For each Participant and rating 'R', the position PR, dispersion DR, and frequency FR of the category of rating 'R' were determined from the frequency distribution fR(s) as the Mean, Standard deviation and Number of samples, respectively.
We define the support of a category of rating 'R' as the interval between the extreme sizes where µR s)>0, the core as the interval between the extreme sizes that compose the 1-cut, and the peripheries as the difference between support and core.
For each global category of rating, an agreement rate was then computed.
We find that nine distinct rate classes, empirically estimated from the data, plus a category of rates estimated to be zero, are sufficient for the Turkic data.
In each analysis, 4 categories of rate variation were used.
ML and BI analyses of the amino acid alignment (i.e., alignment 4) was analyzed under a WAG model of substitution considering corrections for site-to-site rate variation (gamma) with eight categories of rate variation and proportion of invariable sites.
The best likelihood trees were searched under the GTR-GAMMA model with six categories of rate variation (500 bootstrap replicates were undertaken for estimation of node support).
We utilised four categories of rate variation across the amino acid sites and 500 bootstrap replicates were generated for the estimation of node support.
We performed this inference on both untrimmed and BMGE-trimmed versions of the concatenated matrix, using a combination of NNI and SPR heuristic searches, and inferring under the LG+F model with four 'free' (--free-rates) categories of rate variation.
Nucleotide substitution models were obtained from jModeltest (version 2.1, [ 38, 39], testing 11 substitution schemes, each with 4 categories of rate variation among sites) and using the corrected AIC criterion (AICc) to find the best fitting model.
