Summary
The recent evaluation by Fitch (1980) of REH theory for macromolecular divergence is a severely erroneous and distorted analysis of our work over the past decade. We reply to those distortions here. At present, there is no factual basis for believing Fitch's assessment that corrections which move evolutionary estimates of total mutations fixed closer to the true distance must do so at the expense of an increased variance sufficient to compromise the value of the improvement. By direct calculation the variance in the estimates of total mutations fixed given by REH theory is comparable to that of other models now in the literature for the case in which genetic events are equiprobable. A general argument is given that suggests that, as we consider more and more carefully the selective, functional, and structural constraints on the evolution of genes and proteins, this variance may be expected to decrease toward a lower bound.
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Baba ML, Darga L, Goodman M, Czelusniak J (1981) Evolution of cytochromec investigated by the maximum parsimony method. J Mol Evol 17:197–213
Cavender JA (1978) Taxonomy with confidence. Math Bios 40:271–280
Dayhoff M, Park CM, McLaughlin PJ (1972) Building a phylogenetic tree: Cytochromec. In: Dayhoff M (ed) Atlas of protein sequence and structure, vol. 5. National Biomedical Research Fdn., Georgetown University Medical Center, Washington, DC, p 8
Dayhoff M, Schwartz RM, Orcutt BC (1978) A model of evolutionary change in proteins. In: Dayhoff M (ed) Atlas of protein sequence and structure, vol. 5, suppl. 3. National Biomedical Research Fdn., Georgetown University Medical Center, Washington, DC, p 351
Doolittle RF, Blombäck B (1964) Amino-acid sequnce investigations of fibrinopeptides from various mammals: Evolutionary implications. Nature 202:147–152
Felsenstein J (1978) Cases in which parsimony or compatiblity methods will be positively misleading. Syst Zool 27:401–409
Fitch W (1971) Toward defining the course of evolution: Minimum change for a specific tree topology. Syst Zool 20:406–416
Fitch W (1973) Aspects of molecular evolution. Ann Rev Genet 7:343–380
Fitch W (1980) Estimating the total number of nucleotide substitutions since the common ancestor of a pair of homologous genes: Comparison of several methods and three beta hemoglobin mRNAs. J Mol Evol 16:153–209
Fitch W, Margoliash E (1967) Construction of phylogenetic trees. Science 155:279–284
Fitch W, Markowitz E (1970) An improved method for determining codon variablity in a gene and its application to the rate of fixation of mutations in evolution. Biochem Genet 4:579–593
Friday A (1980) The status of immunological distance data in the construction of phylogenetic classifications: A critique. In: Bisby FA, Vaughan JG, Wright CA (eds) Chemosystematics: Principles and practice. Academic Press, London New York
Holmquist R (1972a) Theoretical foundations of paleogenetics. In: LeCam L, Neuman J, Scott EL (eds) Sixth Berkeley Symposium on Mathematical Statistics and Probability, vol. 5, University of California Press, Berkeley, p 315
Holmquist R (1972b) Empirical support for a stochastic model of evolution. J Mol Evol 1:211–222
Holmquist R (1973) The stochastic model and deviations from randomness in eukaryotic tRNAs: Comparison with the PAM approach. J Mol Evol 2:145–148
Holmquist R (1976) Random and nonrandom processes in the molecular evolution of higher organisms. In: Goodman M, Tashian RE, Tashian JH (eds) Molecular anthopology. Plenum Press, New York, p 89
Holmquist R (1978a) The REH theory of protein and nucleic acid divergence: A retrospective update. J Mol Evol 11:361–374
Holmquist R (1978b) A measure of the denseness of a phylogenetic network. J Mol Evol 11:225–231
Holmquist R (1979) The method of parsimony: An experimental test and theoretical analysis of the adequacy of molecular restoration studies. J Mol Biol 135:939–958
Holmquist R (1980) Evolutionary analysis ofα andβ hemoglobin genes by REH theory under the assumption of the equiprobability of genetic events. J Mol Evol 15:149–159
Holmquist R, Cimino JB (1980) A general method for biological inference: Illustrated by the estimation of gene nucleotide transition probabilities. BioSystems: J Mol, Cellular & Behavioral Origins and Evol 12:1–22
