| fdnadist

## Function

Nucleic acid sequence Distance Matrix program

## Description

Computes four different distances between species from nucleic acid sequences. The distances can then be used in the distance matrix programs. The distances are the Jukes-Cantor formula, one based on Kimura's 2- parameter method, the F84 model used in DNAML, and the LogDet distance. The distances can also be corrected for gamma-distributed and gamma-plus-invariant-sites-distributed rates of change in different sites. Rates of evolution can vary among sites in a prespecified way, and also according to a Hidden Markov model. The program can also make a table of percentage similarity among sequences.

## Algorithm

This program uses nucleotide sequences to compute a distance matrix, under four different models of nucleotide substitution. It can also compute a table of similarity between the nucleotide sequences. The distance for each pair of species estimates the total branch length between the two species, and can be used in the distance matrix programs FITCH, KITSCH or NEIGHBOR. This is an alternative to use of the sequence data itself in the maximum likelihood program DNAML or the parsimony program DNAPARS.

The program reads in nucleotide sequences and writes an output file containing the distance matrix, or else a table of similarity between sequences. The four models of nucleotide substitution are those of Jukes and Cantor (1969), Kimura (1980), the F84 model (Kishino and Hasegawa, 1989; Felsenstein and Churchill, 1996), and the model underlying the LogDet distance (Barry and Hartigan, 1987; Lake, 1994; Steel, 1994; Lockhart et. al., 1994). All except the LogDet distance can be made to allow for for unequal rates of substitution at different sites, as Jin and Nei (1990) did for the Jukes-Cantor model. The program correctly takes into account a variety of sequence ambiguities, although in cases where they exist it can be slow.

Jukes and Cantor's (1969) model assumes that there is independent change at all sites, with equal probability. Whether a base changes is independent of its identity, and when it changes there is an equal probability of ending up with each of the other three bases. Thus the transition probability matrix (this is a technical term from probability theory and has nothing to do with transitions as opposed to transversions) for a short period of time dt is:

                  To:    A        G        C        T
                       ---------------------------------
                   A  | 1-3a      a         a       a
           From:   G  |  a       1-3a       a       a
                   C  |  a        a        1-3a     a
                   T  |  a        a         a      1-3a

where a is u dt, the product of the rate of substitution per unit time (u) and the length dt of the time interval. For longer periods of time this implies that the probability that two sequences will differ at a given site is:

          p = 3/4 ( 1 - e- 4/3 u t)

and hence that if we observe p, we can compute an estimate of the branch length ut by inverting this to get

         ut = - 3/4 loge ( 1 - 4/3 p )

The Kimura "2-parameter" model is almost as symmetric as this, but allows for a difference between transition and transversion rates. Its transition probability matrix for a short interval of time is:

                  To:     A        G        C        T
                       ---------------------------------
                   A  | 1-a-2b     a         b       b
           From:   G  |   a      1-a-2b      b       b
                   C  |   b        b       1-a-2b    a
                   T  |   b        b         a     1-a-2b

where a is u dt, the product of the rate of transitions per unit time and dt is the length dt of the time interval, and b is v dt, the product of half the rate of transversions (i.e., the rate of a specific transversion) and the length dt of the time interval.

The F84 model incorporates different rates of transition and transversion, but also allowing for different frequencies of the four nucleotides. It is the model which is used in DNAML, the maximum likelihood nucelotide sequence phylogenies program in this package. You will find the model described in the document for that program. The transition probabilities for this model are given by Kishino and Hasegawa (1989), and further explained in a paper by me and Gary Churchill (1996).

The LogDet distance allows a fairly general model of substitution. It computes the distance from the determinant of the empirically observed matrix of joint probabilities of nucleotides in the two species. An explanation of it is available in the chapter by Swofford et, al. (1996).

The first three models are closely related. The DNAML model reduces to Kimura's two-parameter model if we assume that the equilibrium frequencies of the four bases are equal. The Jukes-Cantor model in turn is a special case of the Kimura 2-parameter model where a = b. Thus each model is a special case of the ones that follow it, Jukes-Cantor being a special case of both of the others.

