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Registro completo
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Biblioteca (s) : |
INIA Las Brujas. |
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Fecha actual : |
10/09/2014 |
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Actualizado : |
18/06/2019 |
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Tipo de producción científica : |
Artículos en Revistas Indexadas Internacionales |
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Circulación / Nivel : |
A - 1 |
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Autor : |
MISZTAL, I.; LEGARRA, A.; AGUILAR, I. |
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Afiliación : |
IGNACY MISZTAL, Universidad de Georgia (UG); ANDRÉS LEGARRA, INRA (Institut National de la Recherche Agronomique); IGNACIO AGUILAR GARCIA, Instituto Nacional de Investigación Agropecuaria (INIA), Uruguay. |
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Título : |
Using recursion to compute the inverse of the genomic relationship matrix. |
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Fecha de publicación : |
2014 |
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Fuente / Imprenta : |
Journal of Dairy Science, 2014, v.97, no.6, p.3943-3952. OPEN ACCESS. |
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ISSN : |
0022-0302 |
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DOI : |
http://dx.doi.org/10.3168/jds.2013-7752 |
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Idioma : |
Inglés |
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Notas : |
Article history: Received November 22, 2013. // Accepted February 10, 2014. |
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Contenido : |
ABSTRACT.
Computing the inverse of the genomic relationship matrix using recursion was investigated. A traditional algorithm to invert the numerator relationship matrix is based on the observation that the conditional expectation for an additive effect of 1 animal given the effects of all other animals depends on the effects of its sire and dam only, each with a coefficient of 0.5. With genomic relationships, such an expectation depends on all other genotyped animals, and the coefficients do not have any set value. For each animal, the coefficients plus the conditional variance can be called a genomic recursion. If such recursions are known, the mixed model equations can be solved without explicitly creating the inverse of the genomic relationship matrix. Several algorithms were developed to create genomic recursions. In an algorithm with sequential updates, genomic recursions are created animal by animal. That algorithm can also be used to update a known inverse of a genomic relationship matrix for additional genotypes. In an algorithm with forward updates, a newly computed recursion is immediately applied to update recursions for remaining animals. The computing costs for both algorithms depend on the sparsity pattern of the genomic recursions, but are lower or equal than for regular inversion. An algorithm for proven and young animals assumes that the genomic recursions for young animals contain coefficients only for proven animals. Such an algorithm generates exact genomic EBV in genomic BLUP and is an approximation in single-step genomic BLUP. That algorithm has a cubic cost for the number of proven animals and a linear cost for the number of young animals. The genomic recursions can provide new insight into genomic evaluation and possibly reduce costs of genetic predictions with extremely large numbers of genotypes.
© 2014 American Dairy Science Association. MenosABSTRACT.
Computing the inverse of the genomic relationship matrix using recursion was investigated. A traditional algorithm to invert the numerator relationship matrix is based on the observation that the conditional expectation for an additive effect of 1 animal given the effects of all other animals depends on the effects of its sire and dam only, each with a coefficient of 0.5. With genomic relationships, such an expectation depends on all other genotyped animals, and the coefficients do not have any set value. For each animal, the coefficients plus the conditional variance can be called a genomic recursion. If such recursions are known, the mixed model equations can be solved without explicitly creating the inverse of the genomic relationship matrix. Several algorithms were developed to create genomic recursions. In an algorithm with sequential updates, genomic recursions are created animal by animal. That algorithm can also be used to update a known inverse of a genomic relationship matrix for additional genotypes. In an algorithm with forward updates, a newly computed recursion is immediately applied to update recursions for remaining animals. The computing costs for both algorithms depend on the sparsity pattern of the genomic recursions, but are lower or equal than for regular inversion. An algorithm for proven and young animals assumes that the genomic recursions for young animals contain coefficients only for proven animals. Such an algorithm generates exact geno... Presentar Todo |
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Palabras claves : |
GENOMIC RELATIONSHIP MATRIX; GENOMIC SELECTION; PRECONDITIONED CONJUGATE GRADIENTE (PCG) ALGORITHM; RECURSION; SINGLE-STEP BLUP. |
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Thesagro : |
GENÓMICA ANIMAL; SELECCIÓN GENÓMICA. |
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Asunto categoría : |
L10 Genética y mejoramiento animal |
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URL : |
http://www.ainfo.inia.uy/digital/bitstream/item/3059/1/Aguilar-I.-2014-Jr.Dairy-Sci.-v.976-p.3943-3952.pdf
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Marc : |
LEADER 02796naa a2200265 a 4500
001 1050106
005 2019-06-18
008 2014 bl uuuu u00u1 u #d
022 $a0022-0302
024 7 $ahttp://dx.doi.org/10.3168/jds.2013-7752$2DOI
100 1 $aMISZTAL, I.
245 $aUsing recursion to compute the inverse of the genomic relationship matrix.$h[electronic resource]
260 $c2014
500 $aArticle history: Received November 22, 2013. // Accepted February 10, 2014.
520 $aABSTRACT. Computing the inverse of the genomic relationship matrix using recursion was investigated. A traditional algorithm to invert the numerator relationship matrix is based on the observation that the conditional expectation for an additive effect of 1 animal given the effects of all other animals depends on the effects of its sire and dam only, each with a coefficient of 0.5. With genomic relationships, such an expectation depends on all other genotyped animals, and the coefficients do not have any set value. For each animal, the coefficients plus the conditional variance can be called a genomic recursion. If such recursions are known, the mixed model equations can be solved without explicitly creating the inverse of the genomic relationship matrix. Several algorithms were developed to create genomic recursions. In an algorithm with sequential updates, genomic recursions are created animal by animal. That algorithm can also be used to update a known inverse of a genomic relationship matrix for additional genotypes. In an algorithm with forward updates, a newly computed recursion is immediately applied to update recursions for remaining animals. The computing costs for both algorithms depend on the sparsity pattern of the genomic recursions, but are lower or equal than for regular inversion. An algorithm for proven and young animals assumes that the genomic recursions for young animals contain coefficients only for proven animals. Such an algorithm generates exact genomic EBV in genomic BLUP and is an approximation in single-step genomic BLUP. That algorithm has a cubic cost for the number of proven animals and a linear cost for the number of young animals. The genomic recursions can provide new insight into genomic evaluation and possibly reduce costs of genetic predictions with extremely large numbers of genotypes. © 2014 American Dairy Science Association.
650 $aGENÓMICA ANIMAL
650 $aSELECCIÓN GENÓMICA
653 $aGENOMIC RELATIONSHIP MATRIX
653 $aGENOMIC SELECTION
653 $aPRECONDITIONED CONJUGATE GRADIENTE (PCG) ALGORITHM
653 $aRECURSION
653 $aSINGLE-STEP BLUP
700 1 $aLEGARRA, A.
700 1 $aAGUILAR, I.
773 $tJournal of Dairy Science, 2014$gv.97, no.6, p.3943-3952. OPEN ACCESS.
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