TREE-PUZZLE - Maximum likelihood analysis
for nucleotide, amino acid, and two-state data

TREE-PUZZLE Manual
Version 5.2 (July 2004)
Copyright 2003-2004 by

Heiko A. Schmidt, Korbinian Strimmer, and Arndt von Haeseler

Copyright 1999-2003 by
Copyright 1995-1999 by

H.A. Schmidt, K. Strimmer, M. Vingron, and A. von Haeseler
K. Strimmer and A. von Haeseler

Heiko A. Schmidt
von Neumann Institute for Computing (NIC),
Research Center Jülich, D-52425 Jülich, Germany.
email: hschmidt @ cs.uni-duesseldorf.de
Korbinian Strimmer
Department of Statistic, University of Munich,Ludwigstr. 33, D-80539 Munich, Germany.
email: strimmer @ stat.uni-muenchen.de
Arndt von Haeseler
von Neumann Institute for Computing (NIC),
Research Center Jülich, D-52425 Jülich, Germany
andBioinformatics, Düsseldorf University,
Universitätsstr. 1, D-40225 Düsseldorf, Germany.
email: haeseler @ cs.uni-duesseldorf.de
Remarks:• A bug has been fixed, which tended to produce less resolved trees. Hence,versions prior to 5.2 should not be used anymore!
• Some menus have been extended. Hence, the order of some options might havechanged. Please check existing scripts and parameter files!
• Until 2000 TREE-PUZZLE was distributed under the name PUZZLE.

General Information
TREE-PUZZLE is a computer program to reconstruct phylogenetic trees frommolecular sequence data by maximum likelihood. It implements a fast tree
search algorithm, quartet puzzling, that allows analysis of large data sets andautomatically assigns estimations of support to each internal branch. TREEPUZZLE also computes pairwise maximum likelihood distances as well as branch
lengths for user specified trees. Branch lengths can be calculated with andwithout the molecular-clock assumption. In addition, TREE-PUZZLE offers
likelihood mapping, a method to investigate the support of a hypothesized internal branch without computing an overall tree and to visualize the phylogenetic
content of a sequence alignment. TREE-PUZZLE also conducts a number ofstatistical tests on the data set (chi-square test for homogeneity of base composition, likelihood ratio to test the clock hypothesis, one and two-sided KishinoHasegawa test, Shimodaira-Hasegawa test, Expected Likelihood Weights). The
models of substitution provided by TREE-PUZZLE are TN, HKY, F84, SH for
nucleotides, Dayhoff, JTT, mtREV24, BLOSUM 62, VT, WAG for amino acids,
and F81 for two-state data. Rate heterogeneity is modeled by a discrete Gamma
distribution and by allowing invariable sites. The corresponding parameters canbe inferred from the data set.
TREE-PUZZLE is available free of charge from• http://www.tree-puzzle.de/ (TREE-PUZZLE home page)• http://www.dkfz-heidelberg.de/tbi/tree-puzzle/ (TREE-PUZZLE
home page mirror at DKFZ)• http://iubio.bio.indiana.edu/soft/molbio/evolve (IUBio-Archive,USA)• ftp://ftp.pasteur.fr/pub/GenSoft (Institut Pasteur, France)
TREE-PUZZLE is written in ANSI/ISO C. It will run on most personal
computers and workstations if compiled by an appropriate C compiler. The tree
reconstruction part of TREE-PUZZLE has been parallelized using the Message
Passing Interface (MPI) library standard (Snir et al., 1998; Gropp et al., 1998).
If desired to run TREE-PUZZLE in parallel you need an implementation of the
MPI library installed on your system. Please read the Installation section (2)for more details.
1

We suggest that this documentation should be read before using TREEPUZZLE the first time. If you do not have the time to read this manual completely please do read at least the sections Input/Output Conventions (3.1) andQuick Start (4) below. Then you should be able to use the TREE-PUZZLE
program, especially if you have some experience with the PHYLIP programs.
The other sections should then be read at a later time.
To find out what’s new in the current version please read the Version History(section 16).

2

Contents
1 Legal Stuff

5

2 Installation
2.1 UNIX/Source Distribution . . . . . . . . . . . . . . . . . . . . . .
2.1.1 Linux (binary distribution) . . . . . . . . . . . . . . . . .
2.1.2 Mac OS X (binary distribution) . . . . . . . . . . . . . . .
2.1.3 Older Mac OSes . . . . . . . . . . . . . . . . . . . . . . .
2.1.4 Windows 95/98/NT/. . . (binary distribution) . . . . . . .
2.1.5 VMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.1.6 Parallel TREE-PUZZLE . . . . . . . . . . . . . . . . . . .
2.2 ANSI/ISO C Compilers . . . . . . . . . . . . . . . . . . . . . . .
2.3 Contributed TREE-PUZZLE Packages . . . . . . . . . . . . . . .

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7
7
8
8
8
8
10
11

3 Introduction
12
3.1 Input/Output Conventions . . . . . . . . . . . . . . . . . . . . . 12
3.1.1 Sequence Input . . . . . . . . . . . . . . . . . . . . . . . . 13
3.1.2 General Output . . . . . . . . . . . . . . . . . . . . . . . . 13
3.1.3 Distance Output . . . . . . . . . . . . . . . . . . . . . . . 14
3.1.4 Tree Output . . . . . . . . . . . . . . . . . . . . . . . . . 15
3.1.5 Tree Input . . . . . . . . . . . . . . . . . . . . . . . . . . 15
3.1.6 Likelihood Mapping Output . . . . . . . . . . . . . . . . . 16
4 Quick Start

17

5 Models of Sequence Evolution
19
5.1 Models of Substitution . . . . . . . . . . . . . . . . . . . . . . . . 19
5.2 Models of Rate Heterogeneity . . . . . . . . . . . . . . . . . . . . 21
6 Possible Analysis
22
6.1 Tree Reconstruction Using Quartet Puzzling . . . . . . . . . . . . 22
6.2 Likelihood Mapping . . . . . . . . . . . . . . . . . . . . . . . . . 23
6.3 Usertree Evaluation and Testing . . . . . . . . . . . . . . . . . . 24
6.4 Consensus Tree Construction . . . . . . . . . . . . . . . . . . . . 25
6.5 Parameter Estimation and Pairwise Distances . . . . . . . . . . . 25

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7 Available Options

26

8 Other Features

31

9 Interpretation and Hints
33
9.1 Quartet Puzzling Support Values . . . . . . . . . . . . . . . . . . 33
9.2 Percentage of Unresolved Quartets . . . . . . . . . . . . . . . . . 33
9.3 Percentage of Ambiguous Characters in the Alignment . . . . . . 34
9.4 Automatic Parameter Estimation . . . . . . . . . . . . . . . . . . 34
9.5 Batch Mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
10 Limits and Error Messages

36

11 Are Quartets Reliable?

37

12 Other Programs
38
12.1 Related Links and Programs . . . . . . . . . . . . . . . . . . . . . 38
12.2 Supporting Programs . . . . . . . . . . . . . . . . . . . . . . . . . 38
12.3 Other Phylogenetic Programs . . . . . . . . . . . . . . . . . . . . 39
12.4 Compilers and Other Software . . . . . . . . . . . . . . . . . . . 39
13 TREE-PUZZLE References and Further Reading40

14 Acknowledgments and Credits

42

15 Known Bugs

46

16 Version History

47

4

Chapter 1

Legal Stuff
TREE-PUZZLE 5.3 is c 1999-2003 Heiko A. Schmidt, Korbinian Strimmer,
Martin Vingron, and Arndt von Haeseler.
Earlier PUZZLE versions were c 1999-2003 by Heiko A. Schmidt, Korbinian
Strimmer, Martin Vingron, and Arndt von Haeseler and under the name PUZZLE
c 1995-1999 by Korbinian Strimmer and Arndt von Haeseler.
The software and its accompanying documentation are provided as is, without guarantee of support or maintenance. The whole package is licensed under
the GNU public license, except for the parts indicated in the sources where
the copyright of the authors does not apply. Please refer to http://www.
opensource.org/licenses/gpl-license.html for details.

5Chapter 2

Installation
The source code of the TREE-PUZZLE software is 100% identical across platforms. However, installation procedures differ. There is a source distribution(tree-puzzle-5.2.tar.gz, tree-puzzle-5.2.tar.zip, tree-puzzle-5.2.tar.sit)
and binary distributions (tree-puzzle-5.2-linux.tar.gz, tree-puzzle-5.2-macosx.sit,
tree-puzzle-5.2-windows.zip) with executables for Linux, Mac OS X, andWindows respectively.

2.1

UNIX/Source Distribution

Get the file tree-puzzle-5.2.tar.gz (or the .sit or .zip file for Mac orWindows). Decompress it first (using gunzip command or another program
capable of handling gz format) and then untar the file withgunzip tree-puzzle-5.2.tar.gz
tar xvf tree-puzzle-5.2.tar
The newly created directory tree-puzzle-5.2 contains four subdirectories
called doc, data, bin, and src. The doc directory contains this manual inHTML format. The data directory contains example input files. The src
directory contains the ANSI/ISO C sources of TREE-PUZZLE. Switch to thisdirectory by typing
cd tree-puzzle-5.2
To compile we recommend the GNU gcc (or GNU egcs) compiler. If gcc is
installed just typesh ./configure
makemake install6and the executable puzzle is compiled and put into the /usr/local/bin
directory. If you want to have puzzle installed into another directory you can
set this by setting the --prefix=/name/of/the/wanted/directory directive at
the sh ./configure command line. The parallel version should have been built
and installed as well, if configure found a known MPI compiler/installation(cf. 2.1.6 Parallel TREE-PUZZLE).
Then typemake clean
and everything will be nicely cleaned up.
If your compiler is not the GNU gcc compiler and not found by configure
you will have to modify that, by setting the CC variable (e.g. setenv CC cc under csh or CC=cc; export CC under sh/bash) before running sh ./configure.
If you still cannot compile properly then your compiler or its runtime libraryis most probably not ANSI compliant (e.g., very old SUN compilers). In mostcases, however, you will succeed to compile by changing some parameters in themakefile. Ask your local Unix expert/system administrator for help.