The Jin and Nei (1990) correction for variation in rate of evolution from site to site can be adapted to all of the first three models. It assumes that the rate of substitution varies from site to site according to a gamma distribution, with a coefficient of variation that is specified by the user. The user is asked for it when choosing this option in the menu.

Each distance that is calculated is an estimate, from that particular pair of species, of the divergence time between those two species. For the Jukes- Cantor model, the estimate is computed using the formula for ut given above, as long as the nucleotide symbols in the two sequences are all either A, C, G, T, U, N, X, ?, or - (the latter four indicate a deletion or an unknown nucleotide. This estimate is a maximum likelihood estimate for that model. For the Kimura 2-parameter model, with only these nucleotide symbols, formulas special to that estimate are also computed. These are also, in effect, computing the maximum likelihood estimate for that model. In the Kimura case it depends on the observed sequences only through the sequence length and the observed number of transition and transversion differences between those two sequences. The calculation in that case is a maximum likelihood estimate and will differ somewhat from the estimate obtained from the formulas in Kimura's original paper. That formula was also a maximum likelihood estimate, but with the transition/transversion ratio estimated empirically, separately for each pair of sequences. In the present case, one overall preset transition/transversion ratio is used which makes the computations harder but achieves greater consistency between different comparisons.

For the F84 model, or for any of the models where one or both sequences contain at least one of the other ambiguity codons such as Y, R, etc., a maximum likelihood calculation is also done using code which was originally written for DNAML. Its disadvantage is that it is slow. The resulting distance is in effect a maximum likelihood estimate of the divergence time (total branch length between) the two sequences. However the present program will be much faster than versions earlier than 3.5, because I have speeded up the iterations.

The LogDet model computes the distance from the determinant of the matrix of co-occurrence of nucleotides in the two species, according to the formula

       D  = - 1/4(loge(|F|) - 1/2loge(fA1fC1fG1fT1fA2fC2fG2fT2))

Where F is a matrix whose (i,j) element is the fraction of sites at which base i occurs in one species and base j occurs in the other. fji is the fraction of sites at which species i has base j. The LogDet distance cannot cope with ambiguity codes. It must have completely defined sequences. One limitation of the LogDet distance is that it may be infinite sometimes, if there are too many changes between certain pairs of nucleotides. This can be particularly noticeable with distances computed from bootstrapped sequences. Note that there is an assumption that we are looking at all sites, including those that have not changed at all. It is important not to restrict attention to some sites based on whether or not they have changed; doing that would bias the distances by making them too large, and that in turn would cause the distances to misinterpret the meaning of those sites that had changed.

For all of these distance methods, the program allows us to specify that "third position" bases have a different rate of substitution than first and second positions, that introns have a different rate than exons, and so on. The Categories option which does this allows us to make up to 9 categories of sites and specify different rates of change for them.

In addition to the four distance calculations, the program can also compute a table of similarities between nucleotide sequences. These values are the fractions of sites identical between the sequences. The diagonal values are 1.0000. No attempt is made to count similarity of nonidentical nucleotides, so that no credit is given for having (for example) different purines at corresponding sites in the two sequences. This option has been requested by many users, who need it for descriptive purposes. It is not intended that the table be used for inferring the tree.

## Usage

Here is a sample session with fdnadist

    % fdnadist
    Nucleic acid sequence Distance Matrix program
    Input (aligned) nucleotide sequence set(s): dnadist.dat
    Distance methods
             f : F84 distance model
             k : Kimura 2-parameter distance
             j : Jukes-Cantor distance
             l : LogDet distance
             s : Similarity table
    Choose the method to use [F84 distance model]:
    Phylip distance matrix output file [dnadist.fdnadist]:

    Distances calculated for species
        Alpha        ....
        Beta         ...
        Gamma        ..
        Delta        .
        Epsilon

    Distances written to file "dnadist.fdnadist"

    Done.

