No. 31

COMPUTER SCIENCE MONOGRAPHS
A Publicationof
The Institute of Statistical Mathematics

INTEROGATE 1.0. EXPLORATION AND TESTING OF STATIONARITY,
REVERSIBILITY AND CLOCK-LIKENESS IN SEQUENCE DATA
byPeter J. Waddell, Hiroshi Mine and Masami Hasegawa

March 2005

Computer Science Monographs

Editors
Junji NANAKO(in chief )Kenji FUKUMIZU
Koji KANEFUJI
Takashi NAKAMURA

The series of Computer Science Monographs publishes the statisticalsoftware and the articles on computer applications originating at The
Institute of Statistical Mathematics.

All communications relating to thispublication should be addressed to the Editorial Office, The Institute of
Statistical Mathematics, 4-6-7 Minami-Azabu, Minato-ku, Tokyo 106-8569,
Japan.

The electronic version of this issue is downloadable at
http://www.ism.ac.jp/

1

INTEROGATE 1.0. Exploration and Testing of Stationarity, Reversibility
and Clock-likeness in Sequence Data.
Peter J. Waddell1,3*, Hiroshi Mine1,4, and Masami Hasegawa1,2.
1Institute of Mathematical Statistics, 4-6-7 Minami-Azabu, Minato-ku, Tokyo, 106-8569, Japan
Department of Biosystems Science, School of Advanced Studies, The Graduate University for
Advanced Studies, Hayama, 240-0193, Japan
3
Present Address, Laboratory of Biometry and Bioinformatics,Graduate School of Agricultureand Life Sciences, University of Tokyo, 1-1-1 Yayoi Bunkyo-ku, Tokyo 113-8657, Japan
4
Present address, 3rd Research Dept. 307U Hitachi, Ltd., Systems Development Lab, Tokyo*
For correspondence: waddell@ab.a.u-tokyo.ac.jp
２

Abstract
INTEROGATE 1.0 is a set of C programs to facilitate the evaluation and editingof molecular sequence data. The package is intended to assist in phylogenetic analyses bygiving the user important statistics on the data in conjunction with inferring anevolutionary tree. These statistics can assist in understanding which sites/models may bemost suitable for analysis, and also which sequences may be significantly atypical. The
user may then want to consider the results of analyses removing sites and/or particularsequences. Conversely, they can be used after inferring initial trees to ask what part, if
any, of the tree may be incorrect. The programs are: Freqnuc, FreqAA and FreqCodon foranalyzing the stationarity, reversibility and relative rate of nucleotide, amino acid andcodon sequences, respectively; Capture, for estimating the proportion of invariant sites;
Pcons, for assessing properties of constant sites; Exclcon, for removing constant sites
from data; Perfect, for removing more rapidly evolving sites from the data or “sitestripping”; Perfect2, for removing the same sites from matched amino acid and codon
data. The manual includes a detailed worked example of these programs use. This
includes sequences used to reconstruct the evolutionary origins of mammals, which gave
unanticipated inferred relationships within the superorder Supraprimates.

INTRODUCTION
INTEROGATE 1.0 is a set of programs to facilitate the evaluation and editing ofmolecular sequence data. The package is intended to assist in phylogenetic analyses bygiving the user important statistics on the data in conjunction with inferring anevolutionary tree. These statistics can assist in understanding which sites/models may bemost suitable for analysis, and also which sequences may be significantly atypical. The
user may then want to consider the results of analyses removing sites and/or particularsequences. Conversely, they can be used after inferring initial trees to ask what part, if
any, of the tree may be incorrect.
A particular strength of the package is the large number of tests for assessing nonstationarity and non-reversibility in nucleotide, amino acid or codon data. These tests are
more sensitive than the standard tests in packages such as PAUP (Swofford 2002), yet
Waddell et al.2004, INTEROGATE 1.0

2still computationally tractable for large data sets and/or large numbers of character states(e.g. amino acids or codons). Many of these tests and methods were introduced in
Waddell et al. (1999b).
In reference to a to a known or estimated phylogeny, these tests may be summed
across a set of nonintersecting paths in order to avoid the loss of independence usuallyassociated with multiple pairwise tests on evolutionary data. This approach is inspired by
the use of pairwise lnL statistics in providing a bound on the likelihood of a tree
(Waddell 1995). The programs will then indicate whether, overall, there is statisticallysignificant evidence that the data violate stationarity and reversibility assumptions. A
further option allows a full set of "non-parametric" parsimony-based tests of whether two
lineages have evolved at the same rate (Waddell et al.1999a). These are useful tests ofwhether there may really be a molecular clock. Unlike parametric likelihood ratio tests
these tests do not rely upon specific assumptions about how characters evolve except thatcharacters are independent.
Full tables of test output between all pairs of sequences can be used to diagnose
which parts of the data are causing the most violation of the null hypothesis ofstationarity or reversibility. To facilitate further analysis, the tables of pairwise test
results (or distances between sequences) are also output as NEXUS files. These may beread directly into PAUP and the whole matrix of results visualized as a tree (essentially ahierarchical cluster analysis of multidimensional data). This tree may indicate thosesequences that are similar to each other in their overall properties and those which aremost different. An alternative to hierarchical clustering to look at structure in the data are
multidimensional scaling methods, and the out distance matrices may also be read into
analysis packages such as R with minimal effort (R development core team 2004).
INTEROGATE also contains tools to allow the researcher to focus on the moreconservative parts of the data and/or remove invariant sites. Removal of invariant sites isoften important when using likelihood or distance based methods (e.g. Lockhart etal.1996). These programs allow the user to do this taking into account a unique character(e.g., base) composition of invariant sites (Waddell and Steel 1997).
Another set of programs remove what appear to be the least conservative or most
rapidly evolving sites. This is called site stripping (Waddell et al. 1999b). In particular,
removing sites that vary within a particular group or groups may be beneficial because
this tends to shorten all edges and in particular the lengths of the edges connecting agroup of species to the rest of the tree. In a non-parametric way, this also removes what
appear to be the fastest evolving sites in each group. Assuming that all sites have thesame evolutionary rates in different groups, these are the sites most likely to be involved
in long edge attraction (Felsenstein 1978, Hendy and Penny 1989) and repulsion(Waddell 1995) effects that may mislead phylogenetic inference. In a severe form, mostuseful on large data sets, the programs can quickly reduce the data to a set of characters
linking major groups (e.g., mammalian orders) that show minimal evidence of change or
homoplasy within groups. Hopefully, these are the most reliable characters for inferring
the relationships between groups.
None of these methods are fool proof. For example, with the removal of variable
sites the total amount of data is reduced so stochastic errors may increase. There is always
the risk that much useful data has been thrown away and what remains is not without

