dnds

Estimate synonymous and nonsynonymous substitution rates

Syntax

[Dn, Ds, Vardn, Vards] = dnds(SeqNT1, SeqNT2)

[Dn, Ds, Vardn, Vards] = dnds(SeqNT1, SeqNT2, ...'GeneticCode', GeneticCodeValue, ...)
[Dn, Ds, Vardn, Vards] = dnds(SeqNT1, SeqNT2, ...'Method', MethodValue, ...)
[Dn, Ds, Vardn, Vards] = dnds(SeqNT1, SeqNT2, ...'Window', WindowValue, ...)
[Dn, Ds, Vardn, Vards] = dnds(SeqNT1, SeqNT2, ...'AdjustStops', AdjustStopsValue, ...)
[Dn, Ds, Vardn, Vards] = dnds(SeqNT1, SeqNT2, ...'Verbose', VerboseValue, ...)

Input Arguments

SeqNT1, SeqNT2Nucleotide sequences. Enter either a string or a structure with the field Sequence.
GeneticCodeValueProperty to specify a genetic code. Enter a Code Number or a string with a Code Name from the table Genetic Code. If you use a Code Name, you can truncate it to the first two characters. Default is 1 or Standard.
MethodValue

String specifying the method for calculating substitution rates. Choices are:

  • NG (default) — Nei-Gojobori method (1986) uses the number of synonymous and nonsynonymous substitutions and the number of potentially synonymous and nonsynonymous sites. Based on the Jukes-Cantor model.

  • LWLLi-Wu-Luo method (1985) uses the number of transitional and transversional substitutions at three different levels of degeneracy of the genetic code. Based on Kimura's two-parameter model.

  • PBLPamilo-Bianchi-Li method (1993) is similar to the Li-Wu-Luo method, but with bias correction. Use this method when the number of transitions is much larger than the number of transversions.

WindowValueInteger specifying the sliding window size, in codons, for calculating substitution rates and variances.
AdjustStopsValueControls whether stop codons are excluded from calculations. Choices are true (default) or false.
VerboseValueProperty to control the display of the codons considered in the computations and their amino acid translations. Choices are true or false (default).

    Tip   Specify true to use this display to manually verify the codon alignment of the two input sequences. The presence of stop codons (*) in the amino acid translation can indicate that SeqNT1 and SeqNT2 are not codon-aligned.

Output Arguments

Dn Nonsynonymous substitution rate(s).
DsSynonymous substitution rate(s).
Vardn Variance for the nonsynonymous substitution rate(s).
Vards Variance for the synonymous substitutions rate(s).

Description

[Dn, Ds, Vardn, Vards] = dnds(SeqNT1, SeqNT2) estimates the synonymous and nonsynonymous substitution rates per site between the two homologous nucleotide sequences, SeqNT1 and SeqNT2, by comparing codons using the Nei-Gojobori method.

dnds returns:

  • Dn — Nonsynonymous substitution rate(s).

  • Ds — Synonymous substitution rate(s).

  • Vardn — Variance for the nonsynonymous substitution rate(s).

  • Vards — Variance for the synonymous substitutions rate(s).

This analysis:

  • Assumes that the nucleotide sequences, SeqNT1 and SeqNT2, are codon-aligned, that is, do not have frame shifts

  • Excludes codons that include ambiguous nucleotide characters or gaps

  • Considers the number of codons in the shorter of the two nucleotide sequences

    Caution   If SeqNT1 and SeqNT2 are too short or too divergent, saturation can be reached, and dnds returns NaNs and a warning message.

[Dn, Ds, Vardn, Vards] = dnds(SeqNT1, SeqNT2, ...'PropertyName', PropertyValue, ...) calls dnds with optional properties that use property name/property value pairs. You can specify one or more properties in any order. Each PropertyName must be enclosed in single quotation marks and is case insensitive. These property name/property value pairs are as follows:


[Dn, Ds, Vardn, Vards] = dnds(SeqNT1, SeqNT2, ...'GeneticCode', GeneticCodeValue, ...)
calculates synonymous and nonsynonymous substitution rates using the specified genetic code. Enter a Code Number or a string with a Code Name from the table Genetic Code. If you use a Code Name, you can truncate it to the first two characters. Default is 1 or Standard.

[Dn, Ds, Vardn, Vards] = dnds(SeqNT1, SeqNT2, ...'Method', MethodValue, ...) allows you to calculate synonymous and nonsynonymous substitution rates using the following algorithms:

  • NG (default) — Nei-Gojobori method (1986) uses the number of synonymous and nonsynonymous substitutions and the number of potentially synonymous and nonsynonymous sites. Based on the Jukes-Cantor model.

