Marker-based estimates of between and within population kinships for the conservation of genetic diversity

In this article coefficients of kinship between and within populations are proposed as a tool to assess genetic diversity for conservation of genetic variation. However, pedigree-based kinships are often not available, especially between populations. A method of estimation of kinship from genetic marker data was applied to simulated data from random breeding populations in order to study the suitability of this method for livestock conservation plans. Average coefficients of kinship between populations can be estimated with low Mean Square Error of Prediction, although a bias will occur from alleles that are alike in state in the founder population. The bias is similar for all populations, so the ranking of populations will not be affected. Possible ways of diminishing this bias are discussed. The estimation of kinships between individuals is imprecise unless the number of marker loci is large (> 200). However, it allows distinction between highly related animals (full sibs, half sibs and equivalent relations) and animals that are not directly related if about 30–50 polymorphic marker genes are used. The marker-based estimates of kinship coefficients yielded higher correlations than genetic distance measures with pedigree-based kinships and thus to this measure of genetic diversity, although correlations were high overall. The relation between coefficients of kinship and genetic distances are discussed. Kinship-based diversity measures conserve the founder population allele frequencies, whereas genetic distances will conserve populations in which allele frequencies are the most different. Marker-based kinship estimates can be used for the selection of breeds and individuals as contributors to a genetic conservation programme.     

Pedigree- and marker-based methods in the estimation of genetic diversity in small groups of Holstein cattle

Genetic diversity is often evaluated using pedigree information. Currently, diversity can be evaluated in more detail over the genome based on large numbers of SNP markers. Pedigree- and SNP-based diversity were compared for two small related groups of Holstein animals genotyped with the 50 k SNP chip, genome-wide, per chromosome and for part of the genome examined. Diversity was estimated with coefficient of kinship (pedigree) and expected heterozygosity (SNP). SNP-based diversity at chromosome regions was determined using 5-Mb sliding windows, and significance of difference between groups was determined by bootstrapping. Both pedigree- and SNP-based diversity indicated more diversity in one of the groups; 26 of the 30 chromosomes showed significantly more diversity for the same group, as did 25.9% of the chromosome regions. Even in small populations that are genetically close, differences in diversity can be detected. Pedigree- and SNP-based diversity give comparable differences, but SNP-based diversity shows on which chromosome regions these differences are based. For maintaining diversity in a gene bank, SNP-based diversity gives a more detailed picture than pedigree-based diversity.     

Effect of selection and selective genotyping for creation of reference on bias and accuracy of genomic prediction

Reference populations for genomic selection usually involve selected individuals, which may result in biased prediction of estimated genomic breeding values (GEBV). In a simulation study, bias and accuracy of GEBV were explored for various genetic models with individuals selectively genotyped in a typical nucleus breeding program. We compared the performance of three existing methods, that is, Best Linear Unbiased Prediction of breeding values using pedigree‐based relationships (PBLUP), genomic relationships for genotyped animals only (GBLUP) and a Single‐Step approach (SSGBLUP) using both. For a scenario with no‐selection and random mating (RR), prediction was unbiased. However, lower accuracy and bias were observed for scenarios with selection and random mating (SR) or selection and positive assortative mating (SA). As expected, bias disappeared when all individuals were genotyped and used in GBLUP. SSGBLUP showed higher accuracy compared to GBLUP, and bias of prediction was negligible with SR. However, PBLUP and SSGBLUP still showed bias in SA due to high inbreeding. SSGBLUP and PBLUP were unbiased provided that inbreeding was accounted for in the relationship matrices. Selective genotyping based on extreme phenotypic contrasts increased the prediction accuracy, but prediction was biased when using GBLUP. SSGBLUP could correct the biasedness while gaining higher accuracy than GBLUP. In a typical animal breeding program, where it is too expensive to genotype all animals, it would be appropriate to genotype phenotypically contrasting selection candidates and use a Single‐Step approach to obtain accurate and unbiased prediction of GEBV.     