Waddell et al.2004, INTEROGATE 1.0

3

problems itself. In a sense, these "site stripping" methods are a form of character
reweighting, where the prespecified groups represent non-nested partitions on the "real"tree. For example, they may non-nested clades. It is hoped that these methods are robust
since they make minimal assumptions about what the true model and phylogeny are (c.f.,
iterative reweighting methods that often make strong assumptions about what thephylogeny is, based on an initial analysis of the data at hand).
Used effectively and together, these methods can give a much better feeling for
how robust the data are and which parts of the tree may be incorrect. They were used
extensively in the published and unpublished analyses that have become the basis of themodern phylogenetic classification of placental mammals (e.g., Waddell et al. 1999c,
Waddell et al. 2001).
EXTRACTING AND COMPILING:
Source code and executables are supplied for Linux, Unix (including OSX for
Macintosh) and Windows machines. The programs are all written in ANSI C. Sourcecode comes tarred and zipped into one file. To extract, first unzip with the command,gunzip filename.tar.Z
then untar with,tar -xvf final.ver.tar
If you have any trouble with the executables supplied, the programs compile
easily once you have cc or gcc installed. To compile each program in its respective
folder:i) for folders with files "matrix.c" and "matrix.h" type,(g)cc programName.c matrix.c -lm -o programNameii) for folders without both "matrix.c" and "matrix.h" type(g)cc programName.c -lm -o programName
The programs should then run by calling them. In Linux either set the path to the
executables, or by go to the directory they are in and type "./programname.exe". The "./"
sets the path to the program to that of the current directory. To run under OSX, open awindow with the "terminal" program and go to directory containing the executable. Then
use the same commands mentioned above for Linux. For Windows, open the folder
where the program resides and double click the console application. A DOS-console
window opens. From this point onwards, the executions of all programs are similar for all
platforms. Upon typing a files name, a brief description of what the program does andhow it runs will appear.
LIST OF PROGRAMS:
Waddell et al.2004, INTEROGATE 1.0

4This software suite includes:(i) Freq-programs: These will perform a wide range of pairwise tests on a set of data.
These tests will detect evidence of non-stationarity (changing base/amino acid/codon
usage) or non-reversible evolution. Non-stationarity tests include those based on
approximate X2 or G2 (=G) statistics (Waddell et al. 1999b), or an asymptoticallymore accurate sum of squares (SS) test (Tavaré 1986). For testing for the nonreversibility of true evolutionary model, there are asymptotically exact X2 and G2 test
statistics (Waddell and Steel 1997). Importantly, these programs automatically
replicate the same tests with grouping of cells (character states) to ensure that
expected frequency counts are high enough to allow a reasonable approximation to a
χ2 distribution under the null hypothesis of stationarity or reversibility. There is an
option to output a full set of "non-parametric" parsimony-based tests of whether
pairs of sequences are evolving at the same rate (Waddell et al. 1999a). Output isalso available in NEXUS format for matrixes of test results.
(a).
Freqnuc.exe – nucleic sequence data(b),Freqaa.exe – amino acid sequence data(c),
Freqcod.exe – codon sequence data(ii) Capture.exe: Using either the capture-recapture method of Sidow et al. (1992) or thatof Waddell et al. (1999b), this program estimates what proportion of sites areinvariant along with the s.e. of this estimate. It uses either nucleotide or amino acidsequences (for the Waddell et al. test) or codon sequences (for the Sidow et al. test).
(iii) Pcons.exe: Makes a test of whether the frequencies of the varied and the unvariedcharacters are equal or not. Works with nucleotide, amino acid or codon sequence
data.
(iv) Exclcon.exe: Will exclude a specified fraction of unvaried sites either in proportion
to the frequencies of all characters or just the unvaried characters. Works with
nucleotide, amino acid or codon sequence data.
(v) Perfect.exe: Removes the most rapidly evolving characters in the data. The user
specifies a set of groups of sequences and any site showing variability in thesegroups is removed (nucleotide, amino acid or codon sequence data). There are
options on how gaps and singletons are treated.
(vi) Perfect2.exe: Reads in an amino acid data set and it corresponding codon data set.
Based on user specified groups of sequences, it will remove characters (amino acids
or codons) that show variability in the amino acid data, and will do this for both data
sets (i.e., if a specific amino acid site is to be removed, so will the correspondingcodon). Thus, it is like Perfect.exe but it is useful when the user wants a matchingamino acid and codon data set (for example to do perform matching nucleotide andamino acid analyses).

Waddell et al.2004, INTEROGATE 1.0

5

DESCRIPTION:
This topic is divided into two sections:i)
Input – provides descriptions of the types of input formats the programs
accept.
ii)
Execution, Output and Worked Example – provides descriptions ofrunning all the programs in INTEROGATE1.0 package. This is done witha worked example of topical data. The format and interpretation of output
from each program is also discussed.
INPUTS
Each program in this package accepts input in a standard format. They have also
been modified to accept a simple NEXUS format. The standard format is a basic noninterleaved input format that will work with both PHYLIP and MOLPHY programs. The
NEXUS format is used by various other phylogenetic software packages (PAUP4.0,
MrBayes, etc). These two formats are further explained in the following section, andexamples are supplied with the programs.
Standard format:
Each program accepts a standard input format that is compatible with PHYLIP(Felsenstein ) and MOLPHY (Adachi and Hasegawa,1996). A standard input file starts
with two numbers; the first indicating the number of sequences and the second indicating
the length of each sequence. On a new line, the name of the sequence is given. Thisshould not use spaces or special characters and be 10 or fewer characters if it is to be
used further with PHYLIP programs (for MOLPHY name length may be at least 25
characters). There is then a new line and the first sequence is a single continuous line ofamino acid or nucleic acid characters (see figure 1 below). Please ensure there thesequences are a continuous stream without line breaks, carriage returns or other special
characters.
5 11
dog
FFINIISLIIP
seal
FMINIISLIIPcat
FMINVLSLIIP
horse
FMINVLLLIVPrhino
FTI--LLLVIP

Figure 1 Standard input data format. Sequences must be of equal lengths and areassumed to be aligned.

Waddell et al.2004, INTEROGATE 1.0

6

NEXUS format:
The programs in INTEROGATE1.0 will read in a simple NEXUS format as longas the file extension ‘.nex’ is used (i.e., filename.nex). The following figure illustrates
this format:#NEXUS
Begin DATA;
Dimensions ntax=42 nchar=344;
Format datatype=PROTEIN gap=-;
Matrix[1
1121…]
Ovis_canadenensis
CWTFMHRKFSSAPCEVYSSRNTAMEWHPHTPSCDIC…
Okapia_johnstoni
CWSFMHRKFSSAPCEVYSPRNAAMEWHPHTPSCDIC…
Lagenorhynchus_obscurus CWIFMHRRFSSAPCEAYSPRNATMEWSSHTTPCDIC…
Balaenoptera_physalus
CWSFMHRKFSSAPCEAYSPRNATMEWSSHTTSCDIC…
.
.
.
Sus_scrofa
CWSFMHRKFSSTPCEVYSPRNATMEWHPHTLNCDIC…
;End;