  • LWL — Li-Wu-Luo method (1985) uses the number of transitional and transversional substitutions at three different levels of degeneracy of the genetic code. Based on Kimura's two-parameter model.

  • PBL — Pamilo-Bianchi-Li method (1993) is similar to the Li-Wu-Luo method, but with bias correction. Use this method when the number of transitions is much larger than the number of transversions.

[Dn, Ds, Vardn, Vards] = dnds(SeqNT1, SeqNT2, ...'Window', WindowValue, ...) performs the calculations over a sliding window, specified in codons. Each output is an array containing a rate or variance for each window.

[Dn, Ds, Vardn, Vards] = dnds(SeqNT1, SeqNT2, ...'AdjustStops', AdjustStopsValue, ...) controls whether stop codons are excluded from calculations. Choices are true (default) or false.

    Tip   When the 'AdjustStops' property is set to true, the following are true:

    • Stop codons are excluded from frequency tables.

    • Paths containing stop codons are not counted in the Nei-Gojobori method.

[Dn, Ds, Vardn, Vards] = dnds(SeqNT1, SeqNT2, ...'Verbose', VerboseValue, ...) controls the display of the codons considered in the computations and their amino acid translations. Choices are true or false (default).

    Tip   Specify true to use this display to manually verify the codon alignment of the two input sequences, SeqNT1 and SeqNT2. The presence of stop codons (*) in the amino acid translation can indicate that SeqNT1 and SeqNT2 are not codon-aligned.

Examples

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Estimate synonymous and nonsynonymous substitution rates between two nucleotide sequences

This example shows how to estimate synonymous and nonsynonymous substitution rates between two nucleotide sequences that are not codon-aligned.

This example uses two nucleotide sequences representing the human HEXA gene (accession number: NM_000520) and mouse HEXA gene (accession number: AK080777).

If you have live internet connection, you can use getgenbank function to retrieve the sequence information from the NCBI data repository and load the data into MATLAB®.

humanHEXA = getgenbank('NM_000520');
mouseHEXA = getgenbank('AK080777');

For your convenience, MATLAB provides these two sequences in the following mat file. Note that data in public databases are frequently updated and curated, and the results in this example may slightly differ if you use the latest data.

load hexosaminidase.mat

Extract the coding regions from the two nucleotide sequences.

humanHEXA_cds = featuresparse(humanHEXA,'feature','CDS','Sequence',true);
mouseHEXA_cds = featuresparse(mouseHEXA,'feature','CDS','Sequence',true);

Align the amino acid sequences converted from the nucleotide sequences.

[sc,al] = nwalign(nt2aa(humanHEXA_cds),nt2aa(mouseHEXA_cds),'extendgap',1);

Use the seqinsertgaps function to copy the gaps from the aligned amino acid sequences to their corresponding nucleotide sequences, thus codon-aligning them.

humanHEXA_aligned = seqinsertgaps(humanHEXA_cds,al(1,:))
mouseHEXA_aligned = seqinsertgaps(mouseHEXA_cds,al(3,:))
humanHEXA_aligned =

