Hot topic: Use of genomic recursions in single-step genomic best linear unbiased predictor (BLUP) with a large number of genotypes

Fragomeni, B. O.; Lourenço, Daniela; Tsuruta, S.; Masuda, Yutaka; Aguilar, Ignácio; Legarra, Andrés; Lawlor, T.J.; Misztal, I.

doi:10.3168/jds.2014-9125

Cited by 63 publications

(104 citation statements)

References 17 publications

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“…The approximate inverse calculated in Apy cannot ever be that of which is singular when . The Apy algorithm will never yield exact GBLUP predictions contrary to the claims in [9, 11], but it has been demonstrated to be a useful approximation for some choices of [11–13]. …”

Section: Introductionmentioning

confidence: 92%

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An efficient exact method to obtain GBLUP and single-step GBLUP when the genomic relationship matrix is singular

2016

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BackgroundThe mixed linear model employed for genomic best linear unbiased prediction (GBLUP) includes the breeding value for each animal as a random effect that has a mean of zero and a covariance matrix proportional to the genomic relationship matrix (), where the inverse of is required to set up the usual mixed model equations (MME). When only some animals have genomic information, genomic predictions can be obtained by an extension known as single-step GBLUP, where the covariance matrix of breeding values is constructed by combining the pedigree-based additive relationship matrix with . The inverse of the combined relationship matrix can be obtained efficiently, provided can be inverted. In some livestock species, however, the number of animals with genomic information exceeds the number of marker covariates used to compute , and this results in a singular . For such a case, an efficient and exact method to obtain GBLUP and single-step GBLUP is presented here.ResultsExact methods are already available to obtain GBLUP when is singular, but these require working with large dense matrices. Another approach is to modify to make it nonsingular by adding a small value to all its diagonals or regressing it towards the pedigree-based relationship matrix. This, however, results in the inverse of being dense and difficult to compute as grows. The approach presented here recognizes that the number r of linearly independent genomic breeding values cannot exceed the number of marker covariates, and the mixed linear model used here for genomic prediction only fits these r linearly independent breeding values as random effects.ConclusionsThe exact method presented here was compared to Apy-GBLUP and to Apy single-step GBLUP, both of which are approximate methods that use a modified that has a sparse inverse which can be computed efficiently. In a small numerical example, predictions from the exact approach and Apy were almost identical, but the MME from Apy had a condition number about 1000 times larger than that from the exact approach, indicating ill-conditioning of the MME from Apy. The practical application of exact SSGBLUP is not more difficult than implementation of Apy.Electronic supplementary materialThe online version of this article (doi:10.1186/s12711-016-0260-7) contains supplementary material, which is available to authorized users.

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Section: Introductionmentioning

confidence: 92%

“…We will refer to this property of the genomic relationships that is required for Apy as the Apy property. Provided this property holds, it is claimed that Apy results in an efficient inverse of that leads to exact calculations of GBLUP [9, 11]. However, when is singular and cannot have an inverse.…”

Section: Theorymentioning

confidence: 99%

An efficient exact method to obtain GBLUP and single-step GBLUP when the genomic relationship matrix is singular

2016

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“…The multivariate Gaussian prior density of u specified in ss-GBLUP is loosely derived by conditioning arguments, i.e., writing p (u) = p (u 1 |u 2 ) p (u 2 ) whereby p (u 2 ) is based on using the realized genomic relationship matrix between genotyped animals, as indicated previously with GBLUP, whereas p (u 1 |u 2 ) is based on imputing realized relationships involving non-genotyped animals based on their pedigree-based relationships with each other and with genotyped animals. The resulting hybrid genetic/genomic relationships, or correlation matrix, between all of u = [ u 1 u 2 ] is typically referred to as the "H" matrix, thereby making its usage particularly amenable for large scale BLUP-based genetic/genomic evaluations (Fragomeni et al 2015) within a GBLUP modeling framework.…”

Section: Combining Information On Genotyped and Non-genotyped Animalsmentioning

confidence: 99%

Statistical and Computational Challenges in Whole Genome Prediction and Genome-Wide Association Analyses for Plant and Animal Breeding

