Random and Nonrandom Processes in the Molecular Evolution of Higher Organisms

  • Richard Holmquist
Part of the Advances in Primatology book series (volume 62)


I will discuss the usefulness of approaching an understanding of evolution through a conceptual analysis of the random and nonrandom processes which occur at the molecular level of proteins and nucleic acids, rather than volunteer an exposition of mathematical methodology available elsewhere in the literature. A qualitatively incorrect concept, however mathematically transformed and quantified, remains biologically uninformative. A correct concept, even though imperfectly quantified, is at least useful; the quantitation can be improved as additional data and insight permit. With cautious optimism, Vogel et al. (this volume) state: “the prospects may not be so poor, provided that we do not expect to develop a final and altogether perfect concept. Our model should be refined step by step. After the first few steps, the picture admittedly may still be oversimplified, but at least the most obvious flaws of the old one are corrected.” On the other hand, the known facts are not likely to be accounted for by an arbitrary choice of model. The evolutionary model presented here embodies both selective (i. e., deterministic) and probabilistic evolutionary mechanisms; it reasonably accounts, both qualitatively and quantitatively, for both the observed random and nonrandom and the Darwinian and selectively neutral patterns of protein and nucleic acid variation. The values for evolutionary divergence between species which were calculated from this model when it was first published in 1972 (Holmquist et al., 1972; Jukes and Holmquist, 1972a) were at that time 2–4 times higher than the values then considered correct.


