Many other authors, who have constructed matrices of substitutions using the mutations accumulated in pseudogene sequences have made the same assumptions [ 15, 16].
The resulting alignment was trimmed using BMGE (Block Mapping and Gathering with Entropy, using the matrix of substitution: BLOSUM30).
One of the main assumptions underlying the phylogenetic models is that homologous sequences have evolved by a Markovian process of amino acid residue substitution, described by a 20 × 20 matrix of substitution rates.
We call V i ∗ = (v i, 1 ∗,..., v i, b ∗,..., v i, m ∗ ) the weighted substitution vectors, with v i, b ∗ = ∑ c ∑ x p ∑ x q Pr (x p, x q, r c | D i, Θ ) × w x p, x q where W = { w x, y } is a matrix of substitution weights.
In effect, even the most rich parameter models of classical available ML methods are stationary and homogeneous (i.e., they assume that the same matrix of substitution applies to all branches of the tree and all sites, therefore compositional biases may lead to wrong topology with high bootstrap and high aLRT branch support).
This is not just a feature of any matrix of substitutions.
In particular, when the null hypothesis of independence between nucleotides is true, that the matrix of dinucleotide substitution probabilities for time t is equal to the Kronecker product of the nested nucleotide substitution matrix for time t, i.e.. Pdinuc = Pnuc ⊗ Pnuc.
A 61×61 matrix of codon substitution rates (excluding the three stop codons) is used, assuming that mutations occur at the three codon positions independently and only single-nucleotide substitutions are permitted to occur at any instant.
Using multivariate genomic selection methodology [ 10] for mastitis traits, it is possible to build a (co variance matrix of allele substitution effects.
(For the detailed description of the model and parameters used for each phylogenetic inference, including the matrix of aa substitution; number of Gamma discrete rate-categories (+G); proportion of invariable sites (+I) and observed amino acid frequencies (+F), see figure captions).
