- NAME
- SYNOPSIS
- DESCRIPTION
- REFERENCES
- FEEDBACK
- AUTHOR - Jason Stajich
- CONTRIBUTORS
- APPENDIX
- new
- distance
- available_distance_methods
- D - distance methods
- D_JukesCantor
- D_F81
- D_Uncorrected
- D_Kimura
- D_Kimura_variance
- D_Tamura
- D_F84
- D_TajimaNei
- D_JinNei
- transversions
- transitions
- Data Methods
- pairwise_stats
- calc_KaKs_pair
- calc_all_KaKs_pairs
- calc_average_KaKs
- get_syn_changes
- dnds_pattern_number

# NAME

Bio::Align::DNAStatistics - Calculate some statistics for a DNA alignment

# SYNOPSIS

```
use Bio::AlignIO;
use Bio::Align::DNAStatistics;
my $stats = Bio::Align::DNAStatistics->new();
my $alignin = Bio::AlignIO->new(-format => 'emboss',
-file => 't/data/insulin.water');
my $aln = $alignin->next_aln;
my $jcmatrix = $stats->distance(-align => $aln,
-method => 'Jukes-Cantor');
print $jcmatrix->print_matrix;
## and for measurements of synonymous /nonsynonymous substitutions ##
my $in = Bio::AlignIO->new(-format => 'fasta',
-file => 't/data/nei_gojobori_test.aln');
my $alnobj = $in->next_aln;
my ($seq1id,$seq2id) = map { $_->display_id } $alnobj->each_seq;
my $results = $stats->calc_KaKs_pair($alnobj, $seq1id, $seq2id);
print "comparing ".$results->[0]{'Seq1'}." and ".$results->[0]{'Seq2'}."\n";
for (sort keys %{$results->[0]} ){
next if /Seq/;
printf("%-9s %.4f \n",$_ , $results->[0]{$_});
}
my $results2 = $stats->calc_all_KaKs_pairs($alnobj);
for my $an (@$results2){
print "comparing ". $an->{'Seq1'}." and ". $an->{'Seq2'}. " \n";
for (sort keys %$an ){
next if /Seq/;
printf("%-9s %.4f \n",$_ , $an->{$_});
}
print "\n\n";
}
my $result3 = $stats->calc_average_KaKs($alnobj, 1000);
for (sort keys %$result3 ){
next if /Seq/;
printf("%-9s %.4f \n",$_ , $result3->{$_});
}
```

# DESCRIPTION

This object contains routines for calculating various statistics and distances for DNA alignments. The routines are not well tested and do contain errors at this point. Work is underway to correct them, but do not expect this code to give you the right answer currently! Use dnadist/distmat in the PHLYIP or EMBOSS packages to calculate the distances.

Several different distance method calculations are supported. Listed in brackets are the pattern which will match

JukesCantor [jc|jukes|jukescantor|jukes-cantor]

Uncorrected [jcuncor|uncorrected]

F81 [f81|felsenstein]

Kimura [k2|k2p|k80|kimura]

Tamura [t92|tamura|tamura92]

F84 [f84|felsenstein84]

TajimaNei [tajimanei|tajima\-nei]

JinNei [jinnei|jin\-nei] (not implemented)

There are also three methods to calculate the ratio of synonymous to non-synonymous mutations. All are implementations of the Nei-Gojobori evolutionary pathway method and use the Jukes-Cantor method of nucleotide substitution. This method works well so long as the nucleotide frequencies are roughly equal and there is no significant transition/transversion bias. In order to use these methods there are several pre-requisites for the alignment.

DNA alignment must be based on protein alignment. Use the subroutine "aa_to_dna_aln" in Bio::Align::Utilities to achieve this.

Therefore alignment gaps must be in multiples of 3 (representing an aa deletion/insertion) and at present must be indicated by a '-' symbol.

Alignment must be solely of coding region and be in reading frame 0 to achieve meaningful results

Alignment must therefore be a multiple of 3 nucleotides long.

All sequences must be the same length (including gaps). This should be the case anyway if the sequences have been automatically aligned using a program like Clustal.

Only the standard codon alphabet is supported at present.

calc_KaKs_pair() calculates a number of statistics for a named pair of sequences in the alignment.

calc_all_KaKs_pairs() calculates these statistics for all pairwise comparisons in an MSA. The statistics returned are:

S_d - Number of synonymous mutations between the 2 sequences.

N_d - Number of non-synonymous mutations between the 2 sequences.

S - Mean number of synonymous sites in both sequences.

N - mean number of synonymous sites in both sequences.

P_s - proportion of synonymous differences in both sequences given by P_s = S_d/S.

P_n - proportion of non-synonymous differences in both sequences given by P_n = S_n/S.

D_s - estimation of synonymous mutations per synonymous site (by Jukes-Cantor).

D_n - estimation of non-synonymous mutations per non-synonymous site (by Jukes-Cantor).

D_n_var - estimation of variance of D_n .

