An Evolutionary Reduction Principle for Mutation Rates at Multiple Loci

Bulletin of Mathematical Biology

Volumn 73, Issue 6, 2011, Pages 1227-1270

  Altenberg, Lee ^a  

^a UNIVERSITY OF HAWAII   (United States)

Author keywords

Evolution; Evolutionary theory; Karlin's theorem; Modifier gene; Mutation rate; Reduction principle; Reversible Markov chain; Spectral analysis

Indexed keywords

ARTICLE; BIOLOGICAL MODEL; MOLECULAR EVOLUTION; MUTATION; PROBABILITY;

EVOLUTION, MOLECULAR; MARKOV CHAINS; MODELS, GENETIC; MUTATION;

EID: 79955536041     PISSN: 00928240     EISSN: 15229602     Source Type: Journal    
DOI: 10.1007/s11538-010-9557-9     Document Type: Article

References (64)

1. Ababneh, F., Jermiin, L. S., and Robinson, J. (2006). Generation of the exact distribution and simulation of matched nucleotide sequences on a phylogenetic tree. J. Math. Model. Algorithms, 5, 291-308.
2. Altenberg, L. (1984). A generalization of theory on the evolution of modifier genes. Ph. D. thesis, Stanford University. Searchable online and available from University Microfilms, Ann Arbor, MI.
3. Altenberg, L. (2009). The evolutionary reduction principle for linear variation in genetic transmission. Bull. Math. Biol., 71, 1264-1284.
4. Altenberg, L., and Feldman, M. W. (1987). Selection, generalized transmission, and the evolution of modifier genes. I. The reduction principle. Genetics, 117, 559-572.
5. Baer, C. F., Miyamoto, M. M., and Denver, D. R. (2007). Mutation rate variation in multicellular eukaryotes: causes and consequences. Nat. Rev. Genet., 8, 619-631.
6. Balkau, B., and Feldman, M. W. (1973). Selection for migration modification. Genetics, 74, 171-174.
7. Brandon, R. N. (1982). The levels of selection. In P. Asquith and T. Nickles (Eds.), PSA 1982 (Vol. 1, pp. 315-323). East Lansing: Philosophy of Science Association.
8. Charlesworth, B. (1990). Mutation-selection balance and the evolutionary advantage of sex and recombination. Genet. Res., 55, 199-221.
9. Charlesworth, B., and Charlesworth, D. (1979). Selection on recombination in clines. Genetics, 91, 581-589.
10. Charlesworth, B., Charlesworth, D., and Strobeck, C. (1979). Selection for recombination in partially self-fertilizing populations. Genetics, 93, 237-244.
11. Deutsch, E., and Neumann, M. (1984). Derivatives of the Perron root at an essentially nonnegative matrix and the group inverse of an M-matrix. J. Math. Anal. Appl., 102, 1-29.
12. Duistermaat, J. J., and Kolk, J. A. C. (2004). Cambridge studies in advanced mathematics: Vol. 86. Multidimensional real analysis I: Differentiation. Cambridge: Cambridge University Press. ISBN 9780521551144.
13. Eyre-Walker, A., and Keightley, P. D. (2007). The distribution of fitness effects of new mutations. Nat. Rev. Genet., 8, 610-618.
14. Feldman, M. W. (1972). Selection for linkage modification: I. Random mating populations. Theor. Popul. Biol., 3, 324-346.
15. Feldman, M. W., and Balkau, B. (1973). Selection for linkage modification II. A recombination balance for neutral modifiers. Genetics, 74, 713-726.
16. Feldman, M. W., and Krakauer, J. (1976). Genetic modification and modifier polymorphisms. In S. Karlin and E. Nevo (Eds.), Population genetics and ecology (pp. 547-583). New York: Academic Press.
17. Feldman, M. W., and Liberman, U. (1986). An evolutionary reduction principle for genetic modifiers. Proc. Natl. Acad. Sci. USA, 83, 4824-4827.
18. Feldman, M. W., Christiansen, F. B., and Brooks, L. D. (1980). Evolution of recombination in a constant environment. Proc. Natl. Acad. Sci. USA, 77, 4838-4841.
