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Sampling genotypes in large pedigrees with loops

Genetics Selection Evolution volume 33, Article number: 337 (2001) Cite this article

Abstract

Markov chain Monte Carlo (MCMC) methods have been proposed to overcome computational problems in linkage and segregation analyses. This approach involves sampling genotypes at the marker and trait loci. Scalar-Gibbs is easy to implement, and it is widely used in genetics. However, the Markov chain that corresponds to scalar-Gibbs may not be irreducible when the marker locus has more than two alleles, and even when the chain is irreducible, mixing has been observed to be slow. These problems do not arise if the genotypes are sampled jointly from the entire pedigree. This paper proposes a method to jointly sample genotypes. The method combines the Elston-Stewart algorithm and iterative peeling, and is called the ESIP sampler. For a hypothetical pedigree, genotype probabilities are estimated from samples obtained using ESIP and also scalar-Gibbs. Approximate probabilities were also obtained by iterative peeling. Comparisons of these with exact genotypic probabilities obtained by the Elston-Stewart algorithm showed that ESIP and iterative peeling yielded genotypic probabilities that were very close to the exact values. Nevertheless, estimated probabilities from scalar-Gibbs with a chain of length 235 000, including a burn-in of 200 000 steps, were less accurate than probabilities estimated using ESIP with a chain of length 10 000, with a burn-in of 5 000 steps. The effective chain size (ECS) was estimated from the last 25 000 elements of the chain of length 125 000. For one of the ESIP samplers, the ECS ranged from 21 579 to 22 741, while for the scalar-Gibbs sampler, the ECS ranged from 64 to 671. Genotype probabilities were also estimated for a large real pedigree consisting of 3 223 individuals. For this pedigree, it is not feasible to obtain exact genotype probabilities by the Elston-Stewart algorithm. ESIP and iterative peeling yielded very similar results. However, results from scalar-Gibbs were less accurate.

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Authors and Affiliations

  1. Department of Animal Science, Iowa State University, 225 Kildee Hall, Ames, IA, 50011, USA

    Soledad A. Fernández, Rohan L. Fernando & Liviu R. Totir

  2. Department of Statistics, Iowa State University, 225 Kildee Hall, Ames, IA, 50011, USA

    Soledad A. Fernández & Alicia L Carriquiry

  3. Lawrence H. Baker Center for Bioinformatics and Biological Statistics, Iowa State University, Ames, IA, 50011, USA

    Rohan L. Fernando & Alicia L Carriquiry

  4. Danish Institute of Animal Science, Foulum, Denmark

    Bernt Guldbrandtsen

Authors
  1. Soledad A. Fernández
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  2. Rohan L. Fernando
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  3. Bernt Guldbrandtsen
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  4. Liviu R. Totir
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  5. Alicia L Carriquiry
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Correspondence to Rohan L. Fernando.

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This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated.

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Fernández, S.A., Fernando, R.L., Guldbrandtsen, B. et al. Sampling genotypes in large pedigrees with loops. Genet Sel Evol 33, 337 (2001). https://doi.org/10.1186/1297-9686-33-4-337

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  • DOI: https://doi.org/10.1186/1297-9686-33-4-337

Keywords

Genetics Selection Evolution

ISSN: 1297-9686