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Genetic trends are a valuable tool for analysing the efficiency of breeding programs. They are calculated by averaging the predicted breeding values for all individuals born within a specific time period. Moreover, partitioned genetic trends allow dissecting the contributions of several selection paths to overall genetic progress. These trends are based on the linear relationship between breeding values and the Mendelian sampling terms of ancestors, enabling genetic trends to be split into contributions from different categories of individuals. However, (1) the use of predicted breeding values in calculating partitioned genetic trends depends on the variance components used and (2) a multiple trait analysis allows accounting for selection on correlated traits. These points are often not considered. To overcome these limitations, we present a software called "TM_TRENDS." This software performs a Bayesian analysis of partitioned genetic trends in a multiple trait model, accounting for uncertainty in the variance components. To illustrate the capabilities of this tool, we analysed the partitioned genetic trends for five traits (Birth Weight, Weight at 210 days, Cold Carcass Weight, Carcass Conformation, and Fatness Conformation) in two Spanish beef cattle breeds, Pirenaica and Rubia Gallega. The global genetic trends showed an increase in Carcass Conformation and a decrease in Birth Weight, Weight at 210 days, Cold Carcass Weight, and Fatness Conformation. These trends were partitioned into six categories: non-reproductive individuals, dams of females and non-reproductive individuals, dams of sires, sires with fewer than 20 progeny, sires between 20 and 50 progeny, and sires with more than 50 progeny. The results showed that the main source of genetic progress comes from sires with more than 50 progenies, followed by dams of males. Additionally, two additional features of the Bayesian analysis are presented: the calculation of the posterior probability of the global and partitioned genetic response between two time points, and the calculation of the posterior probability of positive (or negative) genetic progress., (© 2024 The Author(s). Journal of Animal Breeding and Genetics published by John Wiley & Sons Ltd.)

Background: The Dohne Merino sheep was introduced to Australia from South Africa in the 1990s. It was primarily used in crosses with the Merino breed sheep to improve on attributes such as reproduction and carcass composition. Since then, this breed has continued to expand in Australia but the number of genotyped and phenotyped purebred individuals remains low, calling into question the accuracy of genomic selection. The Australian Merino, on the other hand, has a substantial reference population in a separate genomic evaluation (MERINOSELECT). Combining these resources could fast track the impact of genomic selection on the smaller breed, but the efficacy of this needs to be investigated. This study was based on a dataset of 53,663 genotypes and more than 2 million phenotypes. Its main objectives were (1) to characterize the genetic structure of Merino and Dohne Merino breeds, (2) to investigate the utility of combining their evaluations in terms of quality of predictions, and (3) to compare several methods of genetic grouping. We used the 'LR-method' (Linear Regression) for these assessments., Results: We found very low Fst values (below 0.048) between the different Merino lines and Dohne breed considered in our study, indicating very low genetic differentiation. Principal component analysis revealed three distinct groups, identified as purebred Merino, purebred Dohne, and crossbred animals. Considering the whole population in the reference led to the best quality of predictions and the largest increase in accuracy (from 'LR-method') from pedigree to genomic-based evaluations: 0.18, 0.14 and 0.16 for yearling fibre diameter (YFD), yearling greasy fleece weight (YGFW) and yearling liveweight (YWT), respectively. Combined genomic evaluations showed higher accuracies than the evaluation based on the Dohne reference only (accuracies increased by 0.16, 0.06 and 0.07 for YFD, YGFW, and YWT, respectively). For the combined genomic evaluations, metafounder models were more accurate than Unknown Parent Groups models (accuracies increased by 0.04, 0.04 and 0.06 for YFD, YGFW and YWT, respectively)., Conclusions: We found promising results for the future transition of the Dohne breed from pedigree to genomic selection. A combined genomic evaluation, with the MERINOSELECT evaluation in addition to using metafounders, is expected to enhance the quality of genomic predictions for the Dohne Merino breed., (© 2024. The Author(s).)