atgacaagctccaggctttggttttcgctgctgctggcggcagcgttcgcaggacgggcgacggccctctggccctggcctcagaacttccaaacctccgaccagcgctacgtcctttacccgaacaactttcaattccagtacgatgtcagctcggccgcgcagcccggctgctcagtcctcgacgaggccttccagcgctatcgtgacctgcttttcggttccgggtcttggccccgtccttacctcacagggaaacggcatacactggagaagaatgtgttggttgtctctgtagtcacacctggatgtaaccagcttcctactttggagtcagtggagaattataccctgaccataaatgatgaccagtgtttactcctctctgagactgtctggggagctctccgaggtctggagacttttagccagcttgtttggaaatctgctgagggcacattctttatcaacaagactgagattgaggactttccccgctttcctcaccggggcttgctgttggatacatctcgccattacctgccactctctagcatcctggacactctggatgtcatggcgtacaataaattgaacgtgttccactggcatctggtagatgatccttccttcccatatgagagcttcacttttccagagctcatgagaaaggggtcctacaaccctgtcacccacatctacacagcacaggatgtgaaggaggtcattgaatacgcacggctccggggtatccgtgtgcttgcagagtttgacactcctggccacactttgtcctggggaccaggtatccctggattactgactccttgctactctgggtctgagccctctggcacctttggaccagtgaatcccagtctcaataatacctatgagttcatgagcacattcttcttagaagtcagctctgtcttcccagatttttatcttcatcttggaggagatgaggttgatttcacctgctggaagtccaacccagagatccaggactttatgaggaagaaaggcttcggtgaggacttcaagcagctggagtccttctacatccagacgctgctggacatcgtctcttcttatggcaagggctatgtggtgtggcaggaggtgtttgataataaagtaaagattcagccagacacaatcatacaggtgtggcgagaggatattccagtgaactatatgaaggagctggaactggtcaccaaggccggcttccgggcccttctctctgccccctggtacctgaaccgtatatcctatggccctgactggaaggatttctacatagtggaacccctggcatttgaaggtacccctgagcagaaggctctggtgattggtggagaggcttgtatgtggggagaatatgtggacaacacaaacctggtccccaggctctggcccagagcaggggctgttgccgaaaggctgtggagcaacaagttgacatctgacctgacatttgcctatgaacgtttgtcacacttccgctgtgaattgctgaggcgaggtgtccaggcccaacccctcaatgtaggcttctgtgagcaggagtttgaacagacctga


mouseHEXA_aligned =

atggccggctgcaggctctgggtttcgctgctgctggcggcggcgttggcttgcttggccacggcactgtggccgtggccccagtacatccaaacctaccaccggcgctacaccctgtaccccaacaacttccagttccggtaccatgtcagttcggccgcgcaggcgggctgcgtcgtcctcgacgaggcctttcgacgctaccgtaacctgctcttcggttccggctcttggccccgacccagcttctcaaataaacagcaaacgttggggaagaacattctggtggtctccgtcgtcacagctgaatgtaatgaatttcctaatttggagtcggtagaaaattacaccctaaccattaatgatgaccagtgtttactcgcctctgagactgtctggggcgctctccgaggtctggagactttcagtcagcttgtttggaaatcagctgagggcacgttctttatcaacaagacaaagattaaagactttcctcgattccctcaccggggcgtactgctggatacatctcgccattacctgccattgtctagcatcctggatacactggatgtcatggcatacaataaattcaacgtgttccactggcacttggtggacgactcttccttcccatatgagagcttcactttcccagagctcaccagaaaggggtccttcaaccctgtcactcacatctacacagcacaggatgtgaaggaggtcattgaatacgcaaggcttcggggtatccgtgtgctggcagaatttgacactcctggccacactttgtcctgggggccaggtgcccctgggttattaacaccttgctactctgggtctcatctctctggcacatttggaccggtgaaccccagtctcaacagcacctatgacttcatgagcacactcttcctggagatcagctcagtcttcccggacttttatctccacctgggaggggatgaagtcgacttcacctgctggaagtccaaccccaacatccaggccttcatgaagaaaaagggcttt---actgacttcaagcagctggagtccttctacatccagacgctgctggacatcgtctctgattatgacaagggctatgtggtgtggcaggaggtatttgataataaagtgaaggttcggccagatacaatcatacaggtgtggcgggaagaaatgccagtagagtacatgttggagatgcaagatatcaccagggctggcttccgggccctgctgtctgctccctggtacctgaaccgtgtaaagtatggccctgactggaaggacatgtacaaagtggagcccctggcgtttcatggtacgcctgaacagaaggctctggtcattggaggggaggcctgtatgtggggagagtatgtggacagcaccaacctggtccccagactctggcccagagcgggtgccgtcgctgagagactgtggagcagtaacctgacaactaatatagactttgcctttaaacgtttgtcgcatttccgttgtgagctggtgaggagaggaatccaggcccagcccatcagtgtaggctgctgtgagcaggagtttgagcagacttga

Estimate the synonymous and nonsynonymous substitutions rates of the codon-aligned nucleotide sequences and also display the codons considered in the computations and their amino acid translations.