D_s_var - estimation of variance of S_n.

z_value - calculation of z value.Positive value indicates D_n > D_s, negative value indicates D_s > D_n.

The statistics returned by calc_average_KaKs are:

D_s - Average number of synonymous mutations/synonymous site.

D_n - Average number of non-synonymous mutations/non-synonymous site.

D_s_var - Estimated variance of Ds from bootstrapped alignments.

D_n_var - Estimated variance of Dn from bootstrapped alignments.

z_score - calculation of z value. Positive value indicates D_n >D_s, negative values vice versa.

The design of the code is based around the explanation of the Nei-Gojobori algorithm in the excellent book "Molecular Evolution and Phylogenetics" by Nei and Kumar, published by Oxford University Press. The methods have been tested using the worked example 4.1 in the book, and reproduce those results. If people like having this sort of analysis in BioPerl other methods for estimating Ds and Dn can be provided later.

Much of the DNA distance code is based on implementations in EMBOSS (Rice et al, www.emboss.org) [distmat.c] and PHYLIP (J. Felsenstein et al) [dnadist.c]. Insight also gained from Eddy, Durbin, Krogh, & Mitchison.

# REFERENCES

D_JukesCantor

"Phylogenetic Inference", Swoffrod, Olsen, Waddell and Hillis, in Mol. Systematics, 2nd ed, 1996, Ch 11. Derived from "Evolution of Protein Molecules", Jukes & Cantor, in Mammalian Prot. Metab., III, 1969, pp. 21-132.

D_Tamura

K Tamura, Mol. Biol. Evol. 1992, 9, 678.

D_Kimura

M Kimura, J. Mol. Evol., 1980, 16, 111.

JinNei

Jin and Nei, Mol. Biol. Evol. 82, 7, 1990.

D_TajimaNei

Tajima and Nei, Mol. Biol. Evol. 1984, 1, 269.

# FEEDBACK

## Mailing Lists

User feedback is an integral part of the evolution of this and other Bioperl modules. Send your comments and suggestions preferably to the Bioperl mailing list. Your participation is much appreciated.

```
bioperl-l@bioperl.org - General discussion
http://bioperl.org/wiki/Mailing_lists - About the mailing lists
```

## Support

Please direct usage questions or support issues to the mailing list:

*bioperl-l@bioperl.org*

rather than to the module maintainer directly. Many experienced and reponsive experts will be able look at the problem and quickly address it. Please include a thorough description of the problem with code and data examples if at all possible.

## Reporting Bugs

Report bugs to the Bioperl bug tracking system to help us keep track of the bugs and their resolution. Bug reports can be submitted via the web:

` https://redmine.open-bio.org/projects/bioperl/`

# AUTHOR - Jason Stajich

Email jason-AT-bioperl.org

# CONTRIBUTORS

Richard Adams, richard.adams@ed.ac.uk

# APPENDIX

The rest of the documentation details each of the object methods. Internal methods are usually preceded with a _

## new

```
Title : new
Usage : my $obj = Bio::Align::DNAStatistics->new();
Function: Builds a new Bio::Align::DNAStatistics object
Returns : Bio::Align::DNAStatistics
Args : none
```

## distance

```
Title : distance
Usage : my $distance_mat = $stats->distance(-align => $aln,
-method => $method);
Function: Calculates a distance matrix for all pairwise distances of
sequences in an alignment.
Returns : L<Bio::Matrix::PhylipDist> object
Args : -align => Bio::Align::AlignI object
-method => String specifying specific distance method
(implementing class may assume a default)
See also: L<Bio::Matrix::PhylipDist>
```

## available_distance_methods

```
Title : available_distance_methods
Usage : my @methods = $stats->available_distance_methods();
Function: Enumerates the possible distance methods
Returns : Array of strings
Args : none
```

## D - distance methods

## D_JukesCantor

```
Title : D_JukesCantor
Usage : my $d = $stat->D_JukesCantor($aln)
Function: Calculates D (pairwise distance) between 2 sequences in an
alignment using the Jukes-Cantor 1 parameter model.
Returns : L<Bio::Matrix::PhylipDist>
Args : L<Bio::Align::AlignI> of DNA sequences
double - gap penalty
```

## D_F81

```
Title : D_F81
Usage : my $d = $stat->D_F81($aln)
Function: Calculates D (pairwise distance) between 2 sequences in an
alignment using the Felsenstein 1981 distance model.
Relaxes the assumption of equal base frequencies that is
in JC.
Returns : L<Bio::Matrix::PhylipDist>
Args : L<Bio::Align::AlignI> of DNA sequences
```

## D_Uncorrected

```
Title : D_Uncorrected
Usage : my $d = $stats->D_Uncorrected($aln)
Function: Calculate a distance D, no correction for multiple substitutions
is used. In rare cases where sequences may not overlap, 'NA' is
substituted for the distance.
Returns : L<Bio::Matrix::PhylipDist>
Args : L<Bio::Align::AlignI> (DNA Alignment)
[optional] gap penalty
```

