Hostname: page-component-5c6d5d7d68-xq9c7 Total loading time: 0 Render date: 2024-08-17T14:24:09.841Z Has data issue: false hasContentIssue false
  • English
  • Français

The detection of a recessive visible gene in finite populations*

Published online by Cambridge University Press:  14 April 2009

Samuel Karlin  and
Simon Tavare
Samuel Karlin
Affiliation:
Department of Mathematics, Stanford University, Stanford, California 94305
Simon Tavare
Affiliation:
Department of Mathematics, Stanford University, Stanford, California 94305 Department of Mathematics, University of Utah, Salt Lake City, Utah 84112 (permanent address).

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Robertson, 1978, addressed the interesting problem of ascertaining the distribution of the time to detection of a recessive homozygote in a finite population. He was motivated in part by breeding and artificial selection practices. The same problem arises in the context of evolutionary processes and medical genetics since it refers to the time of first appearance as a homozygote of a new crossover event or a mutant gene.

Type
Research Article
Information
Genetics Research , Volume 37 , Issue 1 , February 1981 , pp. 33 - 46
Copyright
Copyright © Cambridge University Press 1981

References

REFERENCES

SirAiry, G. B. (1838). On the intensity of light in the neighbourhood of a caustic. Transactions of Cambridge Philosophical Society 6, 379–402.Google Scholar
Ewens, W. J. (1979). Mathematical Population Genetics. Springer Verlag. New York.Google Scholar
Gradshteyn, I. S. & Ryzhik, I. M. (1965). Tables of Integrals, Series and Products, 3rd edition. New York: Academic Press.Google Scholar
Kaulin, S. (1973). Sex and infinity, a mathematical analysis of the advantages and disadvantages of genetic recombination. In The Mathematical Theory of the Dynamics of Biological Populations (ed. Bartlett, M. S. and Hiorns, R. W.), pp. 155–194. New York and London: Academic Press.Google Scholar
Karlin, S., McGregor, J. L. & Bodmer, W. F. (1966). The rate of production of recombinants between linked genes in finite populations, Proceedings of 5th Berkeley Symposium on Mathematical Statistics and Probability, vol. iv, University of California Press. pp. 403–414.Google Scholar
Karlin, S. & Tavaré, S. (1981). The detection of particular genotypes in finite populations. Theoretical Population Biology (to appear).Google Scholar
Karlin, S. & Taylor, H. M. (1980). A second Course in Stochastic Processes. New York: Academic Press.Google Scholar
Kimura, M. (1970). Length of time required for a selectively neutral mutant to reach fixation through random drift in a finite population. Genetical Research 15, 131–133.CrossRefGoogle Scholar
Kimura, M. (1971). Theoretical foundations of population genetics at the molecular level. Theoretical Population Biology 2, 174–208.CrossRefGoogle ScholarPubMed
Miller, J. C. P. (1946). The Airy Integral. Mathematical tables. Part-vol. B. Cambridge University Press, England.Google Scholar
Robertson, A. (1960). A theory of limits in artificial selection. Proceedings of the Royal Society of London, B 153, 234–249.Google Scholar
Robertson, A. (1978). The time to detection of recessive visible genes in small populations. Genetical Research 31, 255–264.Google Scholar
Robertson, A. & Narain, P. (1971). The survival of recessive lethals in finite populations. Theoretical Population Biology 2, 24–50.Google Scholar