19. Feller, W. (1971). An introduction to probability theory and its applications, Vol. I (3rd ed.). New York: Wiley.
20. Fox, A., Tuch, B., and Chuang, J. (2008). Measuring the prevalence of regional mutation rates: an analysis of silent substitutions in mammals, fungi, and insects. BMC Evol. Biol., 8, 186.
21. Giraud, A., Matic, I., Tenaillon, O., Clara, A., Radman, M., Fons, M., and Taddei, F. (2001). Costs and benefits of high mutation rates: adaptive evolution of bacteria in the mouse gut. Science, 291.
22. Guillemin, V., and Pollack, A. (1974). Differential topology. Prentice-Hall: Englewood Cliffs.
23. Hirsch, M. W. (1976). Differential topology. New York: Springer.
24. Hoede, C., Denamur, E., and Tenaillon, O. (2006). Selection acts on DNA secondary structures to decrease transcriptional mutagenesis. PLoS Genet., 2, e176. http://dx. plos. org/10. 1371%2Fjournal. pgen. 0020176.
25. Holsinger, K., Feldman, M. W., and Altenberg, L. (1986). Selection for increased mutation rates with fertility differences between matings. Genetics, 112, 909-922.
26. Holsinger, K. E., and Feldman, M. W. (1983a). Linkage modification with mixed random mating and selfing: a numerical study. Genetics, 103, 323-333.
27. Holsinger, K. E., and Feldman, M. W. (1983b). Modifiers of mutation rate: evolutionary optimum with complete selfing. Proc. Natl. Acad. Sci. USA, 80, 6732-6734.
28. Horn, R. A., and Johnson, C. R. (1985). Matrix analysis. Cambridge: Cambridge University Press.
29. Iosifescu, M. (1980). Finite Markov processes and their applications. Bucharest: Wiley.
30. Jayaswal, V., Jermiin, L. S., and Robinson, J. (2005). Estimation of phylogeny using a general Markov model. Evol. Bioinform. Online, 1, 62-80.
31. Karlin, S. (1976). Population subdivision and selection migration interaction. In S. Karlin and E. Nevo (Eds.), Population genetics and ecology (pp. 616-657). New York: Academic Press.
32. Karlin, S. (1982). Classification of selection-migration structures and conditions for a protected polymorphism. In M. K. Hecht, B. Wallace, and G. T. Prance (Eds.), Evolutionary biology (Vol. 14, pp. 61-204). New York: Plenum.
33. Karlin, S., and McGregor, J. (1972a). Application of method of small parameters to multi-niche population genetic models. Theor. Popul. Biol., 3, 186-209.
34. Karlin, S., and McGregor, J. (1972b). The evolutionary development of modifier genes. Proc. Natl. Acad. Sci. USA, 69, 3611-3614.
35. Karlin, S., and McGregor, J. (1974). Towards a theory of the evolution of modifier genes. Theor. Popul. Biol., 5, 59-103.
36. Keilson, J. (1979). Markov chain models: rarity and exponentiality. New York: Springer.
37. King, D. G., and Kashi, Y. (2007). Mutation rate variation in eukaryotes: evolutionary implications of site-specific mechanisms. Nat. Rev. Genet., 8.
38. Kingman, J. F. C. (1978). A simple model for the balance between selection and mutation. J. Appl. Probab., 15, 1-12.
39. Kingman, J. F. C. (1980). Mathematics of genetic diversity. Philadelphia: Society for Industrial and Applied Mathematics. ISBN 0-89871-166-5.
40. Kondrashov, A. S. (1982). Selection against harmful mutations in large sexual and asexual populations. Genet. Res., 40, 325-332.
41. Kondrashov, A. S. (1984). Deleterious mutations as an evolutionary factor. I. The advantage of recombination. Genet. Res., 44, 199-217.
42. Kondrashov, A. S. (1995). Modifiers of mutation-selection balance: general approach and the evolution of mutation rates. Genet. Res., 66, 53-69.
