Mathematical properties of mutation-selection models

Genetica

Volumn 102-103, Issue , 1998, Pages 279-298

  Bürger, Reinhard ^a  

^a UNIVERSITY OF VIENNA   (Austria)

Author keywords

Genetic variance; Mutation load; Mutation selection balance; Quantitative traits

Indexed keywords

ALLELE; GENETIC LINKAGE; GENETIC MODEL; GENETIC VARIANCE; MUTATION;

EID: 7344226239     PISSN: 00166707     EISSN: None     Source Type: Journal    
DOI: 10.1007/978-94-011-5210-5_23     Document Type: Article

References (80)

1. Akin, E., 1979. The Geometry of Population Genetics. Lect. Notes Biomath. 31. Berlin Heidelberg New York: Springer.
2. Barton, N.H., 1986. The maintenance of poly genie variation through a balance between mutation and stabilizing selection. Genet. Res. Camb. 47: 209-216.
3. Barton, N.H., 1989. Divergence of a polygenic system subject to stabilizing selection, mutation and drift. Genet. Res. 54: 59-77.
4. Barton, N.H. & M. Turelli, 1989. Evolutionary quantitative genetics: how little do we know? Annu. Rev. Genet. 23: 337-370.
5. Baum, L.E. & J.A. Eagon. 1967. An inequality with applications to statistical estimation for probability functions of Markov processes and to amodel for ecology. Bull. Amer. Math. Soc. 73: 360-363.
6. Bulmer, M.G., 1972. The genetic variability of polygenic characters under optimising selection, mutation and drift. Genet. Res. 19: 17-25.
7. Bulmer, M.G., 1974. Linkage disequilibrium and genetic variability. Genet. Res. 23: 281-289.
8. Bürger. R., 1983. Dynamics of the classical genetic model for the evolution of dominance. Math. Biosci. 67: 125-143.
9. Bürger. R., 1988. Mutation-selection balance and continuum-of-alleles models. Math. Biosci. 91: 67-83.
10. Bürger. R., 1989. Linkage and the maintenance of heritable variation by mutation-selection balance. Genetics 121: 175-184.
11. Bürger. R. & I.M. Bomze, 1996. Stationary distributions under mutation-selection balance: structure and properties. Adv. Appl. Prob. 28: 227-251.
12. Bürger. R. & J. Hofbauer, 1994. Mutation load and mutation-selection-balance in quantitative genetic Traits. J. Math. Biol. 32: 193-218.
13. Bürger, R. & R. Lande, 1994. On the distribution of the mean and variance of a quantitative Trait under mutation-selection-drift balance. Genetics 138: 901-912.
14. Bürger, R., G.P. Wagner & F. Stettinger, 1989. How much heritable variation can be maintained in finite populations by a mutation-selection balance? Evolution 43: 1748-1766.
15. Butcher, D., 1995. Muller's ratchet, epistasis and mutation effects. Genetics 141: 431-437.
16. Charlesworth, B., 1990. Mutation-selection balance and the evolutionary advantage of sex and recombination. Genet. Res. 55: 199-221.
17. Charlesworth, B., M.T. Morgan & D. Charlesworth, 1991. Multilocus models of inbreeding depression with synergistic selection and partial self-fertilization. Genetical Research 57: 177-194.
18. Charlesworth, D., M.T. Morgan & B. Oiarlesworth, 1993. Mutation accumulation in finite populations. J. of Heredity 84: 321-325.
19. Crow, J.F., 1970. Genetic loads and the cost of natural selection. pp. 128-177 in Mathematical Topics in Population Genetics, edited by K. Kojima. Berlin Heidelberg New York: Springer.
20. Crow, J.F. & M. Kimura, 1964. The theory of genetic loads, pp. 495-505 in Proc. XI Int. Congr. Genetics, vol. 2. Oxford: Pergamon Press.
21. Crow, J.F. & M. Kimura, 1970. An Introduction to Population Genetics Theory. New York: Harper and Row.
22. Eigen, M. & P. Schuster, 1977. The hypercycle. A principle of natural seIf-organization. Part A: Emergence of the hypercycle. Naturwissenschaften 64: 541-565.
23. Felsenstein, J., 1974. The evolutionary advantage of re combination. Genetics 78: 737-756.
24. Fleming, W.H., 1979. Equilibrium distributions of continuous polygenie Traits. SIAM J. Appl. Math. 36: 148-168.
