A rapid method for computing the inverse of the gametic covariance matrix between relatives for a marked Quantitative Trait Locus

Abdel-Azim, G.; Freeman, A.E.

doi:10.1186/1297-9686-33-2-153

Cited by 20 publications

(33 citation statements)

References 19 publications

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“…Abdel-Azim's and Freeman's example [1] is used to demonstrate that G and its inverse are not unique but depend on the mode of gamete identification. With the assumptions made above and a recombination rate r > 0, gamete identification by markers is considered first.…”

Section: Computing G and Its Inversementioning

confidence: 99%

“…where f i is the conditional probability that 2 homologous alleles at the MQTL in individual i are identical by decent, given observed marker genotypes M (conditional inbreeding coefficient of individual i for the MQTL, given M), which can be calculated according to formula (11) in [21], and Abdel-Azim and Freeman [1] gave an algorithm for the decomposition of G by G = BDB , where B is a lower triangular matrix and D is a block diagonal matrix with (2 × 2)-matrices D i from (4) in the ith block. B can be recursively computed as…”

Section: Gametes Are Identified By Markersmentioning

confidence: 99%

“…An alternative mode of gamete identification has been employed by Wang et al [21] and Abdel-Azim and Freeman [1]: for an individual with a heterozygous (1, 2) marker genotype, the gamete with the first (1, in alphanumerical order) marker allele is taken to carry the first and the gamete with the other (2) allele, the second MQTL allele effect. This is denoted as "gamete identification by markers".…”

Section: Introductionmentioning

confidence: 99%

“…Abdel-Azim and Freeman [1] -based on the results of [2] and [21] -developed a numerically efficient algorithm for the computation of G and its inverse. This algorithm has been tailored for situations where G has full row and column rank and the number of MQTL effects is twice the number of animals in the pedigree.…”

Section: Introductionmentioning

confidence: 99%

“…Then a generalization of the Abdel-Azim and Freeman algorithm [1] is developed, allowing for the elimination of linear dependencies in G and its inverse.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Identification of gametes and treatment of linear dependencies in the gametic QTL-relationship matrix and its inverse

2004

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-The estimation of gametic effects via marker-assisted BLUP requires the inverse of the conditional gametic relationship matrix G. Both gametes of each animal can either be identified (distinguished) by markers or by parental origin. By example, it was shown that the conditional gametic relationship matrix is not unique but depends on the mode of gamete identification. The sum of both gametic effects of each animal -and therefore its estimated breeding value -remains however unaffected. A previously known algorithm for setting up the inverse of G was generalized in order to eliminate the dependencies between columns and rows of G. In the presence of dependencies the rank of G also depends on the mode of gamete identification. A unique transformation of estimates of QTL genotypic effects into QTL gametic effects was proven to be impossible. The properties of both modes of gamete identification in the fields of application are discussed. marker assisted selection / best linear unbiased prediction / linkage analysis / gametic relationship matrix

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Section: Computing G and Its Inversementioning

confidence: 99%

Section: Gametes Are Identified By Markersmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…Then a generalization of the Abdel-Azim and Freeman algorithm [1] is developed, allowing for the elimination of linear dependencies in G and its inverse.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Identification of gametes and treatment of linear dependencies in the gametic QTL-relationship matrix and its inverse

2004

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Prediction of identity by descent probabilities from marker-haplotypes

Meuwissen¹,

Goddard

2001

Genet. Sel. Evol.

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-The prediction of identity by descent (IBD) probabilities is essential for all methods that map quantitative trait loci (QTL). The IBD probabilities may be predicted from marker genotypes and/or pedigree information. Here, a method is presented that predicts IBD probabilities at a given chromosomal location given data on a haplotype of markers spanning that position. The method is based on a simplification of the coalescence process, and assumes that the number of generations since the base population and effective population size is known, although effective size may be estimated from the data. The probability that two gametes are IBD at a particular locus increases as the number of markers surrounding the locus with identical alleles increases. This effect is more pronounced when effective population size is high. Hence as effective population size increases, the IBD probabilities become more sensitive to the marker data which should favour finer scale mapping of the QTL. The IBD probability prediction method was developed for the situation where the pedigree of the animals was unknown (i.e. all information came from the marker genotypes), and the situation where, say T, generations of unknown pedigree are followed by some generations where pedigree and marker genotypes are known.identity by descent / haplotype analysis / coalescence process / linkage disequilibrium / QTL mapping

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The covariance between relatives conditional on genetic markers

2002

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-The development of molecular genotyping techniques makes it possible to analyze quantitative traits on the basis of individual loci. With marker information, the classical theory of estimating the genetic covariance between relatives can be reformulated to improve the accuracy of estimation. In this study, an algorithm was derived for computing the conditional covariance between relatives given genetic markers. Procedures for calculating the conditional relationship coefficients for additive, dominance, additive by additive, additive by dominance, dominance by additive and dominance by dominance effects were developed. The relationship coefficients were computed based on conditional QTL allelic transmission probabilities, which were inferred from the marker allelic transmission probabilities. An example data set with pedigree and linked markers was used to demonstrate the methods developed. Although this study dealt with two QTLs coupled with linked markers, the same principle can be readily extended to the situation of multiple QTL. The treatment of missing marker information and unknown linkage phase between markers for calculating the covariance between relatives was discussed.covariance between relatives / molecular marker / QTL / transmission probability / relationship matrix

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A rapid method for computing the inverse of the gametic covariance matrix between relatives for a marked Quantitative Trait Locus

Cited by 20 publications

References 19 publications

Identification of gametes and treatment of linear dependencies in the gametic QTL-relationship matrix and its inverse

Identification of gametes and treatment of linear dependencies in the gametic QTL-relationship matrix and its inverse

Prediction of identity by descent probabilities from marker-haplotypes

The covariance between relatives conditional on genetic markers

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