The impact of using old germplasm on genetic merit and diversity—A cattle breed case study

Artificial selection and high genetic gains in livestock breeds led to a loss of genetic diversity. Current genetic diversity conservation actions focus on long‐term maintenance of breeds under selection. Gene banks play a role in such actions by storing genetic materials for future use and the recent development of genomic information is facilitating characterization of gene bank material for better use. Using the Meuse‐Rhine‐Issel Dutch cattle breed as a case study, we inferred the potential role of germplasm of old individuals for genetic diversity conservation of the current population. First, we described the evolution of genetic merit and diversity over time and then we applied the optimal contribution (OC) strategy to select individuals for maximizing genetic diversity, or maximizing genetic merit while constraining loss of genetic diversity. In the past decades, genetic merit increased while genetic diversity decreased. Genetic merit and diversity were both higher in an OC scenario restricting the rate of inbreeding when old individuals were considered for selection, compared to considering only animals from the current population. Thus, our study shows that gene bank material, in the form of old individuals, has the potential to support long‐term maintenance and selection of breeds.     

Single step genomic evaluation for female fertility in Nordic Red dairy cattle

Joint Nordic (Denmark, Finland, Sweden) genetic evaluation of female fertility is currently based on the multiple trait multilactation animal model (BLUP). Here, single step genomic model (ssGBLUP) was applied for the Nordic Red dairy cattle fertility evaluation. The 11 traits comprised of nonreturn rate and days from first to last insemination in heifers and first three parities, and days from calving to first insemination in the first three parities. Traits had low heritabilities (0.015–0.04), but moderately high genetic correlations between the parities (0.60–0.88). Phenotypic data included 4,226,715 animals with records and pedigree 5,445,392 animals. Unknown parents were assigned into 332 phantom parent groups (PPG). In mixed model equations animals were associated with PPG effects through the pedigree or both the pedigree and genomic information. Genotype information of 46,914 SNPs was available for 33,969 animals in the pedigree. When PPG used pedigree information only, BLUP converged after 2,420 iterations whereas the ssGBLUP evaluation needed over ten thousand iterations. When the PPG effects were solved accounting both the pedigree and the genomic information, the ssGBLUP model converged after 2,406 iterations. Also, with the latter model breeding values by ssGBLUP and BLUP became more consistent and genetic trends followed each other well. Models were validated using forward prediction of the young bulls. Reliabilities and variance inflation of predicted genomic breeding values (values for parent averages in brackets) for the 11 traits ranged 0.22–0.31 (0.10–0.27) and 0.81–0.95 (0.83–1.06), respectively. The ssGBLUP model gave always higher validation reliabilities than BLUP, but largest increases were for the cow fertility traits.     

Use of haplotypes to estimate Mendelian sampling effects and selection limits

Limits to selection and Mendelian sampling (MS) terms can be calculated using haplotypes by summing the individual additive effects on each chromosome. Haplotypes were imputed for 43 382 single-nucleotide polymorphisms (SNP) in 1455 Brown Swiss, 40 351 Holstein and 4064 Jersey bulls and cows using the Fortran program findhap.f90, which combines population and pedigree haplotyping methods. Lower and upper bounds of MS variance were calculated for daughter pregnancy rate (a measure of fertility), milk yield, lifetime net merit (a measure of profitability) and protein yield assuming either no or complete linkage among SNP on the same chromosome. Calculated selection limits were greater than the largest direct genomic values observed in all breeds studied. The best chromosomal genotypes generally consisted of two copies of the same haplotype even after adjustment for inbreeding. Selection of animals rather than chromosomes may result in slower progress, but limits may be the same because most chromosomes will become homozygous with either strategy. Selection on functions of MS could be used to change variances in later generations.     