Go to the input files for this example
Go to the output files for this example

## Command line arguments

       Standard (Mandatory) qualifiers:
      [-sequence]          seqsetall  File containing one or more sequence
                                      alignments
       -method             menu       [F84 distance model] Choose the method to
                                      use (Values: f (F84 distance model); k
                                      (Kimura 2-parameter distance); j
                                      (Jukes-Cantor distance); l (LogDet
                                      distance); s (Similarity table))
      [-outfile]           outfile    [*.fdnadist] Phylip distance matrix output
                                      file

       Additional (Optional) qualifiers (* if not always prompted):
    *  -gamma              menu       [No distribution parameters used] Gamma
                                      distribution (Values: g (Gamma distributed
                                      rates); i (Gamma+invariant sites); n (No
                                      distribution parameters used))
    *  -ncategories        integer    [1] Number of substitution rate categories
                                      (Integer from 1 to 9)
    *  -rate               array      [1.0] Category rates
    *  -categories         properties File of substitution rate categories
       -weights            properties Weights file
    *  -gammacoefficient   float      [1] Coefficient of variation of substitution
                                      rate among sites (Number 0.001 or more)
    *  -invarfrac          float      [0.0] Fraction of invariant sites (Number
                                      from 0.000 to 1.000)
    *  -ttratio            float      [2.0] Transition/transversion ratio (Number
                                      0.001 or more)
    *  -[no]freqsfrom      toggle     [Y] Use empirical base frequencies from
                                      seqeunce input
    *  -basefreq           array      [0.25 0.25 0.25 0.25] Base frequencies for A
                                      C G T/U (use blanks to separate)
       -lower              boolean    [N] Lower triangular distance matrix
       -printdata          boolean    [N] Print data at start of run
       -[no]progress       boolean    [Y] Print indications of progress of run

       Advanced (Unprompted) qualifiers: (none)
       Associated qualifiers:

       "-sequence" associated qualifiers
       -sbegin1            integer    Start of each sequence to be used
       -send1              integer    End of each sequence to be used
       -sreverse1          boolean    Reverse (if DNA)
       -sask1              boolean    Ask for begin/end/reverse
       -snucleotide1       boolean    Sequence is nucleotide
       -sprotein1          boolean    Sequence is protein
       -slower1            boolean    Make lower case
       -supper1            boolean    Make upper case
       -sformat1           string     Input sequence format
       -sdbname1           string     Database name
       -sid1               string     Entryname
       -ufo1               string     UFO features
       -fformat1           string     Features format
       -fopenfile1         string     Features file name

       "-outfile" associated qualifiers
       -odirectory2        string     Output directory

       General qualifiers:
       -auto               boolean    Turn off prompts
       -stdout             boolean    Write standard output
       -filter             boolean    Read standard input, write standard output
       -options            boolean    Prompt for standard and additional values
       -debug              boolean    Write debug output to program.dbg
       -verbose            boolean    Report some/full command line options
       -help               boolean    Report command line options. More
                                      information on associated and general
                                      qualifiers can be found with -help -verbose
       -warning            boolean    Report warnings
       -error              boolean    Report errors
       -fatal              boolean    Report fatal errors
       -die                boolean    Report dying program messages