43. Kondrashov, F. A., and Kondrashov, A. S. (2010). Measurements of spontaneous rates of mutations in the recent past and the near future. Philos. Trans. R. Soc. B, 365, 1169-1176.
44. Lewontin, R. C. (1974). The genetic basis of evolutionary change. New York: Columbia University Press.
45. Liberman, U., and Feldman, M. W. (1986a). A general reduction principle for genetic modifiers of recombination. Theor. Popul. Biol., 30, 341-371.
46. Liberman, U., and Feldman, M. W. (1986b). Modifiers of mutation rate: A general reduction principle. Theor. Popul. Biol., 30, 125-142.
47. Lynch, M. (2010). Rate molecular spectrum, and consequences of human mutation. Proc. Natl. Acad. Sci. USA, 107, 961-968.
48. Lynch, M., Sung, W., Morris, K., Coffey, N., Landry, C. R., Dopman, E. B., Dickinson, W. J., Okamoto, K., Kulkarni, S., Hartl, D. L., and Thomas, W. K. (2008). A genome-wide view of the spectrum of spontaneous mutations in yeast. Proc. Natl. Acad. Sci., 105, 9272-9277.
49. Munkres, J. R. (1975). Topology: a first course. Prentice-Hall: Englewood Cliffs. ISBN 0-13-925495-1.
50. Otto, S. P., and Feldman, M. W. (1997). Deleterious mutations, variable epistatic interactions, and the evolution of recombination. Theor. Popul. Biol., 51, 34-47.
51. Pylkov, K. V., Zhivotovsky, L. A., and Feldman, M. W. (1998). Migration versus mutation in the evolution of recombination under multilocus selection. Genet. Res., 71, 247-256.
52. Roach, J. C., Glusman, G., Smit, A. F. A., Huff, C. D., Hubley, R., Shannon, P. T., Rowen, L., Pant, K. P., Goodman, N., Bamshad, M., Shendure, J., Drmanac, R., Jorde, L. B., Hood, L., and Galas, D. J. (2010). Analysis of genetic inheritance in a family quartet by whole-genome sequencing. Science. http://dx. doi. org/10. 1126/science. 1186802.
53. Rodríguez, F., Oliver, J., Marín, A., and Medina, J. (1990). The general stochastic model of nucleotide substitution. J. Theor. Biol., 142, 485-501.
54. Salmon, W. C. (1971). Statistical explanation and statistical relevance. Pittsburgh: University of Pittsburgh Press.
55. Salmon, W. C. (1984). Scientific explanation and the causal structure of the world. Princeton: Princeton University Press.
56. Singer, I. M., and Thorpe, J. A. (1967). Lecture notes on elementary topology and geometry. New York: Springer. ISBN 0-387-90202-3.
57. Squartini, F., and Arndt, P. F. (2008). Quantifying the stationarity and time reversibility of the nucleotide substitution process. Mol. Biol. Evol., 25, 2525-2535.
58. Teague, R. (1977). A model of migration modification. Theor. Popul. Biol., 12, 86-94.
59. Whelan, S., and Goldman, N. (2004). Estimating the frequency of events that cause multiple-nucleotide changes. Genetics, 167, 2027-2043.
60. Wilkinson, J. H. (1965). The algebraic eigenvalue problem. Oxford: Clarendon Press.
61. Yang, Z. (1995). On the general reversible Markov process model of nucleotide substitution: a reply to Saccone et al. J. Mol. Evol., 41, 254-255.
62. Yang, Z., and Nielsen, R. (2002). Codon-substitution models for detecting molecular adaptation at individual sites along specific lineages. Mol. Biol. Evol., 19, 908-917.
63. Zhivotovsky, L. A., and Feldman, M. W. (1995). The reduction principle for recombination under density-dependent selection. Theor. Popul. Biol., 47, 244-256.
64. Zhivotovsky, L. A., Feldman, M. W., and Christiansen, F. B. (1994). Evolution of recombination among multiple selected loci: A generalized reduction principle. Proc. Natl. Acad. Sci. USA, 91, 1079-1083.