version 3.6
KITSCH -- Fitch-Margoliash and Least Squares Methods
with Evolutionary Clock
(C) Copyright 1986-2002 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 carries out the Fitch-Margoliash and Least Squares
methods, plus a variety of others of the same family, with the
assumption that all tip species are contemporaneous, and that there is
an evolutionary clock (in effect, a molecular clock). This means that
branches of the tree cannot be of arbitrary length, but are constrained
so that the total length from the root of the tree to any species is
the same. The quantity minimized is the same weighted sum of squares
described in the Distance Matrix Methods documentation file.
The options are set using the menu:
Fitch-Margoliash method with contemporary tips, version 3.6a3
Settings for this run:
D Method (F-M, Minimum Evolution)? Fitch-Margoliash
U Search for best tree? Yes
P Power? 2.00000
-
Negative branch lengths allowed? No
L Lower-triangular data matrix? No
R Upper-triangular data matrix? No
S Subreplicates? No
J Randomize input order of species? No. Use input order
M Analyze multiple data sets? No
0 Terminal type (IBM PC, ANSI, none)? (none)
1 Print out the data at start of run No
2 Print indications of progress of run Yes
3 Print out tree Yes
4 Write out trees onto tree file? Yes
-
Y to accept these or type the letter for one to change
Most of the options are described in the Distance Matrix Programs
documentation file.
The D (methods) option allows choice between the Fitch-Margoliash
criterion and the Minimum Evolution method (Kidd and Sgaramella-Zonta,
1971; Rzhetsky and Nei, 1993). Minimum Evolution (not to be confused
with parsimony) uses the Fitch-Margoliash criterion to fit branch
lengths to each topology, but then chooses topologies based on their
total branch length (rather than the goodness of fit sum of squares).
There is no constraint on negative branch lengths in the Minimum
Evolution method; it sometimes gives rather strange results, as it can
like solutions that have large negative branch lengths, as these reduce
the total sum of branch lengths!
Note that the User Trees (used by option U) must be rooted trees (with
a bifurcation at their base). If you take a user tree from FITCH and
try to evaluate it in KITSCH, it must first be rooted. This can be done
using RETREE. Of the options available in FITCH, the O option is not
available, as KITSCH estimates a rooted tree which cannot be rerooted,
and the G option is not available, as global rearrangement is the
default condition anyway. It is also not possible to specify that
specific branch lengths of a user tree be retained when it is read into
KITSCH, unless all of them are present. In that case the tree should be
properly clocklike. Readers who wonder why we have not provided the
feature of holding some of the user tree branch lengths constant while
iterating others are invited to tell us how they would do it. As you
consider particular possible patterns of branch lengths you will find
that the matter is not at all simple.
If you use a User Tree (option U) with branch lengths with KITSCH, and
the tree is not clocklike, when two branch lengths give conflicting
positions for a node, KITSCH will use the first of them and ignore the
other. Thus the user tree:
((A:0.1,B:0.2):0.4,(C:0.06,D:0.01):43);
is nonclocklike, so it will be treated as if it were actually the tree:
((A:0.1,B:0.1):0.4,(C:0.06,D:0.06):44);
The input is exactly the same as described in the Distance Matrix
Methods documentation file. The output is a rooted tree, together with
the sum of squares, the number of tree topologies searched, and, if the
power P is at its default value of 2.0, the Average Percent Standard
Deviation is also supplied. The lengths of the branches of the tree are
given in a table, that also shows for each branch the time at the upper
end of the branch. "Time" here really means cumulative branch length
from the root, going upwards (on the printed diagram, rightwards). For
each branch, the "time" given is for the node at the right (upper) end
of the branch. It is important to realize that the branch lengths are
not exactly proportional to the lengths drawn on the printed tree
diagram! In particular, short branches are exaggerated in the length on
that diagram so that they are more visible.
The method may be considered as providing an estimate of the phylogeny.
Alternatively, it can be considered as a phenetic clustering of the tip
species. This method minimizes an objective function, the sum of
squares, not only setting the levels of the clusters so as to do so,
but rearranging the hierarchy of clusters to try to find alternative
clusterings that give a lower overall sum of squares. When the power
option P is set to a value of P = 0.0, so that we are minimizing a
simple sum of squares of the differences between the observed distance
matrix and the expected one, the method is very close in spirit to
Unweighted Pair Group Arithmetic Average Clustering (UPGMA), also
called Average-Linkage Clustering. If the topology of the tree is fixed
and there turn out to be no branches of negative length, its result
should be the same as UPGMA in that case. But since it tries
alternative topologies and (unless the N option is set) it combines
nodes that otherwise could result in a reversal of levels, it is
possible for it to give a different, and better, result than simple
sequential clustering. Of course UPGMA itself is available as an option
in program NEIGHBOR.
The U (User Tree) option requires a bifurcating tree, unlike FITCH,
which requires an unrooted tree with a trifurcation at its base. Thus
the tree shown below would be written:
((D,E),(C,(A,B)));
If a tree with a trifurcation at the base is by mistake fed into the U
option of KITSCH then some of its species (the entire rightmost furc,
in fact) will be ignored and too small a tree read in. This should
result in an error message and the program should stop. It is important
to understand the difference between the User Tree formats for KITSCH
and FITCH. You may want to use RETREE to convert a user tree that is
suitable for FITCH into one suitable for KITSCH or vice versa.