Figure 2 Sample non-interleaved NEXUS input format
EXECUTION, OUTPUT and WORKED EXAMPLE
The use of these programs will be illustrated with an alignment of 42 sequencesof the RAG1 gene from Waddell and Shelly (2003) covering all orders of placental
mammals. This gene has proven very useful in evaluating the phylogeny of the placental
mammals. Despite the sequenced exonic region being ~800 bp long, trees based on thisdata (e.g., figure 3, Waddell and Shelly 2003) are highly congruent with priorexpectations (e.g. Waddell et al. 1999c, Murphy et al. 2001, Scally et al. 2001, Waddell
et al. 2001). The afore mentioned tree of figure 3 is, however, less congruent within the
superorder Supraprimates (made up of the clades Euarchonta + Glires). The taxa
Primates (represented here by human, Homo, and tarsier, Tarsier) + Dermoptera (flying
lemur, Cynocephalus) + Scandentia (tree shrew, Tupaia) = the clade Euarchonta , while
Rodentia (mouse, Mus, porcupine, Hystrix, south American rodent, Dolichotis) +Lagomorpha (rabbit, Sylvilagus, pika, Ochotona) = Glires. While the internal structure ofSupraprimates is unresolved in the sense that Bayesian posterior probability (pp) values
for edges were less than 0.95 (assuming a specific model and an uninformative prior),
this part of the tree is somewhat unusual. For example, the flying lemur is placed sister tothe rodents and the tree shrew, lagomorphs and primates are not only together, but thetree shrew is sister to tarsier with a fairly high pp value. In particular, we are interested indiagnosing possible reasons why the prior expectations of the flying lemur sister to tree
shrew or flying lemur sister to primates are not favored in these analyses.

Waddell et al.2004, INTEROGATE 1.0

7

Figure 3. Relationships within Supraprimates based on a RAG2 alignment. Values are pp
values under an invariant sites plus gamma HKY model. Reproduced from figure 1 ofWaddell and Shelly (2003).
Freqnuc.exe
We begin with a diagnosis of base composition. Freqnuc.exe tests for stationarityof nucleotide composition, a reversible evolutionary process and clock-like evolution. It
will do this via all possible pairwise tests and as a sum of user specified pairs. If thesepairs are non-interesting on the true phylogeny, and if there is stationarity, thenasymptotically each test result will be close to independent and the summed statistic will
be close to a chi-square (χ2) random variable with summed degrees of freedom (d.f.).
Here, asymptotically means with very long sequences.
Taking our example data "ragCodon" we obtain the following output when the
program is run (here ">" indicates a prompt for input):>Freqnuc.exe
freqnuc Ver. 0.45
Please input the NUC file name > ragCodon
1
295 R : unknown character, eliminated.
...
41
236 Y : unknown character, eliminated.
Please input the OUTPUT file name > example1
1 : Ovis_canadenensis
2 : Okapia_johnstoni...
40 : Cyclopes_didactylus 41 : Choloepus_hoffmani
42 : Dasypus_novemcinctu
Would you like to specify outgroups for performing relative rate test
( atmost two! ) ?
(y/n) > y
If you specify more than two taxa, the program will only take first two!
please specify taxa numbers :41 42
Would you like to specify more outgroups to exclude from the relative rate test?
(y/n) > yplease specify taxa numbers :1 … 22 32 … 40
Which pairs of taxa indicate non-intersecting paths?
Or press Enter/Return for all pairs.
> 24 23 25 26 30 31 27 28
Do you want the output to be in Nexus file format?
(y/n) > yPlease wait...done.

Waddell et al.2004, INTEROGATE 1.0

8

The program reads in the specified file, in this case "ragCodon", which is a
nucleotide file that starts at the first position of a codon and continues in multiples ofthree until the end. It then lists character states it excludes, in this case nucleotide
ambiguity characters. It asks for an output filename, and in this case is given "example1".
Species are then numbered according to input order and their names listed. If you would
like to have the program run relative rate tests, then type "y" then specify up to two taxa
as outgroups, here taxa 41 and 42. The program then asks if you would like to discard
any other taxa from further analysis. In this example we are focusing on justSupraprimates, so we list all other taxa for exclusion. The user is then asked to indicate
pairs of taxa indicating nominally non-intersecting paths in the true phylogeny. These areentered in pairs without punctuation, the pairs here being (23,24), (25, 26), (30,31), (27,28). Having some expectation of the true phylogeny and edge lengths, this set of paths
sum nearly all the edges in the subtree of Supraprimates sequences, leaving out therelatively short external edge to Hystrix. In this case, there is nearly zero chance thesepaths really intersect if our expectations of mammalian phylogeny are correct.
Finally, the program asks the user wants a NEXUS file of output to be produced
in order to facilitate hierarchical clustering using PAUP.
The output as shown below, actual output being in courier font and discussion of
the output is in Times font.
example1 output
freqnuc Ver. 0.45
Ungrouped
Species

Sym

GroupedStat St.All SS

23 Cyncephalu

X2

58.8

96 22.77

24 Tupaia_tan

G2

66.1 103.6 22.85

25 Homo_sapie

X2

23.6 29.2

3.43

26 Tarsius_sy

G228.5 30.1

3.43

27 Mus_muscul

X2

5.9

2.2

0.38

28 Dolichotis

G2

6.1

2.2

0.38

30 Sylvilagus

X2

10.6

4

0.43

31 Ochotona_s

G2

13.4

4.1

0.43

OverallX2

98.9 131.4 27.01

G2

114.1

140

27.1

SymG
57.1

16.1

1.6

4.6

79.4

df Sta2.5 df Sta5 df

58.4 5

96

3

96

SS5
3 57.164.6 5 103.6

3 103.6

3

14.9 429.2

3 29.2

3 16.1

15.6 430.1

3 30.1

3

5.9 6

2.2

3

2.2

3

6.1 6

2.2

3

2.2

3

2.6 4

4

3

4

3

2.6 4

4.1

3

4.1

3

1.6

4.6

81.8 19 131.4 12 131.4

12 79.4

88.9 1912

140 12140

The output begins with a table, like that above, that gives results for just the
specified paths and the summed results. The sequence names and their numerical indices
are listed in the leftmost columns. Reading the first line, results for tests without grouping
cells are given first. To the right are the same tests using the automatic grouping of cells
to have expected values of at least 2.5 or 5. The X2 and G2 test statistics are listed foreach pair of sequences. The first number is 58.8. This is the X2 result for an ungrouped
test of symmetry of the pairwise divergence matrix, F, along the path between species 24
and 23. The number directly below it, 66.1, is the G2 result for a test of symmetry of F (ormodel reversibility) for the same path. (See Waddell and Steel 1997 for further details of
this test) The X2 and G2 results alternate down the table. The next column headed "Stat"lists results for the X2 and G2 results for the stationarity test (Waddell 1995, Waddell etWaddell et al.2004, INTEROGATE 1.0