Maximum Parsimony Codon Position Amino Acid Site Amino Acid Replacement Ancestral Sequence 
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  1. Ayala, F., 1974, Evolution: Natural selection or random walk? Am. Sci 62: 692–701.PubMedGoogle Scholar
  2. Beyer, W., Stein, M., Smith, T., and Ulam, S., 1974, A molecular sequence metric and evolutionary trees, Math. Biosci. 19: 9–25.CrossRefGoogle Scholar
  3. Cameron, I., and Jeter, S. (eds.), 1974, Acidic Proteins of the Nucleus, Academic Press, New York.Google Scholar
  4. Christenson, R., 1963, in: Induction and the Evolution of Language, Arthur D. Little, Inc., Cambridge, Mass.Google Scholar
  5. Crowson, R., 1975, Anti-Darwinism among the molecular biologists, Nature (London) 254: 464.CrossRefGoogle Scholar
  6. Dayhoff, M., 1972a, Hormones, active peptides, and toxins, Atlas of Protein Sequence and Structure 5: D173.Google Scholar
  7. Dayhoff, M., 1972b, Atlas of Protein Sequence and Structure 5:D234, Matrix 24.Google Scholar
  8. Dayhoff, M., Eck, R., and Park, C., 1972, A model of evolutionary change in proteins, Atlas of Protein Sequence and Structure 5: 89–99.Google Scholar
  9. D’Azzo, J., and Houpis, C., 1966, Feedback Control System Analysis and Synthesis, 2nd ed., Chapter 15, McGraw-Hill, New York.Google Scholar
  10. Dickerson, R., 1971, The structure of cytochrome c and the rates of molecular evolution, J. Mol. Evol. 1: 26–45.PubMedCrossRefGoogle Scholar
  11. Farris, J., 1972, Estimating phylogenetic trees from distance matrices, Am. Nat. 106: 645–668.CrossRefGoogle Scholar
  12. Feller, W., 1968, An Introduction to Probability Theory and Its Applications, Vol. 1, Wiley, New York.Google Scholar
  13. Fiers, W., Contreras, R., Duerinck, F., Haegman, G., Merregaert, J., Min Jou, W., Raeymakers, A., Volckaert, G., Ysebaert, M., Van de Kerckhove, J., Nolf, F., and Van Montagu, M., 1975, A-protein gene of bacteriophage MS2, Nature (London) 256: 273–278.CrossRefGoogle Scholar
  14. Fitch, W., 1971, Toward defining the course of evolution: minimum change for a specific tree topology, Syst. Zool. 20: 406–416.CrossRefGoogle Scholar
  15. Fitch, W., and Margoliash, 1967, Construction of phylogenetic tress, Science 155: 279–284.PubMedCrossRefGoogle Scholar
  16. Ganong, W., 1973, Review of Medical Physiology, 6th ed., p. 307, Lange Medical Publications, Los Altos, Calif.Google Scholar
  17. Gatlin, L., 1972, Information Theory and the Living System, Columbia University Press, New York.Google Scholar
  18. Gatlin, L., 1974, Conservation of Shannon’s redundancy for proteins, J. Mol. Evol. 3: 182–208.Google Scholar
  19. Goldstone, A., and Smith, E., 1966, Amino acid sequence of whale heart cytochrome c, J. Biol. Chem. 241: 4480–4486.PubMedGoogle Scholar
  20. Goodman, M., and Moore, G., 1971, Immunodiffusion systematics of the primates. I. The Catarrhini, Syst. Zool. 20: 19–62.CrossRefGoogle Scholar
  21. Goodman, M., Moore, G., Barnabas, J., and Matsuda, G., 1974, The phylogeny of human globin genes investigated by the maximum parsimony method, J. Mol. Evol. 3: 1–48.PubMedCrossRefGoogle Scholar
  22. Gould, S., Raup, D., Schopf, T., and Simberloff, D., 1975, in: Research news (G. B. Kolata, reviewer), Paleobiology: Random events over geological time, Science 189: 625–626, 660.CrossRefGoogle Scholar
  23. Holmquist, R., 1972a, Empirical support for a stochastic model of evolution, J. Mol Evol. 1: 211–222.CrossRefGoogle Scholar
  24. Holmquist, R., 1972b, Theoretical foundations for a quantitative approach to paleogenetics. Part i. DNA, J. Mol Evol 1: 115–133.CrossRefGoogle Scholar
  25. Holmquist, R., 1972c, Theoretical foundations for a quantitative approach to paleogenetics. Part II. Proteins, J. Mol Evol 1: 134–149.CrossRefGoogle Scholar
  26. Holmquist, R., 1972c, Theoretical foundations of paleogenetics, in: Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability: Darwinian, Neo-Darwinian, and Non-Darwinian Evolution, Vol. 5 ( L. LeCam, J. Neyman, and E. Scott, eds.), pp. 315–350, University of California Press, Berkeley.Google Scholar