2.1.1

Linux (binary distribution)

Get the file tree-puzzle-5.2-linux.tar.gz. After decoding this file (if you
have problems, please ask your local Linux expert), you will find a folder called
tree-puzzle-5.2 on your hard disk. This folder contains the subfolders doc,
data, and src. The doc folder contains this manual in PDF format. The data
folder contains example input files. The src folder contains the ANSI/ISO C
sources of TREE-PUZZLE as well as the precompiled executable.
Rename the Linux executable puzzle-linux-gcc-static to puzzle andcopy it to a folder in your PATH, e.g., /usr/local/bin is generally a good
choice.
The Linux executable have been compiled using the GNU C compiler (http://gcc.gnu.org). If you need a compiler to prepare the executable yourself, you
might download one from the list below (section 2.2). Then proceed as describedin the UNIX/Source Installation section (2.1).

2.1.2

Mac OS X (binary distribution)

Get the file tree-puzzle-5.2-macosx.sit. After decoding this file (if you haveproblems, please ask your local Mac OS X expert), you will find a folder called
tree-puzzle-5.2 on your hard disk. This folder contains the subfolders doc,
data, and src. The doc folder contains this manual in PDF format. The data
folder contains example input files. The src folder contains the ANSI/ISO C
sources of TREE-PUZZLE as well as the precompiled executable.
Rename the Mac OS X executable puzzle-macosx-Xcode to puzzle andcopy it to a folder in your PATH, e.g., /usr/local/bin is generally a good
choice.

7

The Mac OS X executable have been compiled using Apple’s Xcode Tools(http://developer.apple.com/macosx/). If you need a compiler to prepare
the executable yourself, you might download one from the list below (section
2.2). Then proceed as described in the UNIX/Source Installation section (2.1).

2.1.3

Older Mac OSes

Due to missing access we do not support Mac OS 9/Classic anymore. We
recommend changing to Mac OS X, which combines the advantages out UNIXsystems with the Mac OS’s graphical interface.
If you want to prepare an executable for your Mac OS yourself, you might
get Metrowerks’ CodeWarrior (refer to section 2.2) to compile the C sources
included in all TREE-PUZZLE distribution packages.

2.1.4

Windows 95/98/NT/. . . (binary distribution)

Get the file tree-puzzle-5.2-windows.zip. After un-zipping this file (if you
have problems, please ask your local Windows expert), you will find a folder
called tree-puzzle-5.2 on your hard disk. This folder contains the subfolders doc, data, and src. The doc folder contains this manual in PDF format. The data folder contains example input files. The src folder contains the
ANSI/ISO C sources of TREE-PUZZLE as well as the precompiled executable.
Rename the Windows executable puzzle-windows-mingw to puzzle andcopy it to a folder in Windows’ search path.
The Windows executable has been compiled using MinGW (http://www.
mingw.org). If you need a compiler to prepare the executable yourself, you
might download one from the list below (section 2.2). Then proceed as describedin the UNIX/Source Installation section (2.1).
If you have a Linux partition on your PC we recommend to install and use
TREE-PUZZLE under Linux (see section 2.1.1) because it runs TREE-PUZZLE
faster than Windows.

2.1.5

VMS

TREE-PUZZLE for VMS is not supported anymore. Nevertheless TREE-PUZZLE
should still be compilable for VMS using the sources (see section 2.1 and ask
your local VMS expert for help).

2.1.6

Parallel TREE-PUZZLE

To compile and run the parallelized TREE-PUZZLE you need an implementation of the Message Passing Interface (MPI) library, a widely used message
passing library standard. Implementations of the MPI libraries are available foralmost all parallel platforms and computer systems, and there are free implementations for most platforms as well.

8

To find an MPI implementation suitable for your platform visit the following
web sites:• http://www.lam-mpi.org/mpi/implementations/• http://www-unix.mcs.anl.gov/mpi/implementations.html• http://WWW.ERC.MsState.Edu/labs/hpcl/projects/mpi/implementations.
html
Although MPI is also available on Macintosh and Windows systems, thedevelopers never ran the parallel version on those platforms.
To install the parallel version of TREE-PUZZLE you need the source distribution for TREE-PUZZLE and install the package on your computer as described above (2.1). The configure should configure the Makefiles appropriately. If there is no known MPI compiler found on the system the parallel version
is not configured. (If problems occur ask your local system administrator for
help.)
Than you should be able to compile the parallel version of TREE-PUZZLE
using the following commands:
sh ./configure
makemake install
and the executable ppuzzle is compiled and put into the /usr/local/bin
directory. If you want to have the executable installed into another directory
please proceed as described in section 2.1.
If your compiler is non out of mpcc (IBM), hcc (LAM), mpicc lam (LAM under LINUX), mpicc mpich (MPICH under LINUX), and mpicc (LAM, MPICH,HP-UX, etc.) and not found by configure you will have to modify that by
setting the MPICC variable (e.g. setenv MPICC /another/mpicc under csh or
MPICC=/another/mpicc; export MPICC under sh) before running sh ./configure.
Some compilers (e.g., IBM) have problems to compile the SPRNG random number generator source code. In this case you can use the old ’leapfrog
generator’ by setting the CFLAGS variable to -DNOSPRNG (e.g., setenv CFLAGS’-DNOSPRNG’ under csh or CFLAGS=’-DNOSPRNG’; export CFLAGS under sh/bash)
before running sh ./configure.
The way you have to start ppuzzle depends on the MPI implementation
installed. So please refer to your MPI manual or ask your local MPI expert for
help.
Note: The parallelization of the tree reconstruction method follows a masterworker-concept, i.e., a master process handles the scheduling of the computation
to the n worker processes, while the worker processes are doing almost all thecomputation work of evaluating the quartets and constructing the puzzling step
trees.

9

Since the master process does not require a lot of CPU time, it can bescheduled sharing one processor with a worker process. Thus, you can run
ppuzzle by assigning n + 1 processes.
If you want to evaluate a usertree or perform likelihood mapping analysis it is
not recommended to do a parallel run, because all the computation will be doneby the master process. Hence a run of the sequential version of TREE-PUZZLE
is more appropriate for usertree or likelihood mapping analysis.

2.2

ANSI/ISO C Compilers

If there is no binary version of TREE-PUZZLE available for your computer or
if you want to compile TREE-PUZZLE yourself, an ANSI/ISO C compiler isneeded to produce an executable suitable for your machine. There are a numberof free compilers available the different operating systems:
GCC - Gnu Compiler Collection (UNIX/Linux, Mac OS X, Windows), available for most OSes, widely spread in the UNIX/Linux community where
it is included in virtually every distribution. GCC is also the basis to mostcompilers mentioned below. (http://gcc.gnu.org)
ICC - Intel C++ Compiler (Linux, Windows), ICC has shown to have good
performance. It is free to a certain extend - please refer to license. (http://www.intel.com/software/products/compilers/)
MinGW - Minimalist GNU for Windows (Windows), a GCC based package that provides all basic tool necessary for software development with
Gnu tools under Windows (http://www.mingw.org)
CygWin - GNU+Cygnus+Windows (Windows), a GCC based package thatprovides the (almost) full Gnu environment and tools known from UNIX/Linuxsystems (including X-Windows). Unfortunately, executables compiled
with CygWin need CygWin installed to be run on other Windows computers. (http://www.cygwin.com)
Xcode Tools (Mac OS X), the GCC based software development tools fromApple for Mac OS X. It seems to be free, but you have to register. Pleasecheck the license. (http://developer.apple.com/macosx/)
CodeWarrior (Mac OS Classic/9/X, Windows), this is a commercial development environment from Metrowerks. Although not supported by the
TREE-PUZZLE developers, CodeWarrior is able to produce executables
for older Mac OSes. (http://www.metrowerks.com/MW/Develop/CodeWarrior.
htm)
For MPI (message passing interface) libraries which are needed to build theparallel version of TREE-PUZZLE refer to the Parallel TREE-PUZZLE section(2.1.6).

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2.3

Contributed TREE-PUZZLE Packages

There are a number of other distributions for different operating systems (ordered alphabetically)
BioLinux.org http://www.biolinux.org/tree-puzzle.html, (thanks to Luc
Ducazu), RPMs for RedHat, Fedora, SuSE
Debian Linux http://packages.debian.org/stable/science/tree-puzzle(thanks to Andreas Tille and Stephane Bortzmeyer)
FreeBSD http://www2.de.freebsd.org/ports/biology.html (thanks to Jan
Lentfer)
NetBSD http://pkgsrc.netbsd.se/?cat=search&34844 (thanks to Marc Baudoin)

11

Chapter 3

Introduction
TREE-PUZZLE is an ANSI/ISO C application to reconstruct phylogenetic trees
from molecular sequence data by maximum likelihood. It implements a fast tree
search algorithm, quartet puzzling, that allows analysis of large data sets andautomatically assigns estimations of support to each internal branch. Rate heterogeneity (invariable sites plus Gamma distributed rates) is incorporated in
all models of substitution available (nucleotides: SH, TN, HKY, F84, and submodels; amino acids: Dayhoff, JTT, mtREV24, BLOSUM 62, VT, and WAG;
two-state data: F81). All parameters including rate heterogeneity can be estimated from the data by maximum likelihood approaches. TREE-PUZZLE also
computes pairwise maximum likelihood distances as well as branch lengths foruser specified trees. In addition, TREE-PUZZLE offers a likelihood mapping toinvestigate the support of internal branches without computing an overall tree.

3.1

Input/Output Conventions

A few things of the name conventions have changed compared to earlier (<5.0) PUZZLE releases. From version 5.0 onwards names of the sequence input
file and the usertree file can be specified at the command line (e.g. ’puzzle
infilename intreename’, where infilename is the name of the sequence fileand intreename is the name of the usertree file). If only the input filename orno filename is given at the command line the TREE-PUZZLE software searches
for input files named infile and/or intree respectively.
The naming conventions of the output files have changed as well. As prefixof the output filenames the name of the sequence input file (or the usertree
file in the usertree analysis case) is used and an extension added to denote thecontent of the file. If no input filename is given at the command line the default
filenames of the earlier versions are used.
The following extensions/default filenames are possible:

12Extension.puzzle.dist.tree.qlist.ptorderfile content
TREE-PUZZLE report
ML distances
final tree(s)list of unresolved quartets
list of unique puzzling step tree
topologies.pstepoutpstep
list of puzzling step tree topologies in chronological order.eps
outlm.eps
EPS graphics file generated in
the likelihood mapping analysis
The file types are described in detail below. In the following ”INFILENAME”
denotes the prefix, which is the sequence input filename or the usertree filename
respectively.

