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Equivalence of multibreed animal models and hierarchical Bayes analysis for maternally influenced traits.

Leguizamón SM, Cantet RJ - Genet. Sel. Evol. (2010)

Bottom Line: Our argument is based on redefining the vectors of breeding values by breed origin such that they do not include individuals with contributions.The extension to include maternal effects and the estimation of the (co)variance components through the hierarchical Bayes analysis are then straightforward.In turn, the contribution of the segregation variance was not significant in either case, which suggests that the allelic frequencies in the two parental breeds were similar.

View Article: PubMed Central - HTML - PubMed

Affiliation: Departamento de Producción Animal, Universidad de Buenos Aires, Argentina. munilla@agro.uba.ar

ABSTRACT

Background: It has been argued that multibreed animal models should include a heterogeneous covariance structure. However, the estimation of the (co)variance components is not an easy task, because these parameters can not be factored out from the inverse of the additive genetic covariance matrix. An alternative model, based on the decomposition of the genetic covariance matrix by source of variability, provides a much simpler formulation. In this study, we formalize the equivalence between this alternative model and the one derived from the quantitative genetic theory. Further, we extend the model to include maternal effects and, in order to estimate the (co)variance components, we describe a hierarchical Bayes implementation. Finally, we implement the model to weaning weight data from an Angus x Hereford crossbred experiment.

Methods: Our argument is based on redefining the vectors of breeding values by breed origin such that they do not include individuals with contributions. Next, we define matrices that retrieve the -row and the -column pattern and, by means of appropriate algebraic operations, we demonstrate the equivalence. The extension to include maternal effects and the estimation of the (co)variance components through the hierarchical Bayes analysis are then straightforward. A FORTRAN 90 Gibbs sampler was specifically programmed and executed to estimate the (co)variance components of the Angus x Hereford population.

Results: In general, genetic (co)variance components showed marginal posterior densities with a high degree of symmetry, except for the segregation components. Angus and Hereford breeds contributed with 50.26% and 41.73% of the total direct additive variance, and with 23.59% and 59.65% of the total maternal additive variance. In turn, the contribution of the segregation variance was not significant in either case, which suggests that the allelic frequencies in the two parental breeds were similar.

Conclusion: The multibreed maternal animal model introduced in this study simplifies the problem of estimating (co)variance components in the framework of a hierarchical Bayes analysis. Using this approach, we obtained for the first time estimates of the full set of genetic (co)variance components. It would be interesting to assess the performance of the procedure with field data, especially when interbreed information is limited.

Show MeSH
Estimated marginal posterior densities for genetic (co)variance components disaggregated by breed source of variability.
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Figure 1: Estimated marginal posterior densities for genetic (co)variance components disaggregated by breed source of variability.

Mentions: Table 3 displays the marginal posterior summaries for the eleven scalar (co)variance components of the fitted model. Additionally, Figure 1 displays the corresponding density shapes that were estimated using a non-parametric technique based on a Gaussian kernel [36]. In general, genetic (co)variance components showed marginal posterior densities with high degree of symmetry, except for those components associated with the segregation between breeds. In particular, while the mean values of direct and maternal segregation variances were respectively = 9.62 kg2 and = 13.37 kg2, the modes for both direct and maternal segregation variances were about 3 Kg2.


Equivalence of multibreed animal models and hierarchical Bayes analysis for maternally influenced traits.

Leguizamón SM, Cantet RJ - Genet. Sel. Evol. (2010)

Estimated marginal posterior densities for genetic (co)variance components disaggregated by breed source of variability.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC2909157&req=5

Figure 1: Estimated marginal posterior densities for genetic (co)variance components disaggregated by breed source of variability.
Mentions: Table 3 displays the marginal posterior summaries for the eleven scalar (co)variance components of the fitted model. Additionally, Figure 1 displays the corresponding density shapes that were estimated using a non-parametric technique based on a Gaussian kernel [36]. In general, genetic (co)variance components showed marginal posterior densities with high degree of symmetry, except for those components associated with the segregation between breeds. In particular, while the mean values of direct and maternal segregation variances were respectively = 9.62 kg2 and = 13.37 kg2, the modes for both direct and maternal segregation variances were about 3 Kg2.

Bottom Line: Our argument is based on redefining the vectors of breeding values by breed origin such that they do not include individuals with contributions.The extension to include maternal effects and the estimation of the (co)variance components through the hierarchical Bayes analysis are then straightforward.In turn, the contribution of the segregation variance was not significant in either case, which suggests that the allelic frequencies in the two parental breeds were similar.

View Article: PubMed Central - HTML - PubMed

Affiliation: Departamento de Producción Animal, Universidad de Buenos Aires, Argentina. munilla@agro.uba.ar

ABSTRACT

Background: It has been argued that multibreed animal models should include a heterogeneous covariance structure. However, the estimation of the (co)variance components is not an easy task, because these parameters can not be factored out from the inverse of the additive genetic covariance matrix. An alternative model, based on the decomposition of the genetic covariance matrix by source of variability, provides a much simpler formulation. In this study, we formalize the equivalence between this alternative model and the one derived from the quantitative genetic theory. Further, we extend the model to include maternal effects and, in order to estimate the (co)variance components, we describe a hierarchical Bayes implementation. Finally, we implement the model to weaning weight data from an Angus x Hereford crossbred experiment.

Methods: Our argument is based on redefining the vectors of breeding values by breed origin such that they do not include individuals with contributions. Next, we define matrices that retrieve the -row and the -column pattern and, by means of appropriate algebraic operations, we demonstrate the equivalence. The extension to include maternal effects and the estimation of the (co)variance components through the hierarchical Bayes analysis are then straightforward. A FORTRAN 90 Gibbs sampler was specifically programmed and executed to estimate the (co)variance components of the Angus x Hereford population.

Results: In general, genetic (co)variance components showed marginal posterior densities with a high degree of symmetry, except for the segregation components. Angus and Hereford breeds contributed with 50.26% and 41.73% of the total direct additive variance, and with 23.59% and 59.65% of the total maternal additive variance. In turn, the contribution of the segregation variance was not significant in either case, which suggests that the allelic frequencies in the two parental breeds were similar.

Conclusion: The multibreed maternal animal model introduced in this study simplifies the problem of estimating (co)variance components in the framework of a hierarchical Bayes analysis. Using this approach, we obtained for the first time estimates of the full set of genetic (co)variance components. It would be interesting to assess the performance of the procedure with field data, especially when interbreed information is limited.

Show MeSH