25. Fraser, G.R., & O. Mayo, 1974. Genetical load in man. Human-genetik 23: 83-110.
26. Hadeler, K.P., 1981. Stable polymorphisms in a selection model with mutation. SIAM J. Appl. Math. 41: 1-7.
27. Haigh, J., 1978. The accumulation of deleterious genes in a population - Muller's ratchet. Theor. Popul. Biol. 14: 251-267.
28. Haldane, J.B.S., 1937. The effect of variation on fitness. Am er. Natur. 71: 337-349.
29. Haldane, J.B.S., 1957. The cost of natural selection. J. Genet. 55: 511-524.
30. Hastings, A., 1989. Linkage disequilibrium and genetic variance under mutation-selection balance. Genetics 121: 857-860.
31. Hastings, A., 1990. Maintenance of poly genie variation through mutation-selection balance: bifurcation analysis of a biallelic model. J. Math. Biol. 28: 329-340.
32. Hill, W.G., 1982. Predictions of response to artificial selection from new mutations. Genet. Res. 40: 255-278.
33. Hofbauer, J., 1985. The selection mutation equation. J. Math. Biol. 23: 41-53.
34. Houle, D., 1989. The maintenance of polygenic variation in finite populations. Evolution 43: 1767-1780.
35. Keightley, P.D. & W.G. Hill, 1988. Quantitative genetic variability maintained by mutation-stabilizing selection balance in finite populations. Genet. Res. 52: 33-43.
36. Kimmel, M. & R. Chakraborty, 1996. Measures of variation at DNA repeat loci under a general stepwise mutation model. Theor. Popul. Biol. 50: 318-367.
37. Kimura, M., 1965. A stochastic model concerning the maintenance of genetic variability in quantitative characters. Proc. Natl. Acad. Sci. U.S.A. 54: 731-736.
38. Kimura, M., 1981. Possibility of extensive neutral evolution under stabilizing selection withspecial reference to nonrandom usage of synonymous codons. Proc. Natl. Acad. Sci., USA 78: 5773-5777.
39. Kimura, M. & T. Maruyama, 1966. The mutational load with epistatic gene interaction in fitness. Genetics 54: 1337-1351.
40. King, J.L., 1966. The gene interaction component of the genetic load. Genetics 53: 403-413.
41. Kingman, J.F.C., 1977. On the properties of bilinear models for the balance between genetic mutation and selection. Math. Proc. Camb. Phil. Soc. 81: 443-453.
42. Kingman, J.F.C., 1978. A simple model for the balance between selection andmutation. J. Appl. Prob. 15: 1-12.
43. Kingman, J.F.C., 1980. Mathematics of Genetic Diversity. Philadelphia: SIAM.
44. Kondrashov, A.S., 1982. Selection against harmful mutations in large sexual and asexual populations. Genet. Res. 40: 325-332.
45. Kondrashov, A.S., 1994. Muller's ratchet under epistatic selection. Genetics 136: 1469-1473.
46. Kondrashov, A.S. & J.F. Crow, 1988. King's formula for the mutation load with epistasis. Genetics 120: 853-856.
47. Lande, R., 1975. The maintenance of genetic variability by mutation in apolygenic character with united loci. Genet. Res. 26: 221-235
48. Lande, R., 1980. Genetic variation and phenotypic evolution during allopatric speciation. Amer. Natur. 116: 463-479.
49. Lande, R., 1994. Risk of population extinction from fixation of new deleterious mutations. Evolution 48: 1460-1469.
50. Latter, B.D.H., 1960. Natural selection for an intermediate optimum. Australian J. of Biol. Sciences 13: 30-35.
51. López, M.A. & C. López-Fanjul, 1993a,b. Spontaneous mutation for a quantitative trait in Drosophila melanogaster. I. Response to artificial selection. Genet. Res. 61: 107-116. II. Distribution of mutant effects on the trait and fitness. Genet. Res. 61: 117-126.
52. López, M.A. & C. López-Fanjul, 1993a,b. Spontaneous mutation for a quantitative trait in Drosophila melanogaster. I. Response to artificial selection. Genet. Res. 61: 107-116. II. Distribution of mutant effects on the trait and fitness. Genet. Res. 61: 117-126.