[nonsynSubRate,synSubRate] = dnds(humanHEXA_aligned,mouseHEXA_aligned,'verbose',true)
DNDS: 
Codons considered in the computations:
ATGACAAGCTCCAGGCTTTGGTTTTCGCTGCTGCTGGCGGCAGCGTTCGCAGGACGGGCGACGGCCCTCTGGCCCTGGCCTCAGAACTTCCAAACCTCCGACCAGCGCTACGTCCTTTACCCGAACAACTTTCAATTCCAGTACGATGTCAGCTCGGCCGCGCAGCCCGGCTGCTCAGTCCTCGACGAGGCCTTCCAGCGCTATCGTGACCTGCTTTTCGGTTCCGGGTCTTGGCCCCGTCCTTACCTCACAGGGAAACGGCATACACTGGAGAAGAATGTGTTGGTTGTCTCTGTAGTCACACCTGGATGTAACCAGCTTCCTACTTTGGAGTCAGTGGAGAATTATACCCTGACCATAAATGATGACCAGTGTTTACTCCTCTCTGAGACTGTCTGGGGAGCTCTCCGAGGTCTGGAGACTTTTAGCCAGCTTGTTTGGAAATCTGCTGAGGGCACATTCTTTATCAACAAGACTGAGATTGAGGACTTTCCCCGCTTTCCTCACCGGGGCTTGCTGTTGGATACATCTCGCCATTACCTGCCACTCTCTAGCATCCTGGACACTCTGGATGTCATGGCGTACAATAAATTGAACGTGTTCCACTGGCATCTGGTAGATGATCCTTCCTTCCCATATGAGAGCTTCACTTTTCCAGAGCTCATGAGAAAGGGGTCCTACAACCCTGTCACCCACATCTACACAGCACAGGATGTGAAGGAGGTCATTGAATACGCACGGCTCCGGGGTATCCGTGTGCTTGCAGAGTTTGACACTCCTGGCCACACTTTGTCCTGGGGACCAGGTATCCCTGGATTACTGACTCCTTGCTACTCTGGGTCTGAGCCCTCTGGCACCTTTGGACCAGTGAATCCCAGTCTCAATAATACCTATGAGTTCATGAGCACATTCTTCTTAGAAGTCAGCTCTGTCTTCCCAGATTTTTATCTTCATCTTGGAGGAGATGAGGTTGATTTCACCTGCTGGAAGTCCAACCCAGAGATCCAGGACTTTATGAGGAAGAAAGGCTTCGAGGACTTCAAGCAGCTGGAGTCCTTCTACATCCAGACGCTGCTGGACATCGTCTCTTCTTATGGCAAGGGCTATGTGGTGTGGCAGGAGGTGTTTGATAATAAAGTAAAGATTCAGCCAGACACAATCATACAGGTGTGGCGAGAGGATATTCCAGTGAACTATATGAAGGAGCTGGAACTGGTCACCAAGGCCGGCTTCCGGGCCCTTCTCTCTGCCCCCTGGTACCTGAACCGTATATCCTATGGCCCTGACTGGAAGGATTTCTACATAGTGGAACCCCTGGCATTTGAAGGTACCCCTGAGCAGAAGGCTCTGGTGATTGGTGGAGAGGCTTGTATGTGGGGAGAATATGTGGACAACACAAACCTGGTCCCCAGGCTCTGGCCCAGAGCAGGGGCTGTTGCCGAAAGGCTGTGGAGCAACAAGTTGACATCTGACCTGACATTTGCCTATGAACGTTTGTCACACTTCCGCTGTGAATTGCTGAGGCGAGGTGTCCAGGCCCAACCCCTCAATGTAGGCTTCTGTGAGCAGGAGTTTGAACAGACC
ATGGCCGGCTGCAGGCTCTGGGTTTCGCTGCTGCTGGCGGCGGCGTTGGCTTGCTTGGCCACGGCACTGTGGCCGTGGCCCCAGTACATCCAAACCTACCACCGGCGCTACACCCTGTACCCCAACAACTTCCAGTTCCGGTACCATGTCAGTTCGGCCGCGCAGGCGGGCTGCGTCGTCCTCGACGAGGCCTTTCGACGCTACCGTAACCTGCTCTTCGGTTCCGGCTCTTGGCCCCGACCCAGCTTCTCAAATAAACAGCAAACGTTGGGGAAGAACATTCTGGTGGTCTCCGTCGTCACAGCTGAATGTAATGAATTTCCTAATTTGGAGTCGGTAGAAAATTACACCCTAACCATTAATGATGACCAGTGTTTACTCGCCTCTGAGACTGTCTGGGGCGCTCTCCGAGGTCTGGAGACTTTCAGTCAGCTTGTTTGGAAATCAGCTGAGGGCACGTTCTTTATCAACAAGACAAAGATTAAAGACTTTCCTCGATTCCCTCACCGGGGCGTACTGCTGGATACATCTCGCCATTACCTGCCATTGTCTAGCATCCTGGATACACTGGATGTCATGGCATACAATAAATTCAACGTGTTCCACTGGCACTTGGTGGACGACTCTTCCTTCCCATATGAGAGCTTCACTTTCCCAGAGCTCACCAGAAAGGGGTCCTTCAACCCTGTCACTCACATCTACACAGCACAGGATGTGAAGGAGGTCATTGAATACGCAAGGCTTCGGGGTATCCGTGTGCTGGCAGAATTTGACACTCCTGGCCACACTTTGTCCTGGGGGCCAGGTGCCCCTGGGTTATTAACACCTTGCTACTCTGGGTCTCATCTCTCTGGCACATTTGGACCGGTGAACCCCAGTCTCAACAGCACCTATGACTTCATGAGCACACTCTTCCTGGAGATCAGCTCAGTCTTCCCGGACTTTTATCTCCACCTGGGAGGGGATGAAGTCGACTTCACCTGCTGGAAGTCCAACCCCAACATCCAGGCCTTCATGAAGAAAAAGGGCTTTACTGACTTCAAGCAGCTGGAGTCCTTCTACATCCAGACGCTGCTGGACATCGTCTCTGATTATGACAAGGGCTATGTGGTGTGGCAGGAGGTATTTGATAATAAAGTGAAGGTTCGGCCAGATACAATCATACAGGTGTGGCGGGAAGAAATGCCAGTAGAGTACATGTTGGAGATGCAAGATATCACCAGGGCTGGCTTCCGGGCCCTGCTGTCTGCTCCCTGGTACCTGAACCGTGTAAAGTATGGCCCTGACTGGAAGGACATGTACAAAGTGGAGCCCCTGGCGTTTCATGGTACGCCTGAACAGAAGGCTCTGGTCATTGGAGGGGAGGCCTGTATGTGGGGAGAGTATGTGGACAGCACCAACCTGGTCCCCAGACTCTGGCCCAGAGCGGGTGCCGTCGCTGAGAGACTGTGGAGCAGTAACCTGACAACTAATATAGACTTTGCCTTTAAACGTTTGTCGCATTTCCGTTGTGAGCTGGTGAGGAGAGGAATCCAGGCCCAGCCCATCAGTGTAGGCTGCTGTGAGCAGGAGTTTGAGCAGACT
Translations:
M  T  S  S  R  L  W  F  S  L  L  L  A  A  A  F  A  G  R  A  T  A  L  W  P  W  P  Q  N  F  Q  T  S  D  Q  R  Y  V  L  Y  P  N  N  F  Q  F  Q  Y  D  V  S  S  A  A  Q  P  G  C  S  V  L  D  E  A  F  Q  R  Y  R  D  L  L  F  G  S  G  S  W  P  R  P  Y  L  T  G  K  R  H  T  L  E  K  N  V  L  V  V  S  V  V  T  P  G  C  N  Q  L  P  T  L  E  S  V  E  N  Y  T  L  T  I  N  D  D  Q  C  L  L  L  S  E  T  V  W  G  A  L  R  G  L  E  T  F  S  Q  L  V  W  K  S  A  E  G  T  F  F  I  N  K  T  E  I  E  D  F  P  R  F  P  H  R  G  L  L  L  D  T  S  R  H  Y  L  P  L  S  S  I  L  D  T  L  D  V  M  A  Y  N  K  L  N  V  F  H  W  H  L  V  D  D  P  S  F  P  Y  E  S  F  T  F  P  E  L  M  R  K  G  S  Y  N  P  V  T  H  I  Y  T  A  Q  D  V  K  E  V  I  E  Y  A  R  L  R  G  I  R  V  L  A  E  F  D  T  P  G  H  T  L  S  W  G  P  G  I  P  G  L  L  T  P  C  Y  S  G  S  E  P  S  G  T  F  G  P  V  N  P  S  L  N  N  T  Y  E  F  M  S  T  F  F  L  E  V  S  S  V  F  P  D  F  Y  L  H  L  G  G  D  E  V  D  F  T  C  W  K  S  N  P  E  I  Q  D  F  M  R  K  K  G  F  E  D  F  K  Q  L  E  S  F  Y  I  Q  T  L  L  D  I  V  S  S  Y  G  K  G  Y  V  V  W  Q  E  V  F  D  N  K  V  K  I  Q  P  D  T  I  I  Q  V  W  R  E  D  I  P  V  N  Y  M  K  E  L  E  L  V  T  K  A  G  F  R  A  L  L  S  A  P  W  Y  L  N  R  I  S  Y  G  P  D  W  K  D  F  Y  I  V  E  P  L  A  F  E  G  T  P  E  Q  K  A  L  V  I  G  G  E  A  C  M  W  G  E  Y  V  D  N  T  N  L  V  P  R  L  W  P  R  A  G  A  V  A  E  R  L  W  S  N  K  L  T  S  D  L  T  F  A  Y  E  R  L  S  H  F  R  C  E  L  L  R  R  G  V  Q  A  Q  P  L  N  V  G  F  C  E  Q  E  F  E  Q  T  
