PUZZLE

Version 4.0
December 1997
Copyright 1995-97 by Korbinian Strimmer and Arndt von Haeseler

Zoologisches Institut, Universität München, München, Germany.

PUZZLE is a computer program 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 and automatically assigns estimations of support to each internal branch. PUZZLE also computes pairwise maximum likelihood distances as well as branch lengths for user specified trees. Branch lengths can also be calculated under the clock-assumption. In addition, PUZZLE offers a novel method, likelihood mapping, to investigate the support of a hypothesized internal branch without computing an overall tree and to visualize the phylogenetic content of a sequence alignment. PUZZLE also conducts a number of statistical tests on the data set (chi-square test for homogeneity of base composition, likelihood ratio to test the clock hypothesis, Kishino-Hasegawa test). The models of substitution provided by PUZZLE are TN, HKY, F84, SH for nucleotides, Dayhoff, JTT, mtREV24, BLOSUM 62 for amino acids, and F81 for two-state data. Rate heterogeneity is modelled by a discrete Gamma distribution and by allowing invariable sites. The corresponding parameters can be inferred from the data set.

PUZZLE is available free of charge from

http://www.zi.biologie.uni-muenchen.de/~strimmer/puzzle.html (PUZZLE home page)

ftp://ftp.ebi.ac.uk/pub/software (European Bioinformatics Institute, UK)

ftp://ftp.pasteur.fr/pub/GenSoft (Institut Pasteur, France)

http://iubio.bio.indiana.edu/soft/molbio/evolve (IUBio archive www, USA)

ftp://iubio.bio.indiana.edu/molbio/evolve (IUBio archive ftp, USA)

We suggest that this documentation should be read before using PUZZLE 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 and Quick Start below. Then you should be able to use the PUZZLE program, especially if you have some experience with the PHYLIP programs. The other sections should be read at a later time, though.

To find out what's new in version 4.0 please read the Version History.

To offer workarounds and fixes for possible bugs present in version 4.0 of PUZZLE we maintain a list of known bugs. Please check this page first if you encounter a problem.

A detailed description of the maximum likelihood methods implemented in PUZZLE can be found in the PhD thesis "Maximum likelihood methods in molecular phylogenetics" (1997) by Korbinian Strimmer. It is available as a book (Herbert Utz Verlag, ISBN 3-89675-252-9) or as PDF file (thesis.pdf, 1.2 MB).

• Legal Stuff
• Installation
• MacOS
• Windows 95/NT and OS/2
• UNIX
• VMS
• Introduction
• Input/Output Conventions
• Sequence Input
• General Output
• Distance Output
• Tree Output
• Tree Input
• Likelihood Mapping Output
• Quick Start
• Models of Sequence Evolution
• Models of Substitution
• Models of Rate Heterogeneity
• Available Options
• Other Features
• Interpretation and Hints
• Quartet Puzzling Support Values
• Percentage of Unresolved Quartets
• Automatic Parameter Estimation
• Likelihood Mapping
• Batch Mode
• Limits and Error Messages
• Are Quartets Reliable?
• Other Programs
• Acknowledgements
• References
• Version History

Legal Stuff

Everyone is granted permission to copy and redistribute this software package and its accompanying documentation, provided that:

1. All copies are identical to the original.
2. No charge is made for this software or works derived from it, with the exception of a distribution fee to cover the cost of materials and/or transmission.

Installation

MacOS

The MacOS executables have been compiled with Metrowerks CodeWarrior 11. The corresponding project files are found in the "SOURCES" folder. PUZZLE runs successfully both on System 7 and Sytem 8.

Windows 95/NT and OS/2

PUZZLE requires Windows 95 or higher, Windows NT version 4.0 or higher, or OS/2. The windows executable, kindly provided by Norman J. Pieniazek, has been compiled using Microsoft Visual C++ version 5. The OS/2 executable, kindly provided by David Bell, has been compiled using GNU gcc. The makefile for Windows 95/NT ("makefile.win") is included in the "SOURCES" folder.

