Technical note: recursive algorithm for inbreeding coefficients assuming nonzero inbreeding of unknown parents

Improved computation of genomic and pedigree inbreeding and relationships accounting for the X chromosome

Breeders for many decades used pedigrees to limit increases in inbreeding, but genomic measures of relationship and inbreeding provide more precise control. Previous calculations of pedigree inbreeding (Fped), genomic inbreeding (Fgen), pedigree expected future inbreeding (EFIped), and genomic expected future inbreeding (EFIgen) included the X chromosome but ignored its influence when estimating relationships. The X chromosome contributes to inbreeding in female progeny, for example, if parents with the same X chromosome are mated. Because the X-specific region has 3.0% of the 79,060 markers used in US genomic evaluation and those markers are coded as 100% homozygous in males, homozygosity of females appeared to be 3% less than for males. Allele frequency also effects the computation of Fgen. Programs to compute pedigree and genomic measures were revised to improve speed and memory use, as well as to better account for the X chromosome. Revised software reduced computational time from 33 h to 13 min (152 times faster) using 32 processors for Fped and EFIped with 88 million animals in the pedigree and from 19 h to 28 min (41 times faster) for Fgen and EFIgen for 3,280,753 genotyped animals of 5 breeds. Correlations were high between Fgen computed using either an allele frequency of 0.5 or a base population frequency for most breeds. Mean Fgen was higher for males than for females, but adjustments for the X chromosome made Fgen means more comparable across genders. The X adjustments did not affect correlations within gender. After adjusting Fgen for the X chromosome using an allele frequency of 0.5, correlations across breeds and gender increased, and X-adjusted Fgen was more similar to Fped. Using an allele frequency of 0.5, mean correlation with Fped across breeds was 0.67 for Fgen, 0.67 for X-adjusted Fgen, and 0.54 for Fgen with base population allele frequency; corresponding EFI correlations were 0.83, 0.83, and 0.84. Breeds with smaller populations were more sensitive to the use of different allele frequencies. Mean correlation of haplotype-based inbreeding with Fped was 0.64. Revision of inbreeding software allowed simpler and more accurate comparison of genomic and pedigree relationships and much faster computation.

Genetic inbreeding load and its individual prediction for milk yield in French dairy sheep

BACKGROUND

The magnitude of inbreeding depression depends on the recessive burden of the individual, which can be traced back to the hidden (recessive) inbreeding load among ancestors. However, these ancestors carry different alleles at potentially deleterious loci and therefore there is individual variability of this inbreeding load. Estimation of the additive genetic value for inbreeding load is possible using a decomposition of inbreeding in partial inbreeding components due to ancestors. Both the magnitude of variation in partial inbreeding components and the additive genetic variance of inbreeding loads are largely unknown. Our study had three objectives. First, based on substitution effect under non-random matings, we showed analytically that inbreeding load of an ancestor can be expressed as an additive genetic effect. Second, we analysed the structure of individual inbreeding by examining the contributions of specific ancestors/founders using the concept of partial inbreeding coefficients in three French dairy sheep populations (Basco-Béarnaise, Manech Tête Noire and Manech Tête Rousse). Third, we included these coefficients in a mixed model as random regression covariates, to predict genetic variance and breeding values of the inbreeding load for milk yield in the same breeds.

RESULTS

Pedigrees included 190,276, 166,028 and 633,655 animals of Basco-Béarnaise, Manech Tête Noire and Manech Tête Rousse, respectively, born between 1985 and 2021. A fraction of 99.1% of the partial inbreeding coefficients were lower than 0.01 in all breeds, meaning that in practice inbreeding occurs in pedigree loops that span several generations backwards. Less than 5% ancestors generate inbreeding, because mating is essentially between unrelated individuals. Inbreeding load estimations involved 658,731, 541,180 and 2,168,454 records of yearly milk yield from 178,123, 151,863 and 596,586 females in Basco-Béarnaise, Manech Tête Noire and Manech Tête Rousse, respectively. Adding the inbreeding load effect to the model improved the fitting (values of the statistic Likelihood Ratio Test between 132 and 383) for milk yield in the three breeds. The inbreeding load variances were equal to 11,804 and 9435 L squared of milk yield for a fully inbred (100%) descendant in Manech Tête Noire and Manech Tête Rousse. In Basco-Béarnaise, the estimate of the inbreeding load variance (11,804) was not significantly different from zero. The correlations between (direct effect) additive genetic and inbreeding load effects were - 0.09, - 0.08 and - 0.12 in Basco-Béarnaise, Manech Tête Noire and Manech Tête Rousse.

CONCLUSIONS

The decomposition of inbreeding in partial coefficients in these populations shows that inbreeding is mostly due to several small contributions of ancestors (lower than 0.001) going back several generations (5 to 7 generations), which is according to the policy of avoiding close matings. There is variation of inbreeding load among animals, although its magnitude does not seem enough to warrant selection based on this criterion.

Impact of inbreeding on production, fertility, and health traits in German Holstein dairy cattle utilizing various inbreeding estimators

In dairy cattle production, it is important to understand how inbreeding affects production, fertility, and health traits. However, there is still limited use of genomic information to estimate inbreeding, despite advancements in genotyping technologies. To address this gap, we investigated the effect of inbreeding on German Holstein dairy cattle using both pedigree-based and genomic-based inbreeding estimators. We employed one method based on pedigree information (Fped) together with 6 genomic-based methods, including 3 genome-wide complex trait analysis software estimators (Fhat1, Fhat2, Fhat3), VanRaden's first method (FVR1, with observed allele frequencies, and FVR0.5, when allele frequencies are set to 0.5), and one based on runs of homozygosity (Froh). Data from 24,489 cows with both phenotypes and genotypes were used, with a pedigree including 232,780 animals born between 1970 and 2018. We analyzed the effects of inbreeding depression on production, fertility, and health traits separately, using single-trait linear animal models as well as threshold models to account for the binary nature of the health traits. For the health traits, we transformed solutions from the liability scale to a probability scale for easier interpretation. Our results showed that the mean inbreeding coefficients from all estimators ranged from -0.003 to 0.243, with negative values observed for most genomic-based methods. We found out that a 1% increase in inbreeding caused a depression ranging from 25.94 kg (Fhat1) to 40.62 kg (Fhat3), 1.18 kg (Fhat2) to 1.70 kg (Fhat3), 0.90 kg (Fhat2) to 1.45 kg (Froh and Fhat3), 0.19 (Fped) to 0.34 d (Fhat3) for 305-d milk yield, fat, protein, and calving interval, respectively. The health traits showed very slight gradual changes when inbreeding was increased steadily from 0% to 50%, with digital dermatitis showing a rather contrasting trend to that of mastitis, which increased the more an animal was inbred. Overall, our study highlights the importance of considering both pedigree-based and genomic-based inbreeding estimators when assessing the impact on inbreeding, emphasizing that not all inbreeding is harmful.

Unraveling inbreeding patterns and selection signals in Alpine Grey cattle

Inbreeding plays a crucial role in livestock breeding, influencing genetic diversity and phenotypic traits. Genomic data have helped address limitations posed by incomplete pedigrees, providing deeper insights into breed genetic diversity. This study assesses inbreeding levels via pedigree and genomic approaches and analyzes old and recent inbreeding using runs of homozygosity (ROH), and selection signals in Alpine Grey cattle. Pedigree data from 165 575 individuals, analyzed with INBUPGF90 software, computed inbreeding coefficients. Genomic-based coefficients derived from PLINK v1.9. or DetectRUNS R package analyses of 1 180 individuals' genotypes. Common single nucleotide polymorphisms within ROH pinpointed genomic regions, aggregating into "ROH islands" indicative of selection pressure. Overlaps with USCS Genome Browser unveiled gene presence. Moderate correlations (0.20-0.54) existed between pedigree and genomic coefficients, with most genomic estimators having higher (>0.8) correlation values. Inbreeding averaged 0.04 in < 8 Mb ROH segments, and 0.03 in > 16 Mb segments; > 90% of ROHs were < 8 Mb, indicating ancient inbreeding prevalence. Recent inbreeding proved less detrimental than in cosmopolitan breeds. Two major ROH islands on chromosomes 6 and 7 harbored genes linked to immune response, disease resistance (PYURF, HERC3), and fertility (EIF4EBP3, SRA1). This study underscores the need for detailed inbreeding analyses to understand genetic characteristics and historical changes in local breeds like Alpine Grey cattle. Genomic insights, especially from ROH, facilitated overcoming pedigree limitations, illuminating breed genetic diversity. Our findings reveal ancient inbreeding's enduring genetic impact and ROH islands potential for selective sweeps, elucidating traits in Alpine Grey cattle.

