mapping of sequence histories from context-independent substitution models, our approach allows for context-dependent nucleotide substitutions to change their relative rates over time. We apply our approach to the analysis of a 0.15 Mb intergenic region from eight primates. In accord with previous findings, we find comparatively little rate variation over time for CpG to TpG substitutions but we find more for other substitution types. We conclude by discussing the limitations and prospects of our approach.

Grouping substitution types into different relaxed molecular clocks

“…Typically, neither is directly observed. Lee et al [8] estimated these sufficient statistics by sampling endpoint-conditioned histories using context-independent substitution models and assuming these histories well approximated a sample of endpoint-conditioned histories from a context-dependent model. Simulation suggested that this approach was reasonable for the primate data analysed by Lee et al [8].…”

“…Lee et al [8] estimated these sufficient statistics by sampling endpoint-conditioned histories using context-independent substitution models and assuming these histories well approximated a sample of endpoint-conditioned histories from a context-dependent model. Simulation suggested that this approach was reasonable for the primate data analysed by Lee et al [8]. If we assume that endpoint-conditioned context-independent histories are a good approximation of context-dependent histories, then the sufficient statistics f b(k)j and n kj can be approximated by their sample means among histories.…”

“…Then, the sample mean among histories can be reported. This latter procedure also facilitates approximation of the variances and covariances of substitution length estimates [8] and is what we refer to here as the 'unweighted procedure'.…”

“…Our extension also employs multidivtime, but has each group rather than each gene or each substitution type with its own independent relaxed clock. For the sake of comparison with Lee et al [8], we analyse the same data as did that study. Specifically, we use an approximately 0.15 Mb subset of data from Kim et al [6] that corresponds to an intergenic part of human chromosome 16 with CpG islands masked by Repeatmasker [14].…”

“…Adding gamma-distributed rate heterogeneity and other contextindependent improvements to the substitution model has the potential to make paths sampled by a context-independent model better approximate the endpoint-conditioned distribution from a context-dependent model. To examine whether incorporating enhancements to the context-independent model would impact divergence time estimates, we also applied the 'unweighted procedure' to obtain substitution lengths from the 312 context-independent sequence paths that were sampled by Lee et al [8]. These 312 paths were generated from the primate dataset with the CAT-GTR model and a four-category discretized gamma treatment of rate heterogeneity (see [8]).…”