Effects of incomplete pedigree on genetic management of the Dutch Landrace goat

Genetic diversity in the Dutch Landrace goat was investigated based on information from the pedigree with about 6500 animals. Annual inbreeding rate after 1985 was below 0.5% and after 1987 close to 0%. However, pedigree information was incomplete, and 350 animals had unknown parents, while for the majority the real parents must have been in the pedigree. To determine the influence of unknown parents, 20 new pedigrees were created by random assignment of animals, alive at the time of birth, as parents to individuals with unknown parents. Only 12 founders remained for these pedigrees, and inbreeding levels varied considerably between these 20 pedigrees. However, inbreeding rates were remarkably constant. They increased to about 0.2%, indicating that the population is not endangered by inbreeding. The optimal contribution theory was used to evaluate possibilities of decreasing the average relationship in the population and thus to increase the genetic diversity of the breed. Optimal contribution decreased the average relationship in the population whether randomly assigned parents were used or not. However, individuals selected as parents for the resampled pedigrees differed from the original pedigree, and only a few animals were selected for all pedigrees. Candidates for inclusion in the genebank were also selected using optimal contribution. Adding animals to the genebank increased the conserved genetic diversity substantially, but as the lists differed between the analysed pedigrees it was not clear which animals were best added to the genebank.     

Consequences for diversity when animals are prioritized for conservation of the whole genome or of one specific allele

When animals are selected for one specific allele, for example for inclusion in a gene bank, this may result in the loss of diversity in other parts of the genome. The aim of this study was to quantify the risk of losing diversity across the genome when targeting a single allele for conservation when storing animals in a gene bank. From a small Holstein population, genotyped for 54 001 SNP loci, animals were prioritized for a single allele while maximizing the genomewide diversity using optimal contribution selection. Selection for a single allele was done for five different target frequencies: (i) no restriction on a target frequency; (ii) target frequency = original frequency in population; (iii) target frequency = 0.50; (iv) target frequency of the major allele = 1 (fixation); and (v) target frequency of the major allele = 0 (elimination). To do this, optimal contribution selection was extended with an extra constraint on the allele frequency of the target SNP marker. Results showed that elimination or fixation of alleles can result in substantial losses in genetic diversity around the targeted locus and also across the rest of the genome, depending on the allele frequency and the target frequency. It was concluded that losses of genetic diversity around the target allele are the largest when the target frequency is very different from the current allele frequency.     

Investigation of genetic diversity and inbreeding in a Japanese native horse breed for suggestions on its conservation

Because native breeds can serve as genetic resources for adapting to environment changes, their conservation is important for future agroecosystems. Using pedigree analysis, we investigated genetic diversity and inbreeding in Japanese Hokkaido native horses, which have adapted to a cold climate and roughage diet. Genetic diversity was measured as the number of founders and the effective number of founders, ancestors and genomes. All metrics imply a decrease in genetic diversity. A comparison of these metrics suggested that pedigree bottlenecks contributed more than did random gene losses to the reduction of genetic diversity. Estimates of marginal contributions of ancestors suggest that the bottlenecks arose mainly because related stallions had been used for breeding. A tendency for an increase in inbreeding coefficients was observed. F‐statistics revealed that a small effective population size majorly contributed to this increase, although non‐random mating in particular regions also contributed. Because the bottlenecks are thought to have reduced the effective population size, our results imply that mitigation of bottlenecks is important for conservation. To this end, breeding should involve genetically diverse stallions. In addition, to prevent non‐random mating observed in particular regions, efforts should be made to plan mating with consideration of kinships.     

Detecting effective starting point of genomic selection by divergent trends from best linear unbiased prediction and single-step genomic best linear unbiased prediction in pigs,beef cattle,and broilers