Interpopulation improvement for crosses of close populations in crops and livestock depends on the amount of heterosis and the amount of variance of dominance deviations in the hybrids. It has been intuited that the further the distance between populations, the lower the amount of dominance variation and the higher the heterosis. Although experience in speciation and interspecific crosses shows, however, that this is not the case when populations are so distant-here we confine ourselves to the case of not-too-distant populations typical in crops and livestock. We present equations that relate the distance between 2 populations, expressed as Nei's genetic distance or as correlation of allele frequencies, quadratically to the amount of dominance deviations across all possible crosses and linearly to the expected heterosis averaging all possible crosses. The amount of variation of dominance deviations decreases with genetic distance until the point where allele frequencies are uncorrelated, and then increases for negatively correlated frequencies. Heterosis always increases with Nei's genetic distance. These expressions match well and complete previous theoretical and empirical findings. In practice, and for close enough populations, they mean that unless frequencies are negatively correlated, selection for hybrids will be more efficient when populations are distant., Competing Interests: Conflicts of interest The author(s) declare no conflict of interest., (© The Author(s) 2023. Published by Oxford University Press on behalf of The Genetics Society of America. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.)

Background: Genetic selection has proven to be a successful strategy for the sustainable control of gastrointestinal parasitism in sheep. However, little is known on the relationship between resistance to parasites and production traits in dairy breeds. In this study, we estimated the heritabilities and genetic correlations for resistance to parasites and milk production traits in the blond-faced Manech breed. The resistance to parasites of 951 rams from the selection scheme was measured through fecal egg counts (FEC) at 30 days post-infection under experimental conditions. Six milk production traits [milk yield (MY), fat yield (FY), protein yield (PY), fat content (FC), protein content (PC) and somatic cell score (LSCS)], were used in this study and were collected on 140,127 dairy ewes in first lactation, as part of the official milk recording. These ewes were related to the 951 rams (65% of the ewes were daughters of the rams)., Results: Fecal egg counts at the end of the first and second infections were moderately heritable (0.19 and 0.37, respectively) and highly correlated (0.93). Heritabilities were moderate for milk yields (ranging from 0.24 to 0.29 for MY, FY and PY) and high for FC (0.35) and PC (0.48). MY was negatively correlated with FC and PC (- 0.39 and - 0.45, respectively). FEC at the end of the second infection were positively correlated with MY, FY and PY (0.28, 0.29 and 0.24, respectively with standard errors of ~ 0.10). These slightly unfavorable correlations indicate that the animals with a high production potential are genetically more susceptible to gastrointestinal parasite infections. A low negative correlation (- 0.17) was also found between FEC after the second infection and LSCS, which suggests that there is a small genetic antagonism between resistance to gastrointestinal parasites and resistance to mastitis, which is another important health trait in dairy sheep., Conclusions: Our results indicate an unfavorable but low genetic relationship between resistance to gastrointestinal parasites and milk production traits in the blond-faced Manech breed. These results will help the breeders' association make decisions about how to include resistance to parasites in the selection objective., (© 2022. The Author(s).)

Background: Multiple breed evaluation using genomic prediction includes the use of data from multiple populations, or from parental breeds and crosses, and is expected to lead to better genomic predictions. Increased complexity comes from the need to fit non-additive effects such as dominance and/or genotype-by-environment interactions. In these models, marker effects (and breeding values) are modelled as correlated between breeds, which leads to multiple trait formulations that are based either on markers [single nucleotide polymorphism best linear unbiased prediction (SNP-BLUP)] or on individuals [genomic(G)BLUP)]. As an alternative, we propose the use of generalized least squares (GLS) followed by backsolving of marker effects using selection index (SI) theory., Results: All investigated options have advantages and inconveniences. The SNP-BLUP yields marker effects directly, which are useful for indirect prediction and for planned matings, but is very large in number of equations and is structured in dense and sparse blocks that do not allow for simple solving. GBLUP uses a multiple trait formulation and is very general, but results in many equations that are not used, which increase memory needs, and is also structured in dense and sparse blocks. An alternative formulation of GBLUP is more compact but requires tailored programming. The alternative of solving by GLS + SI is the least consuming, both in number of operations and in memory, and it uses only single dense blocks. However, it requires dedicated programming. Computational complexity problems are exacerbated when more than additive effects are fitted, e.g. dominance effects or genotype x environment interactions., Conclusions: As multi-breed predictions become more frequent and non-additive effects are more often included, standard equations for genomic prediction based on Henderson's mixed model equations become less practical and may need to be replaced by more efficient (although less general) approaches such as the GLS + SI approach proposed here., (© 2022. The Author(s).)

