
                                 fdnainvar 



Function

   Nucleic acid sequence Invariants method

Description

   For nucleic acid sequence data on four species, computes Lake's and
   Cavender's phylogenetic invariants, which test alternative tree
   topologies. The program also tabulates the frequencies of occurrence
   of the different nucleotide patterns. Lake's invariants are the method
   which he calls "evolutionary parsimony".

Algorithm

   This program reads in nucleotide sequences for four species and
   computes the phylogenetic invariants discovered by James Cavender
   (Cavender and Felsenstein, 1987) and James Lake (1987). Lake's method
   is also called by him "evolutionary parsimony". I prefer Cavender's
   more mathematically precise term "invariants", as the method bears
   somewhat more relationship to likelihood methods than to parsimony.
   The invariants are mathematical formulas (in the present case linear
   or quadratic) in the EXPECTED frequencies of site patterns which are
   zero for all trees of a given tree topology, irrespective of branch
   lengths. We can consider at a given site that if there are no
   ambiguities, we could have for four species the nucleotide patterns
   (considering the same site across all four species) AAAA, AAAC, AAAG,
   ... through TTTT, 256 patterns in all.

   The invariants are formulas in the expected pattern frequencies, not
   the observed pattern frequencies. When they are computed using the
   observed pattern frequencies, we will usually find that they are not
   precisely zero even when the model is correct and we have the correct
   tree topology. Only as the number of nucleotides scored becomes
   infinite will the observed pattern frequencies approach their
   expectations; otherwise, we must do a statistical test of the
   invariants.

   Some explanation of invariants will be found in the above papers, and
   also in my recent review article on statistical aspects of inferring
   phylogenies (Felsenstein, 1988b). Although invariants have some
   important advantages, their validity also depends on symmetry
   assumptions that may not be satisfied. In the discussion below suppose
   that the possible unrooted phylogenies are I: ((A,B),(C,D)), II:
   ((A,C),(B,D)), and III: ((A,D),(B,C)).

  Lake's Invariants, Their Testing and Assumptions

   Lake's invariants are fairly simple to describe: the patterns involved
   are only those in which there are two purines and two pyrimidines at a
   site. Thus a site with AACT would affect the invariants, but a site
   with AAGG would not. Let us use (as Lake does) the symbols 1, 2, 3,
   and 4, with the proviso that 1 and 2 are either both of the purines or
   both of the pyrimidines; 3 and 4 are the other two nucleotides. Thus 1
   and 2 always differ by a transition; so do 3 and 4. Lake's invariants,
   expressed in terms of expected frequencies, are the three quantities:

(1)      P(1133) + P(1234) - P(1134) - P(1233),

(2)      P(1313) + P(1324) - P(1314) - P(1323),

(3)      P(1331) + P(1342) - P(1341) - P(1332),

   He showed that invariants (2) and (3) are zero under Topology I, (1)
   and (3) are zero under topology II, and (1) and (2) are zero under
   Topology III. If, for example, we see a site with pattern ACGC, we can
   start by setting 1=A. Then 2 must be G. We can then set 3=C (so that 4
   is T). Thus its pattern type, making those substitutions, is 1323.
   P(1323) is the expected probability of the type of pattern which
   includes ACGC, TGAG, GTAT, etc.

   Lake's invariants are easily tested with observed frequencies. For
   example, the first of them is a test of whether there are as many
   sites of types 1133 and 1234 as there are of types 1134 and 1233; this
   is easily tested with a chi-square test or, as in this program, with
   an exact binomial test. Note that with several invariants to test, we
   risk overestimating the significance of results if we simply accept
   the nominal 95% levels of significance (Li and Guoy, 1990).

   Lake's invariants assume that each site is evolving independently, and
   that starting from any base a transversion is equally likely to end up
   at each of the two possible bases (thus, an A undergoing a
   transversion is equally likely to end up as a C or a T, and similarly
   for the other four bases from which one could start. Interestingly,
   Lake's results do not assume that rates of evolution are the same at
   all sites. The result that the total of 1133 and 1234 is expected to
   be the same as the total of 1134 and 1233 is unaffected by the fact
   that we may have aggregated the counts over classes of sites evolving
   at different rates.