Effects of inbreeding on production traits and genetic evaluations in Guzerá beef cattle raised under tropical conditions

The objectives of this study were to evaluate the influence of inbreeding on growth traits and body measurements, as well as on the estimation of genetic parameters and genetic trends in Guzerá cattle. Phenotypic records of 4,212 animals selected for postweaning weight from Guzerá Breeding Program of Advanced Beef Cattle Research Center were utilized. The pedigree file contained records from 7,213 animals born from 1928 to 2019. The traits analyzed were: birth weight (BW), weights adjusted to 210, 378 and 550 days of age (W210, W378 and W550, respectively), chest girth at 378 and 550 days of age (CG378 and CG550), scrotal circumference (SC), and hip height at 378 and 550 days of age (HH378 and H550). Linear regression was used to evaluate the effects of inbreeding on traits. Genetic parameters were obtained using models including or not the effect of inbreeding as a covariate. Inbreeding had negative effects (P ≤ 0.01) on BW (-0.09 kg), W378 (-2.86 kg), W550 (-2.95 kg), HH378 (-0.10 cm), and H550 (-0.29 cm). The lowest and highest heritability estimates were obtained for W210 (0.21 ± 0.07) and HH550 (0.57 ± 0.06), respectively. The genetic correlations were strong and positive between all traits, ranging from 0.44 ± 0.08 (SC x HH) to 0.99 ± 0.01 (W378 x W550). Spearman correlations between EBVs obtained with or without inbreeding effect ranged from 0.968 to 0.995 (P < 0.01). The results indicate loss of productive performance in inbred animals. However, the inclusion of inbreeding coefficient in genetic evaluation models did not alter the magnitude of genetic parameters or genetic trends for the traits studied.

Genetic diversity patterns in farmed rainbow trout (Oncorhynchus mykiss) populations using genome-wide SNP and haplotype data

Rainbow trout is one of the most popular aquaculture species worldwide, with a long history of domestication. However, limited information exists about the genetic diversity of farmed rainbow trout populations globally, with most available reports relying on low-throughput genotyping technologies. Notably, no information exists about the genetic diversity status of farmed rainbow trout in Sweden. Double-digest restriction-site-associated DNA sequencing was performed on more than 500 broodfish from two leading producers in Sweden and from the country's national breeding program. Following the detection of single nucleotide polymorphisms (SNPs), genetic diversity was studied by using either individual SNPs (n = 8680; one SNP retained per 300 bp sequence reads) or through SNP haplotypes (n = 20 558; all SNPs retained in 300 bp sequence reads). Similar amounts of genetic diversity were found amongst the three populations when individual SNPs were used. Furthermore, principal component analysis and discriminant analysis of principal components suggested two genetic clusters with the two industry populations grouped together. Genetic differentiation based on the FST fixation index was ~0.01 between the industry populations and ~0.05 when those were compared with the breeding program. Preliminary estimates of effective population size (Ne ) and inbreeding (based on runs of homozygosity; FROH ) were similar amongst the three populations (Ne  ≈ 50-80; median FROH  ≈ 0.11). Finally, the haplotype-based analysis suggested that animals from the breeding program had higher shared coancestry levels than those from the other two populations. Overall, our study provides novel insights into the genetic diversity and structure of Sweden's three main farmed rainbow trout populations, which could guide their future management.

Nonparallel genome changes within subpopulations over time contributed to genetic diversity within the US Holstein population

Maintaining genetic variation in a population is important for long-term genetic gain. The existence of subpopulations within a breed helps maintain genetic variation and diversity. The 20,990 genotyped animals, representing the breeding animals in the year 2014, were identified as the sires of animals born after 2010 with at least 25 progenies, and females measured for type traits within the last 2 yr of data. K-means clustering with 5 clusters (C1, C2, C3, C4, and C5) was applied to the genomic relationship matrix based on 58,990 SNP markers to stratify the selected candidates into subpopulations. The general higher inbreeding resulting from within-cluster mating than across-cluster mating suggests the successful stratification into genetically different groups. The largest cluster (C4) contained animals that were less related to each animal within and across clusters. The average fixation index was 0.03, indicating that the populations were differentiated, and allele differences across the subpopulations were not due to drift alone. Starting with the selected candidates within each cluster, a family unit was identified by tracing back through the pedigree, identifying the genotyped ancestors, and assigning them to a pseudogeneration. Each of the 5 families (F1, F2, F3, F4, and F5) was traced back for 10 generations, allowing for changes in frequency of individual SNPs over time to be observed, which we call allele frequencies change. Alternative procedures were used to identify SNPs changing in a parallel or nonparallel way across families. For example, markers that have changed the most in the whole population, markers that have changed differently across families, and genes previously identified as those that have changed in allele frequency. The genomic trajectory taken by each family involves selective sweeps, polygenic changes, hitchhiking, and epistasis. The replicate frequency spectrum was used to measure the similarity of change across families and showed that populations have changed differently. The proportion of markers that reversed direction in allele frequency change varied from 0.00 to 0.02 if the rate of change was greater than 0.02 per generation, or from 0.14 to 0.24 if the rate of change was greater than 0.005 per generation within each family. Cluster-specific SNP effects for stature were estimated using only females and applied to obtain indirect genomic predictions for males. Reranking occurs depending on SNP effects used. Additive genetic correlations between clusters show possible differences in populations. Further research is required to determine how this knowledge can be applied to maintain diversity and optimize selection decisions in the future.

Comparative analysis of inbreeding parameters and runs of homozygosity islands in 2 Italian autochthonous cattle breeds mainly raised in the Parmigiano-Reggiano cheese production region

Reggiana and Modenese are autochthonous cattle breeds, reared in the North of Italy, that can be mainly distinguished for their standard coat color (Reggiana is red, whereas Modenese is white with some pale gray shades). Almost all milk produced by these breeds is transformed into 2 mono-breed branded Parmigiano-Reggiano cheeses, from which farmers receive the economic incomes needed for the sustainable conservation of these animal genetic resources. After the setting up of their herd books in 1960s, these breeds experienced a strong reduction in the population size that was subsequently reverted starting in the 1990s (Reggiana) or more recently (Modenese) reaching at present a total of about 2,800 and 500 registered cows, respectively. Due to the small population size of these breeds, inbreeding is a very important cause of concern for their conservation programs. Inbreeding is traditionally estimated using pedigree data, which are summarized in an inbreeding coefficient calculated at the individual level (F_PED). However, incompleteness of pedigree information and registration errors can affect the effectiveness of conservation strategies. High-throughput SNP genotyping platforms allow investigation of inbreeding using genome information that can overcome the limits of pedigree data. Several approaches have been proposed to estimate genomic inbreeding, with the use of runs of homozygosity (ROH) considered to be the more appropriate. In this study, several pedigree and genomic inbreeding parameters, calculated using the whole herd book populations or considering genotyping information (GeneSeek GGP Bovine 150K) from 1,684 Reggiana cattle and 323 Modenese cattle, were compared. Average inbreeding values per year were used to calculate effective population size. Reggiana breed had generally lower genomic inbreeding values than Modenese breed. The low correlation between pedigree-based and genomic-based parameters (ranging from 0.187 to 0.195 and 0.319 to 0.323 in the Reggiana and Modenese breeds, respectively) reflected the common problems of local populations in which pedigree records are not complete. The high proportion of short ROH over the total number of ROH indicates no major recent inbreeding events in both breeds. ROH islands spread over the genome of the 2 breeds (15 in Reggiana and 14 in Modenese) identified several signatures of selection. Some of these included genes affecting milk production traits, stature, body conformation traits (with a main ROH island in both breeds on BTA6 containing the ABCG2, NCAPG, and LCORL genes) and coat color (on BTA13 in Modenese containing the ASIP gene). In conclusion, this work provides an extensive comparative analysis of pedigree and genomic inbreeding parameters and relevant genomic information that will be useful in the conservation strategies of these 2 iconic local cattle breeds.

Correlation of Genomic and Pedigree Inbreeding Coefficients in Small Cattle Populations

Simple Summary

This study aimed to evaluate the consistency of different methodologies and sources of information used to estimate inbreeding coefficients in small populations by analyzing the correlation between them in the Holstein population of Mexico and to choose the best option in order to aid breeding programs to improve the productive traits of Holstein cattle in small-specialized populations.

Abstract

This study aimed to identify inbreeding coefficient (F) estimators useful for improvement programs in a small Holstein population through the evaluation of different methodologies in the Mexican Holstein population. F was estimated as follows: (a) from pedigree information (Fped); (b) through runs of homozygosity (Froh); (c) from the number of observed and expected homozygotic SNP in the individuals (Fgeno); (d) through the genomic relationship matrix (Fmg). The study included information from 4277 animals with pedigree records and 100,806 SNP. The average and standard deviation values of F were 3.11 ± 2.30 for Fped, −0.02 ± 3.55 for Fgeno, 2.77 ± 0.71 for Froh and 3.03 ± 3.05 for Fmg. The correlations between coefficients varied from 0.30 between Fped and Froh, to 0.96 between Fgeno and Fmg. Differences in the level of inbreeding among the parent’s country of origin were found regardless of the method used. The correlations among genomic inbreeding coefficients were high; however, they were low with Fped, so further research on this topic is required.

Estimating inbreeding depression for growth and reproductive traits using pedigree and genomic methods in Argentinean Brangus cattle

Inbreeding depression reduces the mean phenotypic value of important traits in livestock populations. The goal of this work was to estimate the level of inbreeding and inbreeding depression for growth and reproductive traits in Argentinean Brangus cattle, in order to obtain a diagnosis and monitor breed management. Data comprised 359,257 (from which 1,990 were genotyped for 40,678 single nucleotide polymorphisms [SNPs]) animals with phenotypic records for at least one of three growth traits: birth weight (BW), weaning weight (WW), and finishing weight (FW). For scrotal circumference (SC), 52,399 phenotypic records (of which 256 had genotype) were available. There were 530,938 animals in pedigree. Three methods to estimate inbreeding coefficients were used. Pedigree-based inbreeding coefficients were estimated accounting for missing parents. Inbreeding coefficients combining genotyped and nongenotyped animal information were also computed from matrix H of the single-step approach. Genomic inbreeding coefficients were estimated using homozygous segments obtained from a Hidden Markov model (HMM) approach. Inbreeding depression was estimated from the regression of the phenotype on inbreeding coefficients in a multiple-trait mixed model framework, either for the whole dataset or for the dataset of genotyped animals. All traits were unfavorably affected by inbreeding depression. A 10% increase in pedigree-based or combined inbreeding would result in a reduction of 0.34 to 0.39 kg in BW, 2.77 to 3.28 kg in WW, and 0.23 cm in SC. For FW, a 10% increase in pedigree-based, genomic, or combined inbreeding would result in a decrease of 8.05 to 11.57 kg. Genomic inbreeding based on the HMM was able to capture inbreeding depression, even in such a compressed genotyped dataset.

Impact of including the cause of missing records on genetic evaluations for growth in commercial pigs

It is of interest to evaluate crossbred pigs for hot carcass weight (HCW) and birth weight (BW); however, obtaining a HCW record is dependent on livability (LIV) and retained tag (RT). The purpose of this study is to analyze how HCW evaluations are affected when herd removal and missing identification are included in the model and examine if accounting for the reasons for missing traits improves the accuracy of predicting breeding values. Pedigree information was available for 1,965,077 purebred and crossbred animals. Records for 503,716 commercial three-way crossbred terminal animals from 2014 to 2019 were provided by Smithfield Premium Genetics. Two pedigree-based models were compared; model 1 (M1) was a threshold-linear model with all four traits (BW, HCW, RT, and LIV), and model 2 (M2) was a linear model including only BW and HCW. The fixed effects used in the model were contemporary group, sex, age at harvest (for HCW only), and dam parity. The random effects included direct additive genetic and random litter effects. Accuracy, dispersion, bias, and Pearson correlations were estimated using the linear regression method. The heritabilities were 0.11, 0.07, 0.02, and 0.04 for BW, HCW, RT, and LIV, respectively, with standard errors less than 0.01. No difference was observed in heritabilities or accuracies for BW and HCW between M1 and M2. Accuracies were 0.33, 0.37, 0.19, and 0.23 for BW, HCW, RT, and LIV, respectively. The genetic correlation between BW and RT was 0.34 ± 0.03, and between BW and LIV was 0.56 ± 0.03. Similarly, the genetic correlation between HCW and RT was 0.26 ± 0.04, and between HCW and LIV was 0.09 ± 0.05, respectively. The positive and moderate genetic correlations between BW and other traits imply a heavier BW resulted in a higher probability of surviving to harvest. Genetic correlations between HCW and other traits were lower due to the large quantity of missing records. Despite the heritable and correlated aspects of RT and LIV, results imply no major differences between M1 and M2; hence, it is unnecessary to include these traits in classical models for BW and HCW.

Grid search approach to discriminate between old and recent inbreeding using phenotypic, pedigree and genomic information

Background

Although inbreeding caused by the mating of animals related through a recent common ancestor is expected to have more harmful effects on phenotypes than ancient inbreeding (old inbreeding), estimating these effects requires a clear definition of recent (new) and ancient (old) inbreeding. Several methods have been proposed to classify inbreeding using pedigree and genomic data. Unfortunately, these methods are largely based on heuristic criteria such as the number of generations from a common ancestor or length of runs of homozygosity (ROH) segments. To mitigate these deficiencies, this study aimed to develop a method to classify pedigree and genomic inbreeding into recent and ancient classes based on a grid search algorithm driven by the assumption that new inbreeding tends to have a more pronounced detrimental effect on traits. The proposed method was tested using a cattle population characterized by a deep pedigree.

Results

Effects of recent and ancient inbreeding were assessed on four growth traits (birth, weaning and yearling weights and average daily gain). Thresholds to classify inbreeding into recent and ancient classes were trait-specific and varied across traits and sources of information. Using pedigree information, inbreeding generated in the last 10 to 11 generations was considered as recent. When genomic information (ROH) was used, thresholds ranged between four to seven generations, indicating, in part, the ability of ROH segments to characterize the harmful effects of inbreeding in shorter periods of time. Nevertheless, using the proposed classification method, the discrimination between new and old inbreeding was less robust when ROH segments were used compared to pedigree. Using several model comparison criteria, the proposed approach was generally better than existing methods. Recent inbreeding appeared to be more harmful across the growth traits analyzed. However, both new and old inbreeding were found to be associated with decreased yearling weight and average daily gain.

Conclusions

The proposed method provided a more objective quantitative approach for the classification of inbreeding. The proposed method detected a clear divergence in the effects of old and recent inbreeding using pedigree data and it was superior to existing methods for all analyzed traits. Using ROH data, the discrimination between old and recent inbreeding was less clear and the proposed method was superior to existing approaches for two out of the four analyzed traits. Deleterious effects of recent inbreeding were detected sooner (fewer generations) using genomic information than pedigree. Difference in the results using genomic and pedigree information could be due to the dissimilarity in the number of generations to a common ancestor. Additionally, the uncertainty associated with the identification of ROH segments and associated inbreeding could have an effect on the results. Potential biases in the estimation of inbreeding effects may occur when new and old inbreeding are discriminated based on arbitrary thresholds. To minimize the impact of inbreeding, mating designs should take the different inbreeding origins into consideration.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12864-021-07872-z.

A genomic‐based vision on the genetic diversity and key performance traits in selectively bred Arctic charr ( Salvelinus alpinus )

Routine implementation of genomic information for guiding selection decisions is not yet common in the majority of aquaculture species. Reduced representation sequencing approaches offer a cost‐effective solution for obtaining genome‐wide information in species with a limited availability of genomic resources. In the current study, we implemented double‐digest restriction site‐associated DNA sequencing (ddRAD‐seq) on an Arctic charr strain with the longest known history of selection (approximately 40 years) aiming to improve selection decisions. In total, 1730 animals reared at four different farms in Sweden and spanning from year classes 2013–2017 were genotyped using ddRAD‐seq. Approximately 5000 single nucleotide polymorphisms (SNPs) were identified, genetic diversity‐related metrics were estimated, and genome‐wide association studies (GWAS) for body length at different time points and age of sexual maturation were conducted. Low genetic differentiation amongst animals from the different farms was observed based on both the results from pairwise F_st values and principal component analysis (PCA). The existence of associations was investigated between the mean genome‐wide heterozygosity of each full‐sib family (year class 2017) and the corresponding inbreeding coefficient or survival to the eyed stage. A moderate correlation (−0.33) was estimated between the mean observed heterozygosity of each full‐sib family and the corresponding inbreeding coefficient, while no linear association was obtained with the survival to the eyed stage. GWAS did not detect loci with major effect for any of the studied traits. However, genomic regions explaining more than 1% of the additive genetic variance for either studied traits were suggested across 14 different chromosomes. Overall, key insights valuable for future selection decisions of Arctic charr have been obtained, suggesting ddRAD as an attractive genotyping platform for obtaining genome‐wide information in a cost‐effective manner.

Modeling genetic differences of combined broiler chicken populations in single-step GBLUP

The introduction of animals from a different environment or population is a common practice in commercial livestock populations. In this study, we modeled the inclusion of a group of external birds into a local broiler chicken population for the purpose of genomic evaluations. The pedigree was composed of 242,413 birds and genotypes were available for 107,216 birds. A five-trait model that included one growth, two yield, and two efficiency traits was used for the analyses. The strategies to model the introduction of external birds were to include a fixed effect representing the origin of parents and to use unknown parent groups (UPG) or metafounders (MF). Genomic estimated breeding values (GEBV) were obtained with single-step GBLUP using the Algorithm for Proven and Young. Bias, dispersion, and accuracy of GEBV for the validation birds, that is, from the most recent generation, were computed. The bias and dispersion were estimated with the linear regression (LR) method,whereas accuracy was estimated by the LR method and predictive ability. When fixed UPG were fit without estimated inbreeding, the model did not converge. In contrast, models with fixed UPG and estimated inbreeding or random UPG converged and resulted in similar GEBV. The inclusion of an extra fixed effect in the model made the GEBV unbiased and reduced the inflation. Genomic predictions with MF were slightly biased and inflated due to the unbalanced number of observations assigned to each metafounder. When combining local and external populations, the greatest accuracy can be obtained by adding an extra fixed effect to account for the origin of parents plus UPG with estimated inbreeding or random UPG. To estimate the accuracy, the LR method is more consistent among scenarios, whereas the predictive ability greatly depends on the model specification.

Determining the stability of accuracy of genomic estimated breeding values in future generations in commercial pig populations

Genomic information has a limited dimensionality (number of independent chromosome segments [M_e]) related to the effective population size. Under the additive model, the persistence of genomic accuracies over generations should be high when the nongenomic information (pedigree and phenotypes) is equivalent to M_e animals with high accuracy. The objective of this study was to evaluate the decay in accuracy over time and to compare the magnitude of decay with varying quantities of data and with traits of low and moderate heritability. The dataset included 161,897 phenotypic records for a growth trait (GT) and 27,669 phenotypic records for a fitness trait (FT) related to prolificacy in a population with dimensionality around 5,000. The pedigree included 404,979 animals from 2008 to 2020, of which 55,118 were genotyped. Two single-trait models were used with all ancestral data and sliding subsets of 3-, 2-, and 1-generation intervals. Single-step genomic best linear unbiased prediction (ssGBLUP) was used to compute genomic estimated breeding values (GEBV). Estimated accuracies were calculated by the linear regression (LR) method. The validation population consisted of single generations succeeding the training population and continued forward for all generations available. The average accuracy for the first generation after training with all ancestral data was 0.69 and 0.46 for GT and FT, respectively. The average decay in accuracy from the first generation after training to generation 9 was −0.13 and −0.19 for GT and FT, respectively. The persistence of accuracy improves with more data. Old data have a limited impact on the predictions for young animals for a trait with a large amount of information but a bigger impact for a trait with less information.

Fine-scale estimation of inbreeding rates, runs of homozygosity and genome-wide heterozygosity levels in the Mangalarga Marchador horse breed

With the availability of high-density SNP panels and the establishment of approaches for characterizing homozygosity and heterozygosity sites, it is possible to access fine-scale information regarding genomes, providing more than just comparisons of different inbreeding coefficients. This is the first study that seeks to access such information for the Mangalarga Marchador (MM) horse breed on a genomic scale. To this end, we aimed to assess inbreeding levels using different coefficients, as well as to characterize homozygous and heterozygous runs in the population. Using Axiom ® Equine Genotyping Array-670k SNP (Thermo Fisher), 192 horses were genotyped. Our results showed different estimates: inbreeding from genomic coefficients (F_ROH ) = 0.16; pedigree-based (F_PED ) = 0.008; and a method based on excess homozygosity (F_HOM ) = 0.010. The correlations between the inbreeding coefficients were low to moderate, and some comparisons showed negative correlations, being practically null. In total, 85,295 runs of homozygosity (ROH) and 10,016 runs of heterozygosity (ROHet) were characterized for the 31 horse autosomal chromosomes. The class with the highest percentage of ROH was 0-2 Mbps, with 92.78% of the observations. In the ROHet results, only the 0-2 class presented observations, with chromosome 11 highlighted in a region with high genetic variability. Three regions from the ROHet analyses showed genes with known functions: tripartite motif-containing 37 (TRIM37), protein phosphatase, Mg²⁺ /Mn²⁺ dependent 1E (PPM1E) and carbonic anhydrase 10 (CA10). Therefore, our findings suggest moderate inbreeding, possibly attributed to breed formation, annulling possible recent inbreeding. Furthermore, regions with high variability in the MM genome were identified (ROHet), associated with the recent selection and important events in the development and performance of MM horses over generations.

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

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.

Comparison of Gene Editing Versus Conventional Breeding to Introgress the POLLED Allele Into the Tropically Adapted Australian Beef Cattle Population

Dehorning is the process of physically removing horns to protect animals and humans from injury, but the process is costly, unpleasant, and faces increasing public scrutiny. Genetic selection for polled (hornless), which is genetically dominant to horned, is a long-term solution to eliminate the need for dehorning. However, due to the limited number of polled Australian Brahman bulls, the northern Australian beef cattle population remains predominantly horned. The potential to use gene editing to produce high-genetic-merit polled cattle was recently demonstrated. To further explore the concept, this study simulated introgression of the POLLED allele into a tropically adapted Australian beef cattle population via conventional breeding or gene editing (top 1% or 10% of seedstock bulls/year) for 3 polled mating schemes and compared results to baseline selection on genetic merit (Japan Ox selection index, $JapOx) alone, over the course of 20 years. The baseline scenario did not significantly decrease the 20-year HORNED allele frequency (80%), but resulted in one of the fastest rates of genetic gain ($8.00/year). Compared to the baseline, the conventional breeding scenarios where polled bulls were preferentially used for breeding, regardless of their genetic merit, significantly decreased the 20-year HORNED allele frequency (30%), but resulted in a significantly slower rate of genetic gain ($6.70/year, P ≤ 0.05). The mating scheme that required the exclusive use of homozygous polled bulls, resulted in the lowest 20-year HORNED allele frequency (8%), but this conventional breeding scenario resulted in the slowest rate of genetic gain ($5.50/year). The addition of gene editing the top 1% or 10% of seedstock bull calves/year to each conventional breeding scenario resulted in significantly faster rates of genetic gain (up to $8.10/year, P ≤ 0.05). Overall, our study demonstrates that, due to the limited number of polled Australian Brahman bulls, strong selection pressure on polled will be necessary to meaningfully increase the number of polled animals in this population. Moreover, these scenarios illustrate how gene editing could be a tool for accelerating the development of high-genetic-merit homozygous polled sires to mitigate the current trade-off of slower genetic gain associated with decreasing HORNED allele frequency in the Australian Brahman population.

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

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.

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.

Genomic and pedigree estimation of inbreeding depression for semen traits in the Basco-Béarnaise dairy sheep breed

Inbreeding depression is associated with a decrease in performance and fitness of the animals. The goal of this study was to evaluate pedigree-based and genomic methods to estimate the level of inbreeding and inbreeding depression for 3 semen traits (volume, concentration, and motility score) in the Basco-Béarnaise sheep breed. Data comprised 16,196 (or 15,071) phenotypic records from 620 rams (of which 533 rams had genotypes of 36,464 SNPs). The pedigree included 8,266 animals, composed of the 620 rams and their ancestors. The number of equivalent complete generations for the 620 rams was 7.04. Inbreeding coefficients were estimated using genomic and pedigree-based information. Genomic inbreeding coefficients were estimated from individual SNP and using segments of homozygous SNP (runs of homozygosity, ROH). Short ROH are of old origin, whereas long ROH are due to recent inbreeding. Considering that the equivalent number of generations in Basco-Béarnaise was 6, inbreeding coefficients for ROH with a length >4 Mb refer to all (recent + old) inbreeding, those with a length >17 Mb correspond to recent inbreeding, and the difference between them indicates old inbreeding. Pedigree-based inbreeding coefficients were also estimated classically, or accounting for nonzero relationships for unknown parents, or including metafounder relationships (estimated using markers) to account for missing pedigree information. Finally, inbreeding coefficients combining genotyped and nongenotyped animal information were computed from matrix H of the single-step approach, also including metafounders. Inbreeding depression was estimated differently depending on the approach used to compute inbreeding coefficients. These 8 estimators of inbreeding coefficients were included as covariates in different animal models. No inbreeding depression was detected for sperm volume or sperm concentration. Inbreeding depression was significant for the motility of spermatozoa. The effect of old and recent inbreeding on motility was null and negative, respectively, demonstrating the existence of purging by selection of deleterious recessive alleles affecting motility. A 10% increase in inbreeding would result in a reduction in mean motility ranging between 0.09 and 0.22 points in the score (from 0 to 5). Motility is unfavorably affected by increasing recent inbreeding but the impact is very small. Runs of homozygosity and metafounders allow us to accurately estimate inbreeding depression and detect recent inbreeding.

Bias in genomic predictions by mating practices for linear type traits in a large-scale genomic evaluation

The objective of this study was to clarify how bias in genomic predictions is created by investigating a relationship among selection intensity, a change in heritability (Δh²), and assortative mating (ASM). A change in heritability, resulting from selection, reflects the impact that the Bulmer effect has on the reduction in between-family variation, whereas assortative mating impacts the within-family variance or Mendelian sampling variation. A partial data set up to 2014, including 841K genotyped animals, was used to calculate genomic predictions with a single-step genomic model for 18 linear type traits in US Holsteins. A full data set up to 2018, including 2.3 million genotyped animals, was used to calculate benchmark genomic predictions. Inbreeding and unknown parent groups for missing parents of animals were included in the model. Genomic evaluation was performed using 2 different genetic parameters: those estimated 14 yr ago, which have been used in the national genetic evaluation for linear type traits in the United States, and those newly estimated with recent records from 2015 to 2018 and those corresponding pedigrees. Genetic trends for 18 type traits were estimated for bulls with daughters and cows with phenotypes in 2018. Based on selection intensity and mating decisions, these traits can be categorized into 3 groups: (a) high directional selection, (b) moderate selection, and (c) intermediate optimum selection. The first 2 categories can be explained by positive assortative mating, and the last can be explained by negative assortative or disassortative mating. Genetic progress was defined by genetic gain per year based on average standardized genomic predictions for cows from 2000 to 2014. Traits with more genetic progress tended to have more "inflated" genomic predictions (i.e., "inflation" means here that genomic predictions are larger in absolute values than expected, whereas "deflation" means smaller than expected). Heritability estimates for 14 out of 18 traits declined in the last 16 yr, and Δh² ranged from -0.09 to 0.04. Traits with a greater decline in heritability tended to have more deflated genomic predictions. Biases (inflation or deflation) in genomic predictions were not improved by using the latest genetic parameters, implying that bias in genomic predictions due to preselection was not substantial for a large-scale genomic evaluation. Moreover, the strong selection intensity was not fully responsible for bias in genomic predictions. The directional selection can decrease heritability; however, positive assortative mating, which was strongly associated with large genetic gains, could minimize the decline in heritability for a trait under strong selection and could affect bias in genomic predictions.

Assessing the potential of improving growth and survival to the eyed stage in selectively bred Arctic charr (Salvelinus alpinus)

The Arctic charr breeding programme has been a main driving force for developing the aquaculture industry in Sweden. Selection has been performed for almost 40 years using animals from a closed breeding nucleus. The aim of the current study was to evaluate the potential of further improving growth-related traits taking into account the existence of genotype-by-environment interaction. Furthermore, we investigated the magnitude of the genetic component associated with survival to the eyed stage and potential associations with inbreeding coefficients. A preliminary heritability estimate of 0.23 (SE 0.20) was obtained for survival to the eyed stage using records spanning from 2000 to 2017 (n = 230). Moreover, moderate-to-high heritability estimates (0.27-0.49) were obtained for growth-related traits (body weight and length), using animals from the latest generation of selection (year class 2017). Those animals (n = 2,776), originating from 55 full-sib families, were split into two groups and reared in separate land-based facilities of commercial fish farms in Sweden. The growth-related traits were recorded twice in both sites when animals were of >1 and >2 years of age. Existence of sexual growth dimorphism was indicated with the males having on average 6%-8% higher total length and 22%-34% higher body weight. Furthermore, high genetic correlations regarding growth traits were obtained amongst animals reared at the two different sites (0.82-0.95). In addition, we assessed the accuracy of best linear unbiased prediction (BLUP)-derived estimated breeding values (EBVs) when phenotypes from each rearing site were subsequently masked and used as a validation set. A mean prediction accuracy of 0.60 (length) and 0.64 (weight) were derived for both rearing sites. Overall, our results suggest that further growth improvements should be possible in the subsequent generations of selection. Finally, even though indications for the existence of an underlying genetic component(s) involved in survival to the eyed stage were obtained additional data will be required for elucidating its magnitude.

Networks of inbreeding coefficients in a selected population of rabbits

The correlation between pedigree and genomic-based inbreeding coefficients is usually discussed in the literature. However, some of these correlations could be spurious. Using partial correlations and information theory, it is possible to distinguish a significant association between two variables which is independent from associations with a third variable. The objective of this study is to implement partial correlations and information theory to assess the relationship between different inbreeding coefficients using a selected population of rabbits. Data from pedigree and genomic information from a 200K SNP chip were available. After applying filtering criteria, the data set comprised 437 animals genotyped for 114,604 autosomal SNP. Fifteen pedigree- and genome-based inbreeding coefficients were estimated and used to build a network. Recent inbreeding coefficient based on runs of homozygosity had 9 edges linking it with different inbreeding coefficients. Partial correlations and information theory approach allowed to infer meaningful associations between inbreeding coefficients and highlighted the importance of the recent inbreeding based on runs of homozygosity, but a good proxy of it could be those pedigree-based definitions reflecting recent inbreeding.

Genetic Variability in the Italian Heavy Draught Horse from Pedigree Data and Genomic Information

This study aimed to investigate the genetic diversity in the Italian Heavy Horse Breed from pedigree and genomic data. Pedigree information for 64,917 individuals were used to assess inbreeding level, effective population size (Ne), and effective numbers of founders and ancestors (fa/fe). Genotypic information from SNP markers were available for 267 individuals of both sexes, and it allowed estimating genomic inbreeding in two methods (observed versus expected homozygosity and from ROH) to study the breed genomic structure and possible selection signatures. Pedigree and genomic inbreeding were greatly correlated (0.65 on average). The inbreeding trend increased over time, apart from periods in which the base population enlarged, when Ne increased also. Recent bottlenecks did not occur in the genome, as fa/fe have shown. The observed homozygosity results were on average lower than expected, which was probably due to the use of French Breton stallions to support the breed genetic variability. High homozygous regions suggested that inbreeding increased in different periods. Two subpopulations were distinguished, which was probably due to the different inclusion of French animals by breeders. Few selection signatures were found at the population level, with possible associations to disease resistance. The almost low inbreeding rate suggested that despite the small breed size, conservation actions are not yet required.

Genetics of Lifetime Reproductive Performance in Italian Heavy Draught Horse Mares

Simple Summary

Fertility is a very important fitness trait in animal production because of its significant economic importance, particularly in species with low reproductive efficiency. For this reason, it should be included as a breeding objective, particularly in horses, where the trait has received less interest than in other species. In this study, we attempted to identify a variable able to detect the lifetime reproductive performance of Italian Heavy Draught Horse (IHDH) mares and to analyze its possible implementation for breeding purposes, with the final aim to increase mares’ fertility efficiency. A phenotypic variable to be used early in life (at least after 3 breeding seasons) has been identified and validated in the study and its genetic component estimated. Results obtained indicated the proposed phenotypic measure of fertility as a good predictor of the lifetime reproductive success in IHDH mares and the variable showed high heritability (that is, the transmittable genetic component) for a fitness trait. Therefore, the use of the lifetime fertility rate proposed in this study for breeding purposes seems feasible, although some limitations could occur in the accuracy of individual breeding value estimates of mares and stallions.

Abstract

Our aims were to find a phenotypic variable to express mares’ lifetime reproductive performance after 6 breeding seasons (BS) in Italian Heavy Draught Horse breed (IHDH), and to estimate its heritability. At first, 1487 mares in a training dataset were used to implement and validate a set of predictive coefficients (LFR-C) or equations (LFR-E) to estimate a lifetime foaling rate (LFR) after 6 BS, i.e., the number of foals generated divided by the opportunities to do so. Then, 3033 mares in a dataset with at least 3 registered BS, was used to estimate LFR for mares with 3, 4, or 5 registered RS. This dataset contained actual (n = 1950) and estimated (n = 1443) LFR, obtained by LFR-C, and LFR-E; Arcsine transformation of LFR-C and LFR-E were also analyzed in single trait animal models to estimate heritability. Overall, the LFR showed a moderate but significant genetic variation, and the heritability of the trait was high (0.24) considering it is a fitness trait. The arcsine transformation of LFR did not show any improvement of heritability. The present study indicates the possible use of a linear LFR variable for breeding purposes in IHDH breed considering both complete and incomplete reproductive careers.

Inbreeding, effective population size, and coancestry in the Latxa dairy sheep breed

Traditionally, breeding programs have estimated and managed inbreeding based on pedigree information. The availability of genomic marker panels has made possible new alternatives to achieve more precise estimates, for example in case of missing pedigree. The objective of the present study was to assess and compare, different estimation methods (pedigree-based methodologies, single SNP-based approach (homozygosity) and runs of homozygosity-based method) to analyze the evolution of genetic diversity measured as inbreeding or as coancestry of 3 selected populations of Latxa dairy sheep (Latxa Cara Rubia and Latxa Cara Negra from Euskadi and Navarre). Genomic data came from 972 artificial insemination rams genotyped with the Illumina OvineSNP50 BeadChip (Illumina Inc., San Diego, CA) whose genealogy consisted of 4,484 animals. Inbreeding estimates based on molecular data were more similar between them than compared with those based on pedigree information. However, the SNP-based approach estimations of effective population size differed more, reflecting the sensitivity of effective population size to small changes in the evolution of inbreeding. The 2 Latxa Cara Negra populations showed increases of inbreeding rates with time and effective population sizes between 64 and 103 animals, depending on breed and methodology used. The Latxa Cara Rubia population did not show an increase in inbreeding rate, mainly due to semen importation from the related French population of Manech Tête Rousse. The effective size estimates based on coancestry increase show a higher variability and they are more sensitive to the source of information and the data structure considered. Realized effective population size based on individual increase in inbreeding were in agreement with the previous estimates. Coancestry evolution analysis based on DNA information showed an increase on coancestry during the last 10 yr in all breeds, as a consequence of the selection process. Moreover, the increase on coancestry between Latxa Cara Rubia and Manech Tête Rousse was more noticeable between than within each of those breeds.

Current status of genomic evaluation

Early application of genomic selection relied on SNP estimation with phenotypes or de-regressed proofs (DRP). Chips of 50k SNP seemed sufficient for an accurate estimation of SNP effects. Genomic estimated breeding values (GEBV) were composed of an index with parent average, direct genomic value, and deduction of a parental index to eliminate double counting. Use of SNP selection or weighting increased accuracy with small data sets but had minimal to no impact with large data sets. Efforts to include potentially causative SNP derived from sequence data or high-density chips showed limited or no gain in accuracy. After the implementation of genomic selection, EBV by BLUP became biased because of genomic preselection and DRP computed based on EBV required adjustments, and the creation of DRP for females is hard and subject to double counting. Genomic selection was greatly simplified by single-step genomic BLUP (ssGBLUP). This method based on combining genomic and pedigree relationships automatically creates an index with all sources of information, can use any combination of male and female genotypes, and accounts for preselection. To avoid biases, especially under strong selection, ssGBLUP requires that pedigree and genomic relationships are compatible. Because the inversion of the genomic relationship matrix (G) becomes costly with more than 100k genotyped animals, large data computations in ssGBLUP were solved by exploiting limited dimensionality of genomic data due to limited effective population size. With such dimensionality ranging from 4k in chickens to about 15k in cattle, the inverse of G can be created directly (e.g., by the algorithm for proven and young) at a linear cost. Due to its simplicity and accuracy, ssGBLUP is routinely used for genomic selection by the major chicken, pig, and beef industries. Single step can be used to derive SNP effects for indirect prediction and for genome-wide association studies, including computations of the P-values. Alternative single-step formulations exist that use SNP effects for genotyped or for all animals. Although genomics is the new standard in breeding and genetics, there are still some problems that need to be solved. This involves new validation procedures that are unaffected by selection, parameter estimation that accounts for all the genomic data used in selection, and strategies to address reduction in genetic variances after genomic selection was implemented.

Controlling bias in genomic breeding values for young genotyped bulls

The objectives of this study were to investigate bias in genomic predictions for dairy cattle and to find a practical approach to reduce the bias. The simulated data included phenotypes, pedigrees, and genotypes, mimicking a dairy cattle population (i.e., cows with phenotypes and bulls with no phenotypes) and assuming selection by breeding values or no selection. With the simulated data, genomic estimated breeding values (GEBV) were calculated with a single-step genomic BLUP and compared with true breeding values. Phenotypes and genotypes were simulated in 10 generations and in the last 4 generations, respectively. Phenotypes in the last generation were removed to predict breeding values for those individuals using only genomic and pedigree information. Complete pedigrees and incomplete pedigrees with 50% missing dams were created to construct the pedigree-based relationship matrix with and without inbreeding. With missing dams, unknown parent groups (UPG) were assigned in relationship matrices. Regression coefficients (b₁) and coefficients of determination (R²) of true breeding values on (G)EBV were calculated to investigate inflation and accuracy in GEBV for genotyped animals, respectively. In addition to the simulation study, 18 linear type traits of US Holsteins were examined. For the 18 type traits, b₁ and R² of GEBV with full data sets on GEBV with partial data sets for young genotyped bulls were calculated. The results from the simulation study indicated inflation in GEBV for genotyped males that were evaluated with only pedigree and genomic information under BLUP selection. However, when UPG for only pedigree-based relationships were included, the inflation was reduced, accuracy was highest, and genetic trends had no bias. For the linear type traits, when UPG for only pedigree-based relationships were included, the results were generally in agreement with those from the simulation study, implying less bias in genetic trends. However, when including no UPG, UPG in pedigree-based relationships, or UPG in genomic relationships, inflation and accuracy in GEBV were similar. The results from the simulation and type traits suggest that UPG must be defined accurately to be estimable and inbreeding should be included in pedigree-based relationships. In dairy cattle, known pedigree information with inbreeding and estimable UPG plays an important role in improving compatibility between pedigree-based and genomic relationship matrices, resulting in more reliable genomic predictions.

Comparison of gene editing versus conventional breeding to introgress the POLLED allele into the US dairy cattle population

Disbudding and dehorning are commonly used cattle management practices to protect animals and humans from injury. They are unpleasant, costly processes subject to increased public scrutiny as an animal welfare issue. Horns are a recessively inherited trait, so one option to eliminate dehorning is to breed for polled (hornlessness). However, due to the low genetic merit and scarcity of polled dairy sires, this approach has not been widely adopted. In March 2018, only 3 Holstein and 0 Jersey active homozygous polled sires were registered with the National Association of Animal Breeders. Alternatively, gene editing to produce high-genetic-merit polled sires has been proposed. To further explore this concept, introgression of the POLLED allele into both the US Holstein and Jersey cattle populations via conventional breeding or gene editing (top 1% of bulls/year) was simulated for 3 polled mating schemes and compared with baseline selection on lifetime net merit (NM$) alone, over the course of 20 yr. Scenarios were replicated 10 times and the changes in HORNED allele frequency, inbreeding, genetic gain (NM$), and number of unique sires used were calculated. Gene editing decreased the frequency of the HORNED allele to <0.1 after 20 yr, which was as fast or faster than conventional breeding for both breeds. In the mating scheme that required the use of only existing homozygous polled sires, inbreeding reached 17% (Holstein) and 14% (Jersey), compared with less than 7% in the baseline scenarios. However, gene editing in the same mating scheme resulted in significantly less inbreeding, 9% (Holstein) and 8% (Jersey). Also, gene editing resulted in significantly higher NM$ after 20 yr compared with conventional breeding for both breeds. Additionally, the gene editing scenarios of both breeds used a significantly greater number of unique sires compared with either the conventional breeding or baseline scenarios. Overall, our simulations show that, given the current genetic merit of horned and polled dairy sires, the use of conventional breeding methods to decrease the frequency of the HORNED allele will increase inbreeding and slow genetic improvement. Furthermore, this study demonstrates how gene editing could be used to rapidly decrease the frequency of the HORNED allele in US dairy cattle populations while maintaining the rate of genetic gain, constraining inbreeding to acceptable levels, and simultaneously addressing an emerging animal welfare concern.

Autozygosity islands and ROH patterns in Nellore lineages: evidence of selection for functionally important traits

Background

The aim of this study was to assess genome-wide autozygosity in a Nellore cattle population and to characterize ROH patterns and autozygosity islands that may have occurred due to selection within its lineages. It attempts also to compare estimates of inbreeding calculated from ROH (F_ROH), genomic relationship matrix (F_GRM), and pedigree-based coefficient (F_PED).

Results

The average number of ROH per animal was 55.15 ± 13.01 with an average size of 3.24 Mb. The Nellore genome is composed mostly by a high number of shorter segments accounting for 78% of all ROH, although the proportion of the genome covered by them was relatively small. The genome autozygosity proportion indicates moderate to high inbreeding levels for classical standards, with an average value of 7.15% (178.70 Mb). The average of F_PED and F_ROH, and their correlations (− 0.05 to 0.26) were low. Estimates of correlation between F_GRM-F_PED was zero, while the correlation (− 0.01 to − 0.07) between F_GRM-F_ROH decreased as a function of ROH length, except for F_{ROH > 8Mb} (− 0.03). Overall, inbreeding coefficients were not high for the genotyped animals. Autozygosity islands were evident across the genome (n = 62) and their genomic location did not largely differ within lineages. Enriched terms (p < 0.01) associated with defense response to bacteria (GO:0042742), immune complex reaction (GO:0045647), pregnancy-associated glycoproteins genes (GO:0030163), and organism growth (GO:0040014) were described within the autozygotic islands.

Conclusions

Low F_PED-F_ROH correlation estimates indicate that F_PED is not the most suitable method for capturing ancient inbreeding when the pedigree does not extend back many generations and F_ROH should be used instead. Enriched terms (p < 0.01) suggest a strong selection for immune response. Non-overlapping islands within the lineages greatly explain the mechanism underlying selection for functionally important traits in Nellore cattle.