We revisited, in a genomic context, the theory of hybrid genetic evaluation models of hybrid crosses of pure lines, as the current practice is largely based on infinitesimal model assumptions. Expressions for covariances between hybrids due to additive substitution effects and dominance and epistatic deviations were analytically derived. Using dense markers in a GBLUP analysis, it is possible to split specific combining ability into dominance and across-groups epistatic deviations, and to split general combining ability (GCA) into within-line additive effects and within-line additive by additive (and higher order) epistatic deviations. We analyzed a publicly available maize data set of Dent × Flint hybrids using our new model (called GCA-model) up to additive by additive epistasis. To model higher order interactions within GCAs, we also fitted "residual genetic" line effects. Our new GCA-model was compared with another genomic model which assumes a uniquely defined effect of genes across origins. Most variation in hybrids is accounted by GCA. Variances due to dominance and epistasis have similar magnitudes. Models based on defining effects either differently or identically across heterotic groups resulted in similar predictive abilities for hybrids. The currently used model inflates the estimated additive genetic variance. This is not important for hybrid predictions but has consequences for the breeding scheme-e.g. overestimation of the genetic gain within heterotic group. Therefore, we recommend using GCA-model, which is appropriate for genomic prediction and variance component estimation in hybrid crops using genomic data, and whose results can be practically interpreted and used for breeding purposes., (© The Author(s) 2021. Published by Oxford University Press on behalf of Genetics Society of America.)

Background: Resilient animals can remain productive under different environmental conditions. Rearing in increasingly heterogeneous environmental conditions increases the need of selecting resilient animals. Detection of environmental challenges that affect an entire population can provide a unique opportunity to select animals that are more resilient to these events. The objective of this study was two-fold: (1) to present a simple and practical data-driven approach to estimate the probability that, at a given date, an unrecorded environmental challenge occurred; and (2) to evaluate the genetic determinism of resilience to such events., Methods: Our method consists of inferring the existence of highly variable days (indicator of environmental challenges) via mixture models applied to frequently recorded phenotypic measures and then using the inferred probabilities of the occurrence of an environmental challenge in a reaction norm model to evaluate the genetic determinism of resilience to these events. These probabilities are estimated for each day (or other time frame). We illustrate the method by using an ovine dataset with daily feed intake (DFI) records., Results: Using the proposed method, we estimated the probability of the occurrence of an unrecorded environmental challenge, which proved to be informative and useful for inclusion as a covariate in a reaction norm animal model. We estimated the breeding values for sensitivity of the genetic potential for DFI of animals to environmental challenges. The level and slope of the reaction norm were negatively correlated (- 0.46 ± 0.21)., Conclusions: Our method is promising and appears to be viable to identify unrecorded events of environmental challenges, which is useful when selecting resilient animals and only productive data are available. It can be generalized to a wide variety of phenotypic records from different species and used with large datasets. The negative correlation between level and slope indicates that a hypothetical selection for increased DFI may not be optimal depending on the presence or absence of stress. We observed a reranking of individuals along the environmental gradient and low genetic correlations between extreme environmental conditions. These results confirm the existence of a G [Formula: see text] E interaction and show that the best animals in one environmental condition are not the best in another one.

