Comparison of models for missing pedigree in single-step genomic prediction

Abstract Pedigree information is often missing for some animals in a breeding program. Unknown-parent groups (UPGs) are assigned to the missing parents to avoid biased genetic evaluations. Although the use of UPGs is well established for the pedigree model, it is unclear how UPGs are integrated into the inverse of the unified relationship matrix (H-inverse) required for single-step genomic best linear unbiased prediction. A generalization of the UPG model is the metafounder (MF) model. The objectives of this study were to derive 3 H-inverses and to compare genetic trends among models with UPG and MF H-inverses using a simulated purebred population. All inverses were derived using the joint density function of the random breeding values and genetic groups. The breeding values of genotyped animals (u2) were assumed to be adjusted for UPG effects (g) using matrix Q2 as u2∗=u2+Q2g before incorporating genomic information. The Quaas–Pollak-transformed (QP) H-inverse was derived using a joint density function of u2∗ and g updated with genomic information and assuming nonzero cov(u2∗,g′). The modified QP (altered) H-inverse also assumes that the genomic information updates u2∗ and g, but cov(u2∗,g′)=0. The UPG-encapsulated (EUPG) H-inverse assumed genomic information updates the distribution of u2∗. The EUPG H-inverse had the same structure as the MF H-inverse. Fifty percent of the genotyped females in the simulation had a missing dam, and missing parents were replaced with UPGs by generation. The simulation study indicated that u2∗ and g in models using the QP and altered H-inverses may be inseparable leading to potential biases in genetic trends. Models using the EUPG and MF H-inverses showed no genetic trend biases. These 2 H-inverses yielded the same genomic EBV (GEBV). The predictive ability and inflation of GEBVs from young genotyped animals were nearly identical among models using the QP, altered, EUPG, and MF H-inverses. Although the choice of H-inverse in real applications with enough data may not result in biased genetic trends, the EUPG and MF H-inverses are to be preferred because of theoretical justification and possibility to reduce biases.

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Estimation of Breeding Values Using Different Densities of Snp to Inform Kinship in Broiler Chickens

10.21203/rs.3.rs-32429/v1 ◽

2020 ◽

Author(s):

Mayara Salvian ◽

Gabriel Costa Monteiro Moreira ◽

Ândrea Plotzki Reis ◽

Brayan Dias Dauria ◽

Fabrício Pilonetto ◽

...

Keyword(s):

Broiler Chickens ◽

Single Step ◽

Regression Coefficients ◽

Whole Genome Sequence ◽

Pedigree Information ◽

Genomic Information ◽

Breeding Values ◽

Genome Wide ◽

Estimated Breeding Values ◽

The Cost

Abstract Background: Traditionally, breeding values are estimated based on phenotypic and pedigree information using the numerator relationship (A) matrix. With the availability of genomic information, genome-wide markers can be included in the estimation of breeding values through genomic kinship. However, the density of genomic information used can impact the cost of implementation. The aim of this study was to compare the rank, accuracy, and bias of estimated breeding values (EBV) for organs [heart (HRT), liver (LIV), gizzard (GIZ), lungs (LUN)] and carcass [breast (BRST), drumstick (DRM) and thigh (THG)] weight traits in a broiler population using pedigree-based BLUP (PBLUP) and single-step genomic BLUP (ssGBLUP) methods using various densities of SNP and variants imputed from whole-genome sequence (WGS). Results: For both PBLUP and ssGBLUP, heritability estimates varied from low (LUN) to high (HRT, LIV, GIZ, BRST, DRM and THG). Regression coefficients values of EBV on genomic estimated breeding values (GEBV) were similar for both the high density (HD) and WGS sets of SNPs, ranging from 0.87 to 0.99 across scenarios. Conclusion: Results show no benefit of using WGS data compared to HD array data using an unweighted ssGBLUP. Our results suggest that 10% of the content of the HD array can yield unbiased and accurate EBV.