  27. Holmquist, R., 1973, The stochastic model and deviations from randomness in eukaryotic tRNAs: Comparison with the PAM approach, J. Mol Evol 2: 145–148.PubMedCrossRefGoogle Scholar
  28. Holmquist, R., 1975, Deviations from compositional randomness in eukaryotic and prokaryotic proteins: The hypothesis of selective-stochastic stability and a principle of charge conservation, J. Mol Evol 4: 277–306.PubMedCrossRefGoogle Scholar
  29. Holmquist, R., and Moise, H., 1975, Compositional non-randomness: A quantitatively conserved evolutionary invariant, J. Mol Evol 6: 1–14.CrossRefGoogle Scholar
  30. Holmquist, R., Cantor, C., and Jukes, T., 1972, Improved procedures for comparing homologous sequences in molecules of proteins and nucleic acids, J. Mol Biol 64: 145–161.PubMedCrossRefGoogle Scholar
  31. Holmquist, R., Jukes, T., and Pangburn, S., 1973, Evolution of transfer RNA, J. Mol Biol 78: 91–116.PubMedCrossRefGoogle Scholar
  32. Holmquist, R., Jukes, T., Moise, H., Goodman, M., and Moore, G., 1976, The evolution of the globin family genes: Concordance of stochastic and augmented maximum parsimony genetic distances for alpha hemoglobin, beta hemoglobin, and myoglobin phylogenies, J. Mol Biol 105: 39–74.PubMedCrossRefGoogle Scholar
  33. Jardine, H., and Sibson, R., 1971, Mathematical Taxonomy, Interscience, New York.Google Scholar
  34. Jaynes, E., 1957, Information theory and statistical mechanics, Phys. Rev. 106: 620–630, 108: 171–190.CrossRefGoogle Scholar
  35. Jukes, T., 1963, Some recent advances in studies of the transcription of the genetic message, Adv. Biol Med. Phys. 9: 1–41.PubMedGoogle Scholar
  36. Jukes, T., 1971, Comparison of the polypeptide chains of globins, J. Mol Evol 1: 46–62.PubMedCrossRefGoogle Scholar
  37. Jukes, T., 1975, Mutations in proteins and base changes in codons, Biochem. Biophys. Res. Commun. 66: 1–8.PubMedCrossRefGoogle Scholar
  38. Jukes, T., and Holmquist, R., 1972a, Estimation of evolutionary changes in certain homologous polypeptide chains, J. Mol Biol 64: 163–179.PubMedCrossRefGoogle Scholar
  39. Jukes, T., and Holmquist, R., 1972b, Evolutionary clock: Non-constancy of rate in different species, Science 177: 530–532.PubMedCrossRefGoogle Scholar
  40. Kimura, M., 1968, Evolutionary rate at the molecular level, Nature (London) 217: 624–626.CrossRefGoogle Scholar
  41. Kimura, M., and Ohta, T., 1974, On some principles governing molecular evolution, Proc. Natl Acad. Sci. U.S.A. 71: 2848–2852.PubMedCrossRefGoogle Scholar
  42. King, J., and Jukes, T., 1969, Non-Darwinian evolution: Random fixation of selectively neutral mutations, Science 164: 788–798.PubMedCrossRefGoogle Scholar
  43. Kolata, G. (reviewer), 1975, Evolution of DNA: Changes in gene regulation, Science 189: 446–447.PubMedCrossRefGoogle Scholar
  44. Langley, C., and Fitch, W., 1974, An examination of the constancy of the rate of molecular evolution, J. Mol Evol 3: 161–177.PubMedCrossRefGoogle Scholar
  45. Li, S., Denney, R., and Yanofsky, C., 1973, Nucleotide sequence divergence in the α-chain structural genes of tryptophan synthetase from Escherichia coli, Salmonella typhimurium, and Aerobactor aerogenes, Proc. Natl Acad. Sci. USA 70: 1112–1116.PubMedCrossRefGoogle Scholar
  46. Lipschutz, S., 1965, Theory and Problems of General Topology, McGraw-Hill, New York.Google Scholar
  47. MacQueen, J., and Marschak, J., 1975, Partial knowledge, entropy, and estimation, Proc. Natl Acad. Sci USA 72: 3819–3824.PubMedCrossRefGoogle Scholar
  48. McLaughlin, P., and Dayhoff, M., 1972, Evolution of species and proteins: a time scale, Atlas of Protein Sequence and Structure 5: 47–52.Google Scholar
  49. Moore, G., 1973, 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
  50. Moore, G., 1976, Proof of the populous path algorithm for missing mutations in parsimony trees, J. Theor. Biol, (in press).Google Scholar
  51. Moore, G., Barnabas, J., and Goodman, M., 1973, A method for constructing maximum parsimony ancestral amino acid sequences on a given network, J Theor. Biol. 38: 459–485.PubMedCrossRefGoogle Scholar