3.1.1

default filename
outfileoutdistouttreeoutqlist
outptorder

Sequence Input

TREE-PUZZLE requests sequence input in PHYLIP INTERLEAVED format(sometimes also called PHYLIP 3.4 format). Many sequence editors and alignment programs (e.g., CLUSTAL W) output data in this format. The data
directory contains four example input files (globin.a, marswolf.n, atp6.a,primates.b) that can be used as templates for own data files. The default
name of the sequence input file is infile, if no input filename is given at thecommand line. If an infile or a file with the given name is not present TREEPUZZLE will request an alternative file name. Sequences names in the input
file are allowed to contain blanks but all blanks will internally be converted tounderscores ’ ’. Sequences can be in upper or lower case, any spaces or control
characters are ignored. The dot ’.’ is recognized as character matching to thefirst sequence, it can be used in all sequences except in the first sequence. Validsymbols for nucleotides are A, C, G, T and U, and for amino acids A, C, D, E,
F, G, H, I, K, L, M, N, P, Q, R, S, T, V, W, and Y. All other visible characters (including gaps, question marks etc.) are treated as N (DNA/RNA) or X
(amino acids). For two-state data the symbols 0 and 1 are allowed. The first
sequence in the data set is considered the default outgroup.

3.1.2

General Output

All results are written to the TREE-PUZZLE report file (INFILENAME.puzzle
or outfile). If the option ”List all unresolved quartets” is invoked a file called”INFILENAME.qlist” or ”outqlist” is created showing all these quartets. If theoption ”List puzzling step trees” is set accordingly the files ”INFILENAME.pstep”
or ”outpstep” and/or ”INFILENAME.ptorder” or ”outptorder” are generated.
The ”INFILENAME.ptorder” or ”outptorder” file contains the unique tree
topologies in PHYLIP format preceded by PHYLIP-format comment (in parenthesis). A typical line in the ptorder file looks like this:[ 2. 60 6.00 2 5 1000 ](chicken,((cat,(horse,(mouse,rat))),13

(opossum,platypus)));
The entries (separated by single blanks) in the parenthesis mean the following:• 2. - Topology occurs second-most among all intermediate tree topologies(= order number).
• 60 - Topology occurs 60 times.
• 6.00 - Topology occurs in 6.00 % of the intermediate tree topologies.
• 2 - unique topology ID (needed for the pstep file)• 5 - Sum of uniquely occurring topologies.
• 1000 - Sum of intermediate trees estimated during the analysis.
The ”INFILENAME.pstep” or ”outpstep” file contains a log of the puzzling
steps performed and the occurring tree topologies.
A typical line in the pstep file contains the following entries (separated by
tabstops):
6. 55 698 3 5 828
The entries in the rows mean the following:• 6. - 6th block of intermediate trees performed.
• 55 - number of intermediate trees inferred in this block.
• 698 - occurrences of this topology so far.
• 3 - unique topology ID (for lookup in the ptorder file).
• 5 - number unique topologies occurred so far.
• 828 - number of puzzling step performed so far.
In the case of a sequential run (puzzle) the entries of this file are more resolved,
because every block consists of one intermediate tree.

3.1.3

Distance Output

TREE-PUZZLE automatically computes pairwise maximum likelihood distances
for all the sequences in the data file. They are written in the TREE-PUZZLE
report file ”INFILENAME.puzzle” or ”outfile” and in the separate file ”INFILENAME.dist” or ”outdist”. The format of distance file is PHYLIP compatible (i.e. it can directly be used as input for PHYLIP distance-based programs
such as neighbor).

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3.1.4

Tree Output

The quartet puzzling tree with its support values and with maximum likelihood branch lengths is displayed as ASCII drawing in the TREE-PUZZLE report in ”INFILENAME.puzzle” or ”outfile”. The same tree is written intothe ”INFILENAME.tree” or ”outtree” file in CLUSTAL W format. If clocklike maximum-likelihood branch lengths are computed there will be both anunrooted and a rooted tree in the ”INFILENAME.puzzle” or ”outfile”. The
tree convention follows the NEWICK format (as implemented in PHYLIP or
CLUSTAL W): the tree topology is described by the usual round brackets(a,b,(c,d)); where branch lengths are written after the colon a:0.22,b:0.33.
Support values for each branch are displayed as internal node labels, i.e., they
follow directly after each node before the branch length to each node. Here isan example:(Gibbon:0.1393, ((Human:0.0414, Chimpanzee:0.0538)99:0.0175,
Gorilla:0.0577)98:0.0531, Orangutan:0.1003);
The likelihood value of each tree is added in parenthesis before the tree string(e.g. ”[ lh=-1621.201605 ]”). Parenthesis mark comments in the Newick or
PHYLIP tree format. In some cases the comment has to be removed before
using them with other programs.
With the programs TreeView and TreeTool it is possible to view a tree bothwith its branch lengths and simultaneously with the support values for the internal branches (here 98% and 99%). Note, the PHYLIP programs DRAWTREEand DRAWGRAM may also be used with the CLUSTAL W treefile format.
However, in the version 3.5 they ignore the internal labels and simply print thetree topology along with branch lengths.

3.1.5

Tree Input

TREE-PUZZLE optionally also reads input trees. The default name for the filecontaining the input tree is intree, if not given at the command line, but if
you choose the input tree option and there is no file with the given name orintree present you will be prompted for an alternative name. The format of
the input trees is identical to the trees in the ”INFILENAME.tree” or ”outtree”
file. However, it is sufficient to provide the tree topology only, you don’t needto specify branch lengths (that are ignored anyway) or internal labels (thatare read, stored, and written back to the ”INFILENAME.tree” or ”outtree”file). The input trees needs not to be unrooted, they can also be rooted. It is
important that sequence names in the input tree file do not contain blanks (useunderscores!). The trees can be multifurcating. The format of the tree input
file is easy: just put the trees into the file. TREE-PUZZLE counts the ’;’ at theend of each tree description to determine how many input trees there are. Anyheader (e.g., with the number of trees) is ignored (this is useful in conjunction
with programs like MOLPHY that need this header). If there is more than one
tree TREE-PUZZLE performs the Shimodaira-Hasegawa test (Shimodaira and15

Hasegawa, 1999), the two-sided and two-sided Kishino-Hasegawa test (Kishinoand Hasegawa, 1989; Goldman et al., 2000) and computes the expected likelihood
weights (ELW Strimmer and Rambaut, 2002) or, if chosen in the menu by theuser, constructs a consensus tree from the input trees.

3.1.6

Likelihood Mapping Output

TREE-PUZZLE also offers likelihood mapping analysis, a method to investigate
support for internal branches of a tree without computing an overall tree and tographically visualize phylogenetic content of a sequence alignment. The resultsof likelihood mapping are written in ASCII to the ”INFILENAME.puzzle” or”outfile” as well as to a file called ”INFILENAME.eps” or ”outlm.eps” respectively. This file contains in encapsulated Postscript format (EPSF) a picture of
the triangle that forms the basis of the likelihood mapping analysis. You may
print it out on a Postscript capable printer or view it with a suitable program.
The ”INFILENAME.eps” or ”outlm.eps” file can be edited by hand (it is plain
ASCII text!) or by drawing programs that understand the Postscript language(e.g., Adobe Illustrator). It can also be converted to other formats with tools
like ghostscript, a free Postscript interpreter which is available for the different
operating systems (http://www.ghostscript.com).

16

Chapter 4

Quick Start
Prepare your sequence input file and, optionally, your tree input file. Then
start the TREE-PUZZLE program. TREE-PUZZLE will choose automaticallythe nucleotide or the amino acid mode. If more than 85% of the characters(not counting ’-’ and ’ ?’) in the sequences are A, C, G, T, U or N, it will beassumed that the sequences consists of nucleotides. If your data set contains
amino acids TREE-PUZZLE suggests whether you have amino acids encodedon mtDNA or on nuclear DNA, and selects the appropriate model of amino acidevolution. If your data set contains nucleotides the default model of sequence
evolution chosen is the HKY model. Parameters need not to be specified, they
will be estimated by a maximum likelihood procedure from the data. If TREEPUZZLE detects a usertree file stated at the command line or one called intree
it automatically switches to the input tree mode.
Then, a menu (PHYLIP ”look and feel”) appears with default options set.
It is possible to change all available options. For example, if you want to incorporate rate heterogeneity you have to select option ’w’ as rate heterogeneity isswitched off by default. Then type ’y’ at the input prompt and start the analysis. You will see a number of status messages on the screen during computation.
When the analysis is finished all output files (e.g., outfile, outtree, outdist,
outqlist, outlm.eps, outpstep, outptlist or INFILENAME.puzzle, INFILENAME.tree, INFILENAME.dist, INFILENAME.qlist, INFILENAME.eps, INFILENAME.pstep, INFILENAME.ptorder) will be in the same directory as the input
files.
To obtain a high quality picture of the output tree (including node labels) you
might want to use use the TreeView program by Roderic Page. It is available
free of charge and runs on Mac OS and MS-Windows. It can be retrieved
from http://taxonomy.zoology.gla.ac.uk/rod/treeview.html. TreeView
understands the CLUSTAL W treefile conventions, reads multifurcating trees
and is able to simultaneously display branch lengths and support values for eachbranch. Open the ”INFILENAME.tree” or ”outtree” file with TreeView, choose”Phylogram” to draw branch lengths, and select ”Show internal edge labels”.
On a Unix you can use the TreeTool program (ftp://rdp.life.uiuc.
17edu/pub/RDP/programs/TreeTool) to display and manipulate TREE-PUZZLE
trees. Precompiled SUN executables are available from the TreeTool homepage. A statically linked version for Linux is available from http://www.
tree-puzzle.de.

18Chapter 5

Models of Sequence
Evolution
Here we give a brief overview over the models implemented in TREE-PUZZLE.