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Applying the Metafounders Approach for Genomic Evaluation in a Multibreed Beef Cattle Population

Frontiers in Genetics ◽

10.3389/fgene.2020.556399 ◽

2020 ◽

Vol 11 ◽

Author(s):

Vinícius Silva Junqueira ◽

Paulo Sávio Lopes ◽

Daniela Lourenco ◽

Fabyano Fonseca e Silva ◽

Fernando Flores Cardoso

Keyword(s):

Beef Cattle ◽

Variance Components ◽

Genetic Relationships ◽

A Priori ◽

Predictive Ability ◽

Single Step ◽

Pedigree Information ◽

Phenotypic Variance ◽

Genomic Information ◽

The Impact

Pedigree information is incomplete by nature and commonly not well-established because many of the genetic ties are not known a priori or can be wrong. The genomic era brought new opportunities to assess relationships between individuals. However, when pedigree and genomic information are used simultaneously, which is the case of single-step genomic BLUP (ssGBLUP), defining the genetic base is still a challenge. One alternative to overcome this challenge is to use metafounders, which are pseudo-individuals that describe the genetic relationship between the base population individuals. The purpose of this study was to evaluate the impact of metafounders on the estimation of breeding values for tick resistance under ssGBLUP for a multibreed population composed by Hereford, Braford, and Zebu animals. Three different scenarios were studied: pedigree-based model (BLUP), ssGBLUP, and ssGBLUP with metafounders (ssGBLUPm). In ssGBLUPm, a total of four different metafounders based on breed of origin (i.e., Hereford, Braford, Zebu, and unknown) were included for the animals with missing parents. The relationship coefficient between metafounders was in average 0.54 (ranging from 0.34 to 0.96) suggesting an overlap between ancestor populations. The estimates of metafounder relationships indicate that Hereford and Zebu breeds have a possible common ancestral relationship. Inbreeding coefficients calculated following the metafounder approach had less negative values, suggesting that ancestral populations were large enough and that gametes inherited from the historical population were not identical. Variance components were estimated based on ssGBLUPm, ssGBLUP, and BLUP, but the values from ssGBLUPm were scaled to provide a fair comparison with estimates from the other two models. In general, additive, residual, and phenotypic variance components in the Hereford population were smaller than in Braford across different models. The addition of genomic information increased heritability for Hereford, possibly because of improved genetic relationships. As expected, genomic models had greater predictive ability, with an additional gain for ssGBLUPm over ssGBLUP. The increase in predictive ability was greater for Herefords. Our results show the potential of using metafounders to increase accuracy of GEBV, and therefore, the rate of genetic gain in beef cattle populations with partial levels of missing pedigree information.

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Evaluating policy feedback rules using the joint density function of a stochastic model

Economics Letters ◽

10.1016/j.econlet.2006.03.035 ◽

2006 ◽

Vol 93 (1) ◽

pp. 1-5 ◽

Cited By ~ 17

Author(s):

R. Barrell ◽

S.G. Hall ◽

I. Hurst

Keyword(s):

Stochastic Model ◽

Density Function ◽

Joint Density ◽

Policy Feedback ◽

Joint Density Function

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Experimental study of velocity filtered joint density function for large eddy simulation

Physics of Fluids ◽

10.1063/1.1776194 ◽

2004 ◽

Vol 16 (10) ◽

pp. 3599-3613 ◽

Cited By ~ 31

Author(s):

Danhong Wang ◽

Chenning Tong ◽

Stephen B. Pope

Keyword(s):

Experimental Study ◽

Large Eddy Simulation ◽

Density Function ◽

Joint Density ◽

Joint Density Function ◽

Eddy Simulation ◽

Large Eddy

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Short communication: Estimation of genetic trends for body weight traits in Markhoz goat at different ages

Spanish Journal of Agricultural Research ◽

10.5424/sjar/2019171-13608 ◽

2019 ◽

Vol 17 (1) ◽

pp. e04SC01 ◽

Cited By ~ 1

Author(s):

Meysam Latifi ◽

Mohammad Razmkabir

Keyword(s):

