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Importantly, modeling rate variation seemed to be an important component.
However, adding parameters for modeling rate variation to either of the two models increased the model likelihood tremendously.
Another striking feature was that once parameters for modeling rate variation had been incorporated into the model, unlinking topologies did not seem to have as pronounced effect on the model likelihood (Table 2), compared to the models without rate variation.
Maximum-likelihood parameters (amino acid frequencies, percent invariant sites, and α for modeling rate variation among sites) were estimated in TREEPUZZLE 5.0 [ 77] under a Jones-Taylor-Thornton (JTT [ 78]) substitution matrix with invariable + Γ (four category) distribution of rates.
In addition to allowing non-clock-like relationships among sequences related by a phylogeny, modeling rate variation among lineages in a gene tree also enable researchers to incorporate multiple calibration points that may not be consistent with a strict molecular clock.
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The authors mistake "relaxed molecular clock" for "approximate molecular clock": approximate molecular clocks correspond to model rate variation over time (e.g. with autocorrelation).
We also include a separate HMM to model rate variation along the sequence since ignoring this can lead to spurious recombination detection (Husmeier and McGuire, 2002).
More sophisticated methods were created to model rate variation and used auto-correlation of rates, local clocks, or the so called "uncorrelated relaxed clock" where substitution rates are assumed to be drawn from a parametric distribution.
Changing a component of the nucleotide substitution model, e.g. adding parameters to model rate variation, had much higher impact on the model likelihood than unlinking parameters among data partition.
However, changing a component of the nucleotide substitution model, e.g. adding parameters to model rate variation, had much higher impact on the model likelihood than unlinking parameters among data partition.
The semi-parametric rate smoothing method implements a stochastic model of rate change based on the hypothesis of rate autocorrelation between adjacent branches [ 31, 35] whereas others attempt to model rate variation across the tree in a Bayesian framework [ 32- 36, 36, 43].
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