Efficient and accurate computation of base generation allele frequencies

A comparison of marker-based estimators of inbreeding and inbreeding depression

BACKGROUND

The availability of genome-wide marker data allows estimation of inbreeding coefficients (F, the probability of identity-by-descent, IBD) and, in turn, estimation of the rate of inbreeding depression (ΔID). We investigated, by computer simulations, the accuracy of the most popular estimators of inbreeding based on molecular markers when computing F and ΔID in populations under random mating, equalization of parental contributions, and artificially selected populations. We assessed estimators described by Li and Horvitz (F_LH1 and F_LH2), VanRaden (F_VR1 and F_VR2), Yang and colleagues (F_YA1 and F_YA2), marker homozygosity (F_HOM), runs of homozygosity (F_ROH) and estimates based on pedigree (F_PED) in comparison with estimates obtained from IBD measures (F_IBD).

RESULTS

If the allele frequencies of a base population taken as a reference for the computation of inbreeding are known, all estimators based on marker allele frequencies are highly correlated with F_IBD and provide accurate estimates of the mean ΔID. If base population allele frequencies are unknown and current frequencies are used in the estimations, the largest correlation with F_IBD is generally obtained by F_LH1 and the best estimator of ΔID is F_YA2. The estimators F_VR2 and F_LH2 have the poorest performance in most scenarios. The assumption that base population allele frequencies are equal to 0.5 results in very biased estimates of the average inbreeding coefficient but they are highly correlated with F_IBD and give relatively good estimates of ΔID. Estimates obtained directly from marker homozygosity (F_HOM) substantially overestimated ΔID. Estimates based on runs of homozygosity (F_ROH) provide accurate estimates of inbreeding and ΔID. Finally, estimates based on pedigree (F_PED) show a lower correlation with F_IBD than molecular estimators but provide rather accurate estimates of ΔID. An analysis of data from a pig population supports the main findings of the simulations.

CONCLUSIONS

When base population allele frequencies are known, all marker-allele frequency-based estimators of inbreeding coefficients generally show a high correlation with F_IBD and provide good estimates of ΔID. When base population allele frequencies are unknown, F_LH1 is the marker frequency-based estimator that is most correlated with F_IBD, and F_YA2 provides the most accurate estimates of ΔID. Estimates from F_ROH are also very precise in most scenarios. The estimators F_VR2 and F_LH2 have the poorest performances.

Polymorphism of prolactin (PRL) gene exon 5 and its association with egg production in IPB-D1 chickens

The prolactin (PRL) gene regulates the egg production and incubation in laying chickens. Local chickens' reproductive systems will disrupt as a result of the incubation period activity, and they will lay fewer eggs. This study aimed to determine the prolactin gene polymorphism in IPB-D1 hens and its relationship to egg production. The polymorphism of the exon 5 prolactin gene was examined on 112 samples of the IPB-D1 chicken DNA collection from the Division of Animal Genetics and Breeding, Faculty of Animal Sciences, IPB University. By performing the phenol-chloroform method, the genomic DNA was obtained. A polymerase chain reaction (PCR) product with a size of 557 bp was produced as a result of the DNA amplification. Three single-nucleotide sequences were discovered. Three single-nucleotide polymorphisms (SNPs), g.7835A  >  G, g.7886A  >  T, and g.8052T  >  C, were found in exon 5 of the PRL gene. Each mutation was polymorphic and in Hardy-Weinberg equilibrium. The point mutation g.8052T  >  C significantly impacted the egg production of IPB-D1 chickens, according to the SNP association analysis on egg production, and may serve as a marker to enhance the selection for the features of egg production in IPB-D1 chickens.

Correcting for base-population differences and unknown parent groups in single-step genomic predictions of Norwegian Red Cattle

Bias and inflation in genomic evaluation with the single-step methods have been reported in several studies. Incompatibility between the base-populations of the pedigree-based and the genomic relationship matrix (G) could be a reason for these biases. Inappropriate ways of accounting for missing parents could be another reason for biases in genetic evaluations with or without genomic information. To handle these problems, we fitted and evaluated a fixed covariate (J) that contains ones for genotyped animals and zeros for unrelated non-genotyped animals, or pedigree-based regression coefficients for related non-genotyped animals. We also evaluated alternative ways of fitting the J covariate together with genetic groups on biases and stability of breeding value estimates, and of including it into G as a random effect. In a whole vs. partial data set comparison, four scenarios were investigated for the partial data: genotypes missing, phenotypes missing, both genotypes and phenotypes missing, and pedigree missing. Fitting J either as fixed or random reduced level-bias and inflation and increased stability of genomic predictions as compared to the basic model where neither J nor genetic groups were fitted. In most models, genomic predictions were largely biased for scenarios with missing genotype and phenotype information. The biases were reduced for models which combined group and J effects. Models with these corrected group covariates performed better than the recently published model where genetic groups were encapsulated and fitted as random via the Quaas and Pollak transformation. In our Norwegian Red cattle data, a model which combined group and J regression coefficients was preferred because it showed least bias and highest stability of genomic predictions across the scenarios.