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., (© 2020.)

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

(1) Background: Ranking traits are used commonly for breeding purposes in several equine populations; however, implementation is complex, because the position of a horse in a competition event is discontinuous and is influenced by the performance of its competitors. One approach to overcoming these limitations is to assume an underlying Gaussian liability that represents a horse's performance and dictates the observed classification in a competition event. That approach can be implemented using Montecarlo Markov Chain (McMC) techniques with a procedure known as the Thurstonian model. (2) Methods: We have developed software (GIBBSTHUR) that analyses ranking traits along with other continuous or threshold traits. The software implements a Gibbs Sampler scheme with a data-augmentation step for the liability of the ranking traits and provides estimates of the variance and covariance components and predictions of the breeding values and the average performance of the competitors in competition events. (3) Results: The results of a simple example are presented, in which it is shown that the procedure can recover the simulated variance and covariance components. In addition, the correlation between the simulated and predicted breeding values and between the estimates of the event effects and the average additive genetic effect of the competitors demonstrates the ability of the software to produce useful predictions for breeding purposes. (4) Conclusions: the GIBBSTHUR software provides a useful tool for the breeding evaluation of ranking traits in horses and is freely available in a public repository (https://github.com/lvaronaunizar/Gibbsthur)., Competing Interests: The authors declare no conflict of interest.

The existence of buffering mechanisms is an emerging property of biological networks, and this results in the buildup of robustness through evolution. So far, there are no explicit methods to find loci implied in buffering mechanisms. However, buffering can be seen as interaction with genetic background. Here we develop this idea into a tractable model for quantitative genetics, in which the buffering effect of one locus with many other loci is condensed into a single statistical effect, multiplicative on the total additive genetic effect. This allows easier interpretation of the results and simplifies the problem of detecting epistasis from quadratic to linear in the number of loci. Using this formulation, we construct a linear model for genome-wide association studies that estimates and declares the significance of multiplicative epistatic effects at single loci. The model has the form of a variance components, norm reaction model and likelihood ratio tests are used for significance. This model is a generalization and explanation of previous ones. We test our model using bovine data: Brahman and Tropical Composite animals, phenotyped for body weight at yearling and genotyped at high density. After association analysis, we find a number of loci with buffering action in one, the other, or both breeds; these loci do not have a significant statistical additive effect. Most of these loci have been reported in previous studies, either with an additive effect or as footprints of selection. We identify buffering epistatic SNPs present in or near genes reported in the context of signatures of selection in multi-breed cattle population studies. Prominent among these genes are those associated with fertility (INHBA, TSHR, ESRRG, PRLR, and PPARG), growth (MSTN, GHR), coat characteristics (KIT, MITF, PRLR), and heat resistance (HSPA6 and HSPA1A). In these populations, we found loci that have a nonsignificant statistical additive effect but a significant epistatic effect. We argue that the discovery and study of loci associated with buffering effects allow attacking the difficult problems, among others, of the release of maintenance variance in artificial and natural selection, of quick adaptation to the environment, and of opposite signs of marker effects in different backgrounds. We conclude that our method and our results generate promising new perspectives for research in evolutionary and quantitative genetics based on the study of loci that buffer effect of other loci., (© The Author(s) 2020. Published by Oxford University Press on behalf of the American Society of Animal Science. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.)

Background: The quantitative genetics theory argues that inbreeding depression and heterosis are founded on the existence of directional dominance. However, most procedures for genomic selection that have included dominance effects assumed prior symmetrical distributions. To address this, two alternatives can be considered: (1) assume the mean of dominance effects different from zero, and (2) use skewed distributions for the regularization of dominance effects. The aim of this study was to compare these approaches using two pig datasets and to confirm the presence of directional dominance., Results: Four alternative models were implemented in two datasets of pig litter size that consisted of 13,449 and 11,581 records from 3631 and 2612 sows genotyped with the Illumina PorcineSNP60 BeadChip. The models evaluated included (1) a model that does not consider directional dominance (Model SN), (2) a model with a covariate b for the average individual homozygosity (Model SC), (3) a model with a parameter λ that reflects asymmetry in the context of skewed Gaussian distributions (Model AN), and (4) a model that includes both b and λ (Model Full). The results of the analysis showed that posterior probabilities of a negative b or a positive λ under Models SC and AN were higher than 0.99, which indicate positive directional dominance. This was confirmed with the predictions of inbreeding depression under Models Full, SC and AN, that were higher than in the SN Model. In spite of differences in posterior estimates of variance components between models, comparison of models based on LogCPO and DIC indicated that Model SC provided the best fit for the two datasets analyzed., Conclusions: Our results confirmed the presence of positive directional dominance for pig litter size and suggested that it should be taken into account when dominance effects are included in genomic evaluation procedures. The consequences of ignoring directional dominance may affect predictions of breeding values and can lead to biased prediction of inbreeding depression and performance of potential mates. A model that assumes Gaussian dominance effects that are centered on a non-zero mean is recommended, at least for datasets with similar features to those analyzed here.

Genomic prediction models have been commonly used in plant breeding but only in reduced datasets comprising a few hundred genotyped individuals. However, pedigree information for an entire breeding population is frequently available, as are historical data on the performance of a large number of selection candidates. The single-step method extends the genomic relationship information from genotyped individuals to pedigree information from a larger number of phenotyped individuals in order to combine relationship information on all members of the breeding population. Furthermore, genomic prediction models that incorporate genotype × environment interactions (G × E) have produced substantial increases in prediction accuracy compared with single-environment genomic prediction models. Our main objective was to show how to use single-step genomic and pedigree models to assess the prediction accuracy of 58,798 CIMMYT wheat ( L.) lines evaluated in several simulated environments in Ciudad Obregon, Mexico, and to predict the grain yield performance of some of them in several sites in South Asia (India, Pakistan, and Bangladesh) using a reaction norm model that incorporated G × E. Another objective was to describe the statistical and computational challenges encountered when developing the pedigree and single-step models in such large datasets. Results indicate that the genomic prediction accuracy achieved by models using pedigree only, markers only, or both pedigree and markers to predict various environments in India, Pakistan, and Bangladesh is higher (0.25-0.38) than prediction accuracy of models that use only phenotypic prediction (0.20) or do not include the G × E term., (Copyright © 2017 Crop Science Society of America.)

Genomic prediction methods based on multiple markers have potential to include nonadditive effects in prediction and analysis of complex traits. However, most developments assume a Hardy-Weinberg equilibrium (HWE). Statistical approaches for genomic selection that account for dominance and epistasis in a general context, without assuming HWE ( e.g. , crosses or homozygous lines), are therefore needed. Our method expands the natural and orthogonal interactions (NOIA) approach, which builds incidence matrices based on genotypic (not allelic) frequencies, to include genome-wide epistasis for an arbitrary number of interacting loci in a genomic evaluation context. This results in an orthogonal partition of the variances, which is not warranted otherwise. We also present the partition of variance as a function of genotypic values and frequencies following Cockerham's orthogonal contrast approach. Then we prove for the first time that, even not in HWE, the multiple-loci NOIA method is equivalent to construct epistatic genomic relationship matrices for higher-order interactions using Hadamard products of additive and dominant genomic orthogonal relationships. A standardization based on the trace of the relationship matrices is, however, needed. We illustrate these results with two simulated F 1 (not in HWE) populations, either in linkage equilibrium (LE), or in linkage disequilibrium (LD) and divergent selection, and pure biological dominant pairwise epistasis. In the LE case, correct and orthogonal estimates of variances were obtained using NOIA genomic relationships but not if relationships were constructed assuming HWE. For the LD simulation, differences were smaller, due to the smaller deviation of the F 1 from HWE. Wrongly assuming HWE to build genomic relationships and estimate variance components yields biased estimates, inflates the total genetic variance, and the estimates are not empirically orthogonal. The NOIA method to build genomic relationships, coupled with the use of Hadamard products for epistatic terms, allows the obtaining of correct estimates in populations either in HWE or not in HWE, and extends to any order of epistatic interactions., (Copyright © 2017 by the Genetics Society of America.)