  Cavender's Invariants, Their Testing and Assumptions

   Cavender's invariants (Cavender and Felsenstein, 1987) are for the
   case of a character with two states. In the nucleic acid case we can
   classify nucleotides into two states, R and Y (Purine and Pyrimidine)
   and then use the two-state results. Cavender starts, as before, with
   the pattern frequencies. Coding purines as R and pyrimidines as Y, the
   patterns types are RRRR, RRRY, and so on until YYYY, a total of 16
   types. Cavender found quadratic functions of the expected frequencies
   of these 16 types that were expected to be zero under a given
   phylogeny, irrespective of branch lengths. Two invariants (called K
   and L) were found for each tree topology. The L invariants are
   particularly easy to understand. If we have the tree topology
   ((A,B),(C,D)), then in the case of two symmetric states, the event
   that A and B have the same state should be independent of whether C
   and D have the same state, as the events determining these happen in
   different parts of the tree. We can set up a contingency table:

                                 C = D         C =/= D
                           ------------------------------
                          |
                   A = B  |   YYYY, YYRR,     YYYR, YYRY,
                          |   RRRR, RRYY      RRYR, RRRY
                          |
                 A =/= B  |   YRYY, YRRR,     YRYR, YRRY,
                          |   RYYY, RYRR      RYYR, RYRY

   and we expect that the events C = D and A = B will be independent.
   Cavender's L invariant for this tree topology is simply the negative
   of the crossproduct difference,

      P(A=/=B and C=D) P(A=B and C=/=D) - P(A=B and C=D) P(A=/=B and C=/=D).

   One of these L invariants is defined for each of the three tree
   topologies. They can obviously be tested simply by doing a chi-square
   test on the contingency table. The one corresponding to the correct
   topology should be statistically indistinguishable from zero. Again,
   there is a possible multiple tests problem if all three are tested at
   a nominal value of 95%.

   The K invariants are differences between the L invariants. When one of
   the tables is expected to have crossproduct difference zero, the other
   two are expected to be nonzero, and also to be equal. So the
   difference of their crossproduct differences can be taken; this is the
   K invariant. It is not so easily tested.

   The assumptions of Cavender's invariants are different from those of
   Lake's. One obviously need not assume anything about the frequencies
   of, or transitions among, the two different purines or the two
   different pyrimidines. However one does need to assume independent
   events at each site, and one needs to assume that the Y and R states
   are symmetric, that the probability per unit time that a Y changes
   into an R is the same as the probability that an R changes into a Y,
   so that we expect equal frequencies of the two states. There is also
   an assumption that all sites are changing between these two states at
   the same expected rate. This assumption is not needed for Lake's
   invariants, since expectations of sums are equal to sums of
   expectations, but for Cavender's it is, since products of expectations
   are not equal to expectations of products.

   It is helpful to have both sorts of invariants available; with further
   work we may appreciate what other invaraints there are for various
   models of nucleic acid change.

Usage

   Here is a sample session with fdnainvar


% fdnainvar -printdata 
Nucleic acid sequence Invariants method
Input sequence: dnainvar.dat
Input file: 
Output file [dnainvar.fdnainvar]: 


Output written to output file "dnainvar.fdnainvar"

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
   -weights            properties (no help text) properties value
  [-outfile]           outfile    Output file name

   Additional (Optional) qualifiers (* if not always prompted):
   -printdata          boolean    Print data at start of run
*  -[no]dotdiff        boolean    Use dot-differencing to display results
   -[no]printpattern   boolean    Print counts of patterns
   -[no]printinvariant boolean    Print invariants
   -[no]progress       boolean    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 deaths


   Standard (Mandatory) qualifiers Allowed values Default
   [-sequence]
   (Parameter 1) File containing one or more sequence alignments Readable
   sets of sequences
   -weights (no help text) properties value Property value(s)
   [-outfile]
   (Parameter 2) Output file name Output file <sequence>.fdnainvar
   Additional (Optional) qualifiers Allowed values Default
   -printdata Print data at start of run Boolean value Yes/No No
   -[no]dotdiff Use dot-differencing to display results Boolean value
   Yes/No Yes
   -[no]printpattern Print counts of patterns Boolean value Yes/No Yes
   -[no]printinvariant Print invariants Boolean value Yes/No Yes
   -[no]progress Print indications of progress of run Boolean value
   Yes/No Yes
   Advanced (Unprompted) qualifiers Allowed values Default
   (none)

Input file format

   fdnainvar reads any normal sequence USAs.