Body Weight ◽

Fixed Effects ◽

Growth Traits ◽

Genetic Selection ◽

Information Criteria ◽

Pedigree Information ◽

Genetic Trend ◽

Breeding Values ◽

Different Ages ◽

Genetic Trends

The objective of the present study was to estimate genetic trends for body weight at different ages in Markhoz goat, including birth weight (BW, n = 4758), weaning weight (WW, n= 3685), 6-month weight (6MW, n = 3420), 9-month weight (9MW, n = 3032) and 12-month weight (12MW, n = 2697). Data and pedigree information were collected from 1992 until 2014 at the Breeding Center of Markhoz goat, Sanandaj, Iran. The GLM procedure of SAS was used for selecting the variables and identifying significant fixed effects in the equation of model. Various animal models were applied for genetic analysis and the best model was determined based on Akaike information criteria (AIC). Breeding values of animals were predicted using Wombat program. Genetic trends were obtained by regressing the average predicted breeding values on birth year for each trait. Based on the best model, direct estimated genetic trends were positive and significance for WW, 6MW, 9MW and 12 MW were 15.51, 26.28, 58.36 and 76.70 g/year, respectively (p<0.001). Maternal genetic trend for BW and WW were 0.61 and 5.47 g/year, respectively (p<0.01). The low and moderate generic trends obtained in the present study, indicated the possibility of growth traits improvements through genetic selection at all ages in Markhoz goat.

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The Effect of Integrating Genomic Information into Genetic Evaluations of Chinese Merino Sheep

Animals ◽

10.3390/ani10040569 ◽

2020 ◽

Vol 10 (4) ◽

pp. 569

Author(s):

Chen Wei ◽

Hanpeng Luo ◽

Bingru Zhao ◽

Kechuan Tian ◽

Xixia Huang ◽

...

Keyword(s):

Rank Correlation ◽

Best Linear Unbiased Prediction ◽

Single Step ◽

Breeding Value ◽

Genomic Information ◽

Linear Unbiased Prediction ◽

Breeding Values ◽

Merino Sheep ◽

Best Linear Unbiased ◽

Unbiased Prediction

Genomic evaluations are a method for improving the accuracy of breeding value estimation. This study aimed to compare estimates of genetic parameters and the accuracy of breeding values for wool traits in Merino sheep between pedigree-based best linear unbiased prediction (PBLUP) and single-step genomic best linear unbiased prediction (ssGBLUP) using Bayesian inference. Data were collected from 28,391 yearlings of Chinese Merino sheep (classified in 1992–2018) at the Xinjiang Gonaisi Fine Wool Sheep-Breeding Farm, China. Subjectively-assessed wool traits, namely, spinning count (SC), crimp definition (CRIM), oil (OIL), and body size (BS), and objectively-measured traits, namely, fleece length (FL), greasy fleece weight (GFW), mean fiber diameter (MFD), crimp number (CN), and body weight pre-shearing (BWPS), were analyzed. The estimates of heritability for wool traits were low to moderate. The largest h2 values were observed for FL (0.277) and MFD (0.290) with ssGBLUP. The heritabilities estimated for wool traits with ssGBLUP were slightly higher than those obtained with PBLUP. The accuracies of breeding values were low to moderate, ranging from 0.362 to 0.573 for the whole population and from 0.318 to 0.676 for the genotyped subpopulation. The correlation between the estimated breeding values (EBVs) and genomic EBVs (GEBVs) ranged from 0.717 to 0.862 for the whole population, and the relative increase in accuracy when comparing EBVs with GEBVs ranged from 0.372% to 7.486% for these traits. However, in the genotyped population, the rank correlation between the estimates obtained with PBLUP and ssGBLUP was reduced to 0.525 to 0.769, with increases in average accuracy of 3.016% to 11.736% for the GEBVs in relation to the EBVs. Thus, genomic information could allow us to more accurately estimate the relationships between animals and improve estimates of heritability and the accuracy of breeding values by ssGBLUP.