5.1

Models of Substitution

The substitution process is modeled as reversible time homogeneous stationary
Markov process. If the corresponding stationary nucleotide (amino acid) frequencies are denoted πi the most general rate matrix for the transition from
nucleotide (amino acid) i to j can be written as

QijP
πj
for i 6= j
Rij =− m Qim πm for i = j
The matrix Qij is symmetric with Qii = 0 (diagonals are zero). For nucleotides
the most general model implemented is the general time reversible or GTR
model (Lanave et al., 1984; Tavaré, 1986; Rodriguez et al., 1990). The GTR
model allows for six different substitution rates (RAC = RCA , RAG = RGA ,RAT = RT A , RCG = RGC , RCT = RT C , RGT = RT G ). However, there is noautomatic parameter estimation implemented (yet) to estimate these parameters from the input data. Hence the parameters have to be entered by the user.
The most general model built into TREE-PUZZLE with parameter estimationis the Tamura-Nei model (TN, Tamura and Nei (1993)).
The matrix Qij for this model equals
 4tγ
 γ+1 for i → j pyrimidine transition
4t
Qij =for i → j purine transition
 γ+1
1
for i → j transversion
The parameter γ is called the ”Y/R transition parameter” whereas t is the”Transition/transversion parameter”. If γ is equal to 1 we get the HKY model
19

(Hasegawa et al., 1985). Note, the ratio of the transition and transversion
rates (without frequencies) is κ = 2t. There is a subtle but important difference between the transition-transversion parameter, the expected transitiontransversion ratio, and the observed transition transversion ratio. The transitiontransversion parameter simply is a parameter in the rate matrix. The expectedtransition-transversion ratio is the ratio of actually occurring transitions to actually occurring transversions taking into account nucleotide frequencies in thealignment. Due to saturation and multiple hits not all substitutions are observable. Thus, the observed transition-transversion ratio counts observabletransitions and transversions only. If the base frequencies in the HKY modelare homogeneous (πi = 0.25) HKY further reduces to the Kimura model. In
this case t is identical to the expected transition/transversion ratio. If t is set
to 0.5 the Jukes-Cantor model is obtained. The F84 model (as implemented
in the various PHYLIP programs, (Felsenstein, 1984) is a special case of the
Tamura-Nei model.
For amino acids the matrix Qij is fixed and does not contain any free parameters. Depending on the type of input data four different Qij matrices
are available in TREE-PUZZLE. The Dayhoff (Dayhoff et al., 1978) and JTT(Jones et al., 1992) matrices are for general use with proteins encoded on nuclear DNA, the mtREV24 (Adachi and Hasegawa, 1996) matrix is for use withproteins encoded on mtDNA.
The WAG matrix has been inferred from a database of 3905 globular protein
sequences, forming 182 distinct gene families spanning a broad range of evolutionary distances (Whelan and Goldman, 2001), and is, hence applicable for awide range of protein families.
The VT model is based an new estimator for amino acid replacement rates,
the resolvent method. The VT matrix has been computed from a large setalignments of varying degree of divergence. Hence VT is for use with proteinsof distant relatedness as well (Müller and Vingron, 2000).
Although implemented in TREE-PUZZLE on request, the BLOSUM 62 matrix (Henikoff and Henikoff, 1992) has been been developed for protein searches.
Hence, it does not represents an evolutionary process and should not really be
used for phylogeny reconstruction.
For doublets (pairs of dependent nucleotides) the SH model (Schöniger andvon Haeseler, 1994) is implemented in TREE-PUZZLE. The corresponding matrix Qij reads 2t for i → j transition substitution
1 for i → j transversion substitution
Qij =
0 for i → j two substitutions
The SH model basically is a F81 model (Felsenstein, 1981) for single substitutions in doublets.

20

5.2

Models of Rate Heterogeneity

Rate heterogeneity is taken into account by considering invariable sites and by
introducing Gamma-distributed rates for the variable sites.
For invariable sites the parameter θ (”Fraction of invariable sites”) determines the probability of a given site to be invariable. If a site is invariable theprobability for the constant site patterns is πi , the frequency of each nucleotide(amino acid).
The rates r for variable sites are determined by a discrete Gamma distribution that approximates the continuous Gamma distribution
g(r) =

αα r αeαr Γ(α)

where the parameter alpha ranges from α = ∞ (no rate heterogeneity) to
α < 1 (strong heterogeneity). The mean expectation of r under this distribution
is 1.
A mixed model of rate heterogeneity (Gamma plus invariable sites) is alsoavailable. In this case the total rate heterogeneity ρ (as defined by Gu et al.
(1995)) computes as ρ = (1+θα)(1+α) .

21

Chapter 6

Possible Analysis
A number of analyses are possible with the TREE-PUZZLE package. The mainones are described in the following.

6.1

Tree Reconstruction Using Quartet Puzzling

The main purpose of the TREE-PUZZLE package is to reconstruct trees. It
uses the quartet puzzling algorithm as described by Strimmer and von Haeseler(1996). Quartet Puzzling is a three step algorithm. Preceeded by an initializing
step that reads input data and infers missing parameters. The three steps are:
ML Step: In this first step, all quartet tree topologies are evaluated to get a
set of quartets, which are best supported by the underlying n sequencealignment. To that end, all n4 quartets, i.e., groups of four sequences,are evaluated using maximum likelihood. The three quartet topologies
ab|cd, ac|bd, and ac|bd (cf. Fig 6.1) are then weighted by their posterior
probabilities. Then one, two, or even all three quartet topologies to the setof supported quartets according to their weights (Strimmer et al., 1997).
Puzzling Step: Starting from one quartet tree the remaining n − 4 sequences
are added one-by-one to get a full n-tree. A sequence is added to thebranch which is least contradicted by the neighborhood relationships fromthe quartet set constructed in the ML step as described by Strimmer andvon Haeseler (1996), ties broken randomly. Differing from their description
we use a recursive O(n4 ) algorithm that gives the same result in faster
time.
This step is repeated very often producing a large number of so-calledintermediate trees.
Consensus Step: From the set of intermediate trees from the ML step a majority consensus tree is built and its branch lengths and ML value are
estimated. By default a 50% majority consensus (M50 consensus sensu
22

A

C

A

B

A

B

B

D

C

D

D

C

AB|CD

AC|BD

AD|BC

Figure 6.1: The 3 fully resolved tree topologies for the quartet (A,B,C,D).
p =
1.0
1

1

L1
L 1 + L 2+ L 3

a

b

d

c

a

c

b

d

a

b

c

d

0.33
1.0

0.33

p =
2

0.33

1.0

p =
3

L2
L 1 + L 2+ L 3

a

b

d

c

a

b

d

c

a

c

d

b

a

b

c

d

L3
L 1 + L 2+ L 3

Figure 6.2: What does the likelihood diagrams show? The posterior weights ofthe three resolved tree topologies for each quartet plotted into 3-dimensional
coordinate system (left side). All points fall into the triangular grey surface.
Hence, shifting the view point produces the triangular diagram.
McMorris and Neumann, 1983) is constructed. However this behavior canbe changed to a relative consensus (Mrel , cf. 6.4 for details) by adding
the ’-consmrel’ flag at the commandline.
For more detailed descriptions of the quartet puzzling algorithm refer toStrimmer and von Haeseler (1996), Strimmer et al. (1997), as well as Schmidt
and von Haeseler (2003). Further informations might also be found in chapters
7, 8, and 9.

6.2

Likelihood Mapping

The quartet topology weighting introduced by Strimmer et al. (1997) led tothree values that add up to 1.0. Plotting these three posterior weights into a
3-dimensional coordinate system makes all points fall into a triangular surface,a so-called simplex (Fig. 6.2). This led enables a way to analyze phylogenetic
information in datasets,likelihood mapping (Strimmer and von Haeseler, 1997).

Plotting all n4 quartets (or a random subsample) in a likelihood mapping
diagram provides an overview of how many quartets cannot be resolved (Fig. 6.3,
left side). The higher this percentage, the less suited a dataset is for phylogenetic
analysis. How can a tree be resolved reliably, if even its quartet subtrees cannot?

23

(a,b)-(c,d)(a,d)-(b,c)(a,c)-(b,d)

32.5%

0.0%
1.8%
%
0.0

0.3

%

0.3%

%

%

0.2%
32.3%

4.4

0.2

0.9%

4.8%

98.0%

33.5%

0.0%

0.8%

89.9%

Figure 6.3: Likelihood mapping diagrams produced from the elongation factor
dataset (EF.phy). Left side: measurement of phylogenetic signal in the dataset
showing only 0.9% unresolved and 0.8 % partly resolved quartets. Right side:grouped likelihood mapping diagram of the branching pattern of EF-2/G sequences. The EF dataset was grouped into 4 clusters: Crenarchaeota (a), Bacteria (b), Eucaryota (c), EF-1α/Tu sequences as outgroup (d). The clusteringof Crenarchaeota (a) and Eucaryota (c) is supported suggesting the Bacteria at
the root of the EF-2/G subtree.
Alternatively, clusters of sequences can be analyzed by likelihood mapping.
This analyzes the support for internal branches or groupings in a tree without having to compute an overall tree. Every internal branch in a completely
resolved tree defines up to four clusters of sequences. Sometimes only the relationship of these groups are of interest and not details of the structure of theclusters themselves. Then a likelihood mapping analysis is sufficient. The corresponding likelihood mapping triangle diagrams (as contained in various output
files generated by TREE-PUZZLE) will elucidate the possible relationships indetail (Fig. 6.3, right side).
For more detailed descriptions refer to Strimmer and von Haeseler (1997) as
well as Schmidt and von Haeseler (2003). Further informations might also befound in chapters 7, 8, and 9.

6.3

Usertree Evaluation and Testing

It is also possible to estimate ML branch lengths and likelihood values for a setof tree topologies provided by the user. If more than one input tree are provided,
several tests are performed to compare these and infer some kind of ’confidence
sets’. The SH test (Shimodaira and Hasegawa, 1999) is a multi-comparison test
taking into account that any tree in the test set could be the maximum likelihood
tree. Two types of Kishino and Hasegawa test (KH test) are implemented tocheck which trees are significantly worse than the best tree. Included are, first,
24the original two-sided KH test as described in Kishino and Hasegawa (1989),
and second, the one-sided KH test (Goldman et al., 2000) using pairwise SH
tests to cope with the fact that we test against the best tree. Goldman et al.
(2000) pointed out the two-sided KH test is not suited for testing against theML tree since all other trees can hardly be better in terms of likelihood (cf. that
paper for details). Furthermore expected likelihood weights (ELW, Strimmer
and Rambaut 2002) are implemented which infer a narrow ’confidence set’ on
the tree set. For the interpretation and applicability of the different tests, thearticles cited above have to be read carefully.