  Input files for usage example

  File: dnainvar.dat

   4   13
Alpha     AACGTGGCCAAAT
Beta      AAGGTCGCCAAAC
Gamma     CATTTCGTCACAA
Delta     GGTATTTCGGCCT

Output file format

   fdnainvar output consists first (if option 1 is selected) of a
   reprinting of the input data, then (if option 2 is on) tables of
   observed pattern frequencies and pattern type frequencies. A table
   will be printed out, in alphabetic order AAAA through TTTT of all the
   patterns that appear among the sites and the number of times each
   appears. This table will be invaluable for computation of any other
   invariants. There follows another table, of pattern types, using the
   1234 notation, in numerical order 1111 through 1234, of the number of
   times each type of pattern appears. In this computation all sites at
   which there are any ambiguities or deletions are omitted. Cavender's
   invariants could actually be computed from sites that have only Y or R
   ambiguities; this will be done in the next release of this program.

   If option 3 is on the invariants are then printed out, together with
   their statistical tests. For Lake's invariants the two sums which are
   expected to be equal are printed out, and then the result of an
   one-tailed exact binomial test which tests whether the difference is
   expected to be this positive or more. The P level is given (but
   remember the multiple-tests problem!).

   For Cavender's L invariants the contingency tables are given. Each is
   tested with a one-tailed chi-square test. It is possible that the
   expected numbers in some categories could be too small for valid use
   of this test; the program does not check for this. It is also possible
   that the chi-square could be significant but in the wrong direction;
   this is not tested in the current version of the program. To check it
   beware of a chi-square greater than 3.841 but with a positive
   invariant. The invariants themselves are computed, as the difference
   of cross-products. Their absolute magnitudes are not important, but
   which one is closest to zero may be indicative. Significantly nonzero
   invariants should be negative if the model is valid. The K invariants,
   which are simply differences among the L invariants, are also printed
   out without any test on them being conducted. Note that it is possible
   to use the bootstrap utility SEQBOOT to create multiple data sets, and
   from the output from sunning all of these get the empirical
   variability of these quadratic invariants.

  Output files for usage example

  File: dnainvar.fdnainvar


Nucleic acid sequence Invariants method, version 3.6b

 4 species,  13  sites

Name            Sequences
----            ---------

Alpha        AACGTGGCCA AAT
Beta         ..G..C.... ..C
Gamma        C.TT.C.T.. C.A
Delta        GGTA.TT.GG CC.



   Pattern   Number of times

     AAAC         1
     AAAG         2
     AACC         1
     AACG         1
     CCCG         1
     CCTC         1
     CGTT         1
     GCCT         1
     GGGT         1
     GGTA         1
     TCAT         1
     TTTT         1


Symmetrized patterns (1, 2 = the two purines  and  3, 4 = the two pyrimidines
                  or  1, 2 = the two pyrimidines  and  3, 4 = the two purines)

     1111         1
     1112         2
     1113         3
     1121         1
     1132         2
     1133         1
     1231         1
     1322         1
     1334         1

Tree topologies (unrooted):

    I:  ((Alpha,Beta),(Gamma,Delta))
   II:  ((Alpha,Gamma),(Beta,Delta))
  III:  ((Alpha,Delta),(Beta,Gamma))



  [Part of this file has been deleted for brevity]

different purine:pyrimidine ratios from 1:1.

  Tree I:

   Contingency Table

      2     8
      1     2

   Quadratic invariant =             4.0

   Chi-square =    0.23111 (not significant)


  Tree II:

   Contingency Table

      1     5
      1     6

   Quadratic invariant =            -1.0

   Chi-square =    0.01407 (not significant)


  Tree III:

   Contingency Table

      1     2
      6     4

   Quadratic invariant =             8.0

   Chi-square =    0.66032 (not significant)




Cavender's quadratic invariants (type K) using purines vs. pyrimidines
 (these are expected to be zero for the correct tree topology)
They will be misled if there are substantially
different evolutionary rate between sites, or
different purine:pyrimidine ratios from 1:1.
No statistical test is done on them here.

  Tree I:              -9.0
  Tree II:              4.0
  Tree III:             5.0

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
   ednacomp DNA compatibility algorithm
   ednadist Nucleic acid sequence Distance Matrix program
   ednainvar Nucleic acid sequence Invariants method
   ednaml Estimates phylogenies from nucleic acid sequence Maximum
   Likelihood
   ednamlk Estimates phylogenies from nucleic acid sequence Maximum
   Likelihood with molecular 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
   fdnadist Nucleic acid sequence Distance Matrix program
   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 pasimony algorithm
   frestboot Bootstrapped restriction sites algorithm
   frestdist Computes 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.
