Inclusion of genetically identical animals to a numerator relationship matrix and modification of its inverse

Abstract In the field of animal breeding, estimation of genetic parameters and prediction of breeding values are routinely conducted by analyzing quantitative traits. Using an animal model and including the direct inverse of a numerator relationship matrix (NRM) into a mixed model has made these ana...
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Autor*in:	Oikawa, Takuro [verfasserIn] Yasuda, Kazuhiro

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2009

Schlagwörter:	Variance Component Genetic Relationship Monozygotic Twin Somatic Cell Nuclear Transfer Lower Triangular Matrix

Anmerkung:	© Oikawa and Yasuda; licensee BioMed Central Ltd. 2009

Übergeordnetes Werk:	Enthalten in: Genetics, selection, evolution - London : BioMed Central, 1989, 41(2009), 1 vom: 03. März
Übergeordnetes Werk:	volume:41 ; year:2009 ; number:1 ; day:03 ; month:03

Links:	Volltext

DOI / URN:	10.1186/1297-9686-41-25

Katalog-ID:	SPR026805227

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allfields	10.1186/1297-9686-41-25 doi (DE-627)SPR026805227 (SPR)1297-9686-41-25-e DE-627 ger DE-627 rakwb eng Oikawa, Takuro verfasserin aut Inclusion of genetically identical animals to a numerator relationship matrix and modification of its inverse 2009 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Oikawa and Yasuda; licensee BioMed Central Ltd. 2009 Abstract In the field of animal breeding, estimation of genetic parameters and prediction of breeding values are routinely conducted by analyzing quantitative traits. Using an animal model and including the direct inverse of a numerator relationship matrix (NRM) into a mixed model has made these analyses possible. However, a method including a genetically identical animal (GIA) in NRM if genetic relationships between pairs of GIAs are not perfect, is still lacking. Here, we describe a method to incorporate GIAs into NRM using a K matrix in which diagonal elements are set to 1.0, off-diagonal elements between pairs of GIAs to (1-x) and the other elements to 0, where x is a constant less than 0.05. The inverse of the K matrix is then calculated directly by a simple formula. Thus, the inverse of the NRM is calculated by the products of the lower triangular matrix that identifies the parents of each individual, its transpose matrix, the inverse of the K matrix and the inverse of diagonal matrix D, in which the diagonal elements comprise a number of known parents and their inbreeding coefficients. The computing method is adaptable to the analysis of a data set including pairs of GIAs with imperfect relationships. Variance Component (dpeaa)DE-He213 Genetic Relationship (dpeaa)DE-He213 Monozygotic Twin (dpeaa)DE-He213 Somatic Cell Nuclear Transfer (dpeaa)DE-He213 Lower Triangular Matrix (dpeaa)DE-He213 Yasuda, Kazuhiro aut Enthalten in Genetics, selection, evolution London : BioMed Central, 1989 41(2009), 1 vom: 03. März (DE-627)312849052 (DE-600)2012369-3 1297-9686 nnns volume:41 year:2009 number:1 day:03 month:03 https://dx.doi.org/10.1186/1297-9686-41-25 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OLC-PHA GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_602 GBV_ILN_2003 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 41 2009 1 03 03
spelling	10.1186/1297-9686-41-25 doi (DE-627)SPR026805227 (SPR)1297-9686-41-25-e DE-627 ger DE-627 rakwb eng Oikawa, Takuro verfasserin aut Inclusion of genetically identical animals to a numerator relationship matrix and modification of its inverse 2009 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Oikawa and Yasuda; licensee BioMed Central Ltd. 2009 Abstract In the field of animal breeding, estimation of genetic parameters and prediction of breeding values are routinely conducted by analyzing quantitative traits. Using an animal model and including the direct inverse of a numerator relationship matrix (NRM) into a mixed model has made these analyses possible. However, a method including a genetically identical animal (GIA) in NRM if genetic relationships between pairs of GIAs are not perfect, is still lacking. Here, we describe a method to incorporate GIAs into NRM using a K matrix in which diagonal elements are set to 1.0, off-diagonal elements between pairs of GIAs to (1-x) and the other elements to 0, where x is a constant less than 0.05. The inverse of the K matrix is then calculated directly by a simple formula. Thus, the inverse of the NRM is calculated by the products of the lower triangular matrix that identifies the parents of each individual, its transpose