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Level-biases in estimated breeding values due to the use of different SNP panels over time in ssGBLUP

Genetics Selection Evolution ◽

10.1186/s12711-019-0517-z ◽

2019 ◽

Vol 51 (1) ◽

Cited By ~ 1

Author(s):

Øyvind Nordbø ◽

Arne B. Gjuvsland ◽

Leiv Sigbjørn Eikje ◽

Theo Meuwissen

Keyword(s):

Value Added ◽

Single Step ◽

Fine Tuning ◽

Genomic Relationship Matrix ◽

Relationship Matrix ◽

Optimal Selection ◽

Breeding Values ◽

Estimated Breeding Values ◽

Snp Panels ◽

Genomic Predictions

Abstract Background The main aim of single-step genomic predictions was to facilitate optimal selection in populations consisting of both genotyped and non-genotyped individuals. However, in spite of intensive research, biases still occur, which make it difficult to perform optimal selection across groups of animals. The objective of this study was to investigate whether incomplete genotype datasets with errors could be a potential source of level-bias between genotyped and non-genotyped animals and between animals genotyped on different single nucleotide polymorphism (SNP) panels in single-step genomic predictions. Results Incomplete and erroneous genotypes of young animals caused biases in breeding values between groups of animals. Systematic noise or missing data for less than 1% of the SNPs in the genotype data had substantial effects on the differences in breeding values between genotyped and non-genotyped animals, and between animals genotyped on different chips. The breeding values of young genotyped individuals were biased upward, and the magnitude was up to 0.8 genetic standard deviations, compared with breeding values of non-genotyped individuals. Similarly, the magnitude of a small value added to the diagonal of the genomic relationship matrix affected the level of average breeding values between groups of genotyped and non-genotyped animals. Cross-validation accuracies and regression coefficients were not sensitive to these factors. Conclusions Because, historically, different SNP chips have been used for genotyping different parts of a population, fine-tuning of imputation within and across SNP chips and handling of missing genotypes are crucial for reducing bias. Although all the SNPs used for estimating breeding values are present on the chip used for genotyping young animals, incompleteness and some genotype errors might lead to level-biases in breeding values.

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Core-dependent changes in genomic predictions using the Algorithm for Proven and Young in single-step genomic best linear unbiased prediction

Journal of Animal Science ◽

10.1093/jas/skaa374 ◽

2020 ◽

Vol 98 (12) ◽

Author(s):

Ignacy Misztal ◽

Shogo Tsuruta ◽

Ivan Pocrnic ◽

Daniela Lourenco

Keyword(s):

Prediction Accuracy ◽

Best Linear Unbiased Prediction ◽

Single Step ◽

Relationship Matrix ◽

Linear Unbiased Prediction ◽

Breeding Values ◽

Best Linear Unbiased ◽

The Impact ◽

Genomic Predictions ◽

Unbiased Prediction

Abstract Single-step genomic best linear unbiased prediction with the Algorithm for Proven and Young (APY) is a popular method for large-scale genomic evaluations. With the APY algorithm, animals are designated as core or noncore, and the computing resources to create the inverse of the genomic relationship matrix (GRM) are reduced by inverting only a portion of that matrix for core animals. However, using different core sets of the same size causes fluctuations in genomic estimated breeding values (GEBVs) up to one additive standard deviation without affecting prediction accuracy. About 2% of the variation in the GRM is noise. In the recursion formula for APY, the error term modeling the noise is different for every set of core animals, creating changes in breeding values. While average changes are small, and correlations between breeding values estimated with different core animals are close to 1.0, based on the normal distribution theory, outliers can be several times bigger than the average. Tests included commercial datasets from beef and dairy cattle and from pigs. Beyond a certain number of core animals, the prediction accuracy did not improve, but fluctuations decreased with more animals. Fluctuations were much smaller than the possible changes based on prediction error variance. GEBVs change over time even for animals with no new data as genomic relationships ties all the genotyped animals, causing reranking of top animals. In contrast, changes in nongenomic models without new data are small. Also, GEBV can change due to details in the model, such as redefinition of contemporary groups or unknown parent groups. In particular, increasing the fraction of blending of the GRM with a pedigree relationship matrix from 5% to 20% caused changes in GEBV up to 0.45 SD, with a correlation of GEBV > 0.99. Fluctuations in genomic predictions are part of genomic evaluation models and are also present without the APY algorithm when genomic evaluations are computed with updated data. The best approach to reduce the impact of fluctuations in genomic evaluations is to make selection decisions not on individual animals with limited individual accuracy but on groups of animals with high average accuracy.

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