Genomic selection has been adopted nationally and internationally in different livestock and plant species. However, understanding whether genomic selection has been effective or not is an essential question for both industry and academia. Once genomic evaluation started being used, estimation of breeding values with pedigree best linear unbiased prediction (BLUP) became biased because this method does not consider selection using genomic information. Hence, the effective starting point of genomic selection can be detected in two possible ways including the divergence of genetic trends and Realized Mendelian sampling (RMS) trends obtained with BLUP and single-step genomic BLUP (ssGBLUP). This study aimed to find the start date of genomic selection for a set of economically important traits in three livestock species by comparing trends obtained using BLUP and ssGBLUP. Three datasets were used for this purpose: 1) a pig dataset with 117k genotypes and 1.3M animals in pedigree, 2) an Angus cattle dataset consisted of ~842k genotypes and 11.5M animals in pedigree, and 3) a purebred broiler chicken dataset included ~154k genotypes and 1.3M birds in pedigree were used. The genetic trends for pigs diverged for the genotyped animals born in 2014 for average daily gain (ADG) and backfat (BF). In beef cattle, the trends started diverging in 2009 for weaning weight (WW) and in 2016 for postweaning gain (PWG), with little divergence for birth weight (BTW). In broiler chickens, the genetic trends estimated by ssGBLUP and BLUP diverged at breeding cycle 6 for two out of the three production traits. The RMS trends for the genotyped pigs diverged for animals born in 2014, more for ADG than for BF. In beef cattle, the RMS trends started diverging in 2009 for WW and in 2016 for PWG, with a trivial trend for BTW. In broiler chickens, the RMS trends from ssGBLUP and BLUP diverged strongly for two production traits at breeding cycle 6, with a slight divergence for another trait. Divergence of the genetic trends from ssGBLUP and BLUP indicates the onset of the genomic selection. The presence of trends for RMS indicates selective genotyping, with or without the genomic selection. The onset of genomic selection and genotyping strategies agrees with industry practices across the three species. In summary, the effective start of genomic selection can be detected by the divergence between genetic and RMS trends from BLUP and ssGBLUP.     

Analysis of pedigrees of Tux-Zillertal, Carinthian Blond and Original Pinzgau cattle population in Austria

The most common goal of animal conservation programmes is to maintain genetic diversity. Various measures for genetic variability based on pedigree information can be used, but most of them are very sensitive to completeness of pedigree information. Different criteria based on probability of identity-by-descent (effective population size via increase in inbreeding N_e) or probability of gene origin (effective number of founders f_e, ancestors f_a and founder genomes N_g) were used to describe the genetic variability of three Austrian cattle breeds [Original Pinzgau (PI), Tux-Zillertal (TZ), Carinthian Blond (CB)]. Reference populations for PI were defined by animals born between 1993 and 1997 and for TZ and CB by all living animals, irrespective of birth year. The numbers of animals in the reference populations were 9706, 471 and 230 for PI, TZ and CB, respectively. The average complete generation equivalent showed the different quality of pedigree information: 5.33 for PI, 2.52 for TZ and 1.73 for CB. The following N_es were calculated: 76 for PI and CB and 43 for TZ. For PI, TZ and CB a f_e-value of 65.4, 21.0 and 29.9, a f_a-value of 32.1, 14.2 and 29.0 and a N_g-value of 19.5, 9.7 and 22.6, respectively, were calculated. In particular, the results for TZ demonstrate the urgent need for a well-planned conservation programme.     

The use of coancestry based on shared segments for maintaining genetic diversity

We have evaluated the use of genomic coancestry coefficients based on shared segments for the maintenance of genetic diversity through optimal contributions methodology for populations of three different Austrian cattle breeds. This coancestry measure has been compared with the genomic coancestry coefficient calculated on a SNP‐by‐SNP basis and with pedigree‐based coancestry. The regressions of the shared segments coancestry on the other two coefficients suggest that the former mainly reflect Identity By Descent but with the advantage over pedigree‐based coancestry of providing the realized Identity By Descent rather than an expectation. The effective population size estimated from the rate of coancestry based on shared segments was very similar to those obtained with the other coefficients and of small magnitude (from 26.24 to 111.90). This result highlights the importance of implementing active management strategies to control the increase of inbreeding and the loss of genetic diversity in livestock breeds, even when the population size is reasonably large. One problem for the implementation of coancestry based on shared segments is the need of estimating the gametic phases of the SNPs which, given the techniques used to obtain the genotypes, are a priori unknown. This study shows, through computer simulations, that using estimates of gametic phases for computing coancestry based on shared segments does not lead to a significant loss in the diversity maintained. This has been shown to be true even when the size of the population is very small as it is usually the case in populations subjected to conservation programmes.     

