A fast indirect method to compute functions of genomic relationships concerning genotyped and ungenotyped individuals, for diversity management

Redefining and interpreting genomic relationships of metafounders

Metafounders are a useful concept to characterize relationships within and across populations, and to help genetic evaluations because they help modelling the means and variances of unknown base population animals. Current definitions of metafounder relationships are sensitive to the choice of reference alleles and have not been compared to their counterparts in population genetics-namely, heterozygosities, FST coefficients, and genetic distances. We redefine the relationships across populations with an arbitrary base of a maximum heterozygosity population in Hardy-Weinberg equilibrium. Then, the relationship between or within populations is a cross-product of the formΓ b , b ' = 2 n 2 p b - 1 2 p b ' - 1 ' with p being vectors of allele frequencies at n markers in populations b and b ' . This is simply the genomic relationship of two pseudo-individuals whose genotypes are equal to twice the allele frequencies. We also show that this coding is invariant to the choice of reference alleles. In addition, standard population genetics metrics (inbreeding coefficients of various forms; FST differentiation coefficients; segregation variance; and Nei's genetic distance) can be obtained from elements of matrix Γ .

Genetic Variance Estimation over Time in Broiler Breeding Programmes for Growth and Reproductive Traits

Monitoring the genetic variance of traits is a key priority to ensure the sustainability of breeding programmes in populations under directional selection, since directional selection can decrease genetic variation over time. Studies monitoring changes in genetic variation have typically used long-term data from small experimental populations selected for a handful of traits. Here, we used a large dataset from a commercial breeding line spread over a period of twenty-three years. A total of 2,059,869 records and 2,062,112 animals in the pedigree were used for the estimations of variance components for the traits: body weight (BWT; 2,059,869 records) and hen-housed egg production (HHP; 45,939 records). Data were analysed with three estimation approaches: sliding overlapping windows, under frequentist (restricted maximum likelihood (REML)) and Bayesian (Gibbs sampling) methods; expected variances using coefficients of the full relationship matrix; and a "double trait covariances" analysis by computing correlations and covariances between the same trait in two distinct consecutive windows. The genetic variance showed marginal fluctuations in its estimation over time. Whereas genetic, maternal permanent environmental, and residual variances were similar for BWT in both the REML and Gibbs methods, variance components when using the Gibbs method for HHP were smaller than the variances estimated when using REML. Large data amounts were needed to estimate variance components and detect their changes. For Gibbs (REML), the changes in genetic variance from 1999-2001 to 2020-2022 were 82.29 to 93.75 (82.84 to 93.68) for BWT and 76.68 to 95.67 (98.42 to 109.04) for HHP. Heritability presented a similar pattern as the genetic variance estimation, changing from 0.32 to 0.36 (0.32 to 0.36) for BWT and 0.16 to 0.15 (0.21 to 0.18) for HHP. On the whole, genetic parameters tended slightly to increase over time. The expected variance estimates were lower than the estimates when using overlapping windows. That indicates the low effect of the drift-selection process on the genetic variance, or likely, the presence of genetic variation sources compensating for the loss. Double trait covariance analysis confirmed the maintenance of variances over time, presenting genetic correlations >0.86 for BWT and >0.82 for HHP. Monitoring genetic variance in broiler breeding programmes is important to sustain genetic progress. Although the genetic variances of both traits fluctuated over time, in some windows, particularly between 2003 and 2020, increasing trends were observed, which warrants further research on the impact of other factors, such as novel mutations, operating on the dynamics of genetic variance.

Reliabilities of estimated breeding values in models with metafounders

BACKGROUND

Reliabilities of best linear unbiased predictions (BLUP) of breeding values are defined as the squared correlation between true and estimated breeding values and are helpful in assessing risk and genetic gain. Reliabilities can be computed from the prediction error variances for models with a single base population but are undefined for models that include several base populations and when unknown parent groups are modeled as fixed effects. In such a case, the use of metafounders in principle enables reliabilities to be derived.

METHODS

We propose to compute the reliability of the contrast of an individual's estimated breeding value with that of a metafounder based on the prediction error variances of the individual and the metafounder, their prediction error covariance, and their genetic relationship. Computation of the required terms demands only little extra work once the sparse inverse of the mixed model equations is obtained, or they can be approximated. This also allows the reliabilities of the metafounders to be obtained. We studied the reliabilities for both BLUP and single-step genomic BLUP (ssGBLUP), using several definitions of reliability in a large dataset with 1,961,687 dairy sheep and rams, most of which had phenotypes and among which 27,000 rams were genotyped with a 50K single nucleotide polymorphism (SNP) chip. There were 23 metafounders with progeny sizes between 100,000 and 2000 individuals.