matrix, the inverse of the K matrix and the inverse of diagonal matrix D, in which the diagonal elements comprise a number of known parents and their inbreeding coefficients. The computing method is adaptable to the analysis of a data set including pairs of GIAs with imperfect relationships. Variance Component (dpeaa)DE-He213 Genetic Relationship (dpeaa)DE-He213 Monozygotic Twin (dpeaa)DE-He213 Somatic Cell Nuclear Transfer (dpeaa)DE-He213 Lower Triangular Matrix (dpeaa)DE-He213 Yasuda, Kazuhiro aut Enthalten in Genetics, selection, evolution London : BioMed Central, 1989 41(2009), 1 vom: 03. März (DE-627)312849052 (DE-600)2012369-3 1297-9686 nnns volume:41 year:2009 number:1 day:03 month:03 https://dx.doi.org/10.1186/1297-9686-41-25 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OLC-PHA GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_602 GBV_ILN_2003 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 41 2009 1 03 03
allfields_unstemmed	10.1186/1297-9686-41-25 doi (DE-627)SPR026805227 (SPR)1297-9686-41-25-e DE-627 ger DE-627 rakwb eng Oikawa, Takuro verfasserin aut Inclusion of genetically identical animals to a numerator relationship matrix and modification of its inverse 2009 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Oikawa and Yasuda; licensee BioMed Central Ltd. 2009 Abstract In the field of animal breeding, estimation of genetic parameters and prediction of breeding values are routinely conducted by analyzing quantitative traits. Using an animal model and including the direct inverse of a numerator relationship matrix (NRM) into a mixed model has made these analyses possible. However, a method including a genetically identical animal (GIA) in NRM if genetic relationships between pairs of GIAs are not perfect, is still lacking. Here, we describe a method to incorporate GIAs into NRM using a K matrix in which diagonal elements are set to 1.0, off-diagonal elements between pairs of GIAs to (1-x) and the other elements to 0, where x is a constant less than 0.05. The inverse of the K matrix is then calculated directly by a simple formula. Thus, the inverse of the NRM is calculated by the products of the lower triangular matrix that identifies the parents of each individual, its transpose matrix, the inverse of the K matrix and the inverse of diagonal matrix D, in which the diagonal elements comprise a number of known parents and their inbreeding coefficients. The computing method is adaptable to the analysis of a data set including pairs of GIAs with imperfect relationships. Variance Component (dpeaa)DE-He213 Genetic Relationship (dpeaa)DE-He213 Monozygotic Twin (dpeaa)DE-He213 Somatic Cell Nuclear Transfer (dpeaa)DE-He213 Lower Triangular Matrix (dpeaa)DE-He213 Yasuda, Kazuhiro aut Enthalten in Genetics, selection, evolution London : BioMed Central, 1989 41(2009), 1 vom: 03. März (DE-627)312849052 (DE-600)2012369-3 1297-9686 nnns volume:41 year:2009 number:1 day:03 month:03 https://dx.doi.org/10.1186/1297-9686-41-25 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OLC-PHA GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_602 GBV_ILN_2003 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 41 2009 1 03 03
allfieldsGer	10.1186/1297-9686-41-25 doi (DE-627)SPR026805227 (SPR)1297-9686-41-25-e DE-627 ger DE-627 rakwb eng Oikawa, Takuro verfasserin aut Inclusion of genetically identical animals to a numerator relationship matrix and modification of its inverse 2009 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Oikawa and Yasuda; licensee BioMed Central Ltd. 2009 Abstract In the field of animal breeding, estimation of genetic parameters and prediction of breeding values are routinely conducted by analyzing quantitative traits. Using an animal model and including the direct inverse of a numerator relationship matrix (NRM) into a mixed model has made these analyses possible. However, a method including a genetically identical animal (GIA) in NRM if genetic relationships between pairs of GIAs are not perfect, is still lacking. Here, we describe a method to incorporate GIAs into NRM using a K matrix in which diagonal elements are set to 1.0, off-diagonal elements between pairs of GIAs to (1-x) and the other elements to 0, where x is a constant less than 0.05. The inverse of the K matrix is then calculated directly by a simple formula. Thus, the inverse of the NRM is calculated by the products of the lower triangular matrix that identifies the parents of each individual, its transpose matrix, the inverse of the K matrix and the inverse of diagonal matrix D, in which the diagonal elements comprise a number of known parents and their