Efficient computation of the genomic relationship matrix and other matrices used in single-step evaluation

Genomic evaluations can be calculated using a unified procedure that combines phenotypic, pedigree and genomic information. Implementation of such a procedure requires the inverse of the relationship matrix based on pedigree and genomic relationships. The objective of this study was to investigate efficient computing options to create relationship matrices based on genomic markers and pedigree information as well as their inverses. SNP maker information was simulated for a panel of 40 K SNPs, with the number of genotyped animals up to 30 000. Matrix multiplication in the computation of the genomic relationship was by a simple 'do' loop, by two optimized versions of the loop, and by a specific matrix multiplication subroutine. Inversion was by a generalized inverse algorithm and by a LAPACK subroutine. With the most efficient choices and parallel processing, creation of matrices for 30 000 animals would take a few hours. Matrices required to implement a unified approach can be computed efficiently. Optimizations can be either by modifications of existing code or by the use of efficient automatic optimizations provided by open source or third-party libraries.     

The impact of the rank of marker variance-covariance matrix in principal component evaluation for genomic selection applications

In genomic selection (GS) programmes, direct genomic values (DGV) are evaluated using information provided by high-density SNP chip. Being DGV accuracy strictly dependent on SNP density, it is likely that an increase in the number of markers per chip will result in severe computational consequences. Aim of present work was to test the effectiveness of principal component analysis (PCA) carried out by chromosome in reducing the marker dimensionality for GS purposes. A simulated data set of 5700 individuals with an equal number of SNP distributed over six chromosomes was used. PCs were extracted both genome-wide (ALL) and separately by chromosome (CHR) and used to predict DGVs. In the ALL scenario, the SNP variance-covariance matrix (S) was singular, positive semi-definite and contained null information which introduces 'spuriousness' in the derived results. On the contrary, the S matrix for each chromosome (CHR scenario) had a full rank. Obtained DGV accuracies were always better for CHR than ALL. Moreover, in the latter scenario, DGV accuracies became soon unsettled as the number of animals decreases, whereas in CHR, they remain stable till 900-1000 individuals. In real applications where a 54k SNP chip is used, the largest number of markers per chromosome is approximately 2500. Thus, a number of around 3000 genotyped animals could lead to reliable results when the original SNP variables are replaced by a reduced number of PCs.     

The unified approach to the use of genomic and pedigree information in genomic evaluations revisited

Previous proposals for a unified approach for amalgamating information from animals with or without genotypes have combined the numerator relationship matrix A with the genomic relationship G estimated from the markers. These approaches have resulted in biased genomic EBV (GEBV), and methodology was developed to overcome these problems. Firstly, a relationship matrix, G(FG) , based on linkage analysis was derived using the same base population as A, which (i) utilizes the genomic information on the same scale as the pedigree information and (ii) permits the regression coefficients used to propagate the genomic data from the genotyped to ungenotyped individuals to be calculated in the light of the genomic information, rather than ignoring it. Secondly, the elements of G were regressed back towards their expected values in the A matrix to allow for their estimation errors. These developments were combined in a methodology LDLAb and tested on simulated populations where either parents were phenotyped and offspring genotyped or vice versa. The LDLAb method was demonstrated to be a unified approach that maximized accuracy of GEBV compared to previous methodologies and removed the bias in the GEBV. Although LDLAb is computationally much more demanding than MLAC, it demonstrates how to make best use the marker information and also shows the computational problems that need to be solved in the future to make best use of the marker data.     

Impact of fitting dominance and additive effects on accuracy of genomic prediction of breeding values in layers

