Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-23T17:32:08.627Z Has data issue: false hasContentIssue false

Linked loci in finite populations

Published online by Cambridge University Press:  14 July 2016

P. Holgate*
Affiliation:
Birkbeck College, London
*
Postal address: Department of Statistics, Birkbeck College, Malet St., London WC1E 7HX, U.K.

Abstract

A finite population of gametes is studied, classified according to the alleles present at k linked loci. A canonical method of following the joint probability distribution of the gametic types from generation to generation is developed. It is shown how the investigation of the rate of first fixation can be systematised. Explicit results are given for k = 2, and, although not so complete, for k = 3.

Type
Research Papers
Copyright
Copyright © Applied Probability Trust 1981 

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.)

References

Abraham, V. M. (1980a) Linearising quadratic transformations in genetic algebras. Proc. London Math. Soc. 40, 346363.CrossRefGoogle Scholar
Abraham, V. M. (1980b) The induced linear transformation in a genetic algebra. Proc. London Math. Soc. 40, 364384.CrossRefGoogle Scholar
Cannings, C. (1974), (1975) The latent roots of certain Markov chains arising in genetics: A new approach. I. Haploid models. Adv. Appl. Prob. 6, 260290; II. Further haploid models. 7, 264–282.CrossRefGoogle Scholar
Hill, W. G. and Robertson, A. (1966) The effect of linkage on limits to artificial selection. Genet. Res. 8, 269294.CrossRefGoogle ScholarPubMed
Hill, W. G. and Robertson, A. (1968) Linkage disequilibrium in finite populations. Theoret. Appl. Genet. 38, 226231.CrossRefGoogle ScholarPubMed
Holgate, P. (1967) Sequences of powers in genetic algebras. J. London Math. Soc. 42, 489496.CrossRefGoogle Scholar
Holgate, P. (1968) The genetic algebra of k linked loci. Proc. London Math. Soc. (3) 18, 315327.CrossRefGoogle Scholar
Holgate, P. (1979) Canonical multiplication in the genetic algebra for linked loci. Linear Alg. Appl. 26, 281286.CrossRefGoogle Scholar
Holgate, P. (1981) Population algebras (with discussion). J. R. Statist. Soc. B 43, 119.Google Scholar
Karlin, S. and Mcgregor, J. (1968) Rates and probabilities of fixation for two locus random mating finite populations without selection. Genetics 58, 141159.CrossRefGoogle ScholarPubMed
Seront, D. and Villard, M. (1972) Linearisation of crossing over and mutation in a finite random mating population. Theoret. Popn Biol. 3, 249257.CrossRefGoogle Scholar
Watterson, G. A. (1970a) The effect of linkage in a finite random mating population. Theoret. Popn Biol. 1, 7287.CrossRefGoogle Scholar
Watterson, G. A. (1970b) On the equivalence of random mating and random union of gametes models in finite monoecious populations. Theoret. Popn Biol. 1, 233250.CrossRefGoogle ScholarPubMed
Wörz-Busekros, A. (1980) Algebras in Genetics. Lecture Notes in Biomathematics 36, Springer-Verlag, Berlin.CrossRefGoogle Scholar