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The constraints of finite size in asexual populations and the rate of the ratchet

Published online by Cambridge University Press:  14 April 2009

Damian D. G. Gessler
Damian D. G. Gessler
Affiliation:
Biology Board of Studies, University of California, Santa Cruz, CA 95064, U.S.A. Phone: (408) 459-5147, Fax: (408) 459-4882. Email: [email protected]

Summary

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An analysis of mutation accumulation in finite, asexual populations shows that by modeling discrete individuals, a necessary condition for mutation–selection balance is often not met. It is found that over a wide parameter range (whenever N e−μ/s < 1, where N is the population size, μ is the genome-wide mutation rate, and s is the realized strength of selection), asexual populations will fail to achieve mutation–selection balance. This is specifically because the steady-state strength of selection on the best individuals is too weak to counter mutation pressure. The discrete nature of individuals means that if the equilibrium level of mutation and selection is such that less than one individual is expected in a class, then equilibration towards this level acts to remove the class. When applied to the classes with the fewest mutations, this drives mutation accumulation. This drive is in addition to the well-known identification of the stochastic loss of the best class as a mechanism for Muller's ratchet. Quantification of this process explains why the distribution of the number of mutations per individual can be markedly hypodispersed compared to the Poisson expectation. The actual distribution, when corrected for stochasticity between the best class and the mean, is akin to a shifted negative binomial. The parameterization of the distribution allows for an approximation for the rate of Muller's ratchet when N e−μ/s < 1. The analysis is extended to the case of variable selection coefficients where incoming mutations assume a distribution of deleterious effects. Under this condition, asexual populations accumulate mutations faster, yet may be able to survive longer, than previously estimated.

Type
Research Article
Information
Genetics Research , Volume 66 , Issue 3 , December 1995 , pp. 241 - 253
Copyright
Copyright © Cambridge University Press 1995

