INPUT FORMAT AND OPTIONS
Input is fairly standard, with one addition. As usual the first line of the file gives the number of species and the number of sites. There follows the characters C or W if the Categories or Weights options are being used.
Next come the species data. Each sequence starts on a new line, has a ten-character species name that must be blank-filled to be of that length, followed immediately by the species data in the one-letter code. The sequences must either be in the "interleaved" or "sequential" formats described in the Molecular Sequence Programs documentation. The I option selects between them. The sequences can have internal blanks in the sequence but there must be no extra blanks at the end of the terminated line. Note that a blank is not a valid symbol for a deletion.
After that are the lines (if any) containing the information for the C, and W options, as described below.
The options are selected using an interactive menu. The menu looks like this:
Nucleic acid sequence Distance Matrix program, version 3.5c Settings for this run: D Distance (Kimura, Jin/Nei, ML, J-C)? Kimura 2-parameter T Transition/transversion ratio? 2.0 C One category of substitution rates? Yes L Form of distance matrix? Square M Analyze multiple data sets? No I Input sequences interleaved? Yes 0 Terminal type (IBM PC, VT52, ANSI)? ANSI 1 Print out the data at start of run No 2 Print indications of progress of run Yes Are these settings correct? (type Y or letter for one to change)The user either types "Y" (followed, of course, by a carriage-return) if the settings shown are to be accepted, or the letter or digit corresponding to an option that is to be changed.
The options M and 0 are the usual ones. They are described in the main documentation file of this package. Option I is the same as in other molecular sequence programs and is described in the molecular sequence programs documentation file.
The D option selects one of the four distance methods. It toggles among the three methods. The default method, if none is specified, is the Kimura 2-
parameter model. If the Nei/Jin distance is selected the user will be asked to supply the coefficient of variation of the rate of substitution among sites. This is different from the parameters used by Nei and Jin but related to them: their parameters a are related to the coefficient of variation by
1/2
CV = 1 / a
or
2
a = 1 / (CV)
(their parameter b is absorbed here by the requirement that time is scaled so
that the mean rate of evolution is 1 per unit time, which means that a = b).
As we consider cases in which the rates are less variable we should set a
larger and larger, as CV gets smaller and smaller.
The F (Frequencies) option appears when the Maximum Likelihood distance is selected. This distance requires that the program be provided with the equilibrium frequencies of the four bases A, C, G, and T (or U). Its default setting is one which may save users much time. If you want to use the empirical frequencies of the bases, observed in the input sequences, as the base frequencies, you simply use the default setting of the F option. These empirical frequencies are not really the maximum likelihood estimates of the base frequencies, but they will often be close to those values (what they are is maximum likelihood estimates under a "star" or "explosion" phylogeny). If you change the setting of the F option you will be prompted for the frequencies of the four bases. These must add to 1 and are to be typed on one line separated by blanks, not commas.
The T option in this program does not stand for Threshold, but instead is the Transition/transversion option. The user is prompted for a real number greater than 0.0, as the expected ratio of transitions to transversions. Note that this is not the ratio of the first to the second kinds of events, but the resulting expected ratio of transitions to transversions. The exact relationship between these two quantities depends on the frequencies in the base pools. The default value of the T parameter if you do not use the T option is 2.0.
The C (Categories) option is the one which species the relative rates of substitution at different sites. The sites are organized into up to nine categories. You are supposed to specify the relative rates of substitution in these categories. The category option asks you to specify how many categories there are to be (up to a maximum of 9) and then to enter the relative rates of change in the categories, as nonnegative real numbers typed on the same line separated by blanks, not commas. If you do not use the C option then there is in effect one category with rate 1.0.
In addition to this line, use of the C option requires one piece of information, which associates sites with categories. That is one or more lines, which are placed after the initial line of the input file, and also after the lines containing the Weights, if any, but before the sequences. It consists of a line whose first characters are ignored, until the maximum length of a species name has been reached (it is therefore convenient, if species names are a maximum of ten characters as in the program as distributed, to put CATEGORIES in the first ten characters of that line, just to remind yourself what it is). The line then contains single digits (1 through 9) indicating which category each site is in. The information can continue to a new line anytime in the middle of these digits. For example the line may read:
CATEGORIES 5555555555 5123123123 1231231231 2344444444 4441231235 5555(that is an example imagining five categories for the three codon positions, intron positions, and flanking sequence positions). A site may in effect be dropped from the analysis by placing it in a category which has an extremely high rate of expected change.
The L option specifies that the output file is to have the distance matrix in lower triangular form.
The W (Weights) option is invoked in the usual way, with only weights 0 and 1 allowed. It selects a set of sites to be analyzed, ignoring the others. The sites selected are those with weight 1. If the W option is not invoked, all sites are analyzed.
As the distances are computed, the program prints on your screen or
terminal the names of the species in turn, followed by one dot (".") for each
other species for which the distance to that species has been computed. Thus
if there are ten species, the first species name is printed out, followed by
nine dots, then on the next line the next species name is printed out followed
by eight dots, then the next followed by seven dots, and so on. The pattern of
dots should form a triangle. When the distance matrix has been written out to
the output file, the user is notified of that.
The output file 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.
The constants that are available to be changed by the user at the
beginning of the program include "maxcategories", the maximum number of site
categories, "iterations", which controls the number of times the program
iterates the EM algorithm that is used to do the maximum likelihood distance,
"namelength", the length of species names in characters, and "epsilon", a
parameter which controls the accuracy of the results of the iterations which
estimate the distances. Making "epsilon" smaller will increase run times but
result in more decimal places of accuracy. This should not be necessary.
The program spends most of its time doing real arithmetic. Any software
or hardware changes that speed up that arithmetic will speed it up by a nearly
proportional amount. For example, microcomputers that have a numeric co-
processor (such as an 8087, 80287, or 80387 chip) will run this program much
faster than ones that do not, if the software calls it. The algorithm, with
separate and independent computations occurring for each pattern, lends itself
readily to parallel processing.
OUTPUT FORMAT
PROGRAM CONSTANTS
TEST DATA SET
5 13
Alpha AACGTGGCCACAT
Beta AAGGTCGCCACAC
Gamma CAGTTCGCCACAA
Delta GAGATTTCCGCCT
Epsilon GAGATCTCCGCCC
CONTENTS OF OUTPUT FILE (with all numerical options on )
Nucleic acid sequence Distance Matrix program, version 3.5c
5 species, 13 sites
Kimura 2-parameter Distance
Base Frequencies:
A 0.25000
C 0.25000
G 0.25000
T(U) 0.25000
Transition/transversion ratio = 2.000000
(Transition/transversion parameter = 1.500000)
Name Sequences
---- ---------
Alpha AACGTGGCCA CAT
Beta ..G..C.... ..C
Gamma C.GT.C.... ..A
Delta G.GA.TT..G .C.
Epsilon G.GA.CT..G .CC
5
Alpha 0.0000 0.2997 0.7820 1.1716 1.4617
Beta 0.2997 0.0000 0.3219 0.8997 0.5653
Gamma 0.7820 0.3219 0.0000 1.4481 1.0726
Delta 1.1716 0.8997 1.4481 0.0000 0.1679
Epsilon 1.4617 0.5653 1.0726 0.1679 0.0000
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Maintained 15 Jul 1996 -- by Martin Hilbers(e-mail:M.P.Hilbers@dl.ac.uk)