A molecular sequence metric and evolutionary trees

Beyer, W. A.; Stein, M. L.; Smith, Temple F.; Ulam, Stanislaw M.

doi:10.1016/0025-5564(74)90028-5

Cited by 76 publications

(44 citation statements)

References 22 publications

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“…For some methods, such as the "Distance Wagner" method of Farris (1972) there is no explicit quantity being optimized. Some authors (Farris, 1972;Beyer et al, 1974;Waterman et al, 1977) place an additional restriction on the fitted trees, namely that for all pairs of tips ij, if the triangle inequality for distances holds, the observed distance between tips A and B in Figure 1 must be less than or equal to the sum ofthe distances A-e and e-B.…”

Section: The Path Length Interpretationmentioning

confidence: 99%

“…Since these original papers, a number of other distance methods have been introduced (Hartigan, 1967;Farris, 1972;Moore et al, 1973;Beyer et al, 1974;Tateno et al, 1982;Chakraborty, 1977;Sattath and Tversky, 1977;Waterman et al, 1977;Fitch, 1981). It is not my intention to review all of these methods here: I have described them briefly elsewhere (Felsenstein, 1982).…”

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Distance Methods for Inferring Phylogenies: A Justification

1984

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Section: The Path Length Interpretationmentioning

confidence: 99%

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confidence: 99%

Distance Methods for Inferring Phylogenies: A Justification

1984

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“…Since early 1970s, (dynamic) time warping (DTW) has been widely used for sequence comparison in various areas, such as phonetic frequency sequences in speech processing [30,31], nucleotides sequences of DNA and RNA in molecular biology [32,33], strings of digits in computer science [34]. Kruskal [35] provided an overview of how widely DTW had been used.…”

Section: Dynamic Time Warpingmentioning

confidence: 99%

Warped factor analysis

Hong

2009

Journal of Chemometrics

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Shifted factor analysis (SFA) is designed to fit overall position shifts of sequential factors as well as the variation of factor weights. SFA is one kind of nonlinear generalization of linear factor models such as the two-mode principal component model and the three-mode Parafac model. Warped factor analysis (WFA), presented here, further generalizes SFA so that it fits factor variation due to not only the position shifts and the systematic weighting but also more flexible shape changes of sequential factors. A quasi alternating least squares (ALS) procedure is developed for WFA, using a simplified warping of segmented sequential factors. The most unique property of WFA is that it allows sequential factors to change shape distinctively, which is unlike what is implicitly assumed in mapping of data profiles, namely that sequential factors change shape together. Unlike the two-mode factor/component models, two-mode SFA was empirically shown to yield an essentially unique solution, using the additional sources of information provided by fitting systematic position shifts. Likewise, factors recovered by two-mode WFA are likely to be essentially unique due to the systematic shape variance fit by the model, provided that the data contain sufficient sources of shape variation.

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“…Given a set of n taxa and the corresponding matrix D of evolutionary distances, the BMEP consists of finding a phylogeny for having minimum length (Catanzaro 2009). The BMEP is based on the minimum evolution criterion of phylogenetic estimation that states that if the evolutionary distances were unbiased estimates of the true evolutionary distances (i.e., the distances that one would obtain if all the molecular data from the analyzed taxa were available), then the true phylogeny would have an expected length shorter than any other possible phylogeny compatible with D. Interestingly, the minimum evolution criterion does not assess that molecular evolution follows minimum paths but states, according to classical evolutionary theory, that a minimum length phylogeny may properly approximate the real phylogeny of well-conserved molecular data, i.e., data whose basic biochemical functions have undergone small change throughout the evolution of the observed taxa (Beyer et al 1974). Because the selective forces acting on taxa may not be constant over time, evolution proceeds by small changes rather than the smallest change (Beyer et al 1974, Waterman et al 1977.…”

Section: Resultsmentioning

confidence: 98%

The Balanced Minimum Evolution Problem

Catanzaro

Pesenti

Salazar-González

2012

INFORMS Journal on Computing

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A phylogeny is an unrooted binary tree that represents the evolutionary relationships of a set of $n$ species. Phylogenies find applications in several scientific areas ranging from medical research, to drug discovery, to epidemiology, to systematics, and to population dynamics. In such applications the available information is usually restricted to the leaves of a phylogeny and is represented by molecular data extracted from the analyzed species, such as DNA, RNA, amino acid or codon fragments. On the contrary, the information about the phylogeny itself is generally missing and is determined by solving an optimization problem, called the Phylogeny Estimation Problem (PEP), whose versions depend on the criterion used to select a phylogeny from among plausible alternatives. In this article we investigate a recent version of the PEP, called the \emph{Balanced Minimum Evolution Problem} (BMEP). We present a mixed integer linear programming model\footnote{See the online supplement for codes and data.} to solve exactly instances of the BMEP and develop branching rules and families of valid inequalities to further strengthen the model. Our results give perspective on the mathematics of the BMEP and suggest new directions on the development of future efficient exact approaches to solution of the problem

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A molecular sequence metric and evolutionary trees

Cited by 76 publications

References 22 publications

Distance Methods for Inferring Phylogenies: A Justification

Distance Methods for Inferring Phylogenies: A Justification

Warped factor analysis

The Balanced Minimum Evolution Problem

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