References

Bardwell, G. E., & Crow, E. L., (1964). A two-parameter family of hyper-Poisson distributions. Journal of the American Statistical Association 59, 133–141.CrossRefGoogle Scholar
Barton, D. E., (1966).Review of P. J. Staff: The displaced Poisson distribution. Mathematical Reviews 32, 6583.Google Scholar
Barton, N. H., (1994). The reduction in fixation probability caused by substitutions at linked loci. Genetical Research 64, 199–208.CrossRefGoogle Scholar
Bell, G., (1982). The Masterpiece of Nature. Berkeley: University of California Press.Google Scholar
Charlesworth, B., (1990). Mutation-selection balance and the evolutionary advantage of sex and recombination. Genetical Research 55, 199–221.CrossRefGoogle ScholarPubMed
Charlesworth, B., (1994). The effect of background selection against deleterious mutations on weakly selected, linked variants. Genetical Research 63, 213–227.CrossRefGoogle ScholarPubMed
Charlesworth, B., Charlesworth, D., & Morgan, M. T., (1990). Genetic loads and estimates of mutation rates in highly inbred plant populations. Nature 347, 380–382.CrossRefGoogle Scholar
Charlesworth, B., Morgan, M. T., & Charlesworth, D., (1993). The effect of deleterious mutations on neutral molecular variation. Genetics. 134, 1289–1303.CrossRefGoogle ScholarPubMed
Charlesworth, D., Morgan, M. T., & Charlesworth, B., (1993). Mutation accumulation in finite outbreeding and inbreeding populations. Genetical Research 61, 39–56.CrossRefGoogle Scholar
Crow, E. L., & Bardwell, G. E., (1965). Estimation of parameters of the hyper-Poisson distributions. In: Classical and Contagious Discrete Distributions (ed. Patil, G. P.), pp. 127–140. Statistical Publishing Society. Calcutta. Oxford: Pergamon Press.Google Scholar
Crow, J. F. (1993 a). How much do we know about spontaneous human mutation rates? Environmental and Molecular Mutagenesis 21, 122–129.CrossRefGoogle ScholarPubMed
Crow, J. F. (1993 b). How much do we know about spontaneous human mutation rates? Correction. Environmental and Molecular Mutagenesis 21, 389.CrossRefGoogle Scholar
Crow, J. F., (1994). Advantages of sexual reproduction. Developmental Genetics 15, 205–213.CrossRefGoogle ScholarPubMed
Crow, J. F., & Simmons, M. J., (1983). The mutation load in Drosophila. In: The Genetics and Biology of Drosophila. Ashburner, M. et al. (eds.), pp. 1–35. London: Academic Press.Google Scholar
Drake, J. W., (1991). A constant rate of spontaneous mutation in DNA-based microbes. Proceedings of the National Academy of Science USA 88, 7160–7164.CrossRefGoogle ScholarPubMed
Ewens, W. J., (1979). Mathematical Population Genetics p. 239. New York: Springer-Verlag.Google Scholar
Felsenstein, J., (1974). The evolutionary advantage of recombination. Genetics 78, 737–756.CrossRefGoogle ScholarPubMed
Gabriel, W., Lynch, M., & Burger, R., (1993). Muller's ratchet and mutational meltdowns. Evolution 47, 1744–1757.CrossRefGoogle ScholarPubMed
Gillespie, J. H., (1991). The Causes of Molecular Evolution, pp. 262–266. New York: Oxford University Press.Google Scholar
Greenwood, M., & Yule, G. U., (1920). An inquiry into the nature of frequency distributions representative of multiple happenings with particular reference to the occurrence of multiple attacks of disease or of repeated accidents. Journal of the Royal Society, Series A. 83, 255–279.Google Scholar
Haigh, J., (1978). The accumulation of deleterious genes in a population—Muller's ratchet. Theoretical Population Biology 14, 251–267.CrossRefGoogle Scholar
Haight, F. A., (1967). Handbook of the Poisson Distribution. New York: John Wiley & Sons.Google Scholar
Haldane, J. B. S., (1937). The effect of variation on fitness. American Naturalist 71, 337–349.CrossRefGoogle Scholar
Higgs, P. G., (1994). Error thresholds and stationary mutant distributions in multi-locus diploid genetics models. Genetical Research 63, 63–78.CrossRefGoogle Scholar
Hill, W. G., & Robertson, A., (1966). The effect of linkage on limits to artificial selection. Genetical Research 8, 269–294.CrossRefGoogle ScholarPubMed
Johnson, N. L., Kotz, S., & Kemp, A. W., (1993). Univariate Discrete Distributions. 2nd ed.New York: John Wiley & Sons.Google Scholar
Keightley, P. D., (1994). The distribution of mutation effects on viability in Drosophila melanogaster. Genetics 138, 1315–1322.CrossRefGoogle ScholarPubMed
Kemp, A. W., & Kemp, C. D., (1966). An alternative derivation of the Hermite distribution. Biometrika 53, 627–628.CrossRefGoogle Scholar
Kemp, C. D., & Kemp, A. W., (1965). Some properties of the ‘Hermite’ distribution. Biometrika 52, 381–394.Google ScholarPubMed
Kimura, M., (1968). Genetic variability maintained in a finite population due to mutational production of neutral and nearly neutral isoalleles. Genetical Research 11, 247–269.CrossRefGoogle Scholar
Kimura, M., (1969). The number of heterozygous nucleotide sites maintained in a finite population due to the steady flux of mutations. Genetics 61, 893–903.CrossRefGoogle Scholar
Kimura, M., (1983). The Neutral Theory of Molecular Evolution. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Kimura, M., & Maruyama, T., (1966). The mutational load with epistatic gene interactions in fitness. Genetics 54, 1337–1351.CrossRefGoogle ScholarPubMed
Kimura, M., Maruyama, T., & Crow, J. F., (1963). The mutation load in small populations. Genetics 48, 1303–1312.CrossRefGoogle ScholarPubMed
Koeberl, D. D., Bottema, C. D. K., Ketterling, R. P., Bridge, P. J., Lillicrap, D. P., & Sommer, S. S., (1990). Mutations causing Hemophila B: Direct estimate of the underlying rates of spontaneous germ-line transitions, transversions, and deletions in a human gene. American Journal of Human Genetics 47, 202–217.Google Scholar
Kondrashov, A. S., (1982). Selection against harmful mutations in large sexual and asexual populations. Genetical Research 40, 325–332.CrossRefGoogle ScholarPubMed
Kondrashov, A. S., & Crow, J. F., (1993). A molecular approach to estimating the human deleterious mutation rate. Human Mutation 2, 229–234.CrossRefGoogle ScholarPubMed
Li, W.-H. (1978). Maintenance of genetic variability under the joint effect of mutation, selection, and random drift. Genetics 90, 349–82.CrossRefGoogle ScholarPubMed
Lynch, M., & Gabriel, W., (1990). Mutation load and the survival of small populations. Evolution 44, 1725–1737.CrossRefGoogle ScholarPubMed
Smith, J. Maynard, (1978). The Evolution of Sex, pp. 33–36. Cambridge: Cambridge University Press.Google Scholar
McKendrick, A. G., (1926). Applications of mathematics to medical problems. Proceedings of the Edinburgh Mathematical Society 44, 98–130.CrossRefGoogle Scholar
Muller, H., (1950). Our load of mutations. American Journal of Human Genetics 1, 111–176.Google Scholar
Muller, H., (1964). The relation of recombination to mutational advance. Mutational Research 1, 2–9.CrossRefGoogle Scholar
Ohta, T., (1977). Extension to the neutral mutation random drift hypothesis. In: Molecular Evolution and Polymorphism (ed. Kimura, M.), pp. 148–167. National Institutes of Genetics.Google Scholar
Pamilo, P., Nei, M., & Li, W.-H., (1987). Accumulation of mutations in sexual and asexual populations. Genetical Research 49, 135–146.CrossRefGoogle ScholarPubMed
Simmons, M. J., & Crow, J. F., (1977). Mutations affecting fitness in Drosophila.populations. Annual Review of Genetics 11, 49–78.CrossRefGoogle ScholarPubMed
Sommer, S. S., (1992). Assessing the underlying pattern of human germline mutations: lessons from the factor IX gene. The FASEB Journal 6, 2767–2774.CrossRefGoogle ScholarPubMed
Staff, P. J., (1964). The displaced Poisson distribution. Australian Journal of Statistics 6, 12–20.CrossRefGoogle Scholar
Staff, P. J., (1967). The displaced Poisson distribution—Region B. Journal of the American Statistical Association 62, 643–654.Google Scholar
Stephan, W., Chao, L., & Smale, J. G., (1993). The advance of Muller's ratchet in a haploid asexual population: approximate solutions based on diffusion theory. Genetical Research 61, 225–231.CrossRefGoogle Scholar
Teicher, H., (1960). On the mixture of distributions. Annals of Mathematical Statistics 31, 55–73.CrossRefGoogle Scholar