Summary
REH theory is extended by deriving the theoretical equations that permit one to analyze the nonrandom molecular divergence of homologous genes and proteins. The nonrandomicities considered are amino acid and base composition, the frequencies with which each of the four nucleotides is replaced by one of the other three, unequal usage of degenerate codons, distribution of fixed base replacements at the three nucleotide positions within codons, and distributions of fixed base replacements among codons. The latter two distributions turn out to dominate the accuracy of genetic distance estimates. The negative binomial density is used to allow for the unequal mutability of different codon sites, and the implications of its two limiting forms, the Poisson and geometric distributions, are considered. It is shown that the fixation intensity — the average number of base replacements per variable codon - is expressible as the simple product of two factors, the first describing the asymmetry of the distribution of base replacements over the gene and the second defining the ratio of the average probability that a codon will fix a mutation to the probability that it will not. Tables are given relating these features to experimentally observable quantities inα hemoglobin,β hemoglobin, myoglobin, cytochromec, and the parvalbumin group of proteins and to the structure of their corre-sponding genes or mRNAs. The principal results are (1) more accurate methods of estimating parameters of evolutionary interest from experimental gene and protein sequence data, and (2) the fact that change in gene and protein structure has been a much less efficient process than previously believed in the sense of requiring many more base replacements to effect a given structural change than earlier estimation procedures had indicated. This inefficiency is directly traceable to Darwinian selection for the nonrandom gene or protein structures necessary for biological function. The application of these methods is illustrated by detailed consideration of the rabbitα -andβ hemoglobin mRNAs and the proteins for which they code. It is found that these two genes are separated by about 425 fixed base replacements, which is a factor of two greater than earlier estimates. The replacements are distributed over approximately 114 codon sites that were free to accept base mutations during the divergence of these two genes.
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References
Barker WC, Ketcham LK, Dayhoff MO (1978) J Mol Evol 10:265–281
Bliss C, Fisher R (1953) Biometrics 53:176–200
Croft LR (1973) Handbook of protein sequences. Joynson-Bruvers, Oxford
Dayhoff MO (1972) Atlas of protein sequence and structure, vol 5. See also Supplement 1 (1973), Supplement 2 (1976) and Supplement 3 (1978)
Efstratiadis A, Kafatos FC, Maniatis T (1977) Cell 10:571–585
Feller W (1968) Elements of combinatorial analysis: binomial coefficients. In: An introduction to probability theory and its applications, vol 1 (2nd edition). John Wiley, New York, p 50
Feller W (1971a) Special densities, randomization. In: An introduction to probability theory and its applications, vol 2. John Wiley, New York, p 47, 57
Feller W (1971b) The exponential and the uniform densities. In: An introduction to probability theory and its applications, vol 2. John Wiley, New York, p 8, 11
Fitch W, Markowitz E (1970) Biochem Gen 4:579–593
Fitch W (1976) Molecular evolutionary clocks. In: Ayala F (ed), Molecular evolution. Sinauer Associates, Sunderland Massachusetts, p 160
Fitch W (1976) J Mol Evol 8:13–40
Goodman M, Moore GW (1977) J Mol Evol 10:4–47, Tables 7, 8, and 9
Heindell HC, Liu A, Paddock GV, Studnicka GM, Salser WA (1978) Cell 15:43–54
Holmquist R (1972) J Mol Evol 1:115–133
Holmquist R (1976a) Random and nonrandom processes in the molecular evolution of higher organisms. In: Goodman M, Tashian R, Tashian J (eds), Molecular anthropology. Plenum Press, New York, p 89
Holmquist R (1976b) J Mol Evol 8:337–349
Holmquist R (1978a) J Mol Evol 11:361–374
Holmquist R (1978b) J Mol Evol 12:17–24
Holmquist R (1978c) J Mol Evol 11:225–231
Holmquist R (1978d) J Mol Evol 11:349–360
Holmquist R (1979) J Mol Biol 135:939–958
Holmquist R (1980) J Mol Evol 15:149–159
Holmquist R, Cimino JB (1980) BioSystems 12:1–22
Holmquist R, Cantor C, Jukes TH (1972) J Mol Biol 64:145–161
Holmquist R, Jukes TH, Moise H, Goodman M, Moore GW (1976) J Mol Biol 105:39–74
Holmquist R, Moise H (1975) J Mol Evol 6:1–14
Iizuka M, Ishiii K, Matsuda H (1975) J Mol Evol 5:249–254
Jukes TH, Holmquist R (1972) J Mol Biol 64:163–179
Kafatos F, Efstratiadis A, Forget B, Weissman S (1977) Proc Nat Acad Sci USA 74: 5618–5622, Figure 1 and Table 2
Karon J (1979) J Mol Evol 12:197–218
King M-C, Wilson AC (1975) Science 188:107–116
Levine RD, Tribus M (eds) (1979) The maximum entropy formalism. MIT Press, Cambridge
Marotta CA, Wilson JT, Forget BG, Weissman SM (1977) J Biol Chem 252:5040–5053
Mood AM (1950) Introduction to the theory of statistics, chapter 8. Point estimation. Mc-Graw Hill, New York, p 147
Moore GW, Goodman M, Callahan C, Holmquist R, Moise H (1976) J Mol Biol 105:15–37
Nichols BP, Yanofsky C (1979) Proc Nat Acad Sci USA 76:5244–1979
Ortega JM, Rheinboldt WC (1970) Iterative solution of nonlinear equations in several variables. Academic Press, New York
Peacock D, Boulter D (1975) J Mol Biol 95:513–527
Schwartz R, Dayhoff MO (1978) Science 199:395–403
Uzzell T, Corbin K (1971) Science 172:1089–1096
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Holmquist, R., Pearl, D. Theoretical foundations for quantitative paleogenetics. J Mol Evol 16, 211–267 (1980). https://doi.org/10.1007/BF01804977
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DOI: https://doi.org/10.1007/BF01804977