inbreeding coefficients. The computing method is adaptable to the analysis of a data set including pairs of GIAs with imperfect relationships. Variance Component (dpeaa)DE-He213 Genetic Relationship (dpeaa)DE-He213 Monozygotic Twin (dpeaa)DE-He213 Somatic Cell Nuclear Transfer (dpeaa)DE-He213 Lower Triangular Matrix (dpeaa)DE-He213 Yasuda, Kazuhiro aut Enthalten in Genetics, selection, evolution London : BioMed Central, 1989 41(2009), 1 vom: 03. März (DE-627)312849052 (DE-600)2012369-3 1297-9686 nnns volume:41 year:2009 number:1 day:03 month:03 https://dx.doi.org/10.1186/1297-9686-41-25 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OLC-PHA GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_602 GBV_ILN_2003 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 41 2009 1 03 03
allfieldsSound	10.1186/1297-9686-41-25 doi (DE-627)SPR026805227 (SPR)1297-9686-41-25-e DE-627 ger DE-627 rakwb eng Oikawa, Takuro verfasserin aut Inclusion of genetically identical animals to a numerator relationship matrix and modification of its inverse 2009 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Oikawa and Yasuda; licensee BioMed Central Ltd. 2009 Abstract In the field of animal breeding, estimation of genetic parameters and prediction of breeding values are routinely conducted by analyzing quantitative traits. Using an animal model and including the direct inverse of a numerator relationship matrix (NRM) into a mixed model has made these analyses possible. However, a method including a genetically identical animal (GIA) in NRM if genetic relationships between pairs of GIAs are not perfect, is still lacking. Here, we describe a method to incorporate GIAs into NRM using a K matrix in which diagonal elements are set to 1.0, off-diagonal elements between pairs of GIAs to (1-x) and the other elements to 0, where x is a constant less than 0.05. The inverse of the K matrix is then calculated directly by a simple formula. Thus, the inverse of the NRM is calculated by the products of the lower triangular matrix that identifies the parents of each individual, its transpose matrix, the inverse of the K matrix and the inverse of diagonal matrix D, in which the diagonal elements comprise a number of known parents and their inbreeding coefficients. The computing method is adaptable to the analysis of a data set including pairs of GIAs with imperfect relationships. Variance Component (dpeaa)DE-He213 Genetic Relationship (dpeaa)DE-He213 Monozygotic Twin (dpeaa)DE-He213 Somatic Cell Nuclear Transfer (dpeaa)DE-He213 Lower Triangular Matrix (dpeaa)DE-He213 Yasuda, Kazuhiro aut Enthalten in Genetics, selection, evolution London : BioMed Central, 1989 41(2009), 1 vom: 03. März (DE-627)312849052 (DE-600)2012369-3 1297-9686 nnns volume:41 year:2009 number:1 day:03 month:03 https://dx.doi.org/10.1186/1297-9686-41-25 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OLC-PHA GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_602 GBV_ILN_2003 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 41 2009 1 03 03
language	English
source	Enthalten in Genetics, selection, evolution 41(2009), 1 vom: 03. März volume:41 year:2009 number:1 day:03 month:03
sourceStr	Enthalten in Genetics, selection, evolution 41(2009), 1 vom: 03. März volume:41 year:2009 number:1 day:03 month:03
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	Variance Component Genetic Relationship Monozygotic Twin Somatic Cell Nuclear Transfer Lower Triangular Matrix
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container_title	Genetics, selection, evolution
authorswithroles_txt_mv	Oikawa, Takuro @@aut@@ Yasuda, Kazuhiro @@aut@@
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author	Oikawa, Takuro
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topic_title	Inclusion of genetically identical animals to a numerator relationship matrix and modification of its inverse Variance Component (dpeaa)DE-He213 Genetic Relationship (dpeaa)DE-He213 Monozygotic Twin (dpeaa)DE-He213 Somatic Cell Nuclear Transfer (dpeaa)DE-He213 Lower Triangular Matrix (dpeaa)DE-He213
topic	misc Variance Component misc Genetic Relationship misc Monozygotic Twin misc Somatic Cell Nuclear Transfer misc Lower Triangular Matrix
topic_unstemmed	misc Variance Component misc Genetic Relationship misc Monozygotic Twin misc Somatic Cell Nuclear Transfer misc Lower Triangular Matrix
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title	Inclusion of genetically identical animals to a numerator relationship matrix and modification of its inverse
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title_full	Inclusion of genetically identical animals to a numerator relationship matrix and modification of its inverse
