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The PHYML program [71], [72] was used for the maximum likelihood analyses (http://atgc.lirmm.fr/phyml/) utilizing the WAG amino acid substitution matrix, with gamma correction (4 categories) and accounting for the number of invariant sites.
The amino acid replacement matrix, the WAG matrix, with gamma distribution was used to reconstruct the phylogenetic tree.
Similarly, we performed ML calculations using the JTT substitution matrix with gamma distribution of rates (JTT+Γ), for each of the six structural classes.
Maximum-likelihood trees for the same set of gene families were found using RAxML [ 81] using the BLOSUM62 substitution rate matrix with gamma distributed rate variation among sites.
ProtTest3 (Darriba et al. 2011) gave the improved general amino-acid replacement matrix, with gamma distributed rates across sites (LG+G) as the best evolutionary model.
The LG amino acid substitution matrix with gamma rate correction was selected based on hierarchical likelihood ratio tests of the optimal tree calculated using the JTT amino acid substitution matrix (the PROTGAMMAJTT model in RAxML) [ 78].
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The JTT matrix with gamma-distributed rate variation among sites was specified in subsequent phylogenetic analyses.
When F is given as a symmetric function f of the eigenvalues (lambda _1, ldots,lambda _n) of the matrix r, with (Gamma ) closed under orthogonal transformations, we will refer to (mathcal F) as orthogonally invariant.
After testing various models with MEGA5 [ 42], we used the WAG substitution matrix with a gamma distribution of substitution rate across sites (the shape parameter α was estimated from the data with four rate categories).
Two independent runs of 800,000 generations were performed from random start trees, using the WAG substitution matrix with a gamma-distributed variation in substitution rate approximated to 4 discrete categories (shape parameter estimated from the data).
Eight independent runs of 200,000 generations were performed from random start trees (initial 40,000 generations discarded) using the WAG substitution matrix with a gamma-distributed variation in substitution rate approximated to 4 discrete categories (shape parameter estimated from the data).
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