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M. Hendy (1991)
A combinatorial description of the closest tree algorithm for finding evolutionary treesDiscret. Math., 96
G. Estabrook, J. Strauch, K. Fiala (1977)
An Application of Compatibility Analysis to the Blackiths' Data on Orthopteroid InsectsSystematic Biology, 26
M. Hendy, David Penny, Mike Steel (1994)
A discrete Fourier analysis for evolutionary trees.Proceedings of the National Academy of Sciences of the United States of America, 91
W. Maddison, D. Maddison (1992)
Macclade: Analysis of Phylogeny and Character Evolution/Version 3
A. Cooper, D. Penny (1997)
Mass Survival of Birds Across the Cretaceous- Tertiary Boundary: Molecular EvidenceScience, 275
M. Hendy, D. Penny (1993)
Spectral analysis of phylogenetic dataJournal of Classification, 10
R. Page (1996)
TreeView: an application to display phylogenetic trees on personal computersComputer applications in the biosciences : CABIOS, 12 4
G. Lento, R. Hickson, Geoffrey Chambers, David Penny (1995)
Use of spectral analysis to test hypotheses on the origin of pinnipeds.Molecular biology and evolution, 12 1
& '( ' '))* BIOINFORMATICS APPLICATION NOTE )*+)) ! "# $ % Motivation: Spectrum is a new Macintosh and Microsoft (Maddison and Maddison, 1992)], and the PHYLIP format Windows program designed to read in phylogenetic four-state (Felsenstein, 1993). Output spectrum files can be saved in or binary data in NEXUS format, and output the corresponding Microsoft Excel format and trees can be saved as TreeV- bipartition spectra. It can be used to find the tree whose iew files (Page, 1996). expected spectrum is closest to the observed spectrum (the The distance spectrum. Spectrum converts a set of distances closest tree; Hendy, Discr. Math., 96, 51–58, 1991). to a distance spectrum (Hendy and Penny, 1993) using the Availability: The program is free and available at relationship between minimal path set lengths and edge {{http://taxonomy.zoology.gla.ac.uk/∼mac/mike.html}}. lengths of trees. It is even possible to ‘correct’ for multiple Contact: michael.charleston@zoology.oxford.ac.uk hits, which, given that the model used accurately reflects the true mechanism of character evolution, renders character- based methods like maximum parsimony able to use distance Spectral analysis was developed by Hendy, Penny and Steel data as their input in a statistically consistent way (Steel et al., (Hendy and Penny, 1993; Hendy et al., 1994; Lento et al., 1993). 1995) allowing investigation of the phylogenetic information The transformations used in Spectrum allow an array of in a data set without forcing a tree. It avoids assumptions (i) characters to be converted to distances or to a spectrum, and that a tree structure is a suitable explanation for the data and from distances to a spectrum. The spectrum itself can be trans- (ii) that the tree used to represent data is the best one possible. formed by the Hadamard conjugation, and eventually lead to The bipartition spectrum is a representation of the amount a phylogenetic tree of support each possible branch of any tree has, for a data set. The nearest neighbourhood of a tree. For a given tree T, there Each branch in a phylogenetic tree corresponds to a bipartition is a set of ‘nearest neighbour’ trees, which may be obtained of the extant taxa into two sets whose union is the whole. In from T by performing nearest neighbour interchange per- a set of aligned sequences, each of which may be in one of two turbations on T (Penny and Cooper, 1997). The nearest neigh- states (say ‘0’ and ‘1’), each site corresponds to a split of the bourhood of T is the set of all the splits of such adjacent trees taxa state ‘0’ and state ‘1’. Hence, there is a simple parallel and those in T, with their support values. Spectrum can pro- between phylogenetic data sets and bipartition spectra. (n – 1) vide this quick method of visualizing the robustness of the For n taxa, there are 2 bipartitions which may be listed phylogenetic signal in the spectrum for the tree found which in a simple order (Hendy and Penny, 1993), and there is a is a good indicator of general trends in the tree. unique number corresponding to each possible split. In a phy- Tree finding. Spectrum provides two methods of finding opti- logenetic data set, there may be finite support for any of these mal trees given input