Tempelman

2015

JABES

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Whole genome prediction (WGP) modeling and genome-wide association (GWA) analyses are big data issues in agricultural quantitative genetics. Both areas require meaningful input from the statistical scholarly community in order to further improve the accuracy of prediction of genetic merit and inference on putative causal variants as well as improving the computational efficiency of existing methods and algorithms. These concerns have become increasingly critical as new sequencing technologies will only exacerbate current model dimensionality problems. We focus primarily on mixed model and hierarchical Bayesian analyses which have been most commonly pursued by animal and plant breeders for WGP thus far. We draw attention to our observation that many such previous analyses have not carefully inferred upon hyperparameters defined at the top levels of the Bayesian model hierarchy, but simply arbitrarily specify their values. We also reassess previous discussions on WGP model dimensionality, believing that useful data augmentation schemes utilized in various Markov Chain Monte Carlo (MCMC) schemes have led to a general misunderstanding that heavy-tailed or variable selection-based WGP models may be highly parameterized relative to more standard mixed model representations. Computational efficiency is addressed with respect to MCMC and competitive, albeit approximate, alternatives. Furthermore, GWA analyses are reassessed, encouraging a greater reliance on shrinkage-based inferences based on critically chosen priors, instead of potentially nonreproducible fixed effects P valuebased inference.

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“…Though construction of H is not easy, the construction of H -1 is feasible (Legarra et al, 2009): (9) where: H -pedigree-genomic relationship matrix A 22 -part of pedigree relationship connected with genotyped animals only (subtraction avoids double counting of relationship)  -weight of genomic in relation to polygenic eff ect (for fi ne tuning more parameters ,  are used) Some technical limitation has been inversion G -1 , if number of genotyped animals was large. Recently recursive algorithm was developed, which allows practically unlimited volume of animals in G (Fragomeni et al, 2015). Masuda et al (2016) used in single-step evaluation more than ½ million of genotyped animals.…”

Section: Single-step Gebv (Ssgblup)mentioning

confidence: 99%

“…Modifi cation, "blending" ssGBLUP (Gao et al, 2012), was used for longevity, where input data for genomic calculation were deregressed proofs (DRP) of all proven bulls from Survival Kit with weights according reliabilities. GEBVs are accompanied by reliabilities calculated according modifi cations of Misztal et al (2013).…”

Section: Gebv Of Holstein In the Czech Republicmentioning

confidence: 99%

GWAS in practical cattle breeding in Czech Republic, single step method, genetic progress

Přibyl

Bauer²,

Čermák³

et al. 2016

Acta fytotechn zootechn

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Development of genetic evaluation of animals is permanent process. It was going from estimated breeding value (EBV) calculated by CC-test, across a BLUP -animal model and RR-TDM, to the genomic enhanced breeding value (GEBV) using genetic markers. Methods of genetic evaluation become a part of marketing strategies of insemination companies. Therefore all countries and association of breeders seek to be compatible with others. Now we are in a period of massive global implementation of genomic evaluation, which combines traditional BLUP with huge quantity of genetic SNP markers. Multi-step procedures are now usual in practice, which work with deregressed proofs. Development of methods attained to the single-step procedure (ssGBLUP) which overcomes some diffi culties of previous methods, improves reliabilities of evaluation and compares all animals, genotyped and ungenotyped, in entire nation-wide population. Genomic evaluation infl uence above all young genotyped animals. In Czech Republic single-step procedure is routinely used for national evaluation of milk, linear type traits, reproduction and longevity. GEBVs are accompanied by genomic reliabilities. Genetic trends over last 20 years are in some traits diff erent for genomic evaluation compared to traditional BLUP evaluation, although input data and genetic parameters (heritability) are the same and genotyped animals were only small proportion from entire evaluated population. Diff erences in genetic trends increase mainly in new batches of animals. Reason of it could be in the changed variability of breeding values and "genomic correction" of relationship between animals, which is expanded from genotyped animals to others individuals in a population.

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Hot topic: Use of genomic recursions in single-step genomic best linear unbiased predictor (BLUP) with a large number of genotypes

Cited by 63 publications

References 17 publications

An efficient exact method to obtain GBLUP and single-step GBLUP when the genomic relationship matrix is singular

An efficient exact method to obtain GBLUP and single-step GBLUP when the genomic relationship matrix is singular

Statistical and Computational Challenges in Whole Genome Prediction and Genome-Wide Association Analyses for Plant and Animal Breeding

GWAS in practical cattle breeding in Czech Republic, single step method, genetic progress

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