Molecular Anthropology pp 117-137 | Cite as
Proof for the Maximum Parsimony (“Red King”) Algorithm
Abstract
In reconstructing hypothetical messenger RNA (mRNA) sequences which were contained in the ancestors of present-day species, we find ourselves in much the same predicament as Alice, sitting in a courtroom for the first time. Alice, who has never seen a judge before, has to infer that the man sitting before her with the “great wig” is a judge. He looks like a judge, so he must be a judge. In examining mRNA sequences from contemporary species (obtained by inference from amino acid sequences and the genetic code), we assume that when two sequences look alike they must be alike, in the sense of sharing a common ancestry. Similarity does not always imply common ancestry, but we assume that that reconstruction of hypothetical ancestors which maximizes the similarity due to common ancestry (and thus minimizes similarity due to parallel and back mutations) is the best reconstruction. This is known as the maximum parsimony hypothesis. Since the judge is really the King of Hearts, or Red King, we call this the Red King hypothesis (see Van Valen, 1974). In this chapter, I shall review the highlights of the proof for the current computer algorithm for reconstructing hypothetical mRNA sequence ancestors consistent with contemporary amino acid sequences and the Red King hypothesis.
Keywords
Maximum Parsimony Accumulation Number Common Ancestry Final Bubble Exterior PointPreview
Unable to display preview. Download preview PDF.
References
- Camin, J. H., and Sokal, R. R., 1965, A method for deducing branching sequences in phylogeny, Evolution 19: 311–326.CrossRefGoogle Scholar
- Cavalli-Sforza, L. L., and Edwards, A. W. F., 1967, Phylogenetic analysis: Models and estimation procedures, Evolution 21: 550–570.CrossRefGoogle Scholar
- Edwards, A. F. W., and Cavalli-Sforza, L. L., 1963, The reconstruction of evolution, Ann. Hum. Genet. 27: 104–105.Google Scholar
- Farris, J. S., 1970, Methods for computing Wagner trees, Syst. Zool. 19: 83–92.CrossRefGoogle Scholar
- Farris, J. S., 1973, Probability model for inferring evolutionary trees, Syst. Zool. 22: 250–256.CrossRefGoogle Scholar
- Felsenstein, J., 1973, Maximum likelihood estimation of evolutionary trees from continuous characters, Am. J. Hum. Genet. 25: 471–492.PubMedGoogle Scholar
- Fitch, W. M., 1971, Toward defining the course of evolution: Minimum change for a specific tree topology, Syst. Zool 20: 406–416.CrossRefGoogle Scholar
- Hartigan, J. A., 1973, Minimum mutation fits to a given tree, Biometrics 29: 53–65.CrossRefGoogle Scholar
- Kolata, G. B., 1974, Analysis of algorithms: Coping with hard problems, Science 186: 520–521.PubMedCrossRefGoogle Scholar
- Moore, G. W., 1971, A mathematical model for the construction of cladograms, Institute of Statistics Mimeograph Series. No. 731, North Carolina State University, Raleigh, N.C.Google Scholar
- Moore, G. W., Goodman, M., and Barnabas, J., 1973a, An iterative approach from the standpoint of the additive hypothesis to the dendrogram problem posed by molecular data sets, J. Theor. Biol. 38: 423–457.PubMedCrossRefGoogle Scholar
- Moore, G. W., Barnabas, J., and Goodman, M., 1973a, A method for constructing maximum parsimony ancestral amino acid sequences on a given network, J. Theor. Biol. 38: 459–485.PubMedCrossRefGoogle Scholar
- Sankoff, D., 1973, Publication Centre de Recherches Mathematiques Technical Report No. 262, University of Montreal, Montreal.Google Scholar
- Sneath, P. H. A., 1957, The application of computers to taxonomy, J. Gen. Microbiol. 17: 201–226.PubMedGoogle Scholar
- Sokal, R. R., and Michener, C. D., 1958, A statistical method for evaluating systematic relationships, Univ. Kan. Sci Bull. 38: 1409–1438.Google Scholar
- Sørenson, T., 1948, Method of establishing groups of equal amplitude in plant sociology based on similarity of, species content and its application to analyses of the vegetation on Danish commons, Biol. Skr. 5: 1–34.Google Scholar
- Van Valen, L., 1974, Molecular evolution as predicted by natural selection, J. Mol. Evol. 3: 89–101.PubMedCrossRefGoogle Scholar