Estimation of individual animal SNP-BLUP reliability using full Monte Carlo sampling

Zaabza, Hafedh Ben; Mäntysaari, Esa; Strandén, Ismo

doi:10.3168/jdsc.2020-0058

Cited by 7 publications

(9 citation statements)

References 9 publications

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“…As can be noticed, the method developed in the present study is much faster than the current methods for approximating reliabilities. For example, Erbe et al (2018) reported that the calculation of genomic reliabilities for 78,000 genotyped animals took 35 min, whereas for 222,619 genotyped animals, Ben Zaabza et al (2020) and Ben Zaabza et al (2021) reported a minimum of 140 and 36 min, respectively. Besides the employed hardware, algorithmic differences explain why our method is much faster than the cited references.…”

Section: Resultsmentioning

confidence: 99%

Efficient approximation of reliabilities for single-step genomic best linear unbiased predictor models with the Algorithm for Proven and Young

Bermann

Lourenço

Misztal

2021

Journal of Animal Science

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The objectives of this study were to develop an efficient algorithm for calculating prediction error variances (PEV) for GBLUP models using the Algorithm for Proven and Young (APY), extend it to single-step GBLUP (ssGBLUP), and to apply this algorithm for approximating the theoretical reliabilities for single and multiple trait models in ssGBLUP. The PEV with APY was calculated by block-sparse inversion, efficiently exploiting the sparse structure of the inverse of the genomic relationship matrix with APY. Single-step GBLUP reliabilities were approximated by combining reliabilities with and without genomic information in terms of effective record contributions. Multi-trait reliabilities relied on single-trait results adjusted using the genetic and residual covariance matrices among traits. Tests involved two datasets provided by the American Angus Association. A small dataset (Data1) was used for comparing the approximated reliabilities with the reliabilities obtained by the inversion of the left-hand side of the mixed model equations. The large dataset (Data2) was used for evaluating the computational performance of the algorithm. Analyses with both datasets used single-trait and three-trait models. The number of animals in the pedigree ranged from 167,951 in Data1 to 10,213,401 in Data2, with 50,000 and 20,000 genotyped animals for single-trait and multiple trait-analysis, respectively, in Data1 and 335,325 in Data2. Correlations between estimated and exact reliabilities obtained by inversion ranged from 0.97 to 0.99, whereas the intercept and slope of the regression of the exact on the approximated reliabilities ranged from 0.00 to 0.04 and from 0.93 to 1.05, respectively. For the three-trait model with the largest dataset (Data2), the elapsed time for the reliability estimation was eleven minutes. The computational complexity of the proposed algorithm increased linearly with the number of genotyped animals and with the number of traits in the model. This algorithm can efficiently approximate the theoretical reliability of genomic estimated breeding values in ssGBLUP with APY for large numbers of genotyped animals at a low cost.

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Section: Resultsmentioning

confidence: 99%

Efficient approximation of reliabilities for single-step genomic best linear unbiased predictor models with the Algorithm for Proven and Young

Bermann

Lourenço

Misztal

2021

Journal of Animal Science

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“…The required computing times in the full-MC-SNP-BLUP were 347 min and 527 min for 120,000 and 160,000 MC samples (Table 8), respectively. These computing times are less than required by GBLUP (3,090 min) using a data of a comparable size, containing 240,000 genotyped animals and 50,000 SNP markers (see Ben Zaabza et al, 2021). Memory requirements for making MME were 115 GB with 120,000 and 204 GB with 160,000 MC samples.…”

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confidence: 99%

“…To overcome the potential computational problem, Ben Zaabza et al (2020) proposed a Monte Carlo (MC)based sampling method to estimate the SNP-BLUP model reliability with an RPG effect (MC-SNP-BLUP), where the MME size depends on the number of markers (m) and MC samples (n mc ) instead of (m + n g ). Further, Ben Zaabza et al (2021) extended the MC-SNP-BLUP to another (MC)-based sampling method called full-MC-SNP-BLUP, where the size of the MME is determined by n mc . This method has a cost of O[(tn mc ) 3 ] for computing times and O[n mc (n g + t 2 n mc )] for memory.…”