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title_sort	inclusion of genetically identical animals to a numerator relationship matrix and modification of its inverse
title_auth	Inclusion of genetically identical animals to a numerator relationship matrix and modification of its inverse
abstract	Abstract In the field of animal breeding, estimation of genetic parameters and prediction of breeding values are routinely conducted by analyzing quantitative traits. Using an animal model and including the direct inverse of a numerator relationship matrix (NRM) into a mixed model has made these analyses possible. However, a method including a genetically identical animal (GIA) in NRM if genetic relationships between pairs of GIAs are not perfect, is still lacking. Here, we describe a method to incorporate GIAs into NRM using a K matrix in which diagonal elements are set to 1.0, off-diagonal elements between pairs of GIAs to (1-x) and the other elements to 0, where x is a constant less than 0.05. The inverse of the K matrix is then calculated directly by a simple formula. Thus, the inverse of the NRM is calculated by the products of the lower triangular matrix that identifies the parents of each individual, its transpose matrix, the inverse of the K matrix and the inverse of diagonal matrix D, in which the diagonal elements comprise a number of known parents and their inbreeding coefficients. The computing method is adaptable to the analysis of a data set including pairs of GIAs with imperfect relationships. © Oikawa and Yasuda; licensee BioMed Central Ltd. 2009
abstractGer	Abstract In the field of animal breeding, estimation of genetic parameters and prediction of breeding values are routinely conducted by analyzing quantitative traits. Using an animal model and including the direct inverse of a numerator relationship matrix (NRM) into a mixed model has made these analyses possible. However, a method including a genetically identical animal (GIA) in NRM if genetic relationships between pairs of GIAs are not perfect, is still lacking. Here, we describe a method to incorporate GIAs into NRM using a K matrix in which diagonal elements are set to 1.0, off-diagonal elements between pairs of GIAs to (1-x) and the other elements to 0, where x is a constant less than 0.05. The inverse of the K matrix is then calculated directly by a simple formula. Thus, the inverse of the NRM is calculated by the products of the lower triangular matrix that identifies the parents of each individual, its transpose matrix, the inverse of the K matrix and the inverse of diagonal matrix D, in which the diagonal elements comprise a number of known parents and their inbreeding coefficients. The computing method is adaptable to the analysis of a data set including pairs of GIAs with imperfect relationships. © Oikawa and Yasuda; licensee BioMed Central Ltd. 2009
abstract_unstemmed	Abstract In the field of animal breeding, estimation of genetic parameters and prediction of breeding values are routinely conducted by analyzing quantitative traits. Using an animal model and including the direct inverse of a numerator relationship matrix (NRM) into a mixed model has made these analyses possible. However, a method including a genetically identical animal (GIA) in NRM if genetic relationships between pairs of GIAs are not perfect, is still lacking. Here, we describe a method to incorporate GIAs into NRM using a K matrix in which diagonal elements are set to 1.0, off-diagonal elements between pairs of GIAs to (1-x) and the other elements to 0, where x is a constant less than 0.05. The inverse of the K matrix is then calculated directly by a simple formula. Thus, the inverse of the NRM is calculated by the products of the lower triangular matrix that identifies the parents of each individual, its transpose matrix, the inverse of the K matrix and the inverse of diagonal matrix D, in which the diagonal elements comprise a number of known parents and their inbreeding coefficients. The computing method is adaptable to the analysis of a data set including pairs of GIAs with imperfect relationships. © Oikawa and Yasuda; licensee BioMed Central Ltd. 2009
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title_short	Inclusion of genetically identical animals to a numerator relationship matrix and modification of its inverse
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Inclusion of genetically identical animals to a numerator relationship matrix and modification of its inverse

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