## D_Kimura

```
Title : D_Kimura
Usage : my $d = $stat->D_Kimura($aln)
Function: Calculates D (pairwise distance) between all pairs of sequences
in an alignment using the Kimura 2 parameter model.
Returns : L<Bio::Matrix::PhylipDist>
Args : L<Bio::Align::AlignI> of DNA sequences
```

## D_Kimura_variance

```
Title : D_Kimura
Usage : my $d = $stat->D_Kimura_variance($aln)
Function: Calculates D (pairwise distance) between all pairs of sequences
in an alignment using the Kimura 2 parameter model.
Returns : array of 2 L<Bio::Matrix::PhylipDist>,
the first is the Kimura distance and the second is
a matrix of variance V(K)
Args : L<Bio::Align::AlignI> of DNA sequences
```

## D_Tamura

```
Title : D_Tamura
Usage : Calculates D (pairwise distance) between 2 sequences in an
alignment using Tamura 1992 distance model.
Returns : L<Bio::Matrix::PhylipDist>
Args : L<Bio::Align::AlignI> of DNA sequences
```

## D_F84

```
Title : D_F84
Usage : my $d = $stat->D_F84($aln)
Function: Calculates D (pairwise distance) between 2 sequences in an
alignment using the Felsenstein 1984 distance model.
Returns : L<Bio::Matrix::PhylipDist>
Args : L<Bio::Align::AlignI> of DNA sequences
[optional] double - gap penalty
```

## D_TajimaNei

```
Title : D_TajimaNei
Usage : my $d = $stat->D_TajimaNei($aln)
Function: Calculates D (pairwise distance) between 2 sequences in an
alignment using the TajimaNei 1984 distance model.
Returns : L<Bio::Matrix::PhylipDist>
Args : Bio::Align::AlignI of DNA sequences
```

## D_JinNei

```
Title : D_JinNei
Usage : my $d = $stat->D_JinNei($aln)
Function: Calculates D (pairwise distance) between 2 sequences in an
alignment using the Jin-Nei 1990 distance model.
Returns : L<Bio::Matrix::PhylipDist>
Args : L<Bio::Align::AlignI> of DNA sequences
```

## transversions

```
Title : transversions
Usage : my $transversions = $stats->transversion($aln);
Function: Calculates the number of transversions between two sequences in
an alignment
Returns : integer
Args : Bio::Align::AlignI
```

## transitions

```
Title : transitions
Usage : my $transitions = Bio::Align::DNAStatistics->transitions($aln);
Function: Calculates the number of transitions in a given DNA alignment
Returns : integer representing the number of transitions
Args : Bio::Align::AlignI object
```

## Data Methods

## pairwise_stats

```
Title : pairwise_stats
Usage : $obj->pairwise_stats($newval)
Function:
Returns : value of pairwise_stats
Args : newvalue (optional)
```

## calc_KaKs_pair

```
Title : calc_KaKs_pair
Useage : my $results = $stats->calc_KaKs_pair($alnobj,
$name1, $name2).
Function : calculates Nei-Gojobori statistics for pairwise
comparison.
Args : A Bio::Align::AlignI compliant object such as a
Bio::SimpleAlign object, and 2 sequence name strings.
Returns : a reference to a hash of statistics with keys as
listed in Description.
```

## calc_all_KaKs_pairs

```
Title : calc_all_KaKs_pairs
Useage : my $results2 = $stats->calc_KaKs_pair($alnobj).
Function : Calculates Nei_gojobori statistics for all pairwise
combinations in sequence.
Arguments: A Bio::Align::ALignI compliant object such as
a Bio::SimpleAlign object.
Returns : A reference to an array of hashes of statistics of
all pairwise comparisons in the alignment.
```

## calc_average_KaKs

```
Title : calc_average_KaKs.
Useage : my $res= $stats->calc_average_KaKs($alnobj, 1000).
Function : calculates Nei_Gojobori stats for average of all
sequences in the alignment.
Args : A Bio::Align::AlignI compliant object such as a
Bio::SimpleAlign object, number of bootstrap iterations
(default 1000).
Returns : A reference to a hash of statistics as listed in Description.
```

## get_syn_changes

```
Title : get_syn_changes
Usage : Bio::Align::DNAStatitics->get_syn_changes
Function: Generate a hashref of all pairwise combinations of codns
differing by 1
Returns : Symetic matrix using hashes
First key is codon
and each codon points to a hashref of codons
the values of which describe type of change.
my $type = $hash{$codon1}->{$codon2};
values are :
1 synonymous
0 non-syn
-1 either codon is a stop codon
Args : none
```

## dnds_pattern_number

```
Title : dnds_pattern_number
Usage : my $patterns = $stats->dnds_pattern_number($alnobj);
Function: Counts the number of codons with no gaps in the MSA
Returns : Number of codons with no gaps ('patterns' in PAML notation)
Args : A Bio::Align::AlignI compliant object such as a
Bio::SimpleAlign object.
```