Hostname: page-component-78c5997874-8bhkd Total loading time: 0 Render date: 2024-11-11T03:18:45.375Z Has data issue: false hasContentIssue false
  • English
  • Français

A natural class of multilocus recombination processes and related measures of crossover interference

Published online by Cambridge University Press:  01 July 2016

Samuel Karlin  and
Uri Liberman
Samuel Karlin*
Affiliation:
Stanford University
Uri Liberman*
Affiliation:
Tel-Aviv University
*
∗Postal address: Department of Mathematics, Stanford University, Stanford, CA 94305, U.S.A.
∗∗Postal address: Department of Statistics, Tel-Aviv University, Ramat-Aviv, Israel. Research carried out while the author was visiting Stanford University.
Get access Rights & Permissions [Opens in a new window]

Abstract

Various classifications and representations of multilocus recombination structures are delimited. A class of recombination distributions called the count–location chiasma process is parametrized by a distribution of the number of crossover events and for such crossover events by a conditional distribution of crossover locations. A number of properties and examples of this recombination structure are developed connecting orderings among the recombination mapping functions and the nature of interference.

Keywords

RECOMBINATION–SEGREGATION DISTRIBUTIONLINKAGE-VALUESNATURAL AND MORE RECOMBINATIONCOUNT–LOCATION CHIASMA PROCESSMAPPING FUNCTION
Type
Research Article
Information
Advances in Applied Probability , Volume 11 , Issue 3 , September 1979 , pp. 479 - 501
Copyright
Copyright © Applied Probability Trust 1979 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

Research supported in part by NIH Grant GM10452-15 and NSF Grant MCS-76-80624-AO1.

References

Anderson, E. G. and Rhoades, M. M. (1931) The distribution of interference in X-chromosome of Drosophila . Pap. Mich. Acad. Sci. 13, 227–239.Google Scholar
Bailey, N. T. J. (1961) Introduction to the Mathematical Theory of Genetic Linkage. Oxford University Press.Google Scholar
Catcheside, D. G. (1977) The Genetics of Recombination. University Park Press, Baltimore, Md.Google Scholar
Geiringer, H. (1944) On the probability theory of linkage in Mendelian heredity. Ann. Math. Statist. 15, 25–57.Google Scholar
Haldane, J. B. S. (1919) The combination of linkage values and the calculation of distance between the loci of linked factors. J. Genet. 8, 299–309.Google Scholar
Jennings, H. S. (1923) The numerical relations in the crossing-over of the genes, with a critical examination of the theory that the genes are arranged in a linear series. Genetics 8, 393–457.Google Scholar
Karlin, S. (1979) Some principles of polymorphism and epistasis based on multilocus theory. Proc. Nat. Acad. Sci. USA 76, 541–545.CrossRefGoogle Scholar
Karlin, S. (1980) Theoretical Population Genetics. Academic Press, New York.Google Scholar
Karlin, S. and Avni, H. (1979) Central equilibria in multilocus systems III: The generalized symmetric heterotic selection regime. To appear.CrossRefGoogle Scholar
Karlin, S. and Liberman, U. (1979a) Central equilibrium in multilocus systems I. Generalized nonepistatic selection regimes. Genetics 91, 777–798.Google Scholar
Karlin, S. and Liberman, U. (1979b) Classifications and comparisons of multilocus recombination distributions. Proc. Nat. Acad. Sci. USA 75, 6332–6336.Google Scholar
Lange, K. and Riche, N. (1978) Comments on lack of interference in the four strand model of crossing over. J. Math. Biol. 5, 55–59.Google Scholar
Mather, K. (1938) Crossing-over. Biol. Rev. 13, 252–292.Google Scholar
Morgan, T. H. (1928) The Theory of Genes. Yale University Press, New Haven, CT.Google Scholar
Owen, A. R. G. (1950) The theory of genetical recombination. Adv. Genetics 3, 111–157.Google ScholarPubMed
Roux, C. Z. (1974) Hardy–Weinberg equilibria in random mating populations. Theoret. Popn Biol. 5, 393–416.Google Scholar
Schnell, F. W. (1961) Some general formulations of linkage effects in inbreeding. Genetics 46, 947–957.Google Scholar