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Bootstrap supports were estimated from 1,000 samples of alignment generated by the SEQBOOT program of PHYLIP v3.69 (Felsenstein 1989).
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After convergence, it permits sampling of alignments.
We therefore define an MH transition kernel that uses collapsed sampling of alignments as a proposal distribution ρ.
A sample of alignments was checked manually for obvious alignment mistakes, none were found, and consequently the alignments were not edited further.
The MCMC approach requires optimal sampling of alignments, each of which ideally represents a single genealogy, to obtain precise estimations of τ and θ.
A sample of alignments and CFs for three genes will be illustrated namely polypyrimidine tract binding protein 2 (PTBP2), FBJ murine osteosarcoma viral oncogene homolog (FOS), and oligodendrocyte transcription factor 1 (OLIG1).
Any nucleotide position in the multiple alignment that failed to have information for at least three samples of the alignment (4.47% of the samples) was deleted on the grounds that it was unlikely to represent homology shared across the alignment.
Quartet Decomposition was performed on 100 topologies per gene family inferred by maximum likelihood from 100 bootstrap samples of each alignment using phyML [66] using the nucleotide substitution models selected above and estimating substitution frequencies and a proportion of invariable sites from the data with 4 rate categories in a gamma distribution where required by the model.
To estimate the level of support for each internal branch, we generated 1,000 non-parametric bootstrap samples of the alignment by using the SEQBOOT program in the PHYLIP package [ 44] and repeated the phylogenetic inference as described above.
While this approach renders a quick way to prepare aligned samples, the extent of alignment is small for high-resolution structural studies on membrane proteins.
We confirmed this conjecture based on random sampling of multiple alignment columns in the WPA so as to match the alignment lengths in the CDA, and as suspected, on average, the sampled WPA reduces the number of cases of asymmetric evolution as compared to WPA and yields a comparable fraction of asymmetric evolution as that for the CDA (Additional file 1: Table S3).
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