title: Identity-by-descent matrix decomposition using latent ancestral allele models.
abstract: Genetic linkage and association studies are empowered by proper modeling of relatedness among individuals. Such relatedness can be inferred from marker and/or pedigree information. In this study, the genetic relatedness among n inbred individuals at a particular locus is expressed as an n x n square matrix Q. The elements of Q are identity-by-descent probabilities, that is, probabilities that two individuals share an allele descended from a common ancestor. In this representation the definition of the ancestral alleles and their number remains implicit. For human inspection and further analysis, an explicit representation in terms of the ancestral allele origin and the number of alleles is desirable. To this purpose, we decompose the matrix Q by a latent class model with K classes (latent ancestral alleles). Let P be an n x K matrix with assignment probabilities of n individuals to K classes constrained such that every element is nonnegative and each row sums to 1. The problem then amounts to approximating Q by PP(T), while disregarding the diagonal elements. This is not an eigenvalue problem because of the constraints on P. An efficient algorithm for calculating P is provided. We indicate the potential utility of the latent ancestral allele model. For representative locus-specific Q matrices constructed for a set of maize inbreds, the proposed model recovered the known ancestry.
authors.affiliation: Biometris, Wageningen University and Research Centre, Wageningen, The Netherlands. cajo.terbraak@wur.nl
authors.forename: Cajo J F
authors.initials: CJ
authors.lastname: ter Braak
authors.forename: Martin P
authors.initials: MP
authors.lastname: Boer
authors.forename: L Radu
authors.initials: LR
authors.lastname: Totir
authors.forename: Christopher R
authors.initials: CR
authors.lastname: Winkler
authors.forename: Oscar S
authors.initials: OS
authors.lastname: Smith
authors.forename: Marco C A M
authors.initials: MC
authors.lastname: Bink
mesh_terms: D000465:Algorithms; D000483:Alleles; D001499:Bayes Theorem; D008040:Genetic Linkage / Q000235:genetics*; D005819:Genetic Markers; D006801:Humans; D010375:Pedigree; D040641:Quantitative Trait Loci / Q000235:genetics*
chemical_list: D005819:Genetic Markers
references.citation: Theor Appl Genet. 2008 Oct;117(6):843-55
references.pmid: 18592205
references.citation: Theor Popul Biol. 2003 Sep;64(2):141-50
references.pmid: 12948676
references.citation: Phys Rev E Stat Nonlin Soft Matter Phys. 2006 Sep;74(3 Pt 2):036104
references.pmid: 17025705
references.citation: Genet Sel Evol. 2001 Nov-Dec;33(6):605-34
references.pmid: 11742632
references.citation: Am J Hum Genet. 2003 Sep;73(3):516-23
references.pmid: 12900793
references.citation: PLoS Genet. 2006 Dec;2(12):e190
references.pmid: 17194218
references.citation: Genetics. 2008 Mar;178(3):1709-23
references.pmid: 18385116
references.citation: Theor Appl Genet. 2010 Jan;120(2):429-40
references.pmid: 19921142
references.citation: Nat Genet. 2006 Aug;38(8):904-9
references.pmid: 16862161
references.citation: Genetics. 2000 Jun;155(2):945-59
references.pmid: 10835412
references.citation: Genet Sel Evol. 2001 Sep-Oct;33(5):453-71
references.pmid: 11712969
references.citation: Nature. 2003 Dec 18;426(6968):789-96
references.pmid: 14685227
references.citation: Genetics. 2009 Jul;182(3):875-88
references.pmid: 19414565
references.citation: Theor Appl Genet. 2006 Jul;113(2):288-300
references.pmid: 16791695
references.citation: Genetics. 2000 May;155(1):421-30
references.pmid: 10790414
references.citation: Am J Hum Genet. 1999 Jul;65(1):220-8
references.pmid: 10364535
references.citation: BMC Bioinformatics. 2007 Nov 13;8:440
references.pmid: 17999749
references.citation: Am J Hum Genet. 2006 Apr;78(4):629-44
references.pmid: 16532393
references.citation: Am J Hum Genet. 1997 Sep;61(3):748-60
references.pmid: 9326339
references.citation: Genet Epidemiol. 2001 Nov;21(3):224-42
references.pmid: 11668579
references.citation: Mol Ecol. 2001 Jun;10(6):1539-49
references.pmid: 11412374
references.citation: Genetics. 2000 Dec;156(4):2081-92
references.pmid: 11102397