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Even S. cerevisiae had an equal substitution of Thr for Ser at this specific site.
For this analysis we consider a nucleotide character which follows the molecular clock assumption and has an equal substitution rate in the internode and four subtending branches in the four-taxon tree of interest (i.e. setting λ0 = λ1 = λ2 = λ3 = λ4 = λ in Figure 1).
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Details of the Z-tests are included in Additional File 5. A free-rate model, where a separate substitution rate was estimated for each branch, had significantly better fit to the data for 4 of our 6 alignments, over an equal-rate mode where terminal branches within a pair had equal substitution rates.
The parameters were as follows: assumed nucleotide frequencies are equal; substitution rate matrix with A-C substitutions = 1.0000, A-G = 2.7002, A-T = 0.7141, C-G = 0.7141, C-T = 3.8573, G-T = 1.0000; proportion of sites assumed to be invariable = 0 and rates for variable sites assumed to follow a gamma distribution with shape parameter = 0.3930.
Essentially, the model is analogous to a JC model [ 85] (equal substitution rates) except that it has a variable number of states (two in our case).
But because these works assume a character with binary states with equal substitution rates, the inconsistency conditions identified by assuming such a simplistic model cannot be directly applied to real-life molecular loci, which typically follow much more complex molecular evolutionary models and vary in rates of evolution.
We compared the likelihoods of two models: an equal-rate model, where terminal branches within a pair are constrained to have equal substitution rates, but substitution rates are allowed to vary between pairs; and a free-rate model, where a separate substitution rate is estimated for each terminal branch.
Given an equal synonymous substitution rate between mat and non-reproductive genes within each reproductive class, this finding indicates that mat-genes evolve faster than the non-reproductive genes.
Under the null model of equal substitution rates among branches, these estimates are expected to be similar (Tajima 1993).
We assume four alternative nucleotide substitution models for the nucleotide character, including from simple to complex the JC model, which assumes equal substitution rates and equal base frequencies at equilibrium, the Kimura 2-Parameter (K2P a.k.a.a
Under the null hypothesis of equal substitution rates in each lineage, the number of nucleotide changes is expected to be equal for the two taxa.
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