Standard (Mandatory) qualifiers | Allowed values | Default
--- | --- | ---
[-sequence] (Parameter 1) | File containing one or more sequence alignments | Readable sets of sequences | Required
-method | Choose the method to use |
f | (F84 distance model)
k | (Kimura 2-parameter distance)
j | (Jukes-Cantor distance)
l | (LogDet distance)
s | (Similarity table)
| F84 distance model
[-outfile] (Parameter 2) | Phylip distance matrix output file | Output file | <*>.fdnadist
Additional (Optional) qualifiers | Allowed values | Default
-gamma | Gamma distribution |
g | (Gamma distributed rates)
i | (Gamma+invariant sites)
n | (No distribution parameters used)
| No distribution parameters used
-ncategories | Number of substitution rate categories | Integer from 1 to 9 | 1
-rate | Category rates | List of floating point numbers | 1.0
-categories | File of substitution rate categories | Property value(s) |
-weights | Weights file | Property value(s) |
-gammacoefficient | Coefficient of variation of substitution rate among sites | Number 0.001 or more | 1
-invarfrac | Fraction of invariant sites | Number from 0.000 to 1.000 | 0.0
-ttratio | Transition/transversion ratio | Number 0.001 or more | 2.0
-[no]freqsfrom | Use empirical base frequencies from seqeunce input | Toggle value Yes/No | Yes
-basefreq | Base frequencies for A C G T/U (use blanks to separate) | List of floating point numbers | 0.25 0.25 0.25 0.25
-lower | Lower triangular distance matrix | Boolean value Yes/No | No
-printdata | Print data at start of run | Boolean value Yes/No | No
-[no]progress | Print indications of progress of run | Boolean value Yes/No | Yes
Advanced (Unprompted) qualifiers | Allowed values | Default
(none)

## Input file format

fdnadist reads any normal sequence USAs.

### Input files for usage example

### File: dnadist.dat

       5   13
    Alpha     AACGTGGCCACAT
    Beta      AAGGTCGCCACAC
    Gamma     CAGTTCGCCACAA
    Delta     GAGATTTCCGCCT
    Epsilon   GAGATCTCCGCCC

## Output file format

fdnadist output contains on its first line the number of species. The distance matrix is then printed in standard form, with each species starting on a new line with the species name, followed by the distances to the species in order. These continue onto a new line after every nine distances. If the L option is used, the matrix or distances is in lower triangular form, so that only the distances to the other species that precede each species are printed. Otherwise the distance matrix is square with zero distances on the diagonal. In general the format of the distance matrix is such that it can serve as input to any of the distance matrix programs.

If the option to print out the data is selected, the output file will precede the data by more complete information on the input and the menu selections. The output file begins by giving the number of species and the number of characters, and the identity of the distance measure that is being used.

If the C (Categories) option is used a table of the relative rates of expected substitution at each category of sites is printed, and a listing of the categories each site is in.

There will then follow the equilibrium frequencies of the four bases. If the Jukes-Cantor or Kimura distances are used, these will necessarily be 0.25 : 0.25 : 0.25 : 0.25. The output then shows the transition/transversion ratio that was specified or used by default. In the case of the Jukes-Cantor distance this will always be 0.5. The transition-transversion parameter (as opposed to the ratio) is also printed out: this is used within the program and can be ignored. There then follow the data sequences, with the base sequences printed in groups of ten bases along the lines of the Genbank and EMBL formats.

The distances printed out are scaled in terms of expected numbers of substitutions, counting both transitions and transversions but not replacements of a base by itself, and scaled so that the average rate of change, averaged over all sites analyzed, is set to 1.0 if there are multiple categories of sites. This means that whether or not there are multiple categories of sites, the expected fraction of change for very small branches is equal to the branch length. Of course, when a branch is twice as long this does not mean that there will be twice as much net change expected along it, since some of the changes may occur in the same site and overlie or even reverse each other. The branch lengths estimates here are in terms of the expected underlying numbers of changes. That means that a branch of length 0.26 is 26 times as long as one which would show a 1% difference between the nucleotide sequences at the beginning and end of the branch. But we would not expect the sequences at the beginning and end of the branch to be 26% different, as there would be some overlaying of changes.

One problem that can arise is that two or more of the species can be so dissimilar that the distance between them would have to be infinite, as the likelihood rises indefinitely as the estimated divergence time increases. For example, with the Jukes-Cantor model, if the two sequences differ in 75% or more of their positions then the estimate of dovergence time would be infinite. Since there is no way to represent an infinite distance in the output file, the program regards this as an error, issues an error message indicating which pair of species are causing the problem, and stops. It might be that, had it continued running, it would have also run into the same problem with other pairs of species. If the Kimura distance is being used there may be no error message; the program may simply give a large distance value (it is iterating towards infinity and the value is just where the iteration stopped). Likewise some maximum likelihood estimates may also become large for the same reason (the sequences showing more divergence than is expected even with infinite branch length). I hope in the future to add more warning messages that would alert the user the this.

