Skip to main content Accessibility help
×
Home

The divergence of a polygenic system subject to stabilizing selection, mutation and drift

  • Nick Barton (a1)

Summary

Polygenic variation can be maintained by a balance between mutation and stabilizing selection. When the alleles responsible for variation are rare, many classes of equilibria may be stable. The rate at which drift causes shifts between equilibria is investigated by integrating the gene frequency distribution 2NΠ(pq)4Nμ−1. This integral can be found exactly, by numerical integration, or can be approximated by assuming that the full distribution of allele frequencies is approximately Gaussian. These methods are checked against simulations. Over a wide range of population sizes, drift will keep the population near an equilibrium which minimizes the genetic variance and the deviation from the selective optimum. Shifts between equilibria in this class occur at an appreciable rate if the product of population size and selection on each locus is small (Nsα2 < 10). The Gaussian approximation is accurate even when the underlying distribution is strongly skewed. Reproductive isolation evolves as populations shift to new combinations of alleles: however, this process is slow, approaching the neutral rate (≈ μ) in small populations.

    • Send article to Kindle

      To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

      Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

      The divergence of a polygenic system subject to stabilizing selection, mutation and drift
      Available formats
      ×

      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

      The divergence of a polygenic system subject to stabilizing selection, mutation and drift
      Available formats
      ×

      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

      The divergence of a polygenic system subject to stabilizing selection, mutation and drift
      Available formats
      ×

Copyright

References

Hide All
Barton, N. H. (1986). The maintenance of polygenic variation through a balance between mutation and stabilizing selection. Genetical Research 47, 209216.
Barton, N. H. (1989). Founder effect speciation. In Speciation and its consequences (ed. Endler, J. A. & Otte, D.. Sinauer Press, Sunderland, Mass.
Barton, N. H. & Charlesworth, B. (1984). Genetic revolutions, founder effects, and speciation. Annual Reviews of Ecology and Systematics 15, 133164.
Barton, N. H. & Rouhani, S. (1987). The frequency of shifts between alternative equilibria. Journal of Theoretical Biology 125, 397418.
Barton, N. H. & Turelli, M. (1987). Adaptive landscapes, genetic distance, and the evolution of quantitative characters. Genetical Research 49, 157174.
Bulmer, M. G. (1972). The genetic variability of polygenic characters under optimizing selection, mutation and drift. Genetical Research 19, 1725.
Bulmer, M. G. (1980). The Mathematical Theory of Quantitative Genetics. Oxford University Press, Oxford.
Burger, R., Wagner, G. P. & Stettinger, F. (1988). How much heritable variation can be maintained in finite populations by a mutation selection balance? Evolution (in press).
Charlesworth, B., Coyne, J. A. & Barton, N. H. (1987). The relative rates of evolution of sex chromosomes and autosomes. American Naturalist 129, 113146.
Coyne, J. & Orr, H. (1989). Patterns of speciation in Drosophila Evolution (in press).
Endler, J. A. (1986). Natural Selection in the Wild. Princeton University Press, Princeton, New Jersey.
Foley, P. (1987). Molecular clock rates at loci under stabilizing selection. Proceedings of the National Academy of Science (USA) 84, 79968000.
Gardiner, C. W. (1983). Handbook of Stochastic Methods. Synergetics, Vol. 13. Springer Verlag, Berlin.
Gillespie, J. H. (1984 a). Molecular evolution over the mutational landscape. Evolution 38, 11161129.
Gillespie, J. H. (1984 b). Pleiotropic overdominance and the maintenance of genetic variation in polygenic characters. Genetics 107, 321330.
Gillespie, J. H. (1986). Variability of evolutionary rates of DNA. Genetics 113, 10771091.
Hastings, A. (1987). Substitution rates under stabilizing selection. Genetics 116, 479486.
Karlin, S. (1979). Principles of polymorphism and epistasis for multilocus systems. Proceedings of the National Academy of Science (USA) 76, 541545.
Kaufmann, S. & Levin, S. A. (1987). Towards a general theory of adaptive walks on a rugged landscape. Journal of Theoretical Biology 128, 1146.
Kimura, M. (1981). Possibility of extensive neutral evolution under stabilizing selection with special reference to non-random usage of synonymous codons. Proceedings of the National Academy of Science (USA) 78, 57735777.
Kimura, M. (1983). The Neutral Theory of Molecular Evolution. Cambridge University Press.
Lande, R. (1975). The maintenance of genetic variability by mutation in a polygenic character with linked loci. Genetical Research 26, 221236.
Latter, B. D. H. (1960). Natural selection for an intermediate optimum. Australian Journal of Biological Sciences 13, 3035.
Maynard Smith, J. (1979). The effects of normalizing and disruptive selection on genes for recombination. Genetical Research 33, 121128.
Nagylaki, T. (1986). The Gaussian approximation for random genetic drift. In Evolutionary Processes and Theory (eds. Karlin, S. & Nevo, E.), pp. 629644. Academic Press, New York.
Provine, W. (1986). Sewall Wright and Evolutionary Biology. University of Chicago Press.
Rouhani, S. & Barton, N. H. (1987). Speciation and the ‘shifting balance’ in a continuous population. Theoretical Population Biology 31, 465492.
Schulman, L. (1981). Techniques and Applications of Path Integration. John Wiley, New York.
Shrimpton, A. E. & Robertson, A. (1988). The isolation of polygenic factors controlling bristle score in Drosophila melanogaster. II. Distribution of the third chromosome bristle effects on chromosome sections. Genetics 118, 445459.
Slatkin, M. (1979). Frequency- and density-dependent selection on a quantitative character. Genetics 93, 755771.
Turelli, M. (1984). Heritable genetic variation via mutation-selection balance: Lerch's zeta meets the abdominal bristle. Theoretical Population Biology 25, 138193.
Turelli, M. (1986). Gaussian versus non-Gaussian genetic analyses of polygenic mutation-selection balance. In Evolutionary Processes and Theory (eds. Karlin, S. & Nevo, E.), pp. 607628. Academic Press, New York.
Turelli, M. & Barton, N. H. (1989). Dynamics of polygenic characters under selection. Manuscript submitted to Genetics.
Wright, S. (1932). The roles of mutation, inbreeding, crossbreeding and selection in evolution. Proceedings of the Sixth International Congress of Genetics 1, 356366.
Wright, S. (1935). Evolution in populations in approximate equilibrium. Journal of Genetics 30, 257266.
Wright, S. (1980). Genetic and organismic selection. Evolution 34, 825843.

The divergence of a polygenic system subject to stabilizing selection, mutation and drift

  • Nick Barton (a1)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed