Estimating genomic relationships of metafounders across and within breeds using maximum likelihood, pseudo-expectation-maximization maximum likelihood and increase of relationships.

BACKGROUND: The theory of "metafounders" proposes a unified framework for relationships across base populations within breeds (e.g. unknown parent groups), and base populations across breeds (crosses) together with a sensible compatibility with genomic relationships. Considering metafounders might be advantageous in pedigree best linear unbiased prediction (BLUP) or single-step genomic BLUP. Existing methods to estimate relationships across metafounders Γ are not well adapted to highly unbalanced data, genotyped individuals far from base populations, or many unknown parent groups (within breed per year of birth). METHODS: We derive likelihood methods to estimate Γ . For a single metafounder, summary statistics of pedigree and genomic relationships allow deriving a cubic equation with the real root being the maximum likelihood (ML) estimate of Γ . This equation is tested with Lacaune sheep data. For several metafounders, we split the first derivative of the complete likelihood in a term related to Γ , and a second term related to Mendelian sampling variances. Approximating the first derivative by its first term results in a pseudo-EM algorithm that iteratively updates the estimate of Γ by the corresponding block of the H-matrix. The method extends to complex situations with groups defined by year of birth, modelling the increase of Γ using estimates of the rate of increase of inbreeding ( Δ F ), resulting in an expanded Γ and in a pseudo-EM+ Δ F algorithm. We compare these methods with the generalized least squares (GLS) method using simulated data: complex crosses of two breeds in equal or unsymmetrical proportions; and in two breeds, with 10 groups per year of birth within breed. We simulate genotyping in all generations or in the last ones. RESULTS: For a single metafounder, the ML estimates of the Lacaune data corresponded to the maximum. For simulated data, when genotypes were spread across all generations, both GLS and pseudo-EM(+ Δ F ) methods were accurate. With genotypes only available in the most recent generations, the GLS method was biased, whereas the pseudo-EM(+ Δ F ) approach yielded more accurate and unbiased estimates. CONCLUSIONS: We derived ML, pseudo-EM and pseudo-EM+ Δ F methods to estimate Γ in many realistic settings. Estimates are accurate in real and simulated data and have a low computational cost.

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 form Γ 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 .

Metabolomic-genomic prediction can improve prediction accuracy of breeding values for malting quality traits in barley.

BACKGROUND: Metabolomics measures an intermediate stage between genotype and phenotype, and may therefore be useful for breeding. Our objectives were to investigate genetic parameters and accuracies of predicted breeding values for malting quality (MQ) traits when integrating both genomic and metabolomic information. In total, 2430 plots of 562 malting spring barley lines from three years and two locations were included. Five MQ traits were measured in wort produced from each plot. Metabolomic features used were 24,018 nuclear magnetic resonance intensities measured on each wort sample. Methods for statistical analyses were genomic best linear unbiased prediction (GBLUP) and metabolomic-genomic best linear unbiased prediction (MGBLUP). Accuracies of predicted breeding values were compared using two cross-validation strategies: leave-one-year-out (LOYO) and leave-one-line-out (LOLO), and the increase in accuracy from the successive inclusion of first, metabolomic data on the lines in the validation population (VP), and second, both metabolomic data and phenotypes on the lines in the VP, was investigated using the linear regression (LR) method. RESULTS: For all traits, we saw that the metabolome-mediated heritability was substantial. Cross-validation results showed that, in general, prediction accuracies from MGBLUP and GBLUP were similar when phenotypes and metabolomic data were recorded on the same plots. Results from the LR method showed that for all traits, except one, accuracy of MGBLUP increased when including metabolomic data on the lines of the VP, and further increased when including also phenotypes. However, in general the increase in accuracy of MGBLUP when including both metabolomic data and phenotypes on lines of the VP was similar to the increase in accuracy of GBLUP when including phenotypes on the lines of the VP. Therefore, we found that, when metabolomic data were included on the lines of the VP, accuracies substantially increased for lines without phenotypic records, but they did not increase much when phenotypes were already known. CONCLUSIONS: MGBLUP is a useful approach to combine phenotypic, genomic and metabolomic data for predicting breeding values for MQ traits. We believe that our results have significant implications for practical breeding of barley and potentially many other species.

Segregation between breeds and local breed proportions in genetic and genomic models for crossbreds.

BACKGROUND: The breeding value of a crossbred individual can be expressed as the sum of the contributions from each of the contributing pure breeds. In theory, the breeding value should account for segregation between breeds, which results from the difference in the mean contribution of loci between breeds, which in turn is caused by differences in allele frequencies between breeds. However, with multiple generations of crossbreeding, how to account for breed segregation in genomic models that split the breeding value of crossbreds based on breed origin of alleles (BOA) is not known. Furthermore, local breed proportions (LBP) have been modelled based on BOA and is a concept related to breed segregation. The objectives of this study were to explore the theoretical background of the effect of LBP and how it relates to breed segregation and to investigate how to incorporate breed segregation (co)variance in genomic BOA models. RESULTS: We showed that LBP effects result from the difference in the mean contribution of loci between breeds in an additive genetic model, i.e. breed segregation effects. We found that the (co)variance structure for BS effects in genomic BOA models does not lead to relationship matrices that are positive semi-definite in all cases. However, by setting one breed as a reference breed, a valid (co)variance structure can be constructed by including LBP effects for all other breeds and assuming them to be correlated. We successfully estimated variance components for a genomic BOA model with LBP effects in a simulated example. CONCLUSIONS: Breed segregation effects and LBP effects are two alternative ways to account for the contribution of differences in the mean effects of loci between breeds. When the covariance between LBP effects across breeds is included in the model, a valid (co)variance structure for LBP effects can be constructed by setting one breed as reference breed and fitting an LBP effect for each of the other breeds.

Genomic evaluation for two-way crossbred performance in cattle.

BACKGROUND: Dairy cattle production systems are mostly based on purebreds, but recently the use of crossbreeding has received increased interest. For genetic evaluations including crossbreds, several methods based on single-step genomic best linear unbiased prediction (ssGBLUP) have been proposed, including metafounder ssGBLUP (MF-ssGBLUP) and breed-specific ssGBLUP (BS-ssGBLUP). Ideally, models that account for breed effects should perform better than simple models, but knowledge on the performance of these methods is lacking for two-way crossbred cattle. In addition, the differences in the estimates of genetic parameters (such as the genetic variance component and heritability) between these methods have rarely been investigated. Therefore, the aims of this study were to (1) compare the estimates of genetic parameters for average daily gain (ADG) and feed conversion ratio (FCR) between these methods; and (2) evaluate the impact of these methods on the predictive ability for crossbred performance. METHODS: Bivariate models using standard ssGBLUP, MF-ssGBLUP and BS-ssGBLUP for the genetic evaluation of ADG and FCR were investigated. To measure the predictive ability of these three methods, we estimated four estimators, bias, dispersion, population accuracy and ratio of population accuracies, using the linear regression (LR) method. RESULTS: The results show that, for both ADG and FCR, the heritabilities were low with the three methods. For FCR, the differences in the estimated genetic parameters were small between the three methods, while for ADG, those estimated with BS-ssGBLUP deviated largely from those estimated with the other two methods. Bias and dispersion were similar across the three methods. Population accuracies for both ADG and FCR were always higher with MF-ssGBLUP than with ssGBLUP, while with BS-ssGBLUP the population accuracy was highest for FCR and lowest for ADG. CONCLUSIONS: Our results indicate that in the genetic evaluation for crossbred performance in a two-way crossbred cattle production system, the predictive ability of MF-ssGBLUP and BS-ssGBLUP is greater than that of ssGBLUP, when the estimated variance components are consistent across the three methods. Compared with BS-ssGBLUP, MF-ssGBLUP is more robust in its superiority over ssGBLUP.

The impact of genotyping strategies and statistical models on accuracy of genomic prediction for survival in pigs.

BACKGROUND: Survival from birth to slaughter is an important economic trait in commercial pig productions. Increasing survival can improve both economic efficiency and animal welfare. The aim of this study is to explore the impact of genotyping strategies and statistical models on the accuracy of genomic prediction for survival in pigs during the total growing period from birth to slaughter.  RESULTS: We simulated pig populations with different direct and maternal heritabilities and used a linear mixed model, a logit model, and a probit model to predict genomic breeding values of pig survival based on data of individual survival records with binary outcomes (0, 1). The results show that in the case of only alive animals having genotype data, unbiased genomic predictions can be achieved when using variances estimated from pedigree-based model. Models using genomic information achieved up to 59.2% higher accuracy of estimated breeding value compared to pedigree-based model, dependent on genotyping scenarios. The scenario of genotyping all individuals, both dead and alive individuals, obtained the highest accuracy. When an equal number of individuals (80%) were genotyped, random sample of individuals with genotypes achieved higher accuracy than only alive individuals with genotypes. The linear model, logit model and probit model achieved similar accuracy. CONCLUSIONS: Our conclusion is that genomic prediction of pig survival is feasible in the situation that only alive pigs have genotypes, but genomic information of dead individuals can increase accuracy of genomic prediction by 2.06% to 6.04%.

Local breed proportions and local breed heterozygosity in genomic predictions for crossbred dairy cows.

For genomic prediction of crossbred animals, models that account for the breed origin of alleles (BOA) in marker genotypes can allow the effects of marker alleles to differ depending on their ancestral breed. Previous studies have shown that genomic estimated breeding values for crossbred cows can be calculated using the marker effects that are estimated in the contributing pure breeds and combined based on estimated BOA in the genotypes of the crossbred cows. In the presented study, we further exploit the BOA information for improving the prediction of genomic breeding values of crossbred dairy cows. We investigated 2 types of BOA-derived breed proportions: global breed proportions, defined as the proportion of marker alleles assigned to each breed across the whole genome; and local breed proportions (LBP), defined as the proportions of alleles on chromosome segments which were assigned to each breed. Further, we investigated 2 BOA-derived measures of heterozygosity for the prediction of total genetic value. First, global breed heterozygosity, defined as the proportion of marker loci that have alleles originating in 2 different breeds over the whole genome. Second, local breed heterozygosity (LBH), defined as proportions of marker loci on chromosome segments that had alleles originating in 2 different breeds. We estimated variance related to LBP and LBH on the remaining variation after accounting for prediction with solutions from the genomic evaluations of the pure breeds and validated alternative models for production traits in 5,214 Danish crossbred dairy cows. The estimated LBP variances were 0.9, 1.2, and 1.0% of phenotypic variance for milk, fat, and protein yield, respectively. We observed no clear LBH effect. Cross-validation showed that models with LBP effects had a numerically small but statistically significantly higher predictive ability than models only including global breed proportions. We observed similar improvement in accuracy by the model having an across crossbred residual additive genetic effect, accounting for the additive genetic variation that was not accounted for by the solutions from purebred. For genomic predictions of crossbred animals, estimated BOA can give useful information on breed proportions, both globally in the genome and locally in genome regions, and on breed heterozygosity.

Genomic predictions for crossbred dairy cows by combining solutions from purebred evaluation based on breed origin of alleles.

Genomic predictions have been applied for dairy cattle for more than a decade with great success, but genomic estimated breeding values (GEBV) are not widely available for crossbred dairy cows. The large reference populations already in place for genomic evaluations of many pure breeds makes it interesting to use the accurate solutions, in particular the estimated marker effects, from these evaluations for calculation of GEBV for crossbred heifers and cows. Effects of marker alleles in crossbred animals can depend on breed origin of the alleles (BOA). Therefore, our aim was to investigate if reliable GEBV for crossbred dairy cows can be obtained by combining estimated marker effects from purebred evaluations based on BOA. We used data on 5,467 Danish crossbred dairy cows with contributions from Holstein, Jersey, and Red Dairy Cattle breeds. We assessed BOA assignment on their genotypes and found that we could assign 99.3% of the alleles to a definite breed of origin. We compared GEBV for 2 traits, protein yield and interval between first and last insemination of cows, with 2 models that both combine estimated marker effects from the genomic evaluations of the pure breeds: a breed of origin model that accounts for BOA and a breed proportion model that only accounts for genomic breed proportions in the crossbred animals. We accounted for the difference in level between the purebred evaluations by including intercepts in the models based on phenotypic averages. The predictive ability for protein yield was significantly higher from the breed of origin model, 0.45 compared with 0.43 from the breed proportion model. Furthermore, for the breed proportion model, the GEBVs had level bias, which made comparison across groups with different breed composition skewed. We therefore concluded that reliable genomic predictions for crossbred dairy cows can be obtained by combining estimated marker effects from the genomic evaluations of purebreds using a model that accounts for BOA.

Genetic evaluation including intermediate omics features.

In animal and plant breeding and genetics, there has been an increasing interest in intermediate omics traits, such as metabolomics and transcriptomics, which mediate the effect of genetics on the phenotype of interest. For inclusion of such intermediate traits into a genetic evaluation system, there is a need for a statistical model that integrates phenotypes, genotypes, pedigree, and omics traits, and a need for associated computational methods that provide estimated breeding values. In this paper, a joint model for phenotypes and omics data is presented, and a formula for the breeding values on individuals is derived. For complete omics data, three equivalent methods for best linear unbiased prediction of breeding values are presented. In all three cases, this requires solving two mixed model equation systems. Estimation of parameters using restricted maximum likelihood is also presented. For incomplete omics data, extensions of two of these methods are presented, where in both cases, the extension consists of extending an omics-related similarity matrix to incorporate individuals without omics data. The methods are illustrated using a simulated data set.

Breed of origin of alleles and genomic predictions for crossbred dairy cows.

BACKGROUND: In dairy cattle, genomic selection has been implemented successfully for purebred populations, but, to date, genomic estimated breeding values (GEBV) for crossbred cows are rarely available, although they are valuable for rotational crossbreeding schemes that are promoted as efficient strategies. An attractive approach to provide GEBV for crossbreds is to use estimated marker effects from the genetic evaluation of purebreds. The effects of each marker allele in crossbreds can depend on the breed of origin of the allele (BOA), thus applying marker effects based on BOA could result in more accurate GEBV than applying only proportional contribution of the purebreds. Application of BOA models in rotational crossbreeding requires methods for detecting BOA, but the existing methods have not been developed for rotational crossbreeding. Therefore, the aims of this study were to develop and test methods for detecting BOA in a rotational crossbreeding system, and to investigate methods for calculating GEBV for crossbred cows using estimated marker effects from purebreds. RESULTS: For detecting BOA in crossbred cows from rotational crossbreeding for which pedigree is recorded, we developed the AllOr method based on the comparison of haplotypes in overlapping windows. To calculate the GEBV of crossbred cows, two models were compared: a BOA model where marker effects estimated from purebreds are combined based on the detected BOA; and a breed proportion model where marker effects are combined based on estimated breed proportions. The methods were tested on simulated data that mimic the first four generations of rotational crossbreeding between Holstein, Jersey and Red Dairy Cattle. The AllOr method detected BOA correctly for 99.6% of the marker alleles across the four crossbred generations. The reliability of GEBV was higher with the BOA model than with the breed proportion model for the four generations of crossbreeding, with the largest difference observed in the first generation. CONCLUSIONS: In rotational crossbreeding for which pedigree is recorded, BOA can be accurately detected using the AllOr method. Combining marker effects estimated from purebreds to predict the breeding value of crossbreds based on BOA is a promising approach to provide GEBV for crossbred dairy cows.

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.

Genetic parameters and genomic prediction for feed intake recorded at the group and individual level in different production systems for growing pigs.

BACKGROUND: In breeding programs, recording large-scale feed intake (FI) data routinely at the individual level is costly and difficult compared with other production traits. An alternative approach could be to record FI at the group level since animals such as pigs are normally housed in groups and fed by a shared feeder. However, to date there have been few investigations about the difference between group- and individual-level FI recorded in different environments. We hypothesized that group- and individual-level FI are genetically correlated but different traits. This study, based on the experiment undertaken in purebred DanBred Landrace (L) boars, was set out to estimate the genetic variances and correlations between group- and individual-level FI using a bivariate random regression model, and to examine to what extent prediction accuracy can be improved by adding information of individual-level FI to group-level FI for animals recorded in groups. For both bivariate and univariate models, single-step genomic best linear unbiased prediction (ssGBLUP) and pedigree-based BLUP (PBLUP) were implemented and compared. RESULTS: The variance components from group-level records and from individual-level records were similar. Heritabilities estimated from group-level FI were lower than those from individual-level FI over the test period. The estimated genetic correlations between group- and individual-level FI based on each test day were on average equal to 0.32 (SD = 0.07), and the estimated genetic correlation for the whole test period was equal to 0.23. Our results demonstrate that by adding information from individual-level FI records to group-level FI records, prediction accuracy increased by 0.018 and 0.032 compared with using group-level FI records only (bivariate vs. univariate model) for PBLUP and ssGBLUP, respectively. CONCLUSIONS: Based on the current dataset, our findings support the hypothesis that group- and individual-level FI are different traits. Thus, the differences in FI traits under these two feeding systems need to be taken into consideration in pig breeding programs. Overall, adding information from individual records can improve prediction accuracy for animals with group records.

Selection and drift reduce genetic variation for milk yield in Manech Tête Rousse dairy sheep.

Decreases in genetic variance over generations reduce future genetic gain. We studied the evolution of genetic variance in the dairy sheep breed Manech Tête Rousse, which has been selected for increasingly complex objectives, including, in this order, milk yield, milk contents, scrapie resistance, and somatic cell score. We estimated base population genetic variance and genetic variance by sex and per year of birth from 1981 to 2014. The data consisted of 1,842,295 milk yield records (from 1978 to 2017) and a pedigree including 530,572 females (96% of them with records) and 3,798 artificial insemination males. As a measure of drift, we computed average relationships for each cohort from which we derived expected reduction of variance due to increased relationships. The difference between observed and expected reductions in genetic variances is the reduction in genetic variance due to selection. Average relationships increased steadily but slowly in both sexes. For females, genetic variance reduced with time until a plateau was reached at around 90% of the initial genetic variance. The reduction due to relationships (roughly 3% cumulated in 30 yr) was smaller than that due to selection (roughly 10% across the last years). A smaller loss due to selection was seen in recent years, possibly due to a change in selection objectives. These results agree well with theoretical expectations. The pattern of the evolution of genetic variance in males was similar to that for females but with a stronger reduction because of strong selection of AI males at birth. We conclude that the reductions in genetic variation due to selection and drift agree with expectations, and none of the reductions are very strong in this population because of control of inbreeding and smooth changes in selection objectives over time.

Prediction of breeding values for group-recorded traits including genomic information and an individually recorded correlated trait.

Records on groups of individuals could be valuable for predicting breeding values when a trait is difficult or costly to measure on single individuals, such as feed intake and egg production. Adding genomic information has shown improvement in the accuracy of genetic evaluation of quantitative traits with individual records. Here, we investigated the value of genomic information for traits with group records. Besides, we investigated the improvement in accuracy of genetic evaluation for group-recorded traits when including information on a correlated trait with individual records. The study was based on a simulated pig population, including three scenarios of group structure and size. The results showed that both the genomic information and a correlated trait increased the accuracy of estimated breeding values (EBVs) for traits with group records. The accuracies of EBV obtained from group records with a size 24 were much lower than those with a size 12. Random assignment of animals to pens led to lower accuracy due to the weaker relationship between individuals within each group. It suggests that group records are valuable for genetic evaluation of a trait that is difficult to record on individuals, and the accuracy of genetic evaluation can be considerably increased using genomic information. Moreover, the genetic evaluation for a trait with group records can be greatly improved using a bivariate model, including correlated traits that are recorded individually. For efficient use of group records in genetic evaluation, relatively small group size and close relationships between individuals within one group are recommended.

Prediction of genetic merit for growth rate in pigs using animal models with indirect genetic effects and genomic information.

BACKGROUND: Several studies have found that the growth rate of a pig is influenced by the genetics of the group members (indirect genetic effects). Accounting for these indirect genetic effects in a selection program may increase genetic progress for growth rate. However, indirect genetic effects are small and difficult to predict accurately. Genomic information may increase the ability to predict indirect genetic effects. Thus, the objective of this study was to test whether including indirect genetic effects in the animal model increases the predictive performance when genetic effects are predicted with genomic relationships. In total, 11,255 pigs were phenotyped for average daily gain between 30 and 94 kg, and 10,995 of these pigs were genotyped. Two relationship matrices were used: a numerator relationship matrix ([Formula: see text]) and a combined pedigree and genomic relationship matrix ([Formula: see text]); and two different animal models were used: an animal model with only direct genetic effects and an animal model with both direct and indirect genetic effects. The predictive performance of the models was defined as the Pearson correlation between corrected phenotypes and predicted genetic levels. The predicted genetic level of a pig was either its direct genetic effect or the sum of its direct genetic effect and the indirect genetic effects of its group members (total genetic effect). RESULTS: The highest predictive performance was achieved when total genetic effects were predicted with genomic information (21.2 vs. 14.7%). In general, the predictive performance was greater for total genetic effects than for direct genetic effects (0.1 to 0.5% greater; not statistically significant). Both types of genetic effects had greater predictive performance when they were predicted with [Formula: see text] rather than [Formula: see text] (5.9 to 6.3%). The difference between predictive performances of total genetic effects and direct genetic effects was smaller when [Formula: see text] was used rather than [Formula: see text]. CONCLUSIONS: This study provides evidence that: (1) corrected phenotypes are better predicted with total genetic effects than with direct genetic effects only; (2) both direct genetic effects and indirect genetic effects are better predicted with [Formula: see text] than [Formula: see text]; (3) using [Formula: see text] rather than [Formula: see text] primarily improves the predictive performance of direct genetic effects.