UNIX

        tar xvf puzzle.tar

        cd PUZZLE/SOURCES

        make

        make -f makefile.gnu

        make -f makefile.hp

If the compilation of the PUZZLE program succeeded without any problem but running the "puzzle" executable does not run the PUZZLE maximum likelihood program rename the executable to "puzzle40" as some UNIX systems come with a preinstalled game that is also called "puzzle".

VMS

Get the file puzzle.uue. After decoding this uuencoded ZIP file (using programs like "UUD" and "UNZIP", ask your local VMS expert for help) you will see a new directory "PUZZLE_40" containing three subdirectories called "EXAMPLES", "MANUAL", and "SOURCES" on your computer. The "MANUAL" directory contains the documentation files for the PUZZLE program in plain text and HTML format. The "EXAMPLES" directory contains some example input files. The "SOURCES" folder contains the ANSI C sources of PUZZLE. Go to this directory by typing

        SET DEF [.PUZZLE.SOURCES]

        @MAKEFILE

        RUN PUZZLE

Introduction

Input/Output Conventions

Sequence Input

General Output

Distance Output

Tree Output

(Gibbon:0.1393, ((Human:0.0414, Chimpanzee:0.0538)99:0.0175, Gorilla:0.0577)98:0.0531, Orangutan:0.1003);

With TreeView and TreeTool it is possible to view a tree with its branch lengths AND simultaneously with the support values for the internal branches (here 98% and 99%). Note, the PHYLIP programs DRAWTREE and DRAWGRAM may also be used with the CLUSTAL W treefile format. However, the current version (3.5) they simply ignores the internal labels and prints only the tree topology with branch lengths.

Tree Input

Likelihood Mapping Output

Quick Start

To obtain a high quality picture of the output tree most conveniently, you can for example use use the TreeView program by Roderic Page. It is available free of charge and runs on MacOS and MS-Windows. It can be retrieved from

http://taxonomy.zoology.gla.ac.uk/rod/treeview.html

On a SUN workstation you can use the TreeTool program to display and manipulate PUZZLE trees (ftp://rdp.life.uiuc.edu/rdp/programs/TreeTool).

Models of Sequence Evolution

Models of Substitution

                |   Q_{ij} pi_j            for i != j
       R_{ij} = |
                | - Sum_m Q_{im} pi_m      for i == j

                | 4*t*gamma/(gamma+1)    for i -> j pyrimidine transition
                |
       Q_{ij} = | 4*t/(gamma+1)          for i -> j purine transition
                |
                | 1                      for i -> j transversion

For amino acids the matrix Q_{ij}is fixed and does not contain any free parameters. Depending on the type of input data four different Q_{ij} are available in PUZZLE. The Dayhoff and JTT matrices are for use with proteins encoded on nuclear DNA, and the mtREV24 matrix is for use with proteins encoded on mtDNA. The BLOSUM 62 model is for more distantly related amino acid sequences (Henikoff and Henikoff 1992).

For doublets (pairs of dependent nucleotides) the SH model is implemented in PUZZLE. The corresponding matrix Q_{ij} reads

                | 2*t       for i -> j transition substitution
                |
       Q_{ij} = | 1         for i -> j transversion substitution
                |
                | 0         for i -> j two substitutions

Models of Rate Heterogeneity

For invariable sites the parameter theta ("Fraction of invariable sites") determines the probability of a given site to be invariable. If a site is invariable the probability for the constant site patterns is pi_i, the frequency of each nucleotide (amino acid).

The rates r for variable sites are determined by a discrete Gamma distribution that approximates the continous Gamma distribution

                                   alpha   alpha-1
                              alpha       r
                      g(r) = ------------------------
                               alpha r
                              e         Gamma(alpha)

In previous versions of PUZZLE instead of alpha the related parameter eta = 1/(1+alpha) was used.

