For each of these groups, we aligned the protein sequences using MAFFT software [ 65] and cleaned alignment using trimAl software [ 66] to remove all positions in the alignment with gaps in 10% or more of the sequences.
Finally we concatenated all the cleaned alignment files, obtaining a multiple alignment of about 5000 7000 columns.
From the filtered and cleaned alignment, augur builds a phylogenetic tree using FastTree (Price et al., 2009), which is then further refined using RAxML (Stamatakis, 2014).
For each cleaned or non-cleaned alignment the best-fit amino acid substitution model was selected using ProtTest from MEGA5 [ 57].
Based on these manually cleaned alignments (Methods S2), we constructed and calibrated HMMs (Methods S3).
Cleaned alignments of representative proteins tend to be more homogeneous than alignments of random proteins.
Maximum likelihood (ML) phylogenetic trees corresponding to the 111 cleaned alignments were inferred with PHYML-3.1 [ 25].
Afterwards, in order to obtain codon-cleaned alignments, we mapped the coding sequences (CDS) of NHX and SOS1 genes to protein alignments.
All cleaned alignments containing codons under positive selection are provided in Additional file 4. For inferring ω on branches, the alignments and the corresponding phylogenies were used as input for mapNH [ 78, 79].
The codon-cleaned alignments and the NJ phylogenetic trees (both rooted and unrooted), were further used in Codeml from the PAML package [ 62] to determine heterogeneous selective pressure on amino acid sites.