Bias and accuracy of dairy sheep evaluations using BLUP and SSGBLUP with metafounders and unknown parent groups.

BACKGROUND: Bias has been reported in genetic or genomic evaluations of several species. Common biases are systematic differences between averages of estimated and true breeding values, and their over- or under-dispersion. In addition, comparing accuracies of pedigree versus genomic predictions is a difficult task. This work proposes to analyse biases and accuracies in the genetic evaluation of milk yield in Manech Tête Rousse dairy sheep, over several years, by testing five models and using the estimators of the linear regression method. We tested models with and without genomic information [best linear unbiased prediction (BLUP) and single-step genomic BLUP (SSGBLUP)] and using three strategies to handle missing pedigree [unknown parent groups (UPG), UPG with QP transformation in the [Formula: see text] matrix (EUPG) and metafounders (MF)]. METHODS: We compared estimated breeding values (EBV) of selected rams at birth with the EBV of the same rams obtained each year from the first daughters with phenotypes up to 2017. We compared within and across models. Finally, we compared EBV at birth of the rams with and without genomic information. RESULTS: Within models, bias and over-dispersion were small (bias: 0.20 to 0.40 genetic standard deviations; slope of the dispersion: 0.95 to 0.99) except for model SSGBLUP-EUPG that presented an important over-dispersion (0.87). The estimates of accuracies confirm that the addition of genomic information increases the accuracy of EBV in young rams. The smallest bias was observed with BLUP-MF and SSGBLUP-MF. When we estimated dispersion by comparing a model with no markers to models with markers, SSGBLUP-MF showed a value close to 1, indicating that there was no problem in dispersion, whereas SSGBLUP-EUPG and SSGBLUP-UPG showed a significant under-dispersion. Another important observation was the heterogeneous behaviour of the estimates over time, which suggests that a single check could be insufficient to make a good analysis of genetic/genomic evaluations. CONCLUSIONS: The addition of genomic information increases the accuracy of EBV of young rams in Manech Tête Rousse. In this population that has missing pedigrees, the use of UPG and EUPG in SSGBLUP produced bias, whereas MF yielded unbiased estimates, and we recommend its use. We also recommend assessing biases and accuracies using multiple truncation points, since these statistics are subject to random variation across years.

Genetic associations between stayability and longevity in commercial crossbred sows, and stayability in multiplier sows.

Longevity in commercial sows is often selected for through stayability traits measured in purebred animals. However, this may not be justifiable because longevity and stayability may be subject to both genotype by environment interaction (G × E) and genotype by genotype interaction (G × G). This study tested the hypothesis that stayability to service after first parity is more strongly genetically correlated with longevity in commercial herds when stayability is measured in commercial herds rather than multiplier herds. The analysis was based on farrowing- and service-records from 470,824 sows (189,263 multiplier; 281,561 commercial) and 300 herds (156 multiplier; 144 commercial sows). Multiplier sows were either purebred Landrace or Yorkshire and commercial sows were mainly rotationally crossbreds between the two breeds. Commercial longevity was defined as age in days when culled (LongC), and stayability to service after first parity was defined for both commercial sows (StayC) and multiplier sows (StayM). The genetic correlations between LongC, StayC, and StayM were estimated by restricted maximum likelihood using linear mixed models. Genetic parameters were estimated separately for Landrace and Yorkshire. In Landrace, the genetic correlations between LongC and StayC, LongC and StayM, and StayC and StayM were 0.86 ± 0.02, 0.24 ± 0.05, and 0.34 ± 0.06, respectively. In Yorkshire, the genetic correlations between LongC and StayC, LongC and StayM, and StayC and StayM were 0.81 ± 0.03, 0.17 ± 0.05, and 0.18 ± 0.7, respectively. Conclusively, longevity in commercial herds is more strongly correlated with stayability when stayability is measured in commercial herds rather than multiplier herds.

Correction to: A bivariate genomic model with additive, dominance and inbreeding depression effects for sire line and three-way crossbred pigs.

An amendment to this paper has been published and can be accessed via the original article.