The total rate heterogeneity rho (Gu et al. 1995) of the model of rate heterogeneity combining invariable sites and a Gamma distribution is rho = (1+ theta alpha)/(1+alpha).

Available Options

GENERAL OPTIONS
 b                     Type of analysis?  Tree reconstruction
 k                Tree search procedure?  Quartet puzzling
 v       Approximate quartet likelihood?  No
 u             List unresolved quartets?  No
 n             Number of puzzling steps?  1000
 j             List puzzling step trees?  No
 o                  Display as outgroup?  Gibbon
 z     Compute clocklike branch lengths?  No
 e                  Parameter estimates?  Approximate (faster)
 x            Parameter estimation uses?  Neighbor-joining tree
SUBSTITUTION PROCESS
 d          Type of sequence input data?  Nucleotides
 m                Model of substitution?  HKY (Hasegawa et al. 1985)
 t    Transition/transversion parameter?  Estimate from data set
 f               Nucleotide frequencies?  Estimate from data set
RATE HETEROGENEITY
 w          Model of rate heterogeneity?  Uniform rate

Confirm [y] or change [menu] settings:

The following table lists in alphabetical order all PUZZLE options. Be aware, however, not all of them are accessible at the same time:

Option	Description
a	Gamma rate heterogeneity parameter alpha. It is the so-called shape parameter of the Gamma distribution.
b	Type of analysis. Allows to switch between tree reconstruction by maximum likelihood and likelihood mapping.
c	Number of rate categories (4-8) for the discrete Gamma distribution (rate heterogeneity).
d	Data type. Specifies whether nucleotide or amino acid sequences serve as input. Is automatically suggested by inspection of the input data.
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 frequency of each nucleotide (amino acid, doublet) as input. 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").
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 the alignment 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 SH model 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. This parameter can be estimated from the data by PUZZLE (only if the approximation option for the likelihood function is turned off).
j	List puzzling steps trees. Writes all intermediate trees (puzzling step trees) of a quartet puzzling tree into a file.
k	Tree search. Determines how the overall tree is obtained. The topology is either computed with the quartet puzzling algorithm or is defined by the user. Maximum likelihood branch lengths will be computed for this tree. Alternatively, a maximum likelihood distance matrix only can also be computed (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 be placed 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 Tamura-Nei (TN) model, the Hasegawa et al. (HKY) model, and the Schöniger & 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 originally proposed model (Schöniger & von Haeseler 1994) is obtained by setting the transition-transversion parameter to 0.5. The Jukes-Cantor (1969), the Felsenstein (1981), and the Kimura (1980) model are all special cases of the HKY model. For amino acid sequence data the Dayhoff et al. (Dayhoff) model, the Jones et al. (JTT) model, the Adachi and Hasegawa (mtREV24) model, and the Henikoff and Henikoff (BLOSUM 62) substitution model are implemented in PUZZLE. The mtREV24 model describes the evolution of amino acids encoded on mtDNA, and BLOSUM 62 is for distantly related amino acid sequences. For more information please read the section in this manual about models of sequence evolution. See also option "w" (model of rate heterogeneity).
n	Number of puzzling steps. Parameter of the quartet puzzling tree search (meaning comparable to the number of bootstrap replicates). Generally, the more sequences are used the more puzzling steps are advised. The dfault value varies depending on he number of sequences.
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 (!) transition-transversion ratio for the F84 model can be entered, and PUZZLE computes the corresponding parameters of the TN model (this depends on base frequencies of the data). This allows to compare the results of PUZZLE and the PHYLIP maximum likelihood programs which use the F84 model.
q	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 q=0.
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 and purine transitions. You don't need to specify this parameter as PUZZLE estimates it from the data. For precise definition please read the section in this manual about models of sequence evolution.
s	Symmetrize doublet frequencies. This option is only available for the SH model. With this option the doublet frequencies are symmetrized. For example, the frequencies of "AT" and "TA" are set to the average of both frequencies.
t	Transition/transversion parameter. For nucleotide data only. You don't need to specify this parameter as PUZZLE estimates it from the data. The precise definition of this parameter is given in the section on models of sequence evolution in this manual.
u	Show unresolved quartets. During the quartet puzzling tree search PUZZLE 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, Goldman, and von Haeseler 1996). If this option is selected you'll get a detailed list of all starlike quartets. Note, for some data sets there may be a lot of unresolved quartets. In this case a list of all unresolved 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. This option was hidden in some previous versions.
w	Model of rate heterogeneity. 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 a mixed model (1 invariable rate + Gamma distributed rates). All necessary parameters can be estimated by 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. See also option "m" (model of substitution).
x	Selects the methods used in the estimation of the model parameters. Neighbor-joining 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.