Holmquist R, Pearl D (1980) Theoretical foundations for quantitative paleogenetics. Part III: The molecular divergence of nucleic acids and proteins for the case of genetic events of unequal probability. J Mol Evol 16:211–267
Holmquist R, Cantor C, Jukes TH (1972) Improved procedures for comparing homologous sequences in molecules of proteins and nucleic acids. J Mol Biol 64:145–161
Holmquist R, Jukes TH, Moise H, Goodman M, Moore GW (1976) The evolution of the globin family genes: concordance of stochastic and augmented maximum parsimony genetic distances forα hemoglobin,β hemoglobin and myoglobin phylogenies. J Mol Biol 105:39–74
Holmquist R, Pearl D, Jukes TH (1981) Nonuniform molecular divergence: The quantitative evolutionary analysis of genes and messenger RNAs under selective structural constraints. In: Goodman M (ed) Macromolecular sequences in systematics and evolutionary biology. Plenum Press, New York
Jaynes ET (1979) Where do we stand on maximum entropy? In: Levine RD, Tribus M (eds) The maximum entropy formalism. MIT Press, Cambridge (Massachusetts), London, p 15
Jukes TH (1963) Some recent advances in studies of the transcription of the genetic message. Adv Biol Med Phys 9:1–41
Jukes TH, Cantor C (1969) Evolution of protein molecules. In Munro HN (ed) Mammalian protein metabolism, III. Academic Press, New York, p 21
Jukes TH, Holmquist R (1972) Estimation of evolutionary changes in certain homologous polypeptide chains. J Mol Biol 64:163–179
Jukes TH, Holmquist R, Moise H (1975) Amino acid composition of proteins: Selection against the genetic code. Science 189:50–51
Karon J (1979) The covarion model for the evolution of proteins: Parameter estimates and comparison with Holmquist, Cantor and Jukes' stochastic model. J Mol Evol 12:197–218
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
Kimura M (1981) Was globin evolution very rapid in its early stages? A dubious case against the rate-constancy hypothesis. J Mol Evol 17:110–113
Kimura M, Ohta T (1972) On the stochastic model for estimation of mutational distance between homologous proteins. J Mol Evol 2:87–90
King JL (1980) Does the information density of amino acid composition increase? J Mol Evol 15:73–75
King JL, Jukes TH (1969) Non-Darwinian evolution. Science 164:788–798
Lawn R, Efstratiadis A, O'Connell C, Maniatis T (1980) The nucleotide sequence of the humanβ-globin gene. Cell 21:647–651
Moore GW (1977) Proof of the populous path algorithm for missing mutations in parsimony trees. J Theor Biol 66:95–106
Moore GW, Goodman M, Callahan C, Holmquist R, Moise H (1976) Stochastic versus augmented maximum parsimony method for estimating superimposed mutations in the divergent evolution of protein sequences. Methods tested on cytochromec amino acid sequences. J Mol Biol 105:15–37
Nei M, Tateno Y (1978) Nonrandom amino acid substitution and estimation of the number of nucleotide substitutions in evolution. J Mol Evol 11:301–310
Ratner VA, Rodin SN, Zharkikh AA (1977) Analysis of the molecular evolution of globins by a more accurate method. In: Ratner VA (ed) Mathematical models of evolution and selection. Academy of Sciences USSR, Novosibirsk, p 67 (Figure 2).
Sattath S, Tversky A (1977) Additive similarity trees. Psychometrika 42:319–345
Shepard RN (1980) Multidimensional scaling, tree-fitting and clustering. Science 210:390–398
Tuppey H (1958) Über die Artspezifität der Proteinstruktur. In: Neuberger A (ed) Symposium on protein structure. John Wiley, New York, pp 66–76
Uzzell T, Corbin KW (1971) Fitting discrete probability distributions to evolutionary events. Science 172:1089–1096
Verhoeyen M, Fang R, Min Jou W, Devos R, Huylebroeck D, Saman E, Fiers W (1980) Antigenic drift between the haemagglutinin of the Hong Kong influenza strains A/Aichi/2/68 and A/Victoria/3/75. Nature (London) 286:771–775
Zuckerkandl E, Pauling L (1965) Evolutionary divergence and convergence in proteins. In: Bryson V, Vogel HJ (eds) Evolving genes and proteins. Academic Press, New York, p 97
Zuckerkandl E, Schroeder WA (1961) Amino-acid composition of the polypeptide chains of gorilla haemoglobin. Nature 192:984–985
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Holmquist, R., Jukes, T.H. The current status of REH theory. J Mol Evol 18, 47–59 (1981). https://doi.org/10.1007/BF01733211
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DOI: https://doi.org/10.1007/BF01733211