Solving efficiently large single‐step genomic best linear unbiased prediction models

Strandén, Ismo; Matilainen, Kaarina; Aamand, G.P.; Mäntysaari, Esa

doi:10.1111/jbg.12257

Cited by 39 publications

(52 citation statements)

References 23 publications

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“…It avoids negative reliabilities, which are puzzling to report. Last, using correctly inbreeding protects from unexpected problems, such as lack of convergence due to not consideration of inbreeding in the

H^{- 1}

matrix in SSGBLUP (Matilainen et al, ; Strandén et al, ).…”

Section: Discussionmentioning

confidence: 99%

“…Again, the use of

H^{* - 1}

(formed as

{bold-italicH}^{* - 1} = {bold-italicA}^{* - 1} + (\begin{matrix} 0 & 0 \\ 0 & {bold-italicG}^{- 1} - {bold-italicA}_{22}^{- 1} \end{matrix})

) implicitly assumes an incorrect matrix of “true” relationships, that is

{()(, {boldH}^{* - 1})}^{- 1} = {boldH}^{*} \neq H

. This resulted in strong convergence problems for large data sets which included inbred animals (Matilainen, Strandén, Aamand, & Mäntysaari, ; Strandén, Matilainen, Aamand, & Mäntysaari, ). It is unclear how ignoring inbreeding when computing

A^{* - 1}

H^{* - 1}

, affects the calculation of PEV (computed by inversion) and therefore accuracies.…”

Section: Methodsmentioning

confidence: 99%

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Effects of ignoring inbreeding in model‐based accuracy for BLUP and SSGBLUP

Aguilar

Fernández²,

Blasco

et al. 2020

J Animal Breeding Genetics

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Model‐based accuracy, defined as the theoretical correlation between true and estimated breeding value, can be obtained for each individual as a function of its prediction error variance (PEV) and inbreeding coefficient F, in BLUP, GBLUP and SSGBLUP genetic evaluations. However, for computational convenience, inbreeding is often ignored in two places. First, in the computation of reliability = 1‐PEV/(1 + F). Second, in the set‐up, using Henderson's rules, of the inverse of the pedigree‐based relationship matrix A. Both approximations have an effect in the computation of model‐based accuracy and result in wrong values. In this work, first we present a reminder of the theory and extend it to SSGBLUP. Second, we quantify the error of ignoring inbreeding with real data in three scenarios: BLUP evaluation and SSGBLUP in Uruguayan dairy cattle, and BLUP evaluations in a line of rabbit closed for >40 generations with steady increase of inbreeding up to an average of 0.30. We show that ignoring inbreeding in the set‐up of the A‐inverse is equivalent to assume that non‐inbred animals are actually inbred. This results in an increase of apparent PEV that is negligible for dairy cattle but considerable for rabbit. Ignoring inbreeding in reliability = 1‐PEV/(1 + F) leads to underestimation of reliability for BLUP evaluations, and this underestimation is very large for rabbit. For SSGBLUP in dairy cattle, it leads to both underestimation and overestimation of reliability, both for genotyped and non‐genotyped animals. We strongly recommend to include inbreeding both in the set‐up of A‐inverse and in the computation of reliability from PEVs.

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H^{- 1}

matrix in SSGBLUP (Matilainen et al, ; Strandén et al, ).…”

Section: Discussionmentioning

confidence: 99%

“…Again, the use of

H^{* - 1}

(formed as

{bold-italicH}^{* - 1} = {bold-italicA}^{* - 1} + (\begin{matrix} 0 & 0 \\ 0 & {bold-italicG}^{- 1} - {bold-italicA}_{22}^{- 1} \end{matrix})

) implicitly assumes an incorrect matrix of “true” relationships, that is

{()(, {boldH}^{* - 1})}^{- 1} = {boldH}^{*} \neq H

A^{* - 1}

H^{* - 1}

, affects the calculation of PEV (computed by inversion) and therefore accuracies.…”

Section: Methodsmentioning

confidence: 99%

Effects of ignoring inbreeding in model‐based accuracy for BLUP and SSGBLUP

Aguilar

Fernández²,

Blasco

et al. 2020

J Animal Breeding Genetics

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“…The GLS equivalent uses the method proposed by McPeek et al (2004) and implemented by Strandén et al (2017) and Garcia-Baccino et al (2017) in which for the ith SNP…”

Section: Methodsmentioning

confidence: 99%

“…Two implementations of this method were made. Our first implementation, referred to as "GLS_Sparse," was similar to that of Strandén et al (2017) in the sense that the vector t A = − 22 1 1 was first computed as a multiplication of sparse matrices by the vector 1, followed by the trivial computation of the scalar…”

Section: Methodsmentioning

confidence: 99%

“…The first method was to run, for each SNP, a BLUP in which the heritability was close to 1 (e.g., 0.99 or smaller; Gengler et al, 2007). The second method was, for each SNP, a general least squares (GLS) estimator using either sparse or dense matrices for the computation of the inverse of pedigree relationship submatrices (McPeek et al, 2004;Garcia-Baccino et al, 2017;Strandén et al, 2017). The BLUP and GLS methods are expected to be very similar because both use pedigree information, but we did not expect them to be exactly the same, although theoretically equivalent (e.g., Henderson, 1984;Mrode, 2005;Garcia-Baccino et al, 2017) differences between estimates of BLUP and GLS methods could be due to the heritability different from 1 and the iterative solver used in the BLUP method.…”

Section: Introductionmentioning

confidence: 99%

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Efficient and accurate computation of base generation allele frequencies

Aldridge

Vandenplas

Calus

2019

Journal of Dairy Science

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Allele frequencies are used for several aspects of genomic prediction, with the assumption that these are equal to the allele frequency in the base generation of the pedigree. The current standard method, however, calculates allele frequencies from the current genotyped population. We compared the current standard method with BLUP and general least squares (GLS) methods explicitly targeting the base population to determine whether there is a more accurate and still efficient method of calculating allele frequencies that better represents the base generation. A data set based on a typical dairy population was simulated for 325,266 animals; the last 100,078 animals in generations 9 to 12 of the population were genotyped, with 1,670 SNP markers. For the BLUP method, several SNP genotypes were analyzed with a multitrait model by assuming a heritability of 0.99 and no genetic correlation among them. This method was limited by the time required for each BLUP to converge (approximately 6 min per BLUP run of 15 SNP). The GLS method had 2 implementations. The first implementation, using imputation on the fly and multiplication of sparse matrices, was very efficient and required just 49 s and 1.3 GB of random access memory. The second implementation, using a dense full A 22 1 − matrix, was very inefficient and required more than 1 d of wall clock time and more than 118.2 GB of random access memory. When no selection was considered in the simulations, all methods predicted equally well. When selection was introduced, higher correlations between the estimated allele frequency and known base generation allele frequency were observed for BLUP (0.96 ± 0.01) and GLS (0.97 ± 0.01) compared with the current standard method (0.87 ± 0.01). The GLS method decreased in accuracy when introducing incomplete pedigree, with 25% of sires in the first 5 generations randomly replaced as unknown to erroneously identify founder animals (0.93 ± 0.01) and a further decrease for 8 generations (0.91 ± 0.01). There was no change in accuracy when introducing 5% genotyping errors (0.97 ± 0.01), 5% missing genotypes (0.97 ± 0.01), or both 5% genotyping errors and missing genotypes (0.97 ± 0.01). The GLS method provided the most accurate estimates of base generation allele frequency and was only slightly slower compared with the current method. The efficient implementation of the GLS method, therefore, is very well suited for practical application and is recommended for implementation.

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