Other Features

PUZZLE also tests with a 5% level chi-square-test whether the base composition of each sequence is identical to the average base composition of the whole alignment. All sequences with deviating composition are listed in the output 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 PUZZLE (since version 2.5) is the employment of a weighting scheme of quartets (Strimmer, Goldman, and von Haeseler 1997) in the quartet puzzling tree search.

PUZZLE also computes the average distance between all pairs of sequences (maximum likelihood distances). The average distances can be viewed as a rough measure for the overall sequence divergence.

If more than one input tree is provided PUZZLE uses the Kishino-Hasegawa test (1989) to check which trees are significantly worse than the best tree.

If clock-like maximum-likelihood branch lengths are computed PUZZLE checks with the help of a likelihood-ratio test (Felsenstein 1988) whether the data set is clock-like.

PUZZLE also detects sequences that occur more than once in the data and that therefore can be removed from the data set.

If rate heterogeneity is taken into account in the analysis PUZZLE also computes the most probable assignment of rate categories to sequence positions, according Felsenstein and Churchill (1996).

Interpretation and Hints

Quartet Puzzling Support Values

Percentage of Unresolved Quartets

Automatic Parameter Estimation

Likelihood Mapping

Batch Mode

puzzle << !
t
10
y
!

Limits and Error Messages

If problems are encountered PUZZLE terminates program execution and returns a plain text error message. Depending on the severity errors are classified 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 memory errors (not enough RAM) or problems with the format of the input files.
Other errors:	Completely uncritical. Occur mostly when options of PUZZLE are being set.

A standard machine (1996 UNIX workstation) with 32 to 64 MB RAM PUZZLE can easily do maximum likelihood tree searches including estimation of support values for data sets with 50-100 sequences. As likelihood mapping is not memory consuming and computationally quite fast it can be applied to large data sets as well.

Are Quartets Reliable?

However, this is not true. According to Hillis findings (Hillis, 1996), quartets can be hard, but extra information helps. That is, if all you have are data on species (A, B, C, D) then it might be relatively difficult to find the correct tree for them. But if you have additional data (species E, F, G, ...) and try 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's 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. 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. etc. should overcome this problem.

The facts about how well PUZZLE actually works have been investigated in the Strimmer and von Haeseler (1996) and Strimmer, Goldman, and von Haeseler (1997) papers. Their results cannot be altered by Hillis's findings. Considered as a heuristic search for maximum likelihood trees, quartet puzzling works very well.

(This section follows N. Goldman, personal communication).

Other Programs

"Tree of Life" software page: http://phylogeny.arizona.edu/tree/programs/programs.html

Joe Felsenstein's list of programs: http://evolution.genetics.washington.edu/software.html

European Bioinformatics Institute: http://www.ebi.ac.uk/biocat/biocat.html

Rod Page's TreeView: http://taxonomy.zoology.gla.ac.uk/rod/treeview.html

TreeTool: ftp://rdp.life.uiuc.edu/rdp/programs/TreeTool

Acknowledgements

References

Adachi, J., and M. Hasegawa. 1996. Model of amino acid substitution in proteins encoded by mitochondrial DNA. J. Mol. Evol. 42: 459-468.