6.4

Consensus Tree Construction

Alternatively, a consensus tree can be constructed from all the trees in a set.
ML branch lengths and ML value are estimated for the consensus topology.
Currently, TREE-PUZZLE by default constructs a 50% majority rule consensus (M50 consensus sensu McMorris and Neumann, 1983), that means all
splits (bipartitions of the sequence set) occurring in more than 50% of thedataset are incorporated in the consensus tree.
A relative majority consensus tree (Mrel consensus) is constructed, if theuser adds the ’-consmrel’ flag at the commandline. In this Mrel consensus
all splits are incorporated into the consensus tree that do not contradict anyother split occurring equally or more often in the set of user trees. This means,
all splits are used, even below 50% occurrence, until the first incongruence isobserved. (This is comparable to a relative majority vote.)
Further informations might also be found in chapters 7, 8, and 9.

6.5

Parameter Estimation and Pairwise Distances

It is also possible to only infer parameters and compute a maximum likelihood
distance matrix. That means, no tree is reconstructed and TREE-PUZZLE
ends after writing the estimated parameters and the pairwise distance matrix
to the according output files (*.puzzle, *.dist).
This can be very useful if one wants TREE-PUZZLE to estimate parameters
for the use in another program, e.g., to perform further analyses.
Further informations might also be found in chapters 7, 5, 8, and 9.

25

Chapter 7

Available Options
All options can be selected and changed after TREE-PUZZLE has read the
input file. Depending on the input files options are preselected and displayed ina menu (”PHYLIP look and feel”):
GENERAL OPTIONSb
Type of analysis?
kTree search procedure?
v
Approximate quartet likelihood?
u
List unresolved quartets?
n
Number of puzzling steps?
j
List puzzling step trees?
o
Display as outgroup?
zCompute clocklike branch lengths?
eParameter estimates?
x
Parameter estimation uses?
SUBSTITUTION PROCESSdType of sequence input data?
mModel of substitution?
tTransition/transversion parameter?
f
Nucleotide frequencies?
RATE HETEROGENEITYw
Model of rate heterogeneity?

Tree reconstruction
Quartet puzzling
No
No
1000
No
GibbonNo
Approximate (faster)
Neighbor-joining tree
Nucleotides
HKY (Hasegawa et al. 1985)
Estimate from data set
Estimate from data set
Uniform rate

Quit [q], confirm [y], or change [menu] settings:
By typing the letters shown in the menu you can either change settings orenter new parameters. Some options (for example ’m’ and ’w’) can be invoked
several times to switch through a number of different settings. The parametersof the models of sequence evolution can be estimated from the data by a variety
of procedures based on maximum likelihood. The analysis is started by typing’y’ at the input prompt. To quit the program type ’q’.

26

The following table lists in alphabetical order all TREE-PUZZLE options.
Be aware, however, not all of them are accessible at the same time:
Option Descriptiona - Gamma rate heterogeneity parameter alpha. This is the so-called shapeparameter of the Gamma distribution.
b - Type of analysis. Allows to switch between tree reconstruction/analysis bymaximum likelihood and likelihood mapping.
c - Number of rate categories (4-16) for the discrete Gamma distribution (rateheterogeneity).
d - Data type. Specifies whether nucleotide, amino acid sequences, or twostate data serve as input. The default is automatically set by inspectionof the input data. After TREE-PUZZLE has selected an appropriate data
type (marked by ’Auto:’) the ’d’-option changes the type in the following order: automatically selected type → Nucleotides → Amino acids →automatically selected type.
e - Approximation option. Determines whether an approximate or the exact
likelihood function is used to estimate parameters of the models of sequence evolution. The approximate likelihood function is in most cases
sufficient and is faster.
f - Base frequencies. The maximum likelihood calculation needs the frequencyof each nucleotide (amino acid, doublet) as input. TREE-PUZZLE estimates these values from the sequence input data. This option allows
specification of other values.
g - Group sequences in clusters. Allows to define clusters of sequences as needed
for the likelihood mapping analysis. Only available when likelihood mapping is selected (’b’ option).
h - Codon positions or definition of doublets. For nucleotide data only. If the
TN or HKY model of substitution is used and the number of sites in thealignment is a multiple of three the analysis can be restricted to each of
the three codon positions and to the 1st and 2nd positions. If the SHmodel is used this options allows to specify that the 1st and 2nd codon
positions in the alignment define a doublet.
i - Fraction of invariable sites. Probability of a site to be invariable. Thisparameter can be estimated from the data by TREE-PUZZLE (only if
the approximation option for the likelihood function is turned off).
j - List puzzling step trees. Writes all intermediate trees (puzzling step trees)
used to compute the quartet puzzling tree into a file, either as a list of
topologies ordered by number of occurrences (*.ptorder), or as list about
the chronological occurrence of the topologies (*.pstep), or both.
27

k - Tree search. Determines how the overall tree is obtained. The topology
is either computed with the quartet puzzling algorithm or a set of trees
is provided by the user. If there are more than two trees in such a set,
maximum likelihood branch lengths will be computed for this tree and anumber of tests (KH-test, SH-test, and ELW) will be performed on thetrees by default. Instead of the evaluation a consensus can be computed
for all the trees for which ML branch lengths and ML value are estimated.
Alternatively, a maximum likelihood distance matrix only can also becomputed (no overall tree).
l - Location of root. Only for computation of clock-like maximum likelihood
branch lengths. Allows to specify the branch where the root should beplaced in an unrooted tree topology. For example, in the tree (a,b,(c,d))l = 1 places the root at the branch leading to sequence a whereas l=5
places the root at the internal branch.
m - Model of substitution. The following models are implemented for nucleotides: the general time reversible model (Tavaré, 1986, GTR, e.g.,)model, the Tamura and Nei (TN) model, the Hasegawa et al. (HKY)model, and the Schöniger and von Haeseler (SH) model. The SH model
describes the evolution of pairs of dependent nucleotides (pairs are the first
and the second nucleotide, the third and the fourth nucleotide and so on).
It allows for specification of the transition-transversion ratio. The original model (Schöniger and von Haeseler, 1994) is obtained by setting thetransition-transversion parameter to 0.5. The Jukes and Cantor (1969),
the Felsenstein (1981), and the Kimura (1980) model are all special casesof the HKY model.
For amino acid sequence data the Dayhoff et al. (Dayhoff) model, theJones et al. (JTT) model, the Adachi and Hasegawa (mtREV24) model,
the Henikoff and Henikoff (BLOSUM 62), the Müller and Vingron (VT),and the Whelan and Goldman (WAG) substitution model are implemented
in TREE-PUZZLE. The mtREV24 model describes the evolution of aminoacids encoded on mtDNA, and BLOSUM 62 is for distantly related aminoacid sequences, as well as the VT model. After TREE-PUZZLE has selected an appropriate amino acid substitution model (marked by ’Auto:’)the ’m’-option changes the model in the following order: automaticallyselected model → Dayhoff → JTT → mtREV24 → BLOSUM62 → VT →WAG → automatically selected model
For more information please read the section in this manual about models
of sequence evolution (p. 19). See also option ’w’ (model of rate heterogeneity).
n - If tree reconstruction is selected: number of puzzling steps. Parameter ofthe quartet puzzling tree search. Generally, the more sequences are used
the more puzzling steps are advised. The default value varies dependingon the number of sequences (at least 1000).

28

If likelihood mapping is selected: number of quartets in a likelihood mapping analysis. Equal to the number of dots in the likelihood mapping
diagram. By default 10000 dots/quartets are assumed. To use all possible
quartets in clustered likelihood mapping you have to specify a value of
n=0.
o - Outgroup. For displaying purposes of the unrooted quartet puzzling tree
only. The default outgroup is the first sequence of the data set.
p - Constrain the TN model to the F84 model. This option is only available
for the Tamura-Nei model. With this option the expected (!) transitiontransversion ratio for the F84 model have to be entered and TREEPUZZLE computes the corresponding parameters of the TN model (thisdepends on base frequencies of the data). This allows to compare the results of TREE-PUZZLE and the PHYLIP maximum likelihood programs
which use the F84 model.
q - Quits analysis.
r - Y/R transition parameter. This option is only available for the TN model.
This parameter is the ratio of the rates for pyrimidine transitions andpurine transitions. You do not need to specify this parameter as TREEPUZZLE estimates it from the data. For precise definition please read thesection in this manual about models of sequence evolution (p. 19).
s - Symmetrize doublet frequencies. This option is only available for the SHmodel. With this option the doublet frequencies are symmetrized. For
example, the frequencies of ”AT” and ”TA” are then set to the average ofboth frequencies.
t - Transition/transversion parameter. For nucleotide data only. You do notneed to specify this parameter as TREE-PUZZLE estimates it from thedata. The precise definition of this parameter is given in the section onmodels of sequence evolution in this manual (p. 19).
u - Show unresolved quartets. During the quartet puzzling tree search TREEPUZZLE counts the number of unresolved quartet trees. An unresolved
quartet is a quartet where the maximum likelihood values for each of
the three possible quartet topologies are so similar that it is not possible
to prefer one of them (Strimmer et al., 1997). If this option is selected
you will get a detailed list of all star-like quartets. Note, for some data
sets there may be a lot of unresolved quartets. In this case a list of allunresolved quartets is probably not very useful and also needs a lot of disk
space.
v - Approximate quartet likelihood. For the quartet puzzling tree search only.
Only for very small data sets it is necessary to compute an exact maximum
likelihood. For larger data sets this option should always be turned on.

29

w - Model of rate heterogeneity. TREE-PUZZLE provides several different
models of rate heterogeneity: uniform rate over all sites (rate homogeneity), Gamma distributed rates, two rates (1 invariable + 1 variable), and amixed model (1 invariable rate + Gamma distributed rates). All necessary
parameters can be estimated by TREE-PUZZLE. Note that whenever invariable sites are taken into account the parameter estimation will invoke
the ’e’ option to use an exact likelihood function. For more detailed information please read the section in this manual about models of sequence
evolution (p. 19). See also option ’m’ (model of substitution).
x - Selects the methods used in the estimation of the model parameters. Neighborjoining tree means that a NJ tree is used to estimate the parameters.
Quartet sampling means that a number of random sets of four sequences
are selected to estimate parameters.
y - Starts analysis.
z - Computation of clock-like maximum likelihood branch lengths. This option
also invokes the likelihood ratio clock test.
1 - The A-C rate RAC = RCA . For nucleotide data with GTR model only.
2 - The A-G rate RAG = RGA . For nucleotide data with GTR model only.
3 - The A-T rate RAT = RT A . For nucleotide data with GTR model only.
4 - The C-G rate RCG = RGC . For nucleotide data with GTR model only.
5 - The C-T rate RCT = RT C . For nucleotide data with GTR model only.
6 - The G-T rate RGT = RT G . For nucleotide data with GTR model only.