Electronic supplementary material

The online version of this article (10.1186/s12864-018-5060-8) contains supplementary material, which is available to authorized users.

Challenges in inbreeding estimation of large populations based on Polish Holstein-Friesian cattle pedigree

The aim of this study was to evaluate observed and future inbreeding level in Polish Holstein-Friesian cattle population. In total, over 9.8 mln animals were used in the analysis coming from the pedigree of Polish Federation of Cattle Breeders and Dairy Farmers. Inbreeding level, as an average per birth year, was estimated with the method accounting for missing parent information with the assumption of year 1950 as the base year of the population. If an animal had no ancestral records, an average inbreeding level from its birth year was assigned. Twice the average inbreeding level served as relatedness of the animal to the population, which enabled estimation of inbreeding in its offspring. The future inbreeding of potential offspring was estimated as an average of animals (bulls and cows) available for mating in a certain year. It was observed that 30-50% of animals born between 1985 and 2015 had no relevant ancestral information, which is caused by a high number of new animals and/or entire farms entering the national milk recordings. For the year 2015, the observed inbreeding level was 3.30%, which was more than twice the inbreeding with the classical approach (without missing parent information) and higher by 0.4% than the future inbreeding. The average increase of inbreeding in years 2010-2015 was 0.10%, which is similar to other countries monitored by World Holstein-Friesian Federation. However, the values might be underestimated due to low pedigree completeness. The estimates of future inbreeding suggested that observed inbreeding could be even lower and also increase slower, which indicates a constant need to monitor rate of increase in inbreeding over time. The most important aspect of presented results is the necessity to advise individual farmers to keep precise recordings of the matings on their farm in order to improve the pedigree completeness of Polish Holstein-Friesian and to use suitable mating programs to avoid too rapid growth of inbreeding.

Assessment of runs of homozygosity islands and estimates of genomic inbreeding in Gyr (Bos indicus) dairy cattle

Background

Runs of homozygosity (ROH) are continuous homozygous segments of the DNA sequence. They have been applied to quantify individual autozygosity and used as a potential inbreeding measure in livestock species. The aim of the present study was (i) to investigate genome-wide autozygosity to identify and characterize ROH patterns in Gyr dairy cattle genome; (ii) identify ROH islands for gene content and enrichment in segments shared by more than 50% of the samples, and (iii) compare estimates of molecular inbreeding calculated from ROH (F_ROH), genomic relationship matrix approach (F_GRM) and based on the observed versus expected number of homozygous genotypes (F_HOM), and from pedigree-based coefficient (F_PED).

Results

ROH were identified in all animals, with an average number of 55.12 ± 10.37 segments and a mean length of 3.17 Mb. Short segments (ROH_{1–2 Mb}) were abundant through the genomes, which accounted for 60% of all segments identified, even though the proportion of the genome covered by them was relatively small. The findings obtained in this study suggest that on average 7.01% (175.28 Mb) of the genome of this population is autozygous. Overlapping ROH were evident across the genomes and 14 regions were identified with ROH frequencies exceeding 50% of the whole population. Genes associated with lactation (TRAPPC9), milk yield and composition (IRS2 and ANG), and heat adaptation (HSF1, HSPB1, and HSPE1), were identified. Inbreeding coefficients were estimated through the application of F_ROH, F_GRM, F_HOM, and F_PED approaches. F_PED estimates ranged from 0.00 to 0.327 and F_ROH from 0.001 to 0.201. Low to moderate correlations were observed between F_PED-F_ROH and F_GRM-F_ROH, with values ranging from −0.11 to 0.51. Low to high correlations were observed between F_ROH-F_HOM and moderate between F_PED-F_HOM and F_GRM-F_HOM. Correlations between F_ROH from different lengths and F_PED gradually increased with ROH length.

Conclusions

Genes inside ROH islands suggest a strong selection for dairy traits and enrichment for Gyr cattle environmental adaptation. Furthermore, low F_PED-F_ROH correlations for small segments indicate that F_PED estimates are not the most suitable method to capture ancient inbreeding. The existence of a moderate correlation between larger ROH indicates that F_ROH can be used as an alternative to inbreeding estimates in the absence of pedigree records.

Electronic supplementary material

The online version of this article (10.1186/s12864-017-4365-3) contains supplementary material, which is available to authorized users.

Using a very low-density SNP panel for genomic selection in a breeding program for sheep

Background

Building an efficient reference population for genomic selection is an issue when the recorded population is small and phenotypes are poorly informed, which is often the case in sheep breeding programs. Using stochastic simulation, we evaluated a genomic design based on a reference population with medium-density genotypes [around 45 K single nucleotide polymorphisms (SNPs)] of dams that were imputed from very low-density genotypes (≤ 1000 SNPs).

Methods

A population under selection for a maternal trait was simulated using real genotypes. Genetic gains realized from classical selection and genomic selection designs were compared. Genomic selection scenarios that differed in reference population structure (whether or not dams were included in the reference) and genotype quality (medium-density or imputed to medium-density from very low-density) were evaluated.

Results

The genomic design increased genetic gain by 26% when the reference population was based on sire medium-density genotypes and by 54% when the reference population included both sire and dam medium-density genotypes. When medium-density genotypes of male candidates and dams were replaced by imputed genotypes from very low-density SNP genotypes (1000 SNPs), the increase in gain was 22% for the sire reference population and 42% for the sire and dam reference population. The rate of increase in inbreeding was lower (from − 20 to − 34%) for the genomic design than for the classical design regardless of the genomic scenario.

Conclusions

We show that very low-density genotypes of male candidates and dams combined with an imputation process result in a substantial increase in genetic gain for small sheep breeding programs.

Pedigree and genomic evaluation of pigs using a terminal-cross model

Background

In crossbreeding schemes, within-line selection of purebreds is performed mainly to improve the performance of crossbred descendants under field conditions. The genetic correlation between purebred and crossbred performance is an important parameter to be assessed because purebred performance can be a poor predictor of the performance of crossbred offspring. With the availability of high-density markers, the feasibility of using crossbred information to evaluate purebred candidates can be reassessed. This study implements and applies a single-step terminal-cross model (GEN) to real data to estimate the genetic parameters of several production and quality traits in pigs.

Methods

Piétrain sires were mated with Piétrain and Large White dams to produce purebred and crossbred male half-sib piglets; growth rate, feed conversion ratio, lean meat, pH of longissimus dorsi muscle, drip loss and intramuscular fat content were recorded on all half-sibs. Animals were genotyped using the Illumina Porcine SNP60 BeadChip. The genetic correlation between purebred and crossbred performance was estimated separately for each trait. Purebred animals were evaluated using an animal model, whereas the additive genetic effect of a crossbred individual was decomposed into the additive effects of the sire and dam and a Mendelian sampling effect that was confounded with the residual effect. Genotypes of the Piétrain animals were integrated in the genetic evaluation by using a single-step procedure. As benchmarks, we used a model that was identical to GEN but only accounted for pedigree information (PED) and also two univariate single-step models (GEN_UNI) that took either purebred or crossbred performance into account.

Results

Genetic correlations between purebred and crossbred performance were high and positive for all traits (>0.69). Accuracies of estimated breeding values of genotyped sires and purebred offspring that were obtained with the GEN model outperformed both those obtained with the PED and the GEN_UNI models. The use of genomic information increased the predictive ability of the GEN model, but it did not substantially outperform the GEN_UNI models.

Conclusions

We present a single-step terminal-cross model that integrates genomic information of purebred and crossbred performance by using available software. It improves the theoretical accuracy of genetic evaluations in breeding programs that are based on crossbreeding.

Analysis of population structure and genetic variability in Iranian buffaloes (Bubalus bubalis) using pedigree information

The objective of this study was to use pedigree analysis to evaluate the population structure, genetic variability and inbreeding in Iranian buffaloes. The analysis was based on the pedigree information of 42 285 buffaloes born from 549 sires and 6376 dams within 1697 herds. Pedigree information used in this study was collected during 1976 to 2012 by the Animal Breeding Centre of Iran. The CFC program was applied to calculate pedigree statistics and genetic structure analysis of the Iranian buffaloes. Also, the INBUPGF90 program was used for calculating regular inbreeding coefficients for individuals in the pedigree. The analysis of pedigree indicated that inbreeding coefficient ranged from 0% to 31% with an average of 3.42% and the trend of inbreeding was significantly positive over the years (P < 0.0001). Average coancestry was increased in recent years and overall generation interval was 6.62 years in Iranian buffaloes. Founder genome equivalent, founder equivalent, effective number of founders and effective number of non-founders were increased from 1976 to 2002, but their values decreased from 2002 onwards. A designed mating system to avoid inbreeding may be applied to this population of buffalo to maintain genetic diversity.