Dayhoff, M. O., R. M. Schwartz, and B. C. Orcutt. 1978. A model of evolutionary change in proteins. In: Dayhoff, M. O. (ed.) Atlas of Protein Sequence Structur, Vol. 5, Suppl. 3. National Biomedical Research Foundation, Washington DC, pp. 345-352.

Felsenstein, J. 1981. Evolutionary trees from DNA sequences: A maximum likelihood approach. J. Mol. Evol. 17: 368-76.

Felsenstein, J. 1988. Phylogenies from molecular sequences: Inference and reliability. Annu. Rev. Genet. 22: 521-565.

Felsenstein, J. 1993. PHYLIP (Phylogeny Inference Package) version 3.5c. Distributed by the author. Department of Genetics, University of Washington, Seattle.

Felsenstein, J., and G.A. Churchill. 1996. A hidden Markov model approach to variation among sites in rate of evolution. Mol. Biol. Evol. 13: 93-104.

Gu, X., Y.-X. Fu, and W.-H. Li. 1995. Maximum likelihood estimation of the heterogeneity of substitution rate among nucleotide sites. Mol. Biol. Evol.12: 546-557.

Hasegawa, M., H. Kishino, and K. Yano. 1985. Dating of the human-ape splitting by a molecular clock of mitochondrial DNA. J. Mol. Evol. 22: 160-174.

Henikoff, S., J. G. Henikoff. 1992. Amino acid substitution matrices from protein blocks. PNAS (USA) 89:10915-10919.

Hillis, D. M. 1996. Inferring complex phylogenies. Nature 383:130-131.

Jukes, T. H., and C. R. Cantor. 1969. Evolution of protein molecules. In: Munro, H. N. (ed.) Mammalian Protein Metabolism, New York: Academic Press, pp. 21-132.

Jones, D. T., W. R. Taylor, and J. M. Thornton. 1992. The rapid generation of mutation data matrices from protein sequences. CABIOS 8: 275-282.

Kimura, M. 1980. A simple method for estimating evolutionary rates of base substitutions through comparative studies of nucleotide sequences. J. Mol. Evol. 16: 111-120.

Kishino, H., and M. Hasegawa. 1989. Evaluation of the maximum likelihood estimate of the evolutionary tree topologies from DNA sequence data, and the branching order in Hominoidea. J. Mol. Evol. 29: 170-179.

Tamura, K., and M. Nei. 1993. Estimation of the number of nucleotide substitutions in the control region of mitochondrial DNA in humans and chimpanzees. Mol. Biol. Evol. 10: 512-526.

Tamura K. 1994. Model selection in the estimation of the number of nucleotide substitutions. Mol. Biol. Evol. 11: 154-157.

Thompson, J. D., D. G. Higgins, and T. J. Gibson. 1994. CLUSTAL W: Improving the sensitivity of progressive multiple sequence alignment through sequence weighting, positions-specific gap penalties and weight matrix choice. Nucl. Acids Res. 22: 4673-4680.

Saitou, N., and M. Nei. 1987. The neighbor-joining method: a new method for reconstructing phylogenetic trees. Mol. Biol. Evol. 4: 1406-425.

Schöniger, M., and A. von Haeseler. 1994. A stochastic model for the evolution of autocorrelated DNA sequences. Mol. Phyl. Evol. 3: 240-247.

Strimmer, K., and A. von Haeseler. 1996. Quartet puzzling: a quartet maximum likelihood method for reconstructing tree topologies. Mol. Biol. Evol. 13: 964-969.

Strimmer, K., N. Goldman, and A. von Haeseler. 1997. Bayesian probabilities and quartet puzzling. Mol. Biol. Evol. 14: 210-211.

Strimmer, K., and A. von Haeseler. 1997. Likelihood-mapping: a simple method to visualize phylogenetic content of a sequence alignment. PNAS (USA). 94:6815-6819.

Yang, Z. 1994. Maximum likelihood phylogenetic estimation from DNA sequences with variable rates over sites: approximate methods. J. Mol. Evol. 39:306-314.

Version History