9al.1999b). The column "St.All" does likewise for a test including all sites (the"traditional" conservative test, e.g. like those in PAUP, e.g., see Swofford et al. 1996).
The column SS is the sum of squares GLS test of stationarity (Taveré 1986), with value
57.1 for this first pair.
The next set of columns headed "Grouped" repeat the tests with grouping of cells.
SymG repeats the earlier G2 test of symmetry for grouped cells, so that expected values
are at least 2.5. Grouping is expected to improve the convergence to the test statistics
under the null hypothesis to a χ2 distribution. The “df” columns indicates the degrees of
freedom after grouping from this pairwise F matrix, in this case the number 5 appears, adrop from 6 degrees of freedom without grouping. The next four columns repeat the testsof stationarity with grouping so expected values are at least 2.5 and 5. The final column
gives the SS5 results, that is the GLS test with expected values of at least 5 and the same
degrees of freedom indicated in the previous “df” column. The most robust tests ofstationarity are those in the SS5 column. These clearly show large values for the pairs
Tupaia and Cyncephalus and also Homo and Tarsius.
The final two rows of the first table give the results of tests summed over theselected paths. The summed result clearly indicates non-stationarity. For example, with
SS5 the summed statistic is 80.2 with 12 degrees of freedom. A χ212 distribution has its
most extreme 1% of values greater than ~26.2 and the test statistic here is much larger.
For symmetry or reversibility the summed grouped results are 82.8 (X2) and 88.2 (G2)with 19 degrees of freedom, while a χ219 distribution has its most extreme 1% of values
greater than ~36.2.
More formally, to make a formal test of non-stationarity consider the following
form. In this case it is a test of stationarity using the new non-intersecting summation
method, grouping and the GLS test statistic,
Set α, the probability of a type1 error (rejecting Ho, when Ho is true), to 0.05
Ho: The sequences are stationary in base frequency
H1: The sequences are non-stationary
The test statistic is 80.2with 12 d.f., p <<0.05, therefore reject Ho in favor of H1,
the sequences have undergone non-stationary evolution
Some of the test results will be closely correlated since non-stationarity coincides
with non-symmetry of F. It is possible to have data that are non-reversible but observe
stationary frequencies, but this requires unlikely conditions. Note also that symmetry of F
arises in two cases, these being a reversible model, or a clock. If the data are close toclock-like it will be harder to detect a non-reversible model. If evolution is clock-like andthe only non-stationarity is a non-equilibrium root-frequency, in which case all tips
evolve towards the same expected value, this too will be hard to detect.
As is elaborated further below, with this type of test, the impact of alternative
pairwise pathsets that may cross over on short internal edges should be considered. A
contrived example here would be Homo/Cyncephalus , Tupaia /Tarsius, Mus/Ochotona,and Dolichotis/Sylvilagus. In this case the summed grouped SS5 test statistic is 40.6 with
12 d.f. and the summed grouped SymG value is 50.8 (X2) and 55.9 (G2) with 21 d.f. Bothtests are still clearly significantly large compared with their matching χ2 distributions andwe have no reason to doubt that the data are in fact non-stationary. The reason for thedrop in the size of the test statistic is that the pair Tupaia /Tarsius contains the two most
Waddell et al.2004, INTEROGATE 1.0

10deviant taxa with respect to base composition and they are deviating in the same general
direction.
To summarize, the tests of stationarity use three statistics, G2, X2 and a
Generalized Sum of Squares (GLS) to compare the base composition of sites that change
between two species. The first two statistics may be close to χ23 distributed for a single
pair (where the subscript indicates with 3 degrees of freedom), but do not converge to χ2.
They compare the sums of row and columns of a square matrix (ignoring just the
diagonal). However, each value in this matrix will appear in both a row and a column,
therefore row and column sums are not independent, but correlated. Failure to adjust forthis correlation tends to make the observed values of G2 and X2 biased upwards.
Therefore, the program also makes a GLS test of stationarity. This, with long sequences,
will converge to χ2 as this takes into account the aforementioned correlations (the test
involves estimating and using the inverse of the variance covariance matrix of row andcolumn sums).
The tests for a reversible evolutionary process are from Waddell and Steel (1997).
They also use G2 and X2 statistics comparing the ij-th and ji-th entries of the square
divergence matrix, F. These pairs of numbers are much closer to independent of eachother and given independence of characters follow a multinomial distribution. With longsequences, these test statistics converge to χ2 with degrees of freedom equal to b(b-1)/2
where b is the number of states (with 4 nucleotides this is 6 degrees of freedom).
In the output, the results according to the user specified pairs (or by default allpairs in the order of the input species) are shown first along with their sum. If thesepairwise paths are non-intersecting on the true phylogeny, then the summed statistic will
be close to a χ2 distribution with degrees of freedom equal to the sum of the degrees of
freedom of the component pairwise tests. Unless the true phylogeny is a star-like tree foran even number of sequences, it will be necessary to leave out some edges of the tree inconstructing non-intersecting paths. Alternatively, if internal edges are short, thencounting multiple pairs that cross them tends to have little effect on the overall result. A
recommended mode of operation is to obtain a reasonable estimate of the tree then plotout one set of non-interesting paths that is near maximal in sum of lengths. Then, plot out
another set of near maximal length paths that may cross each other along poorly resolved
internal edges (hence may not cross if the inferred tree is incorrect). Run both sets and ifthey both reject the null hypothesis, the result is probably trustworthy. This can also bethought of as the “hand” version of a robust Bayesian method. This would calculate aminimal path on each optimal tree from bootstrap replicates, and average the test
statistics across these trees.
When paths are specified, the matrices of pairwise output for testing stationarity
and symmetry of F are for just these sets of sequences. Inspecting the table of results, thelargest value within Supraprimates is clearly between Cyncephalus and Tupaia. This goesa long way to explaining why trees of this data do not support these two as sister taxa or
recover Euarchonta.

Waddell et al.2004, INTEROGATE 1.0

11

The output file then contains a table like that below.
Nucleotids
23 Cyncephalu
proportion
X2
24 Tupaia_tan
proportionX2
25 Homo_sapie
proportion
X2
26 Tarsius_sy
proportion
X2
27 Mus_muscul
proportion
X2
28 Dolichotis
proportion
X2
30 Sylvilagus
proportion
X2
31 Ochotona_s
proportion
X2
Overall
X2
G2
Expected

Adenine Cytosine Guanine Thymine
229
201
192
177
29
25
24
22
3.229
0.011
0.282
0.679
122
185
167
89
22
33
30
16
32.5601.054
5.294
35.984
219
203
202
176
27
25
25
22
1.200
0.061
0.031
0.557
193
223
216
165
24
28
27
21
0.529
2.768
1.365
0.011
220
201
197
176
28
25
25
22
1.359
0.011
0.031
0.557
217
201
209
171
27
25
26
21
0.913
0.011
0.452
0.129
208
192
207
192
26
24
26
24
0.105
0.282
0.282
3.947
219
190
206
185
27
24
26
23
1.200
0.452
0.212
2.085
1627
1596
1596
1331
41.0964.652
7.950
43.94846.361
4.586
8.218
51.058203.38199.50199.50166.38This table gives base frequencies and the percentage of each base in each taxon
along with an X2 test statistic of the observed number against the expected number basedon the mean composition of all taxa. This is like the test made in PAUP. These X2
statistics give some idea how different each cell is from the mean. The summed numbers
however have no known distribution (due to unaccounted for correlations) and should not
be used as a formal test of stationarity. Notable results are that many sequences differ
from the mean by substantial amounts, with Tupaia and Tarsius being enriched in G and
C and depleted in A and T.
X-square test for symmetry df = 6
Species
24 Tupaia_tana