If the similarity table is selected, the table that is produced is not in a format that can be used as input to the distance matrix programs. it has a heading, and the species names are also put at the tops of the columns of the table (or rather, the first 8 characters of each species name is there, the other two characters omitted to save space). There is not an option to put the table into a format that can be read by the distance matrix programs, nor is there one to make it into a table of fractions of difference by subtracting the similarity values from 1. This is done deliberately to make it more difficult for the use to use these values to construct trees. The similarity values are not corrected for multiple changes, and their use to construct trees (even after converting them to fractions of difference) would be wrong, as it would lead to severe conflict between the distant pairs of sequences and the close pairs of sequences.

### Output files for usage example

### File: dnadist.fdnadist

        5
    Alpha       0.000000  0.303893  0.857546  1.158921  1.542897
    Beta        0.303893  0.000000  0.339731  0.913519  0.619666
    Gamma       0.857546  0.339731  0.000000  1.631729  1.293707
    Delta       1.158921  0.913519  1.631729  0.000000  0.165882
    Epsilon     1.542897  0.619666  1.293707  0.165882  0.000000

## Data files

None

## Notes

None.

## References

None.

## Warnings

None.

## Diagnostic Error Messages

None.

## Exit status

It always exits with status 0.

## Known bugs

None.

## See also

Program name | Description
--- | ---
distmat | Creates a distance matrix from multiple alignments
ednacomp | DNA compatibility algorithm
ednadist | Nucleic acid sequence Distance Matrix program
ednainvar | Nucleic acid sequence Invariants method
ednaml | Phylogenies from nucleic acid Maximum Likelihood
ednamlk | Phylogenies from nucleic acid Maximum Likelihood with clock
ednapars | DNA parsimony algorithm
ednapenny | Penny algorithm for DNA
eprotdist | Protein distance algorithm
eprotpars | Protein parsimony algorithm
erestml | Restriction site Maximum Likelihood method
eseqboot | Bootstrapped sequences algorithm
fdiscboot | Bootstrapped discrete sites algorithm
fdnacomp | DNA compatibility algorithm
fdnainvar | Nucleic acid sequence Invariants method
fdnaml | Estimates nucleotide phylogeny by maximum likelihood
fdnamlk | Estimates nucleotide phylogeny by maximum likelihood
fdnamove | Interactive DNA parsimony
fdnapars | DNA parsimony algorithm
fdnapenny | Penny algorithm for DNA
fdolmove | Interactive Dollo or Polymorphism Parsimony
ffreqboot | Bootstrapped genetic frequencies algorithm
fproml | Protein phylogeny by maximum likelihood
fpromlk | Protein phylogeny by maximum likelihood
fprotdist | Protein distance algorithm
fprotpars | Protein parsimony algorithm
frestboot | Bootstrapped restriction sites algorithm
frestdist | Distance matrix from restriction sites or fragments
frestml | Restriction site maximum Likelihood method
fseqboot | Bootstrapped sequences algorithm
fseqbootall | Bootstrapped sequences algorithm

## Author(s)

This program is an EMBOSS conversion of a program written by Joe Felsenstein as part of his PHYLIP package.

Although we take every care to ensure that the results of the EMBOSS version are identical to those from the original package, we recommend that you check your inputs give the same results in both versions before publication.

Please report all bugs in the EMBOSS version to the EMBOSS bug team, not to the original author.

## History

Written (2004) - Joe Felsenstein, University of Washington.

Converted (August 2004) to an EMBASSY program by the EMBOSS team.

## Target users

This program is intended to be used by everyone and everything, from naive users to embedded scripts.