RESULTS

In models with metafounders, directly using the prediction error variance instead of the contrast with a metafounder leads to artificially low reliabilities because they refer to a population with maximum heterozygosity. When only one metafounder is fitted in the model, the reliability of the contrast is shown to be equivalent to the reliability of the individual in a model without metafounders. When there are several metafounders in the model, using a contrast with the oldest metafounder yields reliabilities that are on a meaningful scale and very close to reliabilities obtained from models without metafounders. The reliabilities using contrasts with ssGBLUP also resulted in meaningful values.

CONCLUSIONS

This work provides a general method to obtain reliabilities for both BLUP and ssGBLUP when several base populations are included through metafounders.

Metafounders May Reduce Bias in Composite Cattle Genomic Predictions

Metafounders are pseudo-individuals that act as proxies for animals in base populations. When metafounders are used, individuals from different breeds can be related through pedigree, improving the compatibility between genomic and pedigree relationships. The aim of this study was to investigate the use of metafounders and unknown parent groups (UPGs) for the genomic evaluation of a composite beef cattle population. Phenotypes were available for scrotal circumference at 14 months of age (SC14), post weaning gain (PWG), weaning weight (WW), and birth weight (BW). The pedigree included 680,551 animals, of which 1,899 were genotyped for or imputed to around 30,000 single-nucleotide polymorphisms (SNPs). Evaluations were performed based on pedigree (BLUP), pedigree with UPGs (BLUP_UPG), pedigree with metafounders (BLUP_MF), single-step genomic BLUP (ssGBLUP), ssGBLUP with UPGs for genomic and pedigree relationship matrices (ssGBLUP_UPG) or only for the pedigree relationship matrix (ssGBLUP_UPGA), and ssGBLUP with metafounders (ssGBLUP_MF). Each evaluation considered either four or 10 groups that were assigned based on breed of founders and intermediate crosses. To evaluate model performance, we used a validation method based on linear regression statistics to obtain accuracy, stability, dispersion, and bias of (genomic) estimated breeding value [(G)EBV]. Overall, relationships within and among metafounders were stronger in the scenario with 10 metafounders. Accuracy was greater for models with genomic information than for BLUP. Also, the stability of (G)EBVs was greater when genomic information was taken into account. Overall, pedigree-based methods showed lower inflation/deflation (regression coefficients close to 1.0) for SC14, WWM, and BWD traits. The level of inflation/deflation for genomic models was small and trait-dependent. Compared with regular ssGBLUP, ssGBLUP_MF4 displayed regression coefficient closer to one SC14, PWG, WWM, and BWD. Genomic models with metafounders seemed to be slightly more stable than models with UPGs based on higher similarity of results with different numbers of groups. Further, metafounders can help to reduce bias in genomic evaluations of composite beef cattle populations without reducing the stability of GEBVs.

Why and How to Switch to Genomic Selection: Lessons From Plant and Animal Breeding Experience

The present study is a transversal analysis of the interest in genomic selection for plant and animal species. It focuses on the arguments that may convince breeders to switch to genomic selection. The arguments are classified into three different “bricks.” The first brick considers the addition of genotyping to improve the accuracy of the prediction of breeding values. The second consists of saving costs and/or shortening the breeding cycle by replacing all or a portion of the phenotyping effort with genotyping. The third concerns population management to improve the choice of parents to either optimize crossbreeding or maintain genetic diversity. We analyse the relevance of these different bricks for a wide range of animal and plant species and sought to explain the differences between species according to their biological specificities and the organization of breeding programs.

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

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.

Short communication: Methods to compute genomic inbreeding for ungenotyped individuals

The genomic measure of inbreeding is closer to the actual inbreeding than the pedigree-based measure. However, it cannot be computed for ungenotyped animals. An estimate of genomic inbreeding comes from the diagonal of matrix H used in single-step methods. This matrix projects genomic relationships to all ungenotyped members of the pedigree. The diagonal element of H^-1 gives an estimate of the genomic inbreeding coefficient. However, so far no computational methods are available to compute the diagonal of H. Here we propose 3 exact methods to compute this diagonal. The first uses an already-existing algorithm to compute, for each ungenotyped individual, products of the form Hx to obtain the corresponding diagonal element of H. The second method computes, for each ungenotyped individual, a term that can be written as a quadratic form involving pedigree and genomic relationships. For both methods, the computational burden is linear in the number of ungenotyped animals. The last method reorders the computations of the second method so that they become linear in the number of genotyped animals, which is usually much smaller. We tested the methods in 3 small data sets (with ~2,000 genotyped animals and 30,000-500,000 animals in pedigree) and in a large simulated population (with 1,220,000 animals in pedigree and 36,000 genotyped animals). Tests resulted in satisfactory computing times (<10 min in the largest example using 10 parallel threads). Computing times were much shorter for the third method, as expected. Using these methods, estimates of genomic inbreeding in ungenotyped animals can be obtained on a regular basis.