24

25

58.8

6.5

26.2

3.1

56

24.3

43.4

23.6

3.4
14.6

23 Cyncephalus_volans 25 Homo_sapiens_publ

-

26

-

27

28

26 Tarsius_syrichta

-

-

-

30 Sylvilagus_sp

-

-

-

-

31 Ochotona_sp

-

-

-

-

-

27 Mus_musculus_publ

-

-

-

-

28 Dolichotis_patagonu

SX2Sym= 595.0

30

31

11.2

11.7

11.9

40.8

56.9

63

12

13

13.4

12.9

18.3

18.8

5.9

9.7

9.7

10.7

4.6

-

10.6

Sdf = 168

Following this, there are many fully square tables (matrices) like that above, giving
all possible pairwise statistics amongst the selected taxa (that is, all that were included ina pairwise path). If you want all taxa in the alignment listed, then hit return when asked
to specify paths. The first such matrix is shown in full above. Each matrix begins with adescription of the statistic calculated and how many degrees of freedom it has if thisnumber is constant and it is a test statistic. If cells are grouped then an asterisk follows
each statistic and the following number is the grouped degrees of freedom for just that

Waddell et al.2004, INTEROGATE 1.0

12pairwise statistic. Also provided are matrices of the Euclidean and Manhattan distance
between the base composition of each pair of sequences. At the end of some tables is an
overall sum of the statistic across the whole table and the summed degrees of freedom(e.g. SX2Sym = 620.2, Sdf = 168). Note, these sums do not take into account correlations
and therefore should not be used for making overall tests.
Below is a list of all matrices that may be output.
G-square test for symmetry df = 6
X-square test for stationarity df = 3
G-square test for stationarity df = 3
X-square test for stationarity (all sites) df = 3
Euclidian distance Matrix ( all sites )Manhattan Distance Matrix ( all sites )Proportional Euclidian distance Matrix ( all sites )Proportional Manhattan Distance Matrix ( all sites )G-square test for stationarity ( all sites ) df = 3
Species
23
25

26

30

Test of base composition stationarity ( by GLS SS ) df = 3
X-square test for symmetry ( grouped cells )G-square test for symmetry ( grouped cells )X-square test for stationarity ( grouped cells-2.5 )G-square test for stationarity ( grouped cells-2.5 )X-square test for stationarity ( grouped cells-5 )G-square test for stationarity ( grouped cells-5 )Test of base composition stationarity ( by GLS SS5 )Species
23
25
26

30

31

27

28

Relative Rate test using First Outgroup
Relative Rate test using Second Outgroup
Relative Rate for Liberal Case ( using both outgroups )OGspecies
2
3

4

5

Relative Rate test for Conservative Case ( using both outgroups )OGspecies
2

3

4

5

For the relative rate tests, all species other than those listed as “outgroups” or“outgroups to exclude” are included in the table. If a smaller table is desired, list any
species to exclude as “outgroups to exclude.” Only the fist two species listed as
outgroups are used to make these tests. The number for species i and j in these tables isan X2 statistic following Waddell et al. (1999c). Two further tables are given which also
feature tree independent tests of relative rate, but they use two outgroups and parsimonylike unambiguous reconstructions of characters. The liberal relative rate test counts apattern such as CAAT (where the order is outgroups then ingroups) as indicating achange for the second ingroup, where as the conservative test does not count this and thus
only counts patterns where all character states except one ingroup are the same.

Waddell et al.2004, INTEROGATE 1.0

13

At the very end of the output file, there are warnings advising how many entries
in symmetricized F matrices were small before grouping. Following this is a list of how
many entries in the expected π (here Pexp) base composition vector where small. Finally,a list of cases where the GLS SS test could not be performed on the raw F matrix since
the variance covariance matrix could not be inverted (in none).
Warning.
No. of entries in Fsym that are
0 :
None
0.5:
1( 23,25 )1-5:
2( 23,24 )2( 23,25 )4( 23,30 )2( 23,31 )2( 24,28 )2( 24,30 )3( 25,28 )4( 25,30 )3( 26,30 )2( 26,31 )4( 28,30 )2( 28,31 )3( 23,26 )2( 24,25 )2( 24,31 )3( 25,31 )2( 27,28 )3( 30,31 )2( 23,27 )2( 24,26 )3( 25,26 )2( 26,27 )1( 27,30 )4( 23,28 )1( 24,27 )2( 25,27 )2( 26,28 )2( 27,31 )No. of entries in Pexp that are
0 :
None
1 :
None
2-5:
None
Instances when SS cannot be calculated (as V cannot be inverted)
None

Freqnuc.exe is one of three programs in the Freq suite of programs. It is used totest whether the nucleotide data indicate a non-reversible or non-stationary model. If so,then one should consider using the LogDet distances, and not just the general reversible
distances (or, a non-reversible model for sequence evolution). Looking up the complete
table of pairwise tests for homogeneity and stationarity in the output, one can often gauge
which taxa seem most aberrant. A user may consider removing these to assess how theyaffect the overall tree.
In order to facilitate interpretation of matrices of output and identify taxa that insome way share similar properties, the matrices are also output in NEXUS format andcan be read straight into PAUP. In order to work on one particular matrix all that need bedone is to comment out (enclose) with square brackets the other results. Figure 4 shows
the results of analyzing three of these matrices in PAUP. When making such analyses in
PAUP, we prefer a consensus tree approach like that used in Waddell and Kishino (2000).
We often find a consensus of NJ and OLS+ to be informative, but not overly detailed (e.g.
small edges often collapse suggesting ambiguity in their representation). The consensus
tree for Euclidean distances is shown in figure 4.The impression in figure 4a,which isbased on Euclidean distances, is that base composition is generally similar in all species
except Tarsier and Tupaia which are divergent in the same direction. Figure 4b based on
GLS test distances is similar and confirms that only Tupaia and Tarsier deviatesignificantly. Note, this can be discerned visually by assuming the weighted tree
reasonably represents the underlying pairwise distances and for any of these to correspondto test statistics significant at the 2% level, a distance should be greater than ~10, whichwith the two exceptions, these are not (an exact significance level to work with issomewhat arbitrary, as with most cases of multiple testing without a clear priorhypothesis). Figure 4c shows that the same general pattern emerges using as a distance thereversibility test statistic, and there is a hint of Ocotona diverging most from the others in
its own direction. An alternative and a priori equally valid way to look at these output are

Waddell et al.2004, INTEROGATE 1.0

14with other multidimensional visualization techniques including multi-dimensional scaling(e.g., R core development team) and for nucleotides, the 3-axis plots of Waddell (1995).
Ochotona sp
Cyncephalus volans

Homo

TupaiaSylvilagus sp

Ochotona
Homo sapiens publ

Mus musculus publ

Dolichotis patagonu

Cyncephalus

Sylvilagus
Dolichotis
Mus

Tarsius
Tarsius syrichta
TarsiusMus
Sylvilagus

(a)

Homo

Tupaia tana(b)

0.05 changes

Dolichotis
Ochotona
Cyncephalus

Tupaia(c)

