The effect of the H −1 scaling factors τ and ω on the structure of H in the single-step procedure
Abstract Background The single-step covariance matrix H combines the pedigree-based relationship matrix $${\mathbf {A}}$$ A with the more accurate information on realized relatedness of genotyped individuals represented by the genomic relationship matrix $${\mathbf {G}}$$ G . In particular, to impro...
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doaj-77220b7ad8a9418f9d1d4a01390b3d792020-11-24T20:45:01ZdeuBMCGenetics Selection Evolution1297-96862018-04-015011910.1186/s12711-018-0386-xThe effect of the H −1 scaling factors τ and ω on the structure of H in the single-step procedureJohannes W. R. Martini0Matias F. Schrauf1Carolina A. Garcia-Baccino2Eduardo C. G. Pimentel3Sebastian Munilla4Andres Rogberg-Muñoz5Rodolfo J. C. Cantet6Christian Reimer7Ning Gao8Valentin Wimmer9Henner Simianer10KWS SAAT SEDepartamento de Producción Animal, Facultad de Agronomía, Universidad de Buenos AiresDepartamento de Producción Animal, Facultad de Agronomía, Universidad de Buenos AiresInstitute of Animal Breeding, Bavarian State Research Center for AgricultureDepartamento de Producción Animal, Facultad de Agronomía, Universidad de Buenos AiresDepartamento de Producción Animal, Facultad de Agronomía, Universidad de Buenos AiresDepartamento de Producción Animal, Facultad de Agronomía, Universidad de Buenos AiresAnimal Breeding and Genetics Group, Center for Integrated Breeding Research, University of GoettingenAnimal Breeding and Genetics Group, Center for Integrated Breeding Research, University of GoettingenKWS SAAT SEAnimal Breeding and Genetics Group, Center for Integrated Breeding Research, University of GoettingenAbstract Background The single-step covariance matrix H combines the pedigree-based relationship matrix $${\mathbf {A}}$$ A with the more accurate information on realized relatedness of genotyped individuals represented by the genomic relationship matrix $${\mathbf {G}}$$ G . In particular, to improve convergence behavior of iterative approaches and to reduce inflation, two weights $$\tau$$ τ and $$\omega$$ ω have been introduced in the definition of $${\mathbf {H}}^{-1}$$ H-1 , which blend the inverse of a part of $${\mathbf {A}}$$ A with the inverse of $${\mathbf {G}}$$ G . Since the definition of this blending is based on the equation describing $${\mathbf {H}}^{-1}$$ H-1 , its impact on the structure of $${\mathbf {H}}$$ H is not obvious. In a joint discussion, we considered the question of the shape of $${\mathbf {H}}$$ H for non-trivial $$\tau$$ τ and $$\omega$$ ω . Results Here, we present the general matrix $${\mathbf {H}}$$ H as a function of these parameters and discuss its structure and properties. Moreover, we screen for optimal values of $$\tau$$ τ and $$\omega$$ ω with respect to predictive ability, inflation and iterations up to convergence on a well investigated, publicly available wheat data set. Conclusion Our results may help the reader to develop a better understanding for the effects of changes of $$\tau$$ τ and $$\omega$$ ω on the covariance model. In particular, we give theoretical arguments that as a general tendency, inflation will be reduced by increasing $$\tau$$ τ or by decreasing $$\omega$$ ω .http://link.springer.com/article/10.1186/s12711-018-0386-x |
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DOAJ |
language |
deu |
format |
Article |
sources |
DOAJ |
author |
Johannes W. R. Martini Matias F. Schrauf Carolina A. Garcia-Baccino Eduardo C. G. Pimentel Sebastian Munilla Andres Rogberg-Muñoz Rodolfo J. C. Cantet Christian Reimer Ning Gao Valentin Wimmer Henner Simianer |
spellingShingle |
Johannes W. R. Martini Matias F. Schrauf Carolina A. Garcia-Baccino Eduardo C. G. Pimentel Sebastian Munilla Andres Rogberg-Muñoz Rodolfo J. C. Cantet Christian Reimer Ning Gao Valentin Wimmer Henner Simianer The effect of the H −1 scaling factors τ and ω on the structure of H in the single-step procedure Genetics Selection Evolution |
author_facet |
Johannes W. R. Martini Matias F. Schrauf Carolina A. Garcia-Baccino Eduardo C. G. Pimentel Sebastian Munilla Andres Rogberg-Muñoz Rodolfo J. C. Cantet Christian Reimer Ning Gao Valentin Wimmer Henner Simianer |
author_sort |
Johannes W. R. Martini |
title |
The effect of the H −1 scaling factors τ and ω on the structure of H in the single-step procedure |
title_short |
The effect of the H −1 scaling factors τ and ω on the structure of H in the single-step procedure |
title_full |
The effect of the H −1 scaling factors τ and ω on the structure of H in the single-step procedure |
title_fullStr |
The effect of the H −1 scaling factors τ and ω on the structure of H in the single-step procedure |
title_full_unstemmed |
The effect of the H −1 scaling factors τ and ω on the structure of H in the single-step procedure |
title_sort |
effect of the h −1 scaling factors τ and ω on the structure of h in the single-step procedure |
publisher |
BMC |
series |
Genetics Selection Evolution |
issn |
1297-9686 |
publishDate |
2018-04-01 |
description |
Abstract Background The single-step covariance matrix H combines the pedigree-based relationship matrix $${\mathbf {A}}$$ A with the more accurate information on realized relatedness of genotyped individuals represented by the genomic relationship matrix $${\mathbf {G}}$$ G . In particular, to improve convergence behavior of iterative approaches and to reduce inflation, two weights $$\tau$$ τ and $$\omega$$ ω have been introduced in the definition of $${\mathbf {H}}^{-1}$$ H-1 , which blend the inverse of a part of $${\mathbf {A}}$$ A with the inverse of $${\mathbf {G}}$$ G . Since the definition of this blending is based on the equation describing $${\mathbf {H}}^{-1}$$ H-1 , its impact on the structure of $${\mathbf {H}}$$ H is not obvious. In a joint discussion, we considered the question of the shape of $${\mathbf {H}}$$ H for non-trivial $$\tau$$ τ and $$\omega$$ ω . Results Here, we present the general matrix $${\mathbf {H}}$$ H as a function of these parameters and discuss its structure and properties. Moreover, we screen for optimal values of $$\tau$$ τ and $$\omega$$ ω with respect to predictive ability, inflation and iterations up to convergence on a well investigated, publicly available wheat data set. Conclusion Our results may help the reader to develop a better understanding for the effects of changes of $$\tau$$ τ and $$\omega$$ ω on the covariance model. In particular, we give theoretical arguments that as a general tendency, inflation will be reduced by increasing $$\tau$$ τ or by decreasing $$\omega$$ ω . |
url |
http://link.springer.com/article/10.1186/s12711-018-0386-x |
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