## EMBOSS: PHYLIP

# Original PHYLIP gendist documentation.

This is the original PHYLIP documentation and includes information on the old menu driven program which is now replaced with the EMBOSS acd file.

                                                                       version 3.5c

               GENDIST - Compute genetic distances from gene frequencies

    (c) Copyright  1986-1993  by  Joseph  Felsenstein  and  by  the  University  of
    Washington.  Written by Joseph Felsenstein.  Permission is granted to copy this
    document provided that no fee is charged for it and that this copyright  notice
    is not removed.

         This program computes any one of three measures of genetic distance from a
    set  of  gene frequencies in different populations (or species).  The three are
    Nei's genetic distance (Nei, 1972), Cavalli-Sforza's  chord  measure  (Cavalli-
    Sforza  and  Edwards,  1967) and Reynolds, Weir, and Cockerham's (1983) genetic
    distance.  These are written to an output file in a format that can be read  by
    the distance matrix phylogeny programs FITCH and KITSCH.

         The three measures have somewhat different assumptions.  All  assume  that
    all  differences  between populations arise from genetic drift.  Nei's distance
    is formulated for an infinite isoalleles model of mutation, in which there is a
    rate of neutral mutation and each mutant is to a completely new alleles.  It is
    assumed that all loci have the same rate of  neutral  mutation,  and  that  the
    genetic  variability  initially  in  the  population  is at equilibrium between
    mutation and  genetic  drift,  with  the  effective  population  size  of  each
    population remaining constant.

         Nei's distance is:

                                          __  __
                                          \   \
                                          /_  /_  p   p
                                           m   i   1mi 2mi
               D  =  - ln  ( ---------------------------------------- ).
                               __  __               __  __
                               \   \      2  1/2    \   \      2  1/2
                             [ /_  /_  p    ]     [ /_  /_  p    ]
                                m   i   1mi          m   i   2mi

    where m is summed over loci, i over alleles at the m-th locus, and where

                 p
                  1mi

    is the frequency of the i-th allele at the m-th locus in population 1.  Subject
    to  the  above assumptions, Nei's genetic distance is expected, for a sample of
    sufficiently many equivalent loci, to rise linearly with time.

         The other two genetic distances assume that there is no mutation, and that
    all  gene  frequency  changes  are by genetic drift alone.  However they do not
    assume  that  population  sizes  have  remained  constant  and  equal  in   all
    populations.   They  cope  with changing population size by having expectations
    that rise linearly not with time, but with the sum over time of 1/N, where N is
    the  effective population size.  Thus if population size doubles, genetic drift
    will be taking place more slowly, and the genetic distance will be expected  to
    be  rising  only half as fast with respect to time.  Both genetic distances are
    different estimators of the same quantity under the same model.

         Cavalli-Sforza's chord distance is given by

                       __              __                       __
          2            \               \      1/2     1/2       \
         D     =    4  /_  [  1   -    /_   p      p       ]  / /_  (a  - 1)
                        m               i    1mi    2mi          m    m

    where m indexes the loci, where i is summed over the alleles at the m-th locus,
    and  where  a is the number of alleles at the m-th locus.  It can be shown that
    this distance always satisfies the triangle inequality.   Note  that  as  given
    here  it is divided by the number of degrees of freedom, the sum of the numbers
    of alleles minus one.  The quantity which is expected  to  rise  linearly  with
    amount  of  genetic  drift  (sum  of  1/N over time) is D squared, the quantity
    computed above, and that is what is written out into the distance matrix.

         Reynolds, Weir, and Cockerham's (1983) genetic distance is

                           __   __
                           \    \                    2
                           /_   /_  [ p     -  p    ]
            2               m    i     1mi      2mi
           D     =       ------------------------------------
                             __              __
                             \               \
                          2  /_   [  1   -   /_  p    p     ]
                              m               i   1mi  2mi

    where the notation is as before and D-squared is the quantity that is  expected
    to rise linearly with cumulated genetic drift.

         Having computed one of these genetic distances,  one  which  you  feel  is
    appropriate to the biology of the situation, you can use it as the input to the
    programs FITCH, KITSCH or NEIGHBOR.  Keep in mind that the statistical model in
    those  programs  implicitly  assumes that the distances in the input table have
    independent errors.  For any measure of genetic distance this will not be true,
    as  bursts of random genetic drift, or sampling events in drawing the sample of
    individuals from each population, cause fluctuations  of  gene  frequency  that
    affect  many  distances simultaneously.  While this is not expected to bias the
    estimate of the phylogeny, it does mean that the weighing of evidence from  all
    the  different distances in the table will not be done with maximal efficiency.
    One issue is which value of the P  (Power)  parameter  should  be  used.   This
    depends  on  how  the  variance  of a distance rises with its expectation.  For
    Cavalli-Sforza's chord distance, and for the Reynolds et. al. distance  it  can
    be  shown  that the variance of the distance will be proportional to the square
    of its expectation; this suggests a value of 2 for P, which the  default  value
    for FITCH and KITSCH (there is no P option in NEIGHBOR).

         If you think that the pure genetic drift model  is  appropriate,  and  are
    thus tempted to use the Cavalli-Sforza or Reynolds et. al. distances, you might
    consider  using  the  maximum  likelihood  program  CONTML  instead.   It  will
    correctly  weigh  the  evidence in that case.  Like those genetic distances, it
    uses approximations that break down as loci start  to  drift  all  the  way  to
    fixation.   Although  Nei's distance will not break down in that case, it makes
    other assumptions  about  equality  of  substitution  rates  at  all  loci  and
    constancy of population sizes.