30

Chapter 8

Other Features• For nucleotide data TREE-PUZZLE computes the expected transition/transversion
ratio and the expected pyrimidine transition/purine transition ratio corresponding to the selected model. Base frequencies play an important rolein the calculation of both numbers.
• TREE-PUZZLE also tests with a 5% level chi-square-test whether thebase composition of each sequence is identical to the average base composition of the whole alignment. All sequences with deviating composition
are listed in the TREE-PUZZLE report file. It is desired that no sequence(possibly except for the outgroup) has a deviating base composition. Otherwise a basic assumption implicit in the maximum likelihood calculation
is violated.
• A hidden feature of TREE-PUZZLE (since version 2.5) is the employmentof a weighting scheme of quartets (Strimmer et al., 1997) in the quartet
puzzling tree search.
• TREE-PUZZLE also computes the average distance between all pairs ofsequences (maximum likelihood distances). The average distances can beviewed as a rough measure for the overall sequence divergence.
• If more than one input tree several tests are performed to compare theseand infer some kind of ’confidence sets’. The SH test Shimodaira andHasegawa (1999) is a multi-comparison test taking into account that any
tree in the test set could be the maximum likelihood tree. Two types ofKishino and Hasegawa test (KH test) are used to check which trees are
significantly worse than the best tree, first, the original two-sided KH test
as described in Kishino and Hasegawa (1989) and second, the one-sided
KH test (Goldman et al., 2000) using pairwise SH tests to cope with thefact that we test against the best tree. Furthermore expected likelihood
weights (ELW, Strimmer and Rambaut 2002) are implemented which infers a narrow ’confidence set’ on the tree set. For the interpretation and31

applicability of the different tests, the articles cited above have to be read
carefully.
• If clock-like maximum-likelihood branch lengths are computed TREEPUZZLE checks with the help of a likelihood-ratio test (Felsenstein, 1988)
whether the data set is clock-like.
• To utilize phylogenetic in columns with gaps, gap characters are interpreted as wildcards (like ’N’ in DNA or ’X’ in protein sequences. If thepercentage of gapped columns is very high it might be reasonable to strip
them from the alignment prior to analysis.
• A statistic on the amount of gaps and wildcards is calculated and printed
in the puzzle report file and should be examined carefully. If the percentage of those characters is very high certain sequences or even the wholedataset might lack enough overlapping sequence information for proper
phylogenetic analysis.
• TREE-PUZZLE also detects sequences that occur more than once in thedata and that therefore can be removed from the data set to speed up
analysis. Equal sequences are detected via their evolutionary distance,i.e., if their distance equals zero. Since TREE-PUZZLE treats gaps as
wildcards, two sequences seem identical if they just differ by a gap or
wildcard.
• If rate heterogeneity is taken into account in the analysis TREE-PUZZLE
also computes the most probable assignment of rate categories to sequence
positions, according to Felsenstein (1996).
• If quartet puzzling or likelihood mapping analysis is performed the numberof fully, partly, and completely unresolved quartets is printed into the
puzzle report file for each sequence as well as the whole dataset. These
values can help to identify un-informative sequences and whether they oreven the whole dataset is suited for for phylogenetic analysis.

32

Chapter 9Interpretation and Hints
9.1

Quartet Puzzling Support Values

The quartet puzzling (QP) tree search estimates support values for each internal branch. They can be interpreted in much the same way as bootstrap values(though they should not be confused with them). Branches showing a QP reliability from 90% to 100% can be considered very strongly supported. Brancheswith lower reliability (> 70%) can in principle be also trusted but in this case
it is advisable to check how well the respective internal branch does in comparison to other branches in the tree (i.e. check relative reliability). If you areinterested in a branch with a low confidence it is also important to check thealternative groupings that are not included in the QP tree (they are listed in
the TREE-PUZZLE report file in *.** format). There should be a substantial
gap between the lowest reliability value of the QP tree and the most frequentgrouping that is not included in the QP tree.

9.2

Percentage of Unresolved Quartets

TREE-PUZZLE computes the number and the percentage of resolved, partly
resolved, and completely unresolved maximum likelihood quartets for the wholedataset as well as each sequence, i.e. observing all quartets the sequence is partof. A partly resolved or completely unresolved quartet is a quartet where themaximum likelihood values are so similar for two or all three, respectively, ofthe three possible quartet topologies that it is not possible to prefer only one ofthem Strimmer et al. (1997). The percentage of the unresolved quartets among
all possible quartets is an indicator of the suitability of the data for phylogenetic
analysis. A high percentage usually results in a highly multifurcating quartet
puzzling tree. If you only have a few unresolved quartets we recommend to
invoke option ’u’ to get a list of all these quartets. In a likelihood mapping
analysis the percentage of completely unresolved quartets is shown in the central
region of the triangle diagram.

33

If the reconstructed tree is by and large unresolved, i.e. it contains many
multifurcation, and a single sequences have a high percentage of unresolved
quartets, this sequence should be discarded from the dataset, because it might
be a source of ambiguity.

9.3

Percentage of Ambiguous Characters in the
Alignment

Besides the percentages of the three quartet types (resolved, partly resolved,
and unresolved) TREE-PUZZLE also counts the amount of gap and ambiguous characters per sequence and for the full alignment. Ambiguous characters
are such that stand for several characters, e.g. ’X’ in amino acid and ’N’ innucleotide sequences. Note that TREE-PUZZLE interprets any unknown character as ’X’ or ’N’ according to the data type.
If single sequences contain a large quantity of gaps and ambiguous charactersthey might be another source of inaccuracy due to a lack of information as well
as a possible lack of common sites with other sequences.

9.4

Automatic Parameter Estimation

TREE-PUZZLE estimates both the parameters of the models of substitution(TN, HKY) and of the model of rate variation (Gamma distribution, fractionof invariable sites) without prior knowledge of an overall tree by a number ofdifferent strategies based on maximum likelihood. For all estimated parameters
a corresponding standard error (S.E.) is computed. If you have good arguments
to choose a different set of parameters than the values obtained by TREEPUZZLE don’t hesitate to use them. If sequences are extremely similar it is very
hard for every algorithm to extract information about the model of substitution
from the data set. Also, be careful if the estimated parameter values are very
close to the internal upper and lower bounds:
Parameter (Symbol)
Transition/transversion parameter (t)Y/R transition parameter (γ)
Fraction of invariable sites (θ)
Gamma rate heterogeneity parameter (α)

Minimum
0.20
0.10
0.00
0.01

Maximum
30.00
6.00
0.99
99

It is also possible to use the GTR model (Lanave et al., 1984; Tavaré, 1986;
Rodriguez et al., 1990). Unfortunately, there is no automatic estimation procedure (yet) implemented to estimate the six substitution rates. Hence, to use
GTR the user has to provide these parameter to the program.

34

9.5

Batch Mode

Running TREE-PUZZLE from a Unix batch file is straightforward despite thelack of command line switches. Hence you have to pipe the parameters to thestandard input of the program. For example, to run TREE-PUZZLE with athe transition/transversion parameter equal to 10 the following lines in a shell
script are sufficient:puzzle << EOF
t
10
y
EOF
Another possibility is to pipe a parameter file into it, i.e. puzzle < params
or cat params | puzzle where in this example the parameter file params contains:t10y
All other parameters can also be accessed the same way. Note that the yparameter is always needed at the end.

35

Chapter 10

Limits and Error Messages
TREE-PUZZLE has a built-in limit to allow data sets only up to 257 sequencesin order to avoid overflow of internal integer variables. At least 32767 sites
should be possible depending on the compiler used. Computation time willbe the largest constraint even if sufficient computer memory is available. If
rate heterogeneity is taken into account every additional category slows down
the overall computation by the amount of time needed for one complete run
assuming rate homogeneity.
If problems are encountered TREE-PUZZLE terminates program execution
and returns a plain text error message. Depending on the severity errors can beclassified into three groups:”HALT” errors: Very severe. You should never ever see one of these messages. If so, please contact the developers!
”Unable to proceed” errors: Harmless but annoying. Mostly problems withthe format of the input files and sometimes memory errors (i.e., not enoughRAM).
Other errors: Completely uncritical. Occur mostly when options of TREEPUZZLE are being set.
A standard machine (1996 Unix workstation) with 32 to 64 MB RAM TREEPUZZLE can easily do maximum likelihood tree searches including estimationof support values for data sets with 50-100 sequences. As likelihood mapping
is not memory consuming and computationally quite fast it can be applied tolarge data sets as well.

36

Chapter 11

Are Quartets Reliable?
Quartets may be intrinsically one of the most difficult phylogenies to resolve
accurately (cf. Hillis et al., 1996). It has been asked whether this is a problem
for quartet puzzling because it works with quartets.
However, this is not true. According to Hillis’ findings (Hillis et al., 1996),
quartets can be hard, but extra information helps. That is, if all you have aredata on species (A, B, C, D) then it might be relatively difficult to find thecorrect tree for them. But if you have additional data (species E, F, G, ...) andtry to find a tree for all the species, then that part of the tree relating (A, B,
C, D) will more likely be correct than if you had just the data for (A, B, C,
D). In Hillis’ big ’model’ tree, there are many examples of subsets of 4 species
which in themselves might be hard to resolve correctly, but which are correctly
resolved thanks to the (...large amount of...) additional data. TREE-PUZZLE(quartet puzzling) also gains advantage from extra data in the same way. It’s
’understanding’ or resolution of the quartet (A, B, C, D) might be incorrect, but
the information on the relationships of (A, B, C, D) implicit in its treatment of(A, B, C, E), (A, B, E, D), (A, E, C, D), (E, B, C, D), (A, B, C, F), (A, B, F,
D), (A, F, C, D), (F, B, C, D), (A, B, C, G), etc. should overcome this problem.
The facts about how well TREE-PUZZLE actually works have been investigated in the Strimmer and von Haeseler (1996) and Strimmer et al. (1997)
papers. Their results cannot be altered by Hillis’ findings. Considered as aheuristic search for maximum likelihood trees, quartet puzzling works very well.
(This section follows N. Goldman, personal communication).