  52. Moore, G., Goodman, M., Callahan, C., Holmquist, R., and Moise, H. 1976, Stochastic vs. augmented maximum parsimony method for estimation of superimposed mutations in the divergent evolution of protein sequences—Methods tested on cytochrome c amino acid sequences, J. Mol. Biol. 105: 15–38.PubMedCrossRefGoogle Scholar
  53. Ohta, T., 1975, Statistical analyses of Drosophila and human protein polymorphisms, Proc. Natl. Acad. Sci. USA 72: 3194–3196.CrossRefGoogle Scholar
  54. Ohta, T., and Kimura, M., 1971, On the constancy of the evolutionary rate of cistrons, J. Mol. Evol. 1: 18–25.CrossRefGoogle Scholar
  55. Prager, E., and Wilson, A., 1975, Slow evolutionary loss of the potential for interspecific hybridization in birds: A manifestation of slow regulatory evolution, Proc. Natl. Acad. Sci. USA 72: 200–204.PubMedCrossRefGoogle Scholar
  56. Prager, E., Brush, A., Nolan, R., Nakanishi, M., and Wilson, A., 1974, Slow evolution of transferrin and albumin in birds according to microcomplement fixation analysis, J. Mol. Evol. 3: 243–262.PubMedCrossRefGoogle Scholar
  57. Raup, D., and Gould, S., 1974, Stochastic simulation and evolution of morphology—towards a nomothetic paleontology, Syst. Zool. 23: 305–322.CrossRefGoogle Scholar
  58. Raup, D., Gould, S., Schopf, T., and Simberloff, D., 1973, Stochastic models of phylogeny and the evolution of diversity, J. Geol. 81: 525–542.CrossRefGoogle Scholar
  59. Romero-Herrera, A., Lehmann, H., Joysey, K., and Friday, A., 1973, Molecular evolution of myoglobin and the fossil record: A phylogenetic synthesis, Nature (London) 246: 389–395.CrossRefGoogle Scholar
  60. Sarich, V., and Wilson, A., 1967, Immunological time scale for hominid evolution, Science 158: 1200–1203.PubMedCrossRefGoogle Scholar
  61. Sneath, P., 1966, Relations between chemical structure and biological activity in peptides, J. Theor. Biol. 12: 157–195.PubMedCrossRefGoogle Scholar
  62. Sneath, P., 1974, Phylogeny of micro-organisms, Symp. Soc. Gen. Microbiol. 24: 1–39.Google Scholar
  63. Sneath, P., and Sokal, R., 1973, Numerical Taxonomy, Freeman, San Francisco.Google Scholar
  64. Sokolovsky, M., and Moldovan, M., 1972, Primary structure of cytochrome c from the camel, Camelus dromedarius, Biochemistry 11: 145–149.PubMedCrossRefGoogle Scholar
  65. Stebbins, G., 1969, The Basis of Progressive Evolution, pp. 29, 124, University of North Carolina Press, Chapel Hill, N.C.Google Scholar
  66. Tomkins, G., 1975, The metabolic code, Science 189: 760–763.PubMedCrossRefGoogle Scholar
  67. Tribus, M., 1962, The use of the maximum entropy estimate in the estimation of reliability, in: Recent Developments in Information and Decision Processes ( R. E. Marshall and Paul Grey, eds.), Macmillan, New York.Google Scholar
  68. Tribus, M., Shannon, P., and Evans, R., 1966, Why thermodynamics is a logical consequence of information theory, AIChE J. 12: 244–248.CrossRefGoogle Scholar
  69. Van Valen, L., 1971, Adaptive zones and the orders of mammals, Evolution 25: 420–428.CrossRefGoogle Scholar
  70. Van Valen, L., 1973, A new evolutionary law, Evol. Theory 1: 1–30.Google Scholar
  71. Van Valen, L., 1974, A natural model for the origin of some higher taxa, J. Herpetol. 8: 109–121.CrossRefGoogle Scholar
  72. Wilson, A., Maxson, L., and Sarich, V., 1974a, Two types of molecular evolution: Evidence from studies of interspecific hybridization, Proc. Natl Acad. Sci USA 71: 2843–2847.CrossRefGoogle Scholar
  73. Wilson, A., Sarich, V., and Maxson, L., 1974b, The importance of gene rearrangement in evolution: Evidence from studies on rates of chromosomal, protein, and anatomical evolution, Proc. Natl. Acad. Sci. USA 71: 3028–3030.CrossRefGoogle Scholar
  74. Zuckerkandl, E., and Pauling, L., 1962, Molecular disease, evolution, and genie heterogeneity, in: Horizons in Biochemistry ( M. Kasha and B. Pullman, eds.), pp. 189–225, Academic Press, New York.Google Scholar

Copyright information

© Plenum Press, New York 1976

Authors and Affiliations

  • Richard Holmquist
    • 1
  1. 1.Space Sciences LaboratoryUniversity of CaliforniaBerkeleyUSA

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