         The most important thing to remember is that genetic distance  is  not  an
    abstract,  idealized  measure  of  "differentness".   It  is  an  estimate of a
    parameter (time or cumulated inverse effective population size)  of  the  model
    which  is thought to have generated the differences we see.  As an estimate, it
    has statistical properties that can be assessed, and we should  never  have  to
    choose between genetic distances based on their aesthetic properties, or on the
    personal prestige of their originators.  Considering them as estimates  focuses
    us  on  the  questions  which  genetic distances are intended to answer, for if
    there are none there is no reason to compute them.  For further perspective  on
    genetic  distances,  I  recommend  my  own  paper evaluating properties of some
    genetic distances (Felsenstein,  1985c),  the  paper  by  Reynolds,  Weir,  and
    Cockerham (1983), and the material in Nei's book (Nei, 1987).

                                     INPUT FORMAT

         The input to this program is standard and is  as  described  in  the  Gene
    Frequencies  and  Continuous  Characters Programs documentation file above.  It
    consists of the number of populations (or species), the  number  of  loci,  and
    after that a line containing the numbers of alleles at each of the loci.   Then
    the gene frequencies follow in standard format.

         The options are selected using a menu:

    Genetic Distance Matrix program, version 3.5c

    Settings for this run:
      A   Input file contains all alleles at each locus?  One omitted at each locus
      N                        Use Nei genetic distance?  Yes
      C                Use Cavalli-Sforza chord measure?  No
      R                   Use Reynolds genetic distance?  No
      L                         Form of distance matrix?  Square
      M                      Analyze multiple data sets?  No
      0              Terminal type (IBM PC, VT52, ANSI)?  ANSI
      1            Print indications of progress of run?  Yes

    Are these settings correct? (type Y or the letter for one to change)

    The A option is described in the Gene  Frequencies  and  Continuous  Characters
    Programs documentation file.  As with CONTML, it is the signal that all alleles
    are represented in the gene frequency input, without one  being  left  out  per
    locus.  C, N, and R are the signals to use the Cavalli-Sforza, Nei, or Reynolds
    et. al. genetic distances respectively.  The Nei distance is the  default,  and
    it  will  be  computed  if none of these options is explicitly invoked.   The L
    option is the signal that the distance matrix is to be  written  out  in  Lower
    triangular  form.   The M option is the usual Multiple Data Sets option, useful
    for doing bootstrap analyses with the distance matrix programs.

                                     OUTPUT FORMAT

         The output file simply contains on its first line the  number  of  species
    (or  populations).   Each  species  (or population) starts a new line, with its
    name printed out first, and then and there are up  to  nine  genetic  distances
    printed  on  each  line,  in  the standard format used as input by the distance
    matrix programs.  The output, in its default form, is ready to be used  in  the
    distance matrix programs.

                                       CONSTANTS

         The constants available to be changed  by  the  user  if  the  program  is
    recompiled  are  "namelength"  the  length  of a species name, set to 10 in the
    distribution and "epsilon" which defines a small quantity  that  is  used  when
    checking  whether  allele  frequencies  at a locus sum to more than one: if all
    alleles are input (option A) and the sum differs from 1 by more  than  epsilon,
    or  if  not  all  alleles  are input and the sum is greater than 1 by more then
    epsilon, the program will see this as an error and stop.   You  may  find  this
    causes difficulties if you gene frequencies have been rounded.  I have tried to
    keep epsilon from being too small to prevent such problems.

                                       RUN TIMES

         The program is quite fast and the user should effectively never be limited
    by  the amount of time it takes.  All that the program has to do is read in the
    gene frequency data and then, for each  pair  of  species,  compute  a  genetic
    distance  formula  for  each pair of species.  This should require an amount of
    effort proportional to the total number of alleles over loci, and to the square
    of the number of populations.

                                FUTURE OF THIS PROGRAM

         The main change that will be made to this program in the future is to  add
    provisions  for  taking  into account the sample size for each population.  The
    genetic distance formulas have been modified by their inventors to correct  for
    the  inaccuracy  of  the  estimate of the genetic distances, which on the whole
    should artificially increase the distance between populations by a small amount
    dependent  on  the sample sizes.  The main difficulty with doing this is that I
    have not yet settled on a format for putting the sample size in the input  data
    along with the gene frequency data for a species or population.

         I may also include other distance measures, but only if I think their  use
    is  justified.   There  are  many  very  arbitrary  genetic distances, and I am
    reluctant to include most of them.

    ---------------------------------TEST DATA SET--------------------------

        5    10
    2 2 2 2 2 2 2 2 2 2
    European   0.2868 0.5684 0.4422 0.4286 0.3828 0.7285 0.6386 0.0205
    0.8055 0.5043
    African    0.1356 0.4840 0.0602 0.0397 0.5977 0.9675 0.9511 0.0600
    0.7582 0.6207
    Chinese    0.1628 0.5958 0.7298 1.0000 0.3811 0.7986 0.7782 0.0726
    0.7482 0.7334
    American   0.0144 0.6990 0.3280 0.7421 0.6606 0.8603 0.7924 0.0000
    0.8086 0.8636
    Australian 0.1211 0.2274 0.5821 1.0000 0.2018 0.9000 0.9837 0.0396
    0.9097 0.2976

    ----------------------------TEST SET OUTPUT-------------------------------
        5
    European    0.0000  0.0780  0.0807  0.0668  0.1030
    African     0.0780  0.0000  0.2347  0.1050  0.2273
    Chinese     0.0807  0.2347  0.0000  0.0539  0.0633
    American    0.0668  0.1050  0.0539  0.0000  0.1348
    Australian  0.1030  0.2273  0.0633  0.1348  0.0000