5 changes

5 changes

Figure 4. Tree based visualizations of distance matrices of (a) Euclidean basecomposition distances (b) GLS stationarity test distances (c) G2 (Kullback-Liebler)
reversibility test distances between all pairs of taxa. In figure (c) Mus and Dolichotis arelocated at the end of zero length edges that join the tree at the junction to Ochotona. Notethe is different in each figure, and the orientation is chosen arbitrarily by PAUP whenprinting the trees. For figure (b) a distance of more than 10 has a p-value of ~0,02, for(c) a distance of 15 has a p-value of ~0.02. The trees are produced by taking a strict
consensus tree of an NJ and on OLS+ tree for each data matrix. The edge lengths on thisconsensus tree are then estimated using OLS+ (see Waddell and Kishino 2000 for moredetails and examples). PAUP labels edge lengths as changes, but in this case these are
actually distances.
Another aspect of the output are the relative rate tests. These test for clock-likeevolution without any explicit assumption of the evolutionary tree. They are also model
independent. This can be useful in that model-based tests can give the wrong answer
even if the tree is correct. For the Supraprimates, using two divergent xenarthrans as theoutgroups. the resulting table is obtained.
Relative Rate test for Conservative Case (using both outgroups)
Cyncephalus
Tupaia
Homo

0

223.4

1

149.1

23.4

140.3

138

132.6

223.4

0

248

14.4

148.5

17.1

19.2

19.4 165.8

1

248

0

176.3

34.7

162.4

159.3

158.3

19.2

1.7

2.1

95.2

64.3

62.5

Tarsius

149.1

14.4

176.3

0

Mus

23.4

148.5

34.7

77.2

0

Dolichotis

140.3

17.1

162.4 4.9[10]67.3

Hystrix

77.2 4.9[10]67.3

0 7.2[10] 5.2[10]

138

19.2

159.3

1.7

64.3 7.2[10]Sylvilagus

132.6

19.4

158.3

2.1

62.5 5.2[10] 1.1[100]Ochotona

11.6

165.8

19.2

95.2

1.9

85.9

1.9
85.9

0 1.1[100]

82.3

11.6

82.3

0

94.2

94.2

0

To return to our original question, why does Cyncephalus end up with the rodents
and Tupaia within Primates? Taking everything together, it seems apparent that Tupaia
Waddell et al.2004, INTEROGATE 1.0

15groups with Tarsier in the estimated tree of figure 3 due to these two taxa showing
accelerated rates of evolution and convergent base composition. This gives rise to a highpp value. Why Cynocephallus is not close to Homo or why Glires are not recovered areless immediately apparent. The proximity of the Tarsier/Tupaia group to Homo may be
repelling Cynocephallus. There is no immediate explanation for why Glires is notrecovered, or why lagomorphs end up with Primates. However, unlike the Tupaia/Tarsiergrouping these groups do not have high pp values and it may simply be a lack ofresolution. Indeed, rerunning the analysis with Tupaia and Tarsier excluded, suggests
almost no resolution amongst the deep edges of this subset. That is, the biologically most
reasonable tree (containing Rodentia, Glires and Primatomorpha = Primates +Dermoptera, here being Homo, Tarsier and Cynocephalus) is within 2 lnL units of thebest tree, and a tree with Primatomorpha is within 0.1 lnL of the best tree. The BIC
approximation suggests such trees will not have distinct pp values. One further point ofinterest from figure 4 is that for these data Mus does not seem particularly abnormal inbase composition or evolutionary rate. This is in marked contrast to mtDNA sequences(e.g., Waddell et al. 1999b).
FreqAA.exe and FreqCodon.exe
Running these programs is basically the same as running Freqnuc. However the
input data will need to be amino acid sequences using the standard one letter code orcodon sequences starting with the first position and remaining in frame, respectively.
Following the example data, the first part of the output of FreqAA is shown below. The
string of zeros for the SS GLS test are due to the sparseness of the estimated variancecovariance matrix, preventing it being inverted. In the last columns it can be seen
considerable grouping was necessary, as would be expected, since there are 20 aminoacids, only ~266 residues, and frequencies are unequal in nearly any sequence (e.g.,
tryptophan and cytosine tend to be rare). An interesting point is that the approximate test
statistics for stationarity based on X2 and G2 have converged strongly to the more exact
GLS values. This is expected, since with more cells the overall correlation of a row witha column tends to decrease. Consistent with this, the least grouped results are the mostsimilar to GLS values. The overall result is that there is evidence of non-stationarity ofamino acid frequencies (observed statistic 33.1, 0.05 > p-value > 0.01, based on χ221) but
no evidence of a non-reversible model. Inferring which species show strongest andsignificant divergence in amino acid composition is left as an exercise to the reader. The
similarity of results with nucleotide frequencies suggests there may be a causal link,
which would be made stronger and directed by confirming that third bases of codons
moved in the same direction. Testing of codon frequencies using freqcod.exe reveals
clear evidence of non-stationarity, but an insignificant result for non-reversibility.

Waddell et al.2004, INTEROGATE 1.0

16

Statistics for stationarity and reversibility of amino acid frequencies within
Supraprimates.
Ungrouped
Species
23 Cyncephalus

Sym
+ X2

24 Tupaia

G2

25 Homo+ X2

31 Ochotona
Overall

SymG
0

13.9

29.3 25.6

5.04

0

40.5

32

5.09

32.3 16.4

4.91

0

44.7

19.9

5.01

22

2.89

0

34.7
29.4
100.
X2 125.3
5 26.53124.
G2 171.9
8
26.9

2.9

G2
+ X2

28 Dolichotis
30 Sylvilagus

Stat St.All SS

38.6 36.5 13.69
52 43.5

26 Tarsius
27 MusGrouped

G2
+ X2

25
G2

df

Sta2.5 df

df

SS5

5

22.4

9

21.1

7

9.7

5

24

9

22.6

7

0.5

20

2

10

5

8.4

4

0.5

2

11.1

5

8.9

4

3

5.6

6

4.5

5

4.1

2.7

3

5.8

6

4.6

5

2

5.4

4

1.9

2

1.4

2.6

2

5.6

4

1.9

2

14.4

12

43.5

24

36

18

33

15.5

12

46.4

24

38

18

2.7

2.6

0

Sta5

8.7

7.6

Statistics for stationarity and reversibility of codon frequencies within Supraprimates.
Ungrouped
SpeciesSym

23 Cyncephalu+ X2

24 Tupaia_tan

G2

25 Homo_sapie
26 Tarsius_sy
27 Mus_muscul

GroupedStat

93

St.All SS SymG

98.2

70.34

128.9 130.7

85.74

+ X2

57.3

64.4

27.31

G2

78.1

83.5

30.23

+ X2

75.4

68.7

38.13

28 Dolichotis

G2

103.7

89.4

43.31

30 Sylvilagus

+ X2

64.5

64

24.81

31 Ochotona_s

G2

88.9

84.6

27.06

OverallX2

290.3 295.3

160.6

G2

399.6 388.2 186.35

0df

Sta2.5 df

Sta5

df

SS5

14

7

28.1

16

25.8

11 30.3

15.1

7

33.5

16

30.5

11

8.9

6

16.7

13

23.2

8 25.2

9.4

6

17.4

13

24.6

8

0

5.4

9

21.3

19

21.8

11 17.4

5.6

9

22.2

19

22.9

11

0

4.4

5

29.5

12

21.5

8 17.9

4.5

5

34.7

12

22.7

8

32.8

27

95.5

60

92.2

38 90.7

34.6

27 107.7

60

100.7

38

0

0

Capture.exe
This program will estimate how many sites are invariant using either the methodsof Waddell et al. (1999b) for amino acid or nucleotide data, or the methods of Sidow et al.
(1994) for codon data. For the former method, two groups need to be specified. At least
one of these should be monophyletic.
i) At the first prompt the user is asked to enter an input file with its extension.
ii) Next, the user is asked to enter a name for the output file, where the results
will be stored.
iii) The user is asked whether the data is codon sequence. Enter ‘y’ for yes or ‘n’
for no if the input data is an amino acid or nucleic acid data (and not a coding
sequence).
iv) Then user will be asked to divide the taxa into two groups. List the index
numbers of the taxa in the first group. Separate indices with a space.
For this example, Supraprimates was selected as one group and all other taxa
constituted the other. The estimated proportion of invariant sites was ~11.4%. Using thecodon data the estimate was ~12.8%. These numbers are within sampling error of each