Most genomic prediction studies fit only additive effects in models to estimate genomic breeding values (GEBV). However, if dominance genetic effects are an important source of variation for complex traits, accounting for them may improve the accuracy of GEBV. We investigated the effect of fitting dominance and additive effects on the accuracy of GEBV for eight egg production and quality traits in a purebred line of brown layers using pedigree or genomic information (42K single‐nucleotide polymorphism (SNP) panel). Phenotypes were corrected for the effect of hatch date. Additive and dominance genetic variances were estimated using genomic‐based [genomic best linear unbiased prediction (GBLUP)‐REML and BayesC] and pedigree‐based (PBLUP‐REML) methods. Breeding values were predicted using a model that included both additive and dominance effects and a model that included only additive effects. The reference population consisted of approximately 1800 animals hatched between 2004 and 2009, while approximately 300 young animals hatched in 2010 were used for validation. Accuracy of prediction was computed as the correlation between phenotypes and estimated breeding values of the validation animals divided by the square root of the estimate of heritability in the whole population. The proportion of dominance variance to total phenotypic variance ranged from 0.03 to 0.22 with PBLUP‐REML across traits, from 0 to 0.03 with GBLUP‐REML and from 0.01 to 0.05 with BayesC. Accuracies of GEBV ranged from 0.28 to 0.60 across traits. Inclusion of dominance effects did not improve the accuracy of GEBV, and differences in their accuracies between genomic‐based methods were small (0.01–0.05), with GBLUP‐REML yielding higher prediction accuracies than BayesC for egg production, egg colour and yolk weight, while BayesC yielded higher accuracies than GBLUP‐REML for the other traits. In conclusion, fitting dominance effects did not impact accuracy of genomic prediction of breeding values in this population.     

Selection of core animals in the Algorithm for Proven and Young using a simulation model

The Algorithm for Proven and Young (APY) enables the implementation of single‐step genomic BLUP (ssGBLUP) in large, genotyped populations by separating genotyped animals into core and non‐core subsets and creating a computationally efficient inverse for the genomic relationship matrix ( G ). As APY became the choice for large‐scale genomic evaluations in BLUP‐based methods, a common question is how to choose the animals in the core subset. We compared several core definitions to answer this question. Simulations comprised a moderately heritable trait for 95,010 animals and 50,000 genotypes for animals across five generations. Genotypes consisted of 25,500 SNP distributed across 15 chromosomes. Genotyping errors and missing pedigree were also mimicked. Core animals were defined based on individual generations, equal representation across generations, and at random. For a sufficiently large core size, core definitions had the same accuracies and biases, even if the core animals had imperfect genotypes. When genotyped animals had unknown parents, accuracy and bias were significantly better (p ≤ .05) for random and across generation core definitions.     

基于简化基因组测序的娄门鸭遗传多样性评价

旨在通过分析娄门鸭保种群体的遗传多样性和群体结构来评估保种效果。本研究在娄门鸭保种群中随机选择同一世代163只90日龄的健康个体(39公，124母)，翅静脉采血后提取基因组DNA，利用简化基因组测序技术检测全基因组范围内的单核苷酸多态性(SNPs); 利用R软件计算个体水平的多态信息含量(PIC)、固定指数(Fix-index)、香农信息指数(SHI)、基因多样性指数(Nei)、有效等位基因数(Ne)以及本研究自创的相对多态信息含量(rPIC)等6个遗传多样性指标，并比较分析了不同染色体水平的遗传多样性指标; 同时利用admixture软件分析群体遗传结构，gcta软件分析群体主成分和个体间的亲缘关系，并分析连续性纯合片段(runs of homozygosity，ROH)以及基因组近交系数F_ROH，评估保种效果。结果显示，163只娄门鸭个体共检测到622 205个SNPs位点，质控过滤后得到374 455个高质量SNPs位点，其中50.70%的位点分布在NC_040046、NC_040047、NC_040048和NC_040049四个染色体中。娄门鸭群体PIC、Nei、Ne、SHI和rPIC指标值分别为0.154 1、0.192 9、1.336、0.296 9和0.410 9，对于SNPs而言，该群体38.80%的SNPs位点属于高度多态性位点，遗传多样性较为丰富; Fix-index值为0.320 8，说明娄门鸭群体出现了分化，这与遗传结构、PCA和亲缘关系分析将娄门鸭群体划分为3个群体的结果一致。PIC、Nei、Ne和SHI四个指标分别在不同染色体上的分布规律均一致，且4个指标两两相关性均达到0.97以上，而Fix-index与其他4个指标的相关性较低，在0.23以下，说明可以选择Fix-index以及PIC等少数指标来评估娄门鸭群体的遗传多样性。163只娄门鸭个体共检测到2 966条ROH，ROH片段长度主要集中在0~2 Mb区间; 基于ROH得到的基因组近交系数F_ROH在公、母鸭中分别为0.027 5和0.043 3，说明娄门鸭保种群近交程度较低; 具体到染色体水平，NC_040068、NC_040074染色体的F_ROH值分别达到0.352 4和0.319 3。结果提示，娄门鸭保种群的遗传多样性较丰富，群体基因组近交系数较低，但个别染色体的近交系数较高，且群体出现了部分分化。后续保种中可以将遗传结构分析得到的3个分化的亚群个体之间进行适当的非随机交配，消除目前的群体分化现象，并重点监测染色体近交系数较高的基因组区域，避免个别染色体近交系数上升过快。     