Invited review: Unknown-parent groups and metafounders in single-step genomic BLUP

Single-step genomic BLUP (ssGBLUP) is a method for genomic prediction that integrates matrices of pedigree (A) and genomic (G) relationships into a single unified additive relationship matrix whose inverse is incorporated into a set of mixed model equations (MME) to compute genomic predictions. Pedigree information in dairy cattle is often incomplete. Missing pedigree potentially causes biases and inflation in genomic estimated breeding values (GEBV) obtained with ssGBLUP. Three major issues are associated with missing pedigree in ssGBLUP, namely biased predictions by selection, missing inbreeding in pedigree relationships, and incompatibility between G and A in level and scale. These issues can be solved using a proper model for unknown-parent groups (UPG). The theory behind the use of UPG is well established for pedigree BLUP, but not for ssGBLUP. This study reviews the development of the UPG model in pedigree BLUP, the properties of UPG models in ssGBLUP, and the effect of UPG on genetic trends and genomic predictions. Similarities and differences between UPG and metafounder (MF) models, a generalized UPG model, are also reviewed. A UPG model (QP) derived using a transformation of the MME has a good convergence behavior. However, with insufficient data, the QP model may yield biased genetic trends and may underestimate UPG. The QP model can be altered by removing the genomic relationships linking GEBV and UPG effects from MME. This altered QP model exhibits less bias in genetic trends and less inflation in genomic predictions than the QP model, especially with large data sets. Recently, a new model, which encapsulates the UPG equations into the pedigree relationships for genotyped animals, was proposed in simulated purebred populations. The MF model is a comprehensive solution to the missing pedigree issue. This model can be a choice for multibreed or crossbred evaluations if the data set allows the estimation of a reasonable relationship matrix for MF. Missing pedigree influences genetic trends, but its effect on the predictability of genetic merit for genotyped animals should be negligible when many proven bulls are genotyped. The SNP effects can be back-solved using GEBV from older genotyped animals, and these predicted SNP effects can be used to calculate GEBV for young-genotyped animals with missing parents.

Single-step genomic evaluation with metafounders for feed conversion ratio and average daily gain in Danish Landrace and Yorkshire pigs

Background

The single-step genomic best linear unbiased prediction (SSGBLUP) method is a popular approach for genetic evaluation with high-density genotype data. To solve the problem that pedigree and genomic relationship matrices refer to different base populations, a single-step genomic method with metafounders (MF-SSGBLUP) was put forward. The aim of this study was to compare the predictive ability and bias of genomic evaluations obtained with MF-SSGBLUP and standard SSGBLUP. We examined feed conversion ratio (FCR) and average daily gain (ADG) in DanBred Landrace (LL) and Yorkshire (YY) pigs using both univariate and bivariate models, as well as the optimal weighting factors (ω), which represent the proportions of the genetic variance not captured by markers, for ADG and FCR in SSGBLUP and MF-SSGBLUP.

Results

In general, SSGBLUP and MF-SSGBLUP showed similar predictive abilities and bias of genomic estimated breeding values (GEBV). In the LL population, the predictive ability for ADG reached 0.36 using uni- or bi-variate SSGBLUP or MF-SSGBLUP, while the predictive ability for FCR was highest (0.20) for the bivariate model using MF-SSGBLUP, but differences between analyses were very small. In the YY population, predictive ability for ADG was similar for the four analyses (up to 0.35), while the predictive ability for FCR was highest (0.36) for the uni- and bi-variate MF-SSGBLUP analyses. SSGBLUP and MF-SSGBLUP exhibited nearly the same bias. In general, the bivariate models had lower bias than the univariate models. In the LL population, the optimal ω for ADG was ~ 0.2 in the univariate or bivariate models using SSGBLUP or MF-SSGBLUP, and the optimal ω for FCR was 0.70 and 0.55 for SSGBLUP and MF-SSGBLUP, respectively. In the YY population, the optimal ω ranged from 0.25 to 0. 35 for ADG across the four analyses and from 0.10 to 0.30 for FCR.

Conclusions

Our results indicate that MF-SSGBLUP performed slightly better than SSGBLUP for genomic evaluation. There was little difference in the optimal weighting factors (ω) between SSGBLUP and MF-SSGBLUP. Overall, the bivariate model using MF-SSGBLUP is recommended for single-step genomic evaluation of ADG and FCR in DanBred Landrace and Yorkshire pigs.

Genomic prediction for crossbred performance using metafounders

Future genomic evaluation models to be used routinely in breeding programs for pigs and poultry need to be able to optimally use information of crossbred (CB) animals to predict breeding values for CB performance of purebred (PB) selection candidates. Important challenges in the commonly used single-step genomic best linear unbiased prediction (ssGBLUP) model are the definition of relationships between the different line compositions and the definition of the base generation per line. The use of metafounders (MFs) in ssGBLUP has been proposed to overcome these issues. When relationships between lines are known to be different from 0, the use of MFs generalizes the concept of genetic groups relying on the genotype data. Our objective was to investigate the effect of using MFs in genomic prediction for CB performance on estimated variance components, and accuracy and bias of GEBV. This was studied using stochastic simulation to generate data representing a three-way crossbreeding scheme in pigs, with the parental lines being either closely related or unrelated. Results show that using MFs, the variance components should be scaled appropriately, especially when basing them on estimates obtained with, for example a pedigree-based model. The accuracies of GEBV that were obtained using MFs were similar to accuracies without using MFs, regardless whether the lines involved in the CB were closely related or unrelated. The use of MFs resulted in a model that had similar or somewhat better convergence properties compared to other models. We recommend the use of MFs in ssGBLUP for genomic evaluations in crossbreeding schemes.