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confidence: 99%

“…This method has a cost of O[(tn mc ) 3 ] for computing times and O[n mc (n g + t 2 n mc )] for memory. When m is less than n g and n g is large, the full MC approach is computationally less demanding than the exact GBLUP, which involves the time-consuming task of making and inverting the G matrix (see Ben Zaabza et al, 2021). The full-MC approach was reported to be computationally efficient for large data sets and to provide good approximation to the exact values with only a small upward bias.…”

mentioning

confidence: 99%

“…We examined the efficiency of our multistep procedure using the full-MC approach (Ben Zaabza et al, 2021) in the intermediate step for approximating reliabilities of the genotyped animals on the largest data (data 2). We used MC sample sizes of 120,000 and 160,000 for data 2.…”

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confidence: 99%

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Breeding value reliabilities for multiple-trait single-step genomic best linear unbiased predictor

Zaabza

Taskinen

Mäntysaari

et al. 2022

Journal of Dairy Science

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Approximate multistep methods to calculate reliabilities for estimated breeding values in large genetic evaluations were developed for single-trait (ST-R 2 A) and multitrait (MT-R 2 A) single-step genomic BLUP (ssG-BLUP) models. First, a traditional animal model was used to estimate the amount of nongenomic information for the genotyped animals. Second, this information was used with genomic data in a genomic BLUP model (genomic BLUP/SNP-BLUP) to approximate the total amount of information and ssGBLUP reliabilities for the genotyped animals. Finally, reliabilities for the nongenotyped animals were calculated using a traditional animal model where the increased information due to genomic data for the genotyped animals is accounted for by including pseudo-record counts for the genotyped animals. The approaches were tested using a multipletrait ssGBLUP model on 2 data sets. The first data set (data 1) was small enough such that exact ssGBLUP model reliabilities could be computed by inversion and compared with the approximation method reliabilities. Data 1 had 46,535 first-, 35,290 second-, and 23,780 third-lactation 305-d milk yield records from 47,124 Finnish Red dairy cows. The pedigree comprised 64,808 animals, of which 19,757 were genotyped. We examined the efficiency of the MT-R 2 A approximation on a large data set (data 2) derived from the joint Nordic (Danish, Finnish, and Swedish) Holstein dairy cattle data. Data 2 had 17.8 million 305-d milk records from 8.3 million cows and first 3 lactations. The pedigree had 11 million animals of which 274,145 were genotyped on 46,342 SNP markers. For data 1, correlations between the exact ssGBLUP model and the ST-R 2 A for the genotyped (nongenotyped) animals were 0.995 (0.987), 0.965 (0.984), and 0.950 (0.983) for first, second, and third lactation, respectively. Correspondingly, correlations between exact ssGBLUP reliabilities and MT-R 2 A for the genotyped (nongenotyped) animals were 0.995 (0.993), 0.992 (0.991), and 0.990 (0.990) for first, second, and third lactation, respectively. The regression coefficients (b 1 ) of ssGBLUP reliability on ST-R 2 A for the genotyped (nongenotyped) animals ranged from 0.87 (0.94) for first lactation to 0.68 (0.93) for third lactation, whereas for MT-R 2 A they were between 0.91 (0.99) for first lactation to 0.89 (0.99) for third lactation. Correspondingly, the intercepts varied from 0.11 (0.05) to 0.3 (0.06) for ST-R 2 A and from 0.06 (0.01) to 0.07 (0.02) for MT-R 2 A. The computing time for the approximation method was approximately 12% of that required by the direct exact approach. In conclusion, the developed approximate approach allows calculating estimated breeding value reliabilities in the ssGBLUP model even for large data sets.

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Past, present, and future developments in single-step genomic models

Bermann

Cesarani

Misztal

et al. 2022

Italian Journal of Animal Science

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Estimation of individual animal SNP-BLUP reliability using full Monte Carlo sampling

Cited by 7 publications

References 9 publications

Efficient approximation of reliabilities for single-step genomic best linear unbiased predictor models with the Algorithm for Proven and Young

Efficient approximation of reliabilities for single-step genomic best linear unbiased predictor models with the Algorithm for Proven and Young

Breeding value reliabilities for multiple-trait single-step genomic best linear unbiased predictor

Past, present, and future developments in single-step genomic models

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