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.

Turning Observed Founder Alleles into Expected Relationships in an Intercross Population

Pedigree-derived relationships for individuals from an intercross of several lines cannot easily account for the segregation variance that is mainly caused by loci with alternative alleles fixed in different lines. However, when all founders are genotyped for a large number of markers, such relationships can be derived for descendants as expected genomic relationships conditional on the observed founder allele frequencies. A tabular method was derived in detail for autosomes and the X-chromosome. As a case study, we analyzed litter size and body weights at three different ages in an advanced mouse intercross (29 generations, total pedigree size 19,266) between a line selected for high litter size (FL1) and a highly inbred control line (DUKsi). Approximately 60% of the total genetic variance was due to segregation variance. Estimated heritability values were 0.20 (0.03), 0.34 (0.04), 0.23 (0.03), 0.41 (0.03) and 0.47 (0.02) for litter size, litter weight and body weight at ages of 21, 42 and 63 days, respectively (standard errors in brackets). These values were between 12% and 65% higher than observed in analyses that treated founders as unrelated. Fields of applications include experimental populations (selection experiments or advanced intercross lines) with a limited number of founders, which can be genotyped at a reasonable cost. In principle any number of founder lines can be treated. Additional genotypes from individuals in later generations can be combined into a joint relationship matrix by capitalizing on previously published approaches.

Effects of heterozygosity on performance of purebred and crossbred pigs

BACKGROUND

In pigs, crossbreeding aims at exploiting heterosis, but heterosis is difficult to quantify. Heterozygosity at genetic markers is easier to measure and could potentially be used as an indicator of heterosis. The objective of this study was to investigate the effect of heterozygosity on various maternal and production traits in purebred and crossbred pigs. The proportion of heterozygosity at genetic markers across the genome for each individual was included in the prediction model as a fixed regression across or within breeds.

RESULTS

Estimates of regression coefficients of heterozygosity showed large effects for some traits. For maternal traits, regression coefficient estimates were always in a favourable direction, while for production, meat and slaughter quality traits, they were both favourable and unfavourable. Traits with the largest estimated effects of heterozygosity were total number born, litter weight at 3 weeks, weight at 150 days, and age at 40 kg. Estimates of regression coefficients on heterozygosity differed between breeds. Traits with the largest effect of heterozygosity also showed a significant (P < 0.05) increase in prediction accuracy when heterozygosity was included in the model compared to the model without heterozygosity.

CONCLUSIONS

For traits with the largest estimates of regression coefficients on heterozygosity, the inclusion of heterozygosity in the model improved prediction accuracy. Using models that include heterozygosity would result in selecting different animals for breeding, which has the potential to improve genetic gain for these traits. This is most beneficial when crossbreds or several breeds are included in the estimation of breeding values and is relevant to all species, not only pigs. Thus, our results show that including heterozygosity in the model is beneficial for some traits, likely due to dominant gene action.

From clinics to (cow)mics: a reproductive journey

This manuscript describes the different topics I have been involved in the fields of reproductive physiology and embryo biotechnologies with attempts to address practical issues raised mainly by the breeding industry. The journey started with phenotyping work in the field of reproductive physio-pathology. Other issues were related to the optimization of reproductive biotechnologies to favorize genetic selection. The implementation of genomic selection raised opportunities to develop the use embryo biotechnologies and showed the interest of combining them in the case of embryo genotyping. There is still a need to refine phenotyping for reproductive traits especially for the identification of markers of uterine dysfunction. It is believed that new knowledge generated by combining different molecular approaches will be the source of applications that may benefit AI practice and embryo technologies.

Estimates of genetic trend for single-step genomic evaluations

Background

A common measure employed to evaluate the efficacy of livestock improvement schemes is the genetic trend, which is calculated as the means of predicted breeding values for animals born in successive time periods. This implies that different cohorts refer to the same base population. For genetic evaluation schemes integrating genomic information with records for all animals, genotyped or not, this is often not the case: expected means for pedigree founders are zero whereas values for genotyped animals are expected to sum to zero at the (mean) time corresponding to the frequencies that are used to center marker allele counts when calculating genomic relationships.

Methods

The paper examines estimates of genetic trends from single-step genomic evaluations. After a review of methods which propose to align pedigree-based and genomic relationship matrices, simulation is used to illustrate the effects of alignments and choice of assumed gene frequencies on trajectories of genetic trends.

Results

The results show that methods available to alleviate differences between the founder populations implied by the two types of relationship matrices perform well; in particular, the meta-founder approach is advantageous. An application to data from routine genetic evaluation of Australian sheep is shown, confirming their effectiveness for practical data.

Conclusions

Aligning pedigree and genomic relationship matrices for single step genetic evaluation for populations under selection is essential. Fitting meta-founders is an effective and simple method to avoid distortion of estimates of genetic trends.