Use of molecular markers to improve relationship information in the genetic evaluation of beef cattle tick resistance under pedigree‐based models

The selection of genetically superior individuals is conditional upon accurate breeding value predictions which, in turn, are highly depend on how precisely relationship is represented by pedigree. For that purpose, the numerator relationship matrix is essential as a priori information in mixed model equations. The presence of pedigree errors and/or the lack of relationship information affect the genetic gain because it reduces the correlation between the true and estimated breeding values. Thus, this study aimed to evaluate the effects of correcting the pedigree relationships using single‐nucleotide polymorphism (SNP) markers on genetic evaluation accuracies for resistance of beef cattle to ticks. Tick count data from Hereford and Braford cattle breeds were used as phenotype. Genotyping was carried out using a high‐density panel (BovineHD ‐ Illumina^® bead chip with 777 962 SNPs) for sires and the Illumina BovineSNP50 panel (54 609 SNPs) for their progenies. The relationship between the parents and progenies of genotyped animals was evaluated, and mismatches were based on the Mendelian conflicts counts. Variance components and genetic parameters estimates were obtained using a Bayesian approach via Gibbs sampling, and the breeding values were predicted assuming a repeatability model. A total of 460 corrections in relationship definitions were made (Table 1) corresponding to 1018 (9.5%) tick count records. Among these changes, 97.17% (447) were related to the sire's information, and 2.8% (13) were related to the dam's information. We observed 27.2% (236/868) of Mendelian conflicts for sire–progeny genotyped pairs and 14.3% (13/91) for dam–progeny genotyped pairs. We performed 2174 new definitions of half‐siblings according to the correlation coefficient between the coancestry and molecular coancestry matrices. It was observed that higher‐quality genetic relationships did not result in significant differences of variance components estimates; however, they resulted in more accurate breeding values predictions. Using SNPs to assess conflicts between parents and progenies increases certainty in relationships and consequently the accuracy of breeding value predictions of candidate animals for selection. Thus, higher genetic gains are expected when compared to the traditional non‐corrected relationship matrix.     

The influence of selection and epistasis on inbreeding depression estimates

Inbreeding depression estimates obtained by regression of the individual performance on the inbreeding were studied by stochastic simulation under various genetic models (solely additive, partial dominance, overdominance and epistasis), and mating strategies (random mating versus selection). In all models, inbreeding depression estimates based on the individual pedigree inbreeding coefficients were compared with estimates based on the true level of autozygosity. For the model with partial dominance and selection, the estimates of inbreeding depression from pedigree information were more negative (lower) than those based on true inbreeding coefficients whereas, in contrast, they were less negative (higher) for the models with overdominance and selection. The difference in the variation of true and pedigree individual inbreeding coefficient indicated that biased estimates might occur even in random mating populations. The estimation of inbreeding depression was further complicated when epistatic effects were present. The sign and the magnitude of the inbreeding effect (depression) estimates might be rather heterogeneous if additive by dominance effects are present because they are strongly dependent on the gene frequency. It was also shown that inbreeding depression is possible in models with negative additive by dominance effects. In models with dominance by dominance inheritance it was difficult to assess the non-linear relationship between performance and inbreeding, while at the same time, non-linear estimates based on pedigree information were extremely biased. The results obtained indicate that new or additional methodologies are required if reliable conclusions about consequences of inbreeding depression are needed.