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Fast-evolving sites were identified using the discrete gamma rate category to which they belong [ 73].
Because the actual evolutionary rate of site j is unknown, the likelihood of the site j data is integrated against all possible rates, using the discrete gamma approximation and removing explicit dependence on the site-specific rate r j.
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The Dayhoff model of amino acid substitution was used and the discrete gamma distribution model, with four rate categories and an estimated alpha parameter, was implemented.
ML bootstrap values were calculated with the program phyml [ 74], using a discrete gamma model with four rate categories and 100 resamplings; the gamma parameter alpha was calculated individually for each resampled dataset.
In total, 48 different amino acid substitution models were tested by the MEGA 5.2.2 software using a discrete Gamma distribution.
Based on the Kimura 2-parameter model using a discrete Gamma distribution (K2 + G) with 5 rate categories selected by the corrected Akaike Information Criterion (AICc) implemented in MEGA5, a single ML tree (log likelihood = −4114.9869) was recovered (Figure 6A).
The amino acids substitution model described by Whelan and Goldman [ 61] using a discrete Gamma distribution with five categories, was chosen as the best substitution model, since it gave the lowest Bayesian Information Criterion values and corrected Akaike Information Criterion values [ 62] in MEGA5 [ 60].
Using this tree, Bayesian time inference was performed with phylobayes v3.3 using a discrete gamma distribution with eight categories under the GTR matrix of exchange rates, using a log-normal autocorrelated relaxed clock together with a uniform prior on divergence times.
Fast-evolving positions for each dataset were identified individually using a discrete gamma rate category and sites belonging to the most rapidly evolving eighth gamma category were removed.
The Tamura 3-parameter model (T92) with evolutionary rates among sites modeled by using a discrete Gamma distribution (+G) with 5 rate categories had the highest fit (lowest BIC value) among the 24 different nucleotide substitution models tested by maximum likelihood.
The HKY+G model of nucleotide substitution36 was selected based on the Bayesian information criterion using Modelgenerator37, with rate heterogeneity among sites modelled using a discrete gamma distribution with six rate categories.
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