---
_id: '3624'
abstract:
- lang: eng
  text: 'The state of a diploid population segregating for two alleles at each of
    n loci is described by 22(n) genotype frequencies, or equivalently, by allele
    frequencies and by multilocus moments or cumulants of various orders. These measures
    of linkage disequilibrium cannot usually be determined, both because one cannot
    tell whether a gene came from the maternal or paternal gamete, and because such
    a large number of parameters cannot be estimated even from large samples. Simplifying
    assumptions must therefore be made. This paper sets out methods for estimating
    multilocus genotype frequencies which are appropriate for unlinked neutral loci,
    and for populations that are ultimately derived by mixing of two source populations.
    In such a hybrid population, all multilocus associations depend primarily on the
    number of loci involved that derive from the maternal genome, and the number derived
    from the paternal genome Allele frequencies may differ across loci, and the contribution
    of each locus to multilocus associations may be scaled by the difference in allele
    frequency between source populations for that locus (δp ≤ 1). For example, the
    cumulant describing the association between genes i, j, k from the maternal genome,
    and genes i, l from the paternal genome is K(tJ,k,iλ*), = δp(i)/2 δp(J) δp(k)
    δp(l) κ3,2. The state of the population is described by n allele frequencies;
    n divergences, δp; and by a symmetric matrix of cumulants, κ(J,K) (J = 0 ,...,
    n, K = 0 ,..., n). Expressions for these cumulants under short- and long-range
    migration are given. Two methods for estimating the cumulants are described: a
    simple method based on multivariate moments, and a maximum likelihood procedure,
    which uses the Metropolis algorithm. Both methods perform well when tested against
    simulations with two or four loci.'
acknowledgement: This work was supported by grant MMI09726 from the BBSRC/EPSRC, and
  by the Darwin Trust of Edinburgh. I am grateful to W. G. Hill, L. Kruuk and M. Orive,
  and to the referees, for their helpful comments on the manuscript.
article_processing_charge: No
article_type: original
author:
- first_name: Nicholas H
  full_name: Barton, Nicholas H
  id: 4880FE40-F248-11E8-B48F-1D18A9856A87
  last_name: Barton
  orcid: 0000-0002-8548-5240
citation:
  ama: Barton NH. Estimating multilocus linkage disequilibria. <i>Heredity</i>. 2000;84(3):373-389.
    doi:<a href="https://doi.org/10.1046/j.1365-2540.2000.00683.x">10.1046/j.1365-2540.2000.00683.x</a>
  apa: Barton, N. H. (2000). Estimating multilocus linkage disequilibria. <i>Heredity</i>.
    Nature Publishing Group. <a href="https://doi.org/10.1046/j.1365-2540.2000.00683.x">https://doi.org/10.1046/j.1365-2540.2000.00683.x</a>
  chicago: Barton, Nicholas H. “Estimating Multilocus Linkage Disequilibria.” <i>Heredity</i>.
    Nature Publishing Group, 2000. <a href="https://doi.org/10.1046/j.1365-2540.2000.00683.x">https://doi.org/10.1046/j.1365-2540.2000.00683.x</a>.
  ieee: N. H. Barton, “Estimating multilocus linkage disequilibria,” <i>Heredity</i>,
    vol. 84, no. 3. Nature Publishing Group, pp. 373–389, 2000.
  ista: Barton NH. 2000. Estimating multilocus linkage disequilibria. Heredity. 84(3),
    373–389.
  mla: Barton, Nicholas H. “Estimating Multilocus Linkage Disequilibria.” <i>Heredity</i>,
    vol. 84, no. 3, Nature Publishing Group, 2000, pp. 373–89, doi:<a href="https://doi.org/10.1046/j.1365-2540.2000.00683.x">10.1046/j.1365-2540.2000.00683.x</a>.
  short: N.H. Barton, Heredity 84 (2000) 373–389.
date_created: 2018-12-11T12:04:18Z
date_published: 2000-03-01T00:00:00Z
date_updated: 2023-05-02T12:04:03Z
day: '01'
doi: 10.1046/j.1365-2540.2000.00683.x
extern: '1'
external_id:
  pmid:
  - '10762407'
intvolume: '        84'
issue: '3'
language:
- iso: eng
main_file_link:
- url: https://www.nature.com/articles/6886830
month: '03'
oa_version: None
page: 373 - 389
pmid: 1
publication: Heredity
publication_identifier:
  issn:
  - 0018-067X
publication_status: published
publisher: Nature Publishing Group
publist_id: '2759'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Estimating multilocus linkage disequilibria
type: journal_article
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
volume: 84
year: '2000'
...