Waddell et al.2004, INTEROGATE 1.0

17

other. The number of amino acid positions that were totally constant (no "-" or "*"characters either) was 53.
capture Ver. 0.02
1: Ovis …
42: DasypGroup1 : 23 24 25 26 27 28 29 30 31Group2 : 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 32 33 34 35 36
37 38 39 40 41 42
Result : V1 = 171 V2 = 154 V12 = 111
Capture-Recapture estimates
Invariant sites
PinvStandard
29.8 (s.e.=7.048)
0.11145 (s.e.=0.02640)
Unbiased
30.0 (s.e.=6.966)
0.11223 (s.e.=0.02609)
Total Sites (Codons): 801 (267)Constant Sites (Codons) : 144 (48)Result : V1 = 199 V2 = 174 V12 = 154
Capture-Recapture estimates
Invariant codons
Standard
42.2 (s.e.=2.921)
Unbiased
42.2 (s.e.=2.899)

Pinv
0.15789 (s.e.=0.01094)
0.15803 (s.e.=0.01086)

Pcons.exe
This program tests whether the character composition in the varied and theconstant sites of the data are the same or not. The output begins with a table of thefrequencies of each character among the constant sites (marked “Fc” in the output below).
Cystine (CYS) is the highest at 14. PFc is the predicted proportion of sites that should beconstant if the character state composition of all sites is the same (this is just the overall
proportion of this character state times the number of constant sites). X2c is the X2statistic for the comparison of these two numbers (nominally 1 degree of freedom, butcells are not independent). Fv, PFv and X2v are the corresponding numbers among thevariable sites. At the end of the table the total number of sites, C, is listed (here 344), then
the number constant, Sc (here 53) and some other numbers for checking results. The test
statistics are SX2c or the sum of X2 for the constant sites (here 61.97) and SX2v the sumof X2 for the variable sites (here 11.27). Under the hypothesis that the frequencies ofthese two types of character are the same in expectation, the sum of these two statistics (=73.24) will converge asymptotically to a χ2 value with degrees of freedom equal to thenumber of character states minus one (in this case 20 -1 = 19). The p-value under the null
hypothesis is extremely low (< 0.0001). Care should be taken that expected values are in
the range that gives reasonable convergence to a X2 else the test result could be spurious.
In this case expected values of constant sites are moderately even and between 1 and 4.
Although there are a couple of constant sites with low expected frequencies, these do notcontribute much to the overall statistic. The predominant contribution and reason forrejecting the null hypothesis are that cystine residues have a reasonably large expectedvalue. It can be concluded the test result is not spurious and there really is a difference inthe residue frequencies for these two classes of sites.
i) At the first prompt the user is asked to enter an input file with its extension.
For example, file aatest.dat, user will input ‘aatest.dat’ and not just ‘aatest’.
ii) At the second prompt, user is asked whether to consider the symbol ‘-‘ asbeing a different state to others or to be effectively ignored. The user may
judge these as absence of evidence (note: insertions or deletions do indicate
Waddell et al.2004, INTEROGATE 1.0

18

the region may have a higher than usual rate of evolution, so to beconservative, these would be treated as a different state).
iii) At the next prompt user is asked to enter a name for the output file, where theresults will be stored.
iv) The user is asked to select sequences to be included in the calculations. Enterthe respective taxa number from the list separated by a space.
v) Next the calculations are and results are printed on the screen and stored in thespecified output file.
Output of Pcons with Rag amino acid data.
Sample : 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27
28 29 30 31 32 33 34 35 36 37 38 39 40 41 42
AA :
Ala
Arg
Asn
Asp
Cys
Gln
Glu
Gly
His
Ile
Fc :
2
8
3
5
15
3
5
5
9
1
PFc:
6.1
8.3
2.8
2.9
6.7
3.9
5.6
2.7
5.8
4.6
X2c:
2.8
0.0
0.0
1.5 10.2
0.2
0.1
2.0
1.8
2.8
Fv : 13.8 13.5
4.3
2.5
2.4
7.1
9.6
1.9
6.0 10.9PFv:
9.7 13.2
4.5
4.6 10.7
6.2
9.0
4.3
9.2
7.3
X2v:
1.7
0.0
0.0
1.0
6.4
0.1
0.0
1.3
1.1
1.8
AA :
Fc :
PFc:
X2c:
Fv :
PFv:
X2v:

Leu
17
10.1
4.7
9.1
16.1
3.0

Lys
7
10.1
1.0
19.2
16.1
0.6

Met
0
1.9
1.9
4.8
3.0
1.2

Phe
4
3.6
0.0
5.4
5.8
0.0

Pro
5
5.1
0.0
8.1
8.0
0.0

C = 267
Sc = 103
Sv = 164
SX2c = 36.4444 SX2v = 22.8888

Ser
4
9.1
2.9
19.6
14.5
1.8

SFv = 162

Thr
2
3.9
0.9
8.1
6.2
0.6

Trp
2
0.8
2.0
0.0
1.2
1.2

SPFc= 102

Tyr
0
1.6
1.6
4.2
2.6
1.0

Val
6
6.7
0.1
11.4
10.7
0.0

SPFv = 163

Exclcon.exe
This program reads in a file, asks you if the data are amino acids, then excludes acertain number of constant sites in proportion to either the overall composition or thefrequencies at the constant sites alone. In order to estimate how many of which type ofsite to exclude the program multiplies the number to be excluded by the proportion ofthat character state among the constant sites. For example, for ARG the calculation is 39
x 3.77/100 = 1.47. Normal rounding would see 1 such site excluded. However, theprogram rounds such that the total number of excluded sites is exactly 39, so the cut off
for rounding may be slightly larger or smaller than 0.5 (in this case it was slightly
smaller).
i) At the first prompt user is asked to enter an input file with its extension.
ii) At the next prompt user is asked to enter a name for the output file, where theresults will be stored.
iii) This program treats ‘-‘ as a different state. This is indicated to the user duringexecution, by an onscreen warning. this means that a column of alone state
except for one of these characters is not considered constant.
iv) At the next prompt user is asked whether the data is an amino acid sequence.
Enter ‘y’ for yes or ‘n’ for no if the input data is a codon or nucleic acid data.
v) Subsequently the user is asked to choose the species that he/she wants toinclude in the output file. Select the preceding number of the taxa in order tochoose the species as with other programs.