spectra: the ‘closest tree’ (Hendy, 1991) bipartitions, and it is the list of all the support values for the and ‘Manhattan tree’ (Charleston, 1994). Both operate under bipartitions which make up the bipartition spectrum. the assumption that the observed spectrum is likely to be Closely connected with spectral analysis is the Hadamard ‘closest’ in some sense to the expected spectrum of the true conjugation (Hendy and Charleston, 1993; Hendy et al., 1994), a transformation of the bipartition spectrum which al- (underlying) tree. The closest tree is that tree whose expected (n – 1) lows consistent correction for multiple character state changes spectrum is closest in Euclidean [2 ]-dimensional space under the symmetric two-state (one parameter) model of Ca- to the observed (or Hadamard conjugated) spectrum. In the vender (1978) and the symmetric four-state (three parameter) ‘Manhattan tree’ the distance measure used is the ‘Manhattan’ model of Hasegawa et al. (1985). The two-state model is ac- or ‘city-block’ measure. commodated with the Spectrum program. Data constraints. The maximum number of characters per se- Spectrum provides intuitive graphical representation of quence which may be accommodated is 5000, and the maxi- phylogenetic information. Features include drag and drop of mum number of taxa is 23. This latter constraint is imposed input files, full cut, copy and paste facility of graphics and text by the computational complexity of the Hadamard conjuga- windows, and extensive balloon and on-line help. tion (Hendy et al., 1994). The program supports standard phylogenetic input formats In Figure 1 is shown a typical display of Spectrum. The [NEXUS, as used by PAUP (Swofford, 1993) and MACCLADE sequences are converted to a distance matrix, transformed Oxford University Press 98 Spectral analysis of phylogenetic data Fig. 1. A typical display from Spectrum. A log window showing progress with details of input files, transformations used, etc., is shown on the left. Upper right is the Manhattan tree for the spectrum. Below right is a Lento plot showing support values for each split; grey for terminal branches, black for those in the tree, the remainder above and below the horizontal axis show the relative amount of conflict with each split above. Hendy,M.D. and Charleston,M.A. (1993) Hadamard conjugation: a using Tamura and Nei’s formula (1993), and then the dis- versatile tool for modelling sequence evolution. N. Z. J. Bot., 31, tance spectrum calculated. 231–237. Hendy,M.D. and Penny,D. (1993) Spectral analysis of phylogenetic Acknowledgements data. J. Classif., 10, 5–24. Hendy,M.D., Penny,D. and Steel,M.A. (1994) A discrete Fourier Spectrum was written with support from NERC grant analysis for evolutionary trees. Proc. Natl Acad. Sci. USA, 91, GR3/1A095 and from Rod Page, who provided extensive 3339–3343. interface and programming aid. Lento,G.M., Hickson,R.E., Chambers,G.K. and Penny,D. (1995) Use of spectral analysis to test hypotheses on the origin of pinnipeds. Mol. Biol. Evol., 12, 28–52. Maddison,W.P. and Maddison,D.R. (1992) MacClade: Analysis of References Phylogeny and Character Evolution, Version 3.0. Computer program. Page,R.D.M. (1996) TreeView: an application to display phylogenetic Charleston,M.A. (1994) Factors affecting the performance of phyloge- trees on personal computers. Comput. Applic. Biosci., 12, 357–358. netic methods. PhD Thesis, Massey University, Palmerston North, Penny,D. and Cooper,A. (1997) Mass survival of birds across the New Zealand. cretaceous-tertiary boundary: molecular evidence. Science, 275, Estabrook,G.F., Strauch,J.J.G. and Fiala,K.L. (1977) An application of 1109–1113. compatibility analysis to the Blackiths’ data on orthopteroid insects. Steel,M.A., Hendy,M.D. and Penny,D. (1993) Parsimony can be Syst. Zool., 26, 269–276. consistent! Syst. Biol., 42, 581–587. Felsenstein,J. (1993) Phylip: Phylogeny Inference Package. Computer program, University of Washington, Seattle. Swofford,D.L. (1993) Paup: Phylogenetic Analysis Using Parsimony, Hendy,M.D. (1991) A combinatorial description of the closest tree Version 3.1.1. Computer program distributed by the Illinois Natural algorithm for finding evolutionary trees. Discr. Math., 96, 51–58. History Survey.
Bioinformatics – Oxford University Press
Published: Jan 1, 1998
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