53. Lynch, M., & W.G. Hill, 1986. Phenotypic evolution by neutral mutation. Evolution 40: 915-935.
54. Lynch, M. & W. Gabriel, 1990. Mutation load and the survival of small populations. Evolution 44: 1725-1737.
55. Lynch, M., J. Conery & R. Bürger, 1995. Mutation accumulation and the extinction of small populations. Amer. Natur. 146: 489-518.
56. Mackay, T.F.C., R. Lyman, M.S. Jackson, C. Terzian, & W.G. Hill, 1992. Polygenic mutation in Drosophila melanogaster: estimates from divergence among inbred strains. Evolution 46: 300-316.
57. Moran, PA.P., 1976. Global stability of genetic systems governed by mutation and selection. Math. Proc. Camb. Phil. Soc. 80: 331-336.
58. Moran, PA.P., 1977. Global stability of genetic systems governed by mutation and selection. II. Math. Proc. Camb. Phil. Soc. 81: 435-441.
59. Muller, H.J., 1950. Our load of mutations. Amer. J. Hum. Genet. 2: 111-176.
60. Muller, H.J., 1964. The relation of recombination to mutational advance. Mutat. Res. 1: 2-9.
61. Nagylaki, T., 1984. Selection on a quantitative character, pp. 275-306 in Human Population Genetics: The Pittsburgh Symposium, edited by A. Chakravarti. New York: Van Nostrand.
62. Nagylaki, T., 1989. The maintenance of genetic variability in two- locus models of stabilizing selection. Genetics 122: 235-248.
63. Nagylaki, T., 1992. Introduction to Theoretical Population Genetics. Berlin Heidelberg New York: Springer.
64. Norman, M.F., 1974. A central limit theorem for Markov processes that move by small steps. Ann. Prob. 2: 1065-1074.
65. Ohta, T. & M. Kimura, 1973. A model of mutation appropriate to estimate the number of electrophoretically detectable alleles in a finite population. Genet. Res. 22: 201-204.
66. Peck, J.R., 1994. A ruby in the rubbish: beneficial mutations, deleterious mutations and the evolution of sex. Genetics 137: 597-606.
67. Schlötterer, C., C. Vogl, & D. Tautz, 1997. Polymorphism and locus-specific effects on the polymorphism at microsatellite loci in natural Drosophila melanogaster populations. Genetics 146: 309-320.
68. Seneta, E., 1973. Non-Negative Matrices. London: Alien and Unwin.
69. Slatkin, M., 1987. Heritable variation and heterozygosity under a balance between mutations and stabilzing selection. Genet. Res. 50: 53-62.
70. Swetina, J. & P. Schuster, 1982. Self-replication with errors. A model for poylnucleotide replication. Biophys. Chem. 16: 329-345.
71. Thompson, C.J. & J.L. McBride, 1974. On Eigen's theory of self-organization of matter and the evolution of biological macro-molecules. Math. Biosci. 21: 127-142.
72. Turelli, M., 1984. Heritable genetic variation via mutation-selection balance: Lerch's zeta meets the abdominal bristle. Theor. Pop. Biol. 25: 138-193.
73. Turelli, M. & N.H. Barton, 1990. Dynamics of polygenic characters under selection. Theor. Pop. Biol. 38: 1-57.
74. Wagner, G.P. & P. Krall, 1993. What is the difference between models of error thresholds and Muller's ratchet? J. Math. Biol. 32: 33-44.
75. Wright, S., 1935a. The analysis of variance and the correlations between relatives with respect to deviations from an optimum. J. of Genetics 30: 243-256
76. Wright, S., 1935b. Evolution in populations in approximate equilibrium. J. Genetics 30: 257-266.
77. Wright, S., 1949. Adaptation and Selection, pp. 365-89 in Genetics, Paleontology, and Evolution edited by G.L. Jepson, G.G. Simpson, and E. Mayr). Princeton: Univ. Press.
78. Wright, S., 1969. Evolution and the Genetics of Populations. Vol. 2. The Theory of Gene Frequencies. Chicago: University Press.
79. Zeng, Z.B. & C.C. Cockerham, 1993. Mutation models and quantitative genetic variation. Genetics 133: 729-736.
80. Zhivotovsky, L.A. & M.W. Feldman, 1995. Microsatellite variability and genetic distances. Proc. Natl. Acad. Sci. USA 92: 11549-11552.