Waddell et al.2004, INTEROGATE 1.019vi) The total number of sites and total number of constant sites are printed on thescreen. User is now asked to enter the number of sites he/she wants to exclude
from the data.
vii) The next option is whether the constant sites are removed in proportion to thetotal number of constant sites. The program "XXX" may be used to test for asignificant difference in these compositions.
viii) The number of each type of character excluded is written to screen.
Below is output of Exclcon.exe for the ragaa.nex file after excluding 39 constantsites in proportion to the frequencies at the constant sites. “Pr” indicates the percentage ofsuch amino acids among the constant sites, while “Ex” indicates how many of each typewere actually excluded.
Total = 267, Constant = 53
How many constant sites do you want to exclude? > 30
Remove constant sites in proportions of constant sites? (y/n) yWarning : number of sites adjusted.
Warning : number of sites adjusted.
Warning : number of sites adjusted.
Constant = 53, Excluded = 30
AA
Pr
Ex

Ala
0.00
0

Arg
3.77
1

Asn
1.89
1

Asp
Cys
5.66 26.42
2
8

Gln
0.00
0

Glu
3.77
1

Gly
1.89
1

His
7.55
2

Ile
1.89
1

AA
Leu
Pr 15.09
Ex
2

Lys
5.66
2

Met
0.00
0

Phe
5.66
2

Ser
5.66
2

Thr
1.89
1

Trp
1.89
1

Tyr
0.00
0

Val
3.77
1

Pro
7.55
2

Perfect.exe
Perfect.exe allows the user to remove sites that show variability in specified
groups. Selects sites that show evidence of slow rates and conservatism. This program
allows the user to select a subset of the sites that are generally more slowly evolving andas such, should be more robust to deviations from the model used to reconstruct the tree.
The basic idea is to remove sites within a monophyletic group that show evidence ofchange. It is these sites that are likely to evolve faster. Doing this, is also analogous tochoosing to replace that monophyletic group's taxa with a set of just those sites for which
an ancestral sequence can be built based on a unanimous consensus sequence.
i) At the first prompt user is asked to enter an input file with its extension.
ii) At the next prompt user is asked to enter a name for the output file.
iii) For the next two prompts, user is then asked whether to consider certain states as
being different to others or to be effectively ignored. The first option is whether asingle member of the group having a different state should exclude the site. The
second is whether a single member of any of the selected groups having a uniquestate not found in any other member of any group should exclude the site. The
final question is whether a gap character "-" should exclude a state.
iv) User is then asked to specify groups that should be monophyletic species or atleast correspond to edges on the true unrooted tree. This is done by listing theWaddell et al.2004, INTEROGATE 1.0

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number of groups and then listing the members of each group. Finally the user is
asked if they want to retain any species (and their sites) in the output if they are
not included in the specified groups.
v) The program removes all sites showing variation in any of the defined groups.
The sequences are then written to an output file with all sites with ‘?’ removed.
Also generated is a file in which just the position of sites that do or do not showchange in the monophyletic groups is recorded (e.g. sites with ‘??’). These may
be copied directly into a NEXUS file to use as a character weight set (and so canbe included or excluded at will).
There is no limit on the number of groups or the number of taxa within eachgroup. There are a series of options allowing the user to refine their definition of variable.
For example, should a singleton (a unique character state found in only one taxa at a
specific site) result in the site being excluded? Should a gap result in it being excluded?
Sites remaining after such a treatment tend to be closer to the ancestral sequences of eachgroup defined. Assuming an i.i.d. model with unequal rates across sites, sites that are
excluded will be biased towards the faster evolving sites. This approach has also becalled site stripping (Waddell et al. 1999b). It allows the analyst to query the data in more
depth, and its usefulness as a tool tends to be most limited by the users ability to devise
appropriate hypotheses to test.
Consider, for example, our test data. The key question is should Tupaia be closer to
Tarsier than Tarsier is to Homo? The evidence already suggests that Tupaia and Tarsier
are GC rich. How might this probable attraction be mitigated, so we can then ask if there
is any residual evidence that Tupaia is within Primates? For this data one way to do thisis to remove characters that differ between Tupaia and Homo. Doing this produces
something close to an ancestral sequence of these two taxa. If Tupaia is indeed a Primate
or a clear sister to them, this treatment would not be expected to readily disrupt this (i.e.,any characters that evolved on a common edge to these three species should still bepresent in the data). Further, when removing characters, one can even be a bit more
liberal and allow either Tupaia or Homo to have singletons. Such sites may retain useful
information in other parts of the tree, but do not afford much opportunity for convergence
between Tupaia and Tarsier based purely on base composition. On the flip side,
following this treatment, if Tupaia is only attracted to primates due to its basecompositional similarity to Tarsier then it move any where in the tree. However, it is along external edge and as such there might be some tendency to attract to other longedges. The next longest edge in this data is that to Mus. Removing all sites that vary
between Homo and Tariser except those due to singleton states, then analyzing the datawith the most general likelihood model in PAUP, the best tree places Tupaia sister toMus. A tree following Waddell et al. (1999c) has a worse lnL of 1.9 units. Thus, there isno clear evidence that Tupaia is within Primates.
The results are consistent with no resolution within Supraprimates above thesuperordinal level. A final check of this may be made by retaining just those charactersthat show no change within the orders of Supraprimates represented by more than two
species. All but one of the 16 retained characters define orders and this single charactergroups Primates, Cynocephalus plus Lagomorpha vs Rodentia and Tupaia. This helps to

Waddell et al.2004, INTEROGATE 1.0

21

confirm the overall impression there is no apparent signal in this data relating orders
within Supraprimates.
Perfect2.exe
A variant of Perfect.exe that reads in a matching amino acid and codon file. It
evaluates which sites to keep and which to exclude based on the amino acid data, thenexcludes sites that are variable within certain groups of taxa from both the amino aciddata set and then the corresponding codons in the codon data set. This is useful if you
want to analyze the exact same data at the nucleotide and amino acid level.
i) At the first prompt user is asked to enter an input file of amino acid data.
ii) At the second prompt user is asked to enter an input file of codon data thatmatches species to species and codon site to amino acid the first file.
iii) At the next prompt user is asked to enter a name for the output file.
iv) For the next two prompts, user is then asked whether to consider certain states as
being different to others or to be effectively ignored as in the program Perfect.exe.
v) User is then asked to specify groups of monophyletic species again as in
Perfect.exe.
SUMMARY
In conclusion, the programs allow the user to become more familiar with theirdata and to plan analyses accordingly. Use of these programs was an important
determinant in why the tree of Waddell et al. (1999a) was the first accurate tree of therelationships of the 18 orders of placental mammals. The programs should be useful in all
situations where systematic error needs to be considered in addition to stochastic error
affecting the estimated tree.
Acknowledgements: Thanks to JSPS Postdoctoral Fellowships (1997-1999) for
supporting P.J.W. during the development of these programs. H.M. was supported by
JSPS grant funds. Amit Patel worked on part of the program, as a student programmer,
including initial coding of NEXUS formats and relative rate tests (see Waddell et al.,2004).

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