37

Chapter 12

Other Programs
12.1

Related Links and Programs

Some links related to TREE-PUZZLE:
Puzzle-Server: a web interface to TREE-PUZZLE.
http://bioweb.pasteur.fr/seqanal/interfaces/Puzzle.html
PUZZLEBOOT: a program to perform bootstrap analyses with TREE-PUZZLE.
http://hades.biochem.dal.ca/Rogerlab/Software/software.html

12.2

Supporting Programs

An (incomplete) list of programs supporting TREE-PUZZLE by providing graphical presentation of results produced by PUZZLE are:
TreeView: (UNIX/Linux, Mac OS X, Windows) a tree viewer
http://taxonomy.zoology.gla.ac.uk/rod/treeview.html
TreeTool: (UNIX/Linux) a tree viewer
ftp://rdp.life.uiuc.edu/pub/RDP/programs/TreeTool/, a staticallylinked Linux executable is available from http://www.tree-pzzle.deGhostView: (UNIX/Linux, Mac OS X, Windows) a free PostScript viewer/converter
http://www.ghostscript.com
epstopdf: (UNIX/Linux, Mac OS X, Windows) a free encapsulated PostScript(EPS) to PDF converter. The program needs GhostScript (see above) and
Perl (http://www.cpan.org) installed.
http://www.ctan.org/tex-archive/support/epstopdf/

38

12.3

Other Phylogenetic Programs

There are a number of other very useful and widespread programs to reconstruct phylogenetic relationships and to analyze molecular sequence data thatare available free of charge. Here are the URLS of some web pages that provide
links to most of them (including the PHYLIP package and the MOLPHY and
PAML maximum likelihood programs):• Joe Felsenstein’s list of programs (well-organized and pretty exhaustive):
http://evolution.genetics.washington.edu/phylip/software.html• ”Tree of Life” software page:
http://phylogeny.arizona.edu/tree/programs/programs.html• European Bioinformatics Institute:
http://www.ebi.ac.uk/biocat/biocat.html

12.4

Compilers and Other Software

A list of available compilers is provided in section 2.2. Links to lists of implementations of the Message Passing Interface (MPI) library for parallel computing
are given in section 2.1.6.

39

Chapter 13

TREE-PUZZLE Referencesand Further Reading
To get more hands-on details on the usage of the program we recommend torefer toSchmidt, H.A. and A. von Haeseler (2003) Maximum-Likelihood
Analysis Using TREE-PUZZLE. In A.D. Baxevanis, D.B. Davison,
R.D.M. Page, G. Stormo, and L. Stein (eds.) Current Protocols in
Bioinformatics, Unit 6.6, Wiley and Sons, New York. ISBN 0-47125093-7 ISBN 0-471-25093-7
More information can be gained also from the following:If you intend to use TREE-PUZZLE in a publication please cite the programasSchmidt, H.A., K. Strimmer, M. Vingron, and A. von Haeseler(2002) TREE-PUZZLE: maximum likelihood phylogenetic analysis
using quartets and parallel computing. Bioinformatics. 18:502-504.
(PubMed: 11934758)
for the current TREE-PUZZLE version andStrimmer, K., and A. von Haeseler (1996) Quartet puzzling: A quartet maximum likelihood method for reconstructing tree topologies.
Mol. Biol. Evol. 13: 964-969.
for the quartet puzzling algorithm.
For likelihood mapping please use:
Strimmer, K., and A. von Haeseler (1997) Likelihood-mapping: A
simple method to visualize phylogenetic content of a sequence alignment. Proc. Natl. Acad. Sci. USA. 94:6815-6819. (PubMed:
9192648)
40

For the quartet selection taking into account 2nd and 3rd best quartets:
Strimmer, K., N. Goldman and A. von Haeseler (1997) Bayesian
Probabilities and Quartet Puzzling. Mol. Biol. Evol. 14:210-213.
For the current parallel version of TREE-PUZZLE please use:
Schmidt, H.A., K. Strimmer, M. Vingron, and A. von Haeseler(2002) TREE-PUZZLE: maximum likelihood phylogenetic analysis
using quartets and parallel computing. Bioinformatics. 18:502-504.
(PubMed: 11934758)
More information on the performance of the parallel implementation can befound in
H.A. Schmidt, E. Petzold, M. Vingron, and A. von Haeseler (2003)
Molecular Phylogenetics: Parallelized Parameter Estimation andQuartet Puzzling. J. Parallel Distrib. Comput., 63, 719-727. DOI:
10.1016/S0743-7315(03)00129-1

41

Chapter 14

Acknowledgments andCredits
The maximum likelihood kernel of TREE-PUZZLE is an offspring of the program NucML/ProtML version 2.2 by Jun Adachi and Masami Hasegawa (ftp://sunmh.ism.ac.jp/pub/molphy). We thank them for generously allowing us
to use the source code of their program. As a scalable random number generator
we use source code of SPRNG (Scalable Pseudo Random Number Generator)
library (Mascagni and Srinivasan, 2000).
We would also like to thank the European Bioinformatics Institute (EBI),
the Institut Pasteur, and the University of Indiana (i.e., Don Gilbert) for kindly
distributing the TREE-PUZZLE program.
We especially thank Stephane Bortzmeyer, Ross H. Crozier, Peter Foster for
their help in debugging and their valuable remarks and suggestions, Ekkehard
Petzold for the parallelizing the parameter estimation part.
We also thank John M. Archibald, Andreas Bernauer, Christian Blouin,
Steve Cannon, Ignazio Carbone, Iñaki Comas, Ross H. Crozier, Anthony A.
Echelle, Nick Goldman, Matthias Görlach, David Horner, Nicolas Joly, Patrick
Joost, Jan Lentfer, Pawel Mackiewicz, Benoit Moury, Aris Parmakelis, Ekkehard
Petzold, Herve Philippe, Jean-Pierre Szikora, Atro Tossavainen, Falk Tschierske,
Lutz Voigt, Felipe Wettstein, Simin Whelan, Olga Zhaxybayeva, Christian Zmasek(in alphabetical order), and many others for contributions, tips, suggestions, bug
reports, and other contributions.
Furthermore we thank for preparing packages and making TREE-PUZZLE
available in various formats: Jan Lentfer (FreeBSD), Marc Baudoin (NetBSD),
Andreas Tille and Stephane Bortzmeyer (Debian Linux), Luc Ducazu (BioLinux.org).
Finally we thank the Deutsche Forschungsgemeinschaft and the Max-PlanckSociety and the von-Neumann-Institute for Computing (NIC), FZ Jülich, forfinancial support.

42

Bibliography
Adachi, J. and Hasegawa, M. (1996) Model of amino acid substitution in proteins encoded by mitochondrial DNA. J. Mol. Evol., 42, 459–468.
Dayhoff, M. O., Schwartz, R. M. and Orcutt, B. C. (1978) A model of evolutionary change in proteins. In Dayhoff, M. O. (ed.), Atlas of Protein Sequence
Structure, volume 5, pp. 345–352, National Biomedical Research Foundation,
Washington DC.
Felsenstein, J. (1981) Evolutionary trees from DNA sequences: a maximum
likelihood approach. J. Mol. Evol., 17, 368–376.
Felsenstein, J. (1984) Distance methods for inferring phylogenies: A justification. Evolution, 38, 16–24.
Felsenstein, J. (1988) Phylogenies from molecular sequences: Inference and reliability. Annu. Rev. Genet., 22, 521–565.
Felsenstein, J. (1996) Inferring phylogenies from protein sequences by parsimony, distance, and likelihood methods. Methods Enzymol., 266, 418–427.
Goldman, N., Anderson, J. P. and Rodrigo, A. G. (2000) Likelihood-based tests
of topologies in phylogenetics. Syst. Biol., 49, 652–670.
Gropp, W., Huss-Lederman, S., Lumsdaine, A., Lusk, E., Nitzberg, B., Saphir,W. and Snir, M. (1998) MPI: The Complete Reference - The MPI Extensions,volume 2. 2nd edition, The MIT Press, Cambridge, Massachusetts.
Gu, X., Fu, Y.-X. and Li, W.-H. (1995) Maximum likelihood estimation of theheterogeneity of substitution rate among nucleotide sites. Mol. Biol. Evol.,12, 546–557.
Hasegawa, M., Kishino, H. and Yano, T.-A. (1985) Dating of the human–ape
splitting by a molecular clock of mitochondrial DNA. J. Mol. Evol., 22, 160–
174.
Henikoff, S. and Henikoff, J. G. (1992) Amino acid substitution matrices fromprotein blocks. Proc. Natl. Acad. Sci. USA, 89, 10915–10919.

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Hillis, D. M., Moritz, C. and Mable, B. K. (eds.) (1996) Molecular Systematics.
2nd edition, Sinauer Associates, Sunderland, Massachusetts.
Jones, D. T., Taylor, W. R. and Thornton, J. M. (1992) The rapid generationof mutation data matrices from protein sequences. Comput. Appl. Biosci., 8,
275–282.
Jukes, T. H. and Cantor, C. R. (1969) Evolution of protein molecules. In Munro,
H. N. (ed.), Mammalian Protein Metabolism, volume 3, pp. 21–123, Academic
Press, New York.
Kimura, M. (1980) A simple method for estimating evolutionary rates of basesubstitutions through comparative studies of nucleotide sequences. J. Mol.
Evol., 16, 111–120.
Kishino, H. and Hasegawa, M. (1989) Evaluation of the maximum likelihood
estimate of the evolutionary tree topologies from DNA sequence data, andthe branching order in Hominoidea. J. Mol. Evol., 29, 170–179.
Lanave, C., Preparata, G., Saccone, C. and Serio, G. (1984) A new method for
calculating evolutionary substitution rates. J. Mol. Evol., 20, 86–93.
Mascagni, M. and Srinivasan, A. (2000) SPRNG: A scalable library for pseudorandom number generation. ACM Trans. Math. Software, 26, 436–461.
McMorris, F. R. and Neumann, D. A. (1983) Consensus functions defined ontrees. Math. Soc. Sci, 4, 131–136.
Müller, T. and Vingron, M. (2000) Modeling amino acid replacement. J. Comput. Biol., 7, 761–776.
Rodriguez, F., Oliver, J. L., Main, A. and Medina, J. R. (1990) The general
stochastic model of nucleotide substitution. J. theor. Biol., 142, 485–501.
Schmidt, H. A. and von Haeseler, A. (2003) Maximum likelihood analysis using TREE-PUZZLE. In Baxevanis, A. D., Davison, D. B., Page, R. D. M.,
Stormo, G. and Stein, L. (eds.), Current Protocols in Bioinformatics, pp.
6.6.1–6.6.25, Wiley and Sons, New York, USA.
Schöniger, M. and von Haeseler, A. (1994) A stochastic model for the evolutionof autocorrelated DNA sequences. Mol. Phylogenet. Evol., 3, 240–247.
Shimodaira, H. and Hasegawa, M. (1999) Multiple comparisons of loglikelihoods with applications to phylogenetic inference. Mol. Biol. Evol., 16,1114–1116.
Snir, M., Otto, S. W., Huss-Lederman, S., Walker, D. W. and Dongarra, J.
(1998) MPI: The Complete Reference - The MPI Core, volume 1. 2nd edition,
The MIT Press, Cambridge, Massachusetts.

