
Nucleic acid sequence Invariants method, version 3.7a

 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))


Lake's linear invariants
 (these are expected to be zero for the two incorrect tree topologies.
  This is tested by testing the equality of the two parts
  of each expression using a one-sided exact binomial test.
  The null hypothesis is that the first part is no larger than the second.)

 Tree                             Exact test P value    Significant?

   I      1    -     0   =     1       0.5000               no
   II     0    -     0   =     0       1.0000               no
   III    0    -     0   =     0       1.0000               no


Cavender's quadratic invariants (type L) using purines vs. pyrimidines
 (these are expected to be zero, and thus have a nonsignificant
  chi-square, 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.

  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