M  A  G  C  R  L  W  V  S  L  L  L  A  A  A  L  A  C  L  A  T  A  L  W  P  W  P  Q  Y  I  Q  T  Y  H  R  R  Y  T  L  Y  P  N  N  F  Q  F  R  Y  H  V  S  S  A  A  Q  A  G  C  V  V  L  D  E  A  F  R  R  Y  R  N  L  L  F  G  S  G  S  W  P  R  P  S  F  S  N  K  Q  Q  T  L  G  K  N  I  L  V  V  S  V  V  T  A  E  C  N  E  F  P  N  L  E  S  V  E  N  Y  T  L  T  I  N  D  D  Q  C  L  L  A  S  E  T  V  W  G  A  L  R  G  L  E  T  F  S  Q  L  V  W  K  S  A  E  G  T  F  F  I  N  K  T  K  I  K  D  F  P  R  F  P  H  R  G  V  L  L  D  T  S  R  H  Y  L  P  L  S  S  I  L  D  T  L  D  V  M  A  Y  N  K  F  N  V  F  H  W  H  L  V  D  D  S  S  F  P  Y  E  S  F  T  F  P  E  L  T  R  K  G  S  F  N  P  V  T  H  I  Y  T  A  Q  D  V  K  E  V  I  E  Y  A  R  L  R  G  I  R  V  L  A  E  F  D  T  P  G  H  T  L  S  W  G  P  G  A  P  G  L  L  T  P  C  Y  S  G  S  H  L  S  G  T  F  G  P  V  N  P  S  L  N  S  T  Y  D  F  M  S  T  L  F  L  E  I  S  S  V  F  P  D  F  Y  L  H  L  G  G  D  E  V  D  F  T  C  W  K  S  N  P  N  I  Q  A  F  M  K  K  K  G  F  T  D  F  K  Q  L  E  S  F  Y  I  Q  T  L  L  D  I  V  S  D  Y  D  K  G  Y  V  V  W  Q  E  V  F  D  N  K  V  K  V  R  P  D  T  I  I  Q  V  W  R  E  E  M  P  V  E  Y  M  L  E  M  Q  D  I  T  R  A  G  F  R  A  L  L  S  A  P  W  Y  L  N  R  V  K  Y  G  P  D  W  K  D  M  Y  K  V  E  P  L  A  F  H  G  T  P  E  Q  K  A  L  V  I  G  G  E  A  C  M  W  G  E  Y  V  D  S  T  N  L  V  P  R  L  W  P  R  A  G  A  V  A  E  R  L  W  S  S  N  L  T  T  N  I  D  F  A  F  K  R  L  S  H  F  R  C  E  L  V  R  R  G  I  Q  A  Q  P  I  S  V  G  C  C  E  Q  E  F  E  Q  T  

nonsynSubRate =

    0.0933


synSubRate =

    0.5181

References

[1] Li, W., Wu, C., and Luo, C. (1985). A new method for estimating synonymous and nonsynonymous rates of nucleotide substitution considering the relative likelihood of nucleotide and codon changes. Molecular Biology and Evolution 2(2), 150–174.

[2] Nei, M., and Gojobori, T. (1986). Simple methods for estimating the numbers of synonymous and nonsynonymous nucleotide substitutions. Molecular Biology and Evolution 3(5), 418–426.

[3] Nei, M., and Jin, L. (1989). Variances of the average numbers of nucleotide substitutions within and between populations. Molecular Biology and Evolution 6(3), 290–300.

[4] Nei, M., and Kumar, S. (2000). Synonymous and nonsynonymous nucleotide substitutions" in Molecular Evolution and Phylogenetics (Oxford University Press).

[5] Pamilo, P., and Bianchi, N. (1993). Evolution of the Zfx And Zfy genes: rates and interdependence between the genes. Molecular Biology and Evolution 10(2), 271–281.

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