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Strimmer, K., Goldman, N. and von Haeseler, A. (1997) Bayesian probabilities
and quartet puzzling. Mol. Biol. Evol., 14, 210–213.
Strimmer, K. and von Haeseler, A. (1996) Quartet puzzling: A quartet
maximum–likelihood method for reconstructing tree topologies. Mol. Biol.
Evol., 13, 964–969.
Strimmer, K. and von Haeseler, A. (1997) Likelihood–mapping: A simple
method to visualize phylogenetic content of a sequence alignment. Proc. Natl.
Acad. Sci. USA, 94, 6815–6819.
Strimmer, K. and Rambaut, A. (2002) Inferring confidence sets of possibly misspecified gene trees. Proc. R. Soc. Lond. B, 269, 137–142.
Tamura, K. and Nei, M. (1993) Estimation of the number of nucleotide substitutions in the control region of mitochondrial DNA in humans and chimpanzees.
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Tavaré, S. (1986) Some probabilistic and statistical problems on the analysis of
DNA sequences. Lec. Math. Life Sci., 17, 57–86.
Whelan, S. and Goldman, N. (2001) A general empirical model of protein evolution derived from multiple protein families using a maximum likelihood
approach. Mol. Biol. Evol., 18, 691–699.

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Chapter 15

Known Bugs
On Alpha based computers floating point exception errors have occurred. We
hope that we have fixed them all.
For occurrences of floating point exceptions or other errors we need information about the operating system to reproduce and debug those errors. The
datasets and options used when such errors occurred would be very helpful.
Optimizations and Estimations of model parameters and branch lengths arein general performed sequentially until the increase of quality (i.e., likelihood)
is below certain thresholds. Additionally TREE-PUZZLE uses upper and lower
bounds for parameters (cf. 9.4) and branch lenghts. These thresholds andbounds are a tradeoff between accuracy and and speed. Hence, the inferredlikelihood values might differ from other programs. However, these values should
only be ’shifted’ compared to other programs, but should never show different
results in general like, e.g., in the order of the likelihoods of a user defined setof trees.
If you observe such behavior or other bugs please contact the developers!

46

Chapter 16

Version History
The TREE-PUZZLE program has first been distributed in 1995 under the name
PUZZLE. Since then it has been continually improved. Here is a list of the mostimportant changes.
5.2 The quartet puzzling step is now implemented as a fast O(n4 ) algorithm.
The GTR model is possible to be used for DNA sequences. However, theparameters have to be provided by the user. The threshold of 4 <= n <=257 has been removed for tree evaluation, pairwise distance computation,and likelihood mapping. The limits are still there for ML quartet based
tree reconstruction using quartet puzzling. Beside the evaluation of a set ofuser trees, also a consensus tree can now be constructed from these trees.
The random number generation has been changed SPRNG (Mascagni and
Srinivasan, 2000, Scalable Parallel Pseudo Random Number Generators
Library) which has better performance both for the sequential as wellas the parallel code. Furthermore, the parameter estimation has beenparallelized in close collaboration with Ekkehard Petzold.
Some bug fixes have been incorporated: The WAG matrix has been fixedwith corrected data provided by the authors. A bug that tended to maketrees reconstructed less resolved has been rectified. KH tests have beenaltered to not artificially reject a tree if the variance between it and thebest tree is too small. Several minor bug fixes have been applied.
5.1 The TREE-PUZZLE manual is now distributed as a PDF file. Quartet
and ambiguous character statistics per sequence/dataset added. One
sided Kishino-Hasegawa test, Shimodaira-Hasegawa test, and ELW (expected likelihood weights, Strimmer-Rambaut) added for usertree comparison.“ Prints all congruent splits before the consensus step, even if below
50%. Gaps and ambiguous characters statistics per sequence/dataset tothe puzzle report. The programm stops if there are sequences with only
gaps/wildcards.
Several minor bugs fixed: File input fixed to accept also Mac and Windows file formats/linefeeds. (Fixes the bug that restricted user trees to47

be in one line.) root search bug, rate categories output bug, output of
infile name fixed, if the not named ’infile’, minor clock bug corrected, VT
matrix corrected by its authors, radixsort renamed to tp radixsort toavoid name clashes on Mac OS X and FreeBSD. Compiler linker flag order
fixed. 200% bug fixed. FPE errors fixed on Compaq Alpha machines.
5.0 Puzzle tree reconstruction part is now parallelized using the MPI standard(Message Passing Interface).
Possibility added to specify the names of the input file and the user
tree file at the command line. Output files renamed to the form PREFIX.EXTENSION, where PREFIX is the input file name or, if used, theuser tree file name. The EXTENSION could be one of the following:
puzzle (PUZZLE report), tree (tree file), dist (ML distance file), eps(likelihood mapping output in eps format), qlist (unresolved quartets),
qstep (puzzling step tree IDs as they occur in the analysis), or qtorder(sorted unique list of puzzling step trees).
The tree likelihood value is added to the treefile as a leading comment (’[lh=x.xxx ]’) to the tree string.
VT (variable time) matrix (Müller and Vingron, 2000) and WAG matrix(Whelan and Goldman, 2001) are added to the AA substitution models.
The Data type and AA-model options in the menu now show the automatically set type/model first. These can now be changed by using the’d’ or ’m’ key independently from the type/model selected. This makes it
possible to select a desired AA substitution model or data type by piping
letters to the standard input without knowing PUZZLE’s preselection.
Parameters are written to file when estimated before evaluation of thequartets.
The inconsistency with respect to other programs in handling invariable
sites has been fixed.
Some minor bug fixes (e.g. the clockbug and another in the optimization
routine have been fixed).
Source code organization adopted to the GNU standards (configure,make, make install under UNIX)
4.0.2 Update to provide precompiled Windows 95/98/NT executables. In addition: Internal rearrangement of rate matrices. Improved BLOSUM 62
matrix. Endless input loop for input files restricted to 10 trials. Sourcecode clean up to remove compile time warnings. Explicit quit option inmenu. Changes in NJ tree code. Updates of documentation (addresschanges, correction of errors).
4.0.1 Maintenance release. Correction of mtREV matrix. Fix of the ”intreebug”. Removal of stringent runtime-compatibility check to allow out-ofthe-box compile on Alpha. More accurate gamma distribution allowing
16 instead of 8 categories and ensuring a better alpha > 1.0. Update of
documentation (mainly address changes). More Unix-like file layout, andchange of license to GPL.
48

4.0 Executables for Windows 95/NT and OS/2 instead of MS-DOS. Computation of clock-like branch lengths (also for amino acids and for non-binary
trees). Automatic likelihood ratio clock test. Model for two-state sequences data (0,1) included. Display of most probable assignment of rates
to sites. Identification of groups of identical sequences. Possibility toread multiple input trees. Kishino-Hasegawa test to check whether trees
are significantly different. BLOSUM 62 model of amino acid substitution (Henikoff and Henikoff, 1992). Use of parameter alpha instead of
η = 1/(1 + α) (for rate heterogeneity).
Improvements to user interface. SH model can be applied to 1st and2nd codon positions. Automatic check for compatible compiler settings.
Workaround for severe runtime problem when the gcc compiler was used.
3.1 Much improved user interface to rate heterogeneity (less confusing menu,
rearranged outfile, additional out-of-range check). Possibility to readrooted input trees (automatic removal of basal bifurcation). Computation of average distance between all pairs of sequences. Fix of a bug thatcaused PUZZLE 3.0 to crash on some systems (DEC Alpha). Cosmeticchanges in program and documentation.
3.0 Rate heterogeneity included in all models of substitution (Gamma distribution plus invariable sites). Likelihood mapping analysis with Postscript
output added. Much more sophisticated maximum likelihood parameter
estimation for all model parameters including those of rate heterogeneity. Codon positions selectable. Update to mtREV24. New icon. Less
verbose runtime messages. HTML documentation. Better internal error
classification. More information in outfile (number of constant positionsetc.).
2.5.1 Fix of a bug (present only in version 2.5) related to computation of thevariance of the maximum likelihood branch lengths that caused occasional
crashes of PUZZLE on some systems when applied to data sets containing
many very similar sequences. Drop of support for non-FPU Macintosh
version. Corrections in manual.
2.5 Improved QP algorithm (Strimmer et al., 1997). Bug fixes in ML engine,computation of ML distances and ML branch lengths, optional input of auser tree, F84 model added, estimation of all TN model parameters andcorresponding standard errors, CLUSTAL W treefile convention adopted
to allow to show branch lengths and QP support values simultaneously,
display of unresolved quartets, update of mtREV matrix, source code morecompatible with some almost-ANSI compilers, more safety checks in thecode.
2.4 Automatic data type recognition, chi-square-test on base composition, automatic selection of best amino acid model, estimation of transition-transversion
parameter, ASCII plot of quartet puzzling tree into the outfile.

49

2.3 More models, many usability improvements, built-in consensus tree routines, more supported systems, bug fixes, no more dependencies of input
order. First EBI distributed version.
2.2 Optimized internal data structure requiring much less computer memory.
Bug fixes.
2.1 Bug fixes concerning algorithm and transition/transversion parameter.
2.0 Complete revision merging the maximum likelihood and the quartet puzzling
routines into one user friendly program. First electronic distribution.
1.0 First public release, presented at the 1995 phylogenetic workshop (June
15-17, 1995) at the University of Bielefeld, Germany.

50