Ancestral Relationships Using Metafounders: Finite Ancestral Populations and Across Population Relationships

Recent use of genomic (marker-based) relationships shows that relationships exist within and across base population (breeds or lines). However, current treatment of pedigree relationships is unable to consider relationships within or across base populations, although such relationships must exist due to finite size of the ancestral population and connections between populations. This complicates the conciliation of both approaches and, in particular, combining pedigree with genomic relationships. We present a coherent theoretical framework to consider base population in pedigree relationships. We suggest a conceptual framework that considers each ancestral population as a finite-sized pool of gametes. This generates across-individual relationships and contrasts with the classical view which each population is considered as an infinite, unrelated pool. Several ancestral populations may be connected and therefore related. Each ancestral population can be represented as a "metafounder," a pseudo-individual included as founder of the pedigree and similar to an "unknown parent group." Metafounders have self- and across relationships according to a set of parameters, which measure ancestral relationships, i.e., homozygozities within populations and relationships across populations. These parameters can be estimated from existing pedigree and marker genotypes using maximum likelihood or a method based on summary statistics, for arbitrarily complex pedigrees. Equivalences of genetic variance and variance components between the classical and this new parameterization are shown. Segregation variance on crosses of populations is modeled. Efficient algorithms for computation of relationship matrices, their inverses, and inbreeding coefficients are presented. Use of metafounders leads to compatibility of genomic and pedigree relationship matrices and to simple computing algorithms. Examples and code are given.

Population genetic structure analysis and effect of inbreeding on body weights at different ages in Iranian Mehraban sheep

The objective of this study was to describe the population structure and inbreeding, and to quantify their effects on weights at different ages of Mehraban sheep in Iran. The analysis was based on the pedigree information of 26990 animals and 10278 body weight records from birth to yearling age. Data and pedigree information were collected during 1994 to 2011 by the breeding station of Mehraban sheep. The population structure was analyzed using the CFC program. Inbreeding of all animals was calculated by INBUPGF90 program. All animals were grouped into three classes according to their inbreeding coefficients: the first class included non-inbred animals (F=0); and the second and third classes included inbred animals (0<F<0.05 and F≥0.05, respectively). The average inbreeding in Mehraban sheep was 1.69%. Founder equivalent (f_e) values were estimated to be 4244, 3116 and 2965 during 1994-1999, 2000-2005 and 2006-2011, respectively. The effective population sizes (N_e) were 363, 5080 and 5740 during 1994-1999, 2000-2005 and 2006-2011, respectively. Generation interval was 2.15 years for this breed of sheep. Regression coefficients of birth weight, 3-month weight, 6-month weight and yearling weight on lamb inbreeding were estimated to be -6.34±0.69, -14.68±5.33, 48.00±9.43 and 98.65±15.65, respectively. Both positive and negative inbreeding effects were found in the current study. The utilization of a program for designed mating system, in the present flock, could be a suitable approach to keep the level of inbreeding under control.

Effective population size and inbreeding depression on litter size in rabbits. A case study

The purpose of this study is to use demographic and litter size data on four Spanish maternal lines of rabbits (A, V, H and LP), as a case study, in order to: (i) estimate the effective population size of the lines, as a measure of the rate of increase of inbreeding, and (ii) study whether the inbreeding effect on litter size traits depends on the pattern of its accumulation over time. The lines are being selected for litter size at weaning and are kept closed at the same selection nucleus under the same selection and management programme. The study considered 47,794 l and a pedigree of 14,622 animals. Some practices in mating and selection management allow an increase of the inbreeding coefficient lower than 0.01 per generation in these lines of around 25 males and 125 females. Their effective population size (Ne) was around 57.3, showing that the effect of selection, increasing the inbreeding, was counterbalanced by the management practices, intended to reduce the rate of inbreeding increase. The inbreeding of each individual was broken down into three components: old, intermediate and new inbreeding. The coefficients of regression of the old, intermediate and new inbreeding on total born (TB), number born alive (NBA) and number weaned (NW) per litter showed a decreasing trend from positive to negative values. Regression coefficients significantly different from zero were those for the old inbreeding on TB (6.79 ± 2.37) and NBA (5.92 ± 2.37). The contrast between the coefficients of regression between the old and new inbreeding were significant for the three litter size traits: 7.57 ± 1.72 for TB; 6.66 ± 1.73 for NBA and 5.13 ± 1.67 for NW. These results have been interpreted as the combined action of purging unfavourable genes and artificial selection favoured by the inbreeding throughout the generations of selection.

MIM: an indirect method to assess inbreeding and coancestry in large incomplete pedigrees of selected dairy cattle

In real data, inbreeding is usually underestimated because of missing pedigree information. A method adapted to the dairy cattle situation is presented to approximate inbreeding when the stored population pedigree is incomplete. Missing parents in incomplete pedigrees were given a dummy identification and assigned to groups (up to nine for a given birth date of progeny). These groups were linked to contemporary reference groups with known parents. An explicit model considered that polygenic breeding values in a censored group were centred on a function of the average breeding value in the corresponding reference group and deviated independently. Inbreeding coefficients were obtained progressively over birth dates starting from founders. For each date considered, the parameters pertaining to its groups were computed using the parameters already obtained from groups belonging to the previous dates. The updating algorithms were given in detail. An indirect method was implemented to expedite mass computations of the relationship coefficients involved (MIM). MIM was compared to Van Raden's (VR) method using simulated populations with 20 overlapping generations and different rates of missing sires and dams. In the situation of random matings, the average inbreeding coefficients by date obtained by MIM were close to true values, whereas they were strongly underestimated by VR. In the situation of assortative matings, MIM gave average inbreeding coefficients moderately underestimated, whereas those of VR's method were still strongly underestimated. The main conclusion of this study adapted to the situation of dairy cattle with incomplete pedigrees was that corrections for inbreeding and coancestry coefficients are more efficient with an explicit appropriate genetic model than without.

Genealogical analyses in open populations: the case of three Arab-derived Spanish horse breeds

This research assesses the genetic composition of three Arab-derived Spanish horse breeds as an example to highlight the major shortcomings related to genealogical analyses in open populations and to propose approaches useful to deal with this task. The studbooks of three Spanish Arab (SA)-derived horse breeds, Spanish Anglo-Arab (dAA), Hispano-Arab (dHA) and Spanish Sport Horse (dSSH) and those of their parental breeds SA, Spanish Purebred (SPB) and Thoroughbred (TB), totalling 211 754 individuals, were available. The genealogies of the dAA, dHA and dSSH were analysed not only using the corresponding studbook (breed exclusive dataset) but also including the genealogies of the founders from parental breeds (completed dataset). Coancestry analyses revealed that the present SA-derived populations share more genes with the Arab than with the other parental breeds. Effective population size was computed by accounting for migration rates to obtain an equivalent closed-population effective size ((eq)N(e)) of 39.2 for the dAA, 56.3 for dHA and 114.1 for dSSH. The essayed methodologies were useful for characterising populations involving migration. The consequences of the management of the analysed breeds are discussed. The results emphasize the need to include the complete genealogies of the individuals to attain reliable genealogical parameters.

Computing procedures for genetic evaluation including phenotypic, full pedigree, and genomic information

Currently, genomic evaluations use multiple-step procedures, which are prone to biases and errors. A single-step procedure may be applicable when genomic predictions can be obtained by modifying the numerator relationship matrix A to H = A + A(Delta), where A(Delta) includes deviations from expected relationships. However, the traditional mixed model equations require H(-1), which is usually difficult to obtain for large pedigrees. The computations with H are feasible when the mixed model equations are expressed in an alternate form that also applies for singular H and when those equations are solved by the conjugate gradient techniques. Then the only computations involving H are in the form of Aq or A(Delta)q, where q is a vector. The alternative equations have a nonsymmetric left-hand side. Computing A(Delta)q is inexpensive when the number of nonzeros in A(Delta) is small, and the product Aq can be calculated efficiently in linear time using an indirect algorithm. Generalizations to more complicated models are proposed. The data included 10.2 million final scores on 6.2 million Holsteins and were analyzed by a repeatability model. Comparisons involved the regular and the alternative equations. The model for the second case included simulated A(Delta). Solutions were obtained by the preconditioned conjugate gradient algorithm, which works only with symmetric matrices, and by the bi-conjugate gradient stabilized algorithm, which also works with nonsymmetric matrices. The convergence rate associated with the nonsymmetric solvers was slightly better than that with the symmetric solver for the original equations, although the time per round was twice as much for the nonsymmetric solvers. The convergence rate associated with the alternative equations ranged from 2 times lower without A(Delta) to 3 times lower for the largest simulated A(Delta). When the information attributable to genomics can be expressed as modifications to the numerator relationship matrix, the proposed methodology may allow the upgrading of an existing evaluation to incorporate the genomic information.