An important use of this method will be to do a formal statistical test
of the evolutionary clock hypothesis. This can be done by comparing the
sums of squares achieved by FITCH and by KITSCH, BUT SOME CAVEATS ARE
NECESSARY. First, the assumption is that the observed distances are
truly independent, that no original data item contributes to more than
one of them (not counting the two reciprocal distances from i to j and
from j to i). THIS WILL NOT HOLD IF THE DISTANCES ARE OBTAINED FROM
GENE FREQUENCIES, FROM MORPHOLOGICAL CHARACTERS, OR FROM MOLECULAR
SEQUENCES. It may be invalid even for immunological distances and
levels of DNA hybridization, provided that the use of common standard
for all members of a row or column allows an error in the measurement
of the standard to affect all these distances simultaneously. It will
also be invalid if the numbers have been collected in experimental
groups, each measured by taking differences from a common standard
which itself is measured with error. Only if the numbers in different
cells are measured from independent standards can we depend on the
statistical model. The details of the test and the assumptions are
discussed in my review paper on distance methods (Felsenstein, 1984a).
For further and sometimes irrelevant controversy on these matters see
the papers by Farris (1981, 1985, 1986) and myself (Felsenstein, 1986,
1988b).
A second caveat is that the distances must be expected to rise linearly
with time, not according to any other curve. Thus it may be necessary
to transform the distances to achieve an expected linearity. If the
distances have an upper limit beyond which they could not go, this is a
signal that linearity may not hold. It is also VERY important to choose
the power P at a value that results in the standard deviation of the
variation of the observed from the expected distances being the P/2-th
power of the expected distance.
To carry out the test, fit the same data with both FITCH and KITSCH,
and record the two sums of squares. If the topology has turned out the
same, we have N = n(n-1)/2 distances which have been fit with 2n-3
parameters in FITCH, and with n-1 parameters in KITSCH. Then the
difference between S(K) and S(F) has d[1] = n-2 degrees of freedom. It
is statistically independent of the value of S(F), which has d[2] =
N-(2n-3) degrees of freedom. The ratio of mean squares
should, under the evolutionary clock, have an F distribution with n-2
and N-(2n-3) degrees of freedom respectively. The test desired is that
the F ratio is in the upper tail (say the upper 5%) of its
distribution. If the S (subreplication) option is in effect, the above
degrees of freedom must be modified by noting that N is not n(n-1)/2
but is the sum of the numbers of replicates of all cells in the
distance matrix read in, which may be either square or triangular. A
further explanation of the statistical test of the clock is given in a
paper of mine (Felsenstein, 1986).
The program uses a similar tree construction method to the other
programs in the package and, like them, is not guaranteed to give the
best-fitting tree. The assignment of the branch lengths for a given
topology is a least squares fit, subject to the constraints against
negative branch lengths, and should not be able to be improved upon.
KITSCH runs more quickly than FITCH.
The constant available for modification at the beginning of the program
is "epsilon", which defines a small quantity needed in some of the
calculations. There is no feature saving multiply trees tied for best,
because exact ties are not expected, except in cases where it should be
obvious from the tree printed out what is the nature of the tie (as
when an interior branch is of length zero).
__________________________________________________________________
TEST DATA SET
7
Bovine 0.0000 1.6866 1.7198 1.6606 1.5243 1.6043 1.5905
Mouse 1.6866 0.0000 1.5232 1.4841 1.4465 1.4389 1.4629
Gibbon 1.7198 1.5232 0.0000 0.7115 0.5958 0.6179 0.5583
Orang 1.6606 1.4841 0.7115 0.0000 0.4631 0.5061 0.4710
Gorilla 1.5243 1.4465 0.5958 0.4631 0.0000 0.3484 0.3083
Chimp 1.6043 1.4389 0.6179 0.5061 0.3484 0.0000 0.2692
Human 1.5905 1.4629 0.5583 0.4710 0.3083 0.2692 0.0000
__________________________________________________________________
TEST SET OUTPUT FILE (with all numerical options on)
-
7 Populations
-
Fitch-Margoliash method with contemporary tips, version 3.6a3
-
__ __ 2
\ \ (Obs - Exp)
Sum of squares = /_ /_ ------------
2
i j Obs
-
negative branch lengths not allowed
-
Name Distances
--- ---------
-
Bovine 0.00000 1.68660 1.71980 1.66060 1.52430 1.60430
1.59050
Mouse 1.68660 0.00000 1.52320 1.48410 1.44650 1.43890
1.46290
Gibbon 1.71980 1.52320 0.00000 0.71150 0.59580 0.61790
0.55830
Orang 1.66060 1.48410 0.71150 0.00000 0.46310 0.50610
0.47100
Gorilla 1.52430 1.44650 0.59580 0.46310 0.00000 0.34840
0.30830
Chimp 1.60430 1.43890 0.61790 0.50610 0.34840 0.00000
0.26920
Human 1.59050 1.46290 0.55830 0.47100 0.30830 0.26920
0.00000
-
+-------Human
+-6
+----5 +-------Chimp
! !
+---4 +---------Gorilla
! !
+------------------------3 +--------------Orang
! !
+----2 +------------------Gibbon
! !
-
-1 +-------------------------------------------Mouse
!
+------------------------------------------------Bovine
-
Sum of squares = 0.107
-
Average percent standard deviation = 5.16213
-
From To Length Height
--- -- ------ ------
6 Human 0.13460 0.81285
5 6 0.02836 0.67825
6 Chimp 0.13460 0.81285
4 5 0.07638 0.64990
5 Gorilla 0.16296 0.81285
3 4 0.06639 0.57352
4 Orang 0.23933 0.81285
2 3 0.42923 0.50713
3 Gibbon 0.30572 0.81285
1 2 0.07790 0.07790
2 Mouse 0.73495 0.81285
1 Bovine 0.81285 0.81285
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