The vast amount of sequence data generated to analyze complex traits is posing new challenges in terms of the analysis and interpretation of the results. Although simulation is a fundamental tool to investigate the reliability of genomic analyses and to optimize experimental design, existing software cannot realistically simulate complete genomes. To remedy this, we have developed a new strategy (Sequence-Based Virtual Breeding, SBVB) that uses real sequence data and simulates new offspring genomes and phenotypes in a very efficient and flexible manner. Using this tool, we studied the efficiency of full sequence in genomic prediction compared to SNP arrays. We used real porcine sequences from three breeds as founder genomes of a 2500-animal pedigree and two genetic architectures: "neutral" and "selective." In the neutral architecture, frequencies and allele effects were sampled independently whereas, in the selective case, SNPs were sites putatively under selection after domestication and a negative correlation between effect and frequency was induced. We compared the effectiveness of different genotyping strategies for genomic selection, including the use of full sequence commercial arrays or randomly chosen SNP sets in both outbred and crossbred experimental designs. We found that accuracy increases using sequence instead of commercial chips but modestly, perhaps by ≤ 4%. This result was robust to extreme genetic architectures. We conclude that full sequence is unlikely to offset commercial arrays for predicting genetic value when the number of loci is relatively large and the prior given to each SNP is uniform. Using sequence to improve selection thus requires optimized prior information and, likely, increased population sizes. The code and manual for SBVB are available at https://github.com/mperezenciso/sbvb0., (Copyright © 2017 by the Genetics Society of America.)

Background: In pedigreed populations with a major gene segregating for a quantitative trait, it is not clear how to use pedigree, genotype and phenotype information when some individuals are not genotyped. We propose to consider gene content at the major gene as a second trait correlated to the quantitative trait, in a gene content multiple-trait best linear unbiased prediction (GCMTBLUP) method., Results: The genetic covariance between the trait and gene content at the major gene is a function of the substitution effect of the gene. This genetic covariance can be written in a multiple-trait form that accommodates any pattern of missing values for either genotype or phenotype data. Effects of major gene alleles and the genetic covariance between genotype at the major gene and the phenotype can be estimated using standard EM-REML or Gibbs sampling. Prediction of breeding values with genotypes at the major gene can use multiple-trait BLUP software. Major genes with more than two alleles can be considered by including negative covariances between gene contents at each different allele. We simulated two scenarios: a selected and an unselected trait with heritabilities of 0.05 and 0.5, respectively. In both cases, the major gene explained half the genetic variation. Competing methods used imputed gene contents derived by the method of Gengler et al. or by iterative peeling. Imputed gene contents, in contrast to GCMTBLUP, do not consider information on the quantitative trait for genotype prediction. GCMTBLUP gave unbiased estimates of the gene effect, in contrast to the other methods, with less bias and better or equal accuracy of prediction. GCMTBLUP improved estimation of genotypes in non-genotyped individuals, in particular if these individuals had own phenotype records and the trait had a high heritability. Ignoring the major gene in genetic evaluation led to serious biases and decreased prediction accuracy., Conclusions: CGMTBLUP is the best linear predictor of additive genetic merit including pedigree, phenotype, and genotype information at major genes, since it considers missing genotypes. Simulations confirm that it is a simple, efficient and theoretically sound method for genetic evaluation of traits influenced by polygenic inheritance and one or several major genes.

Background: The development of next-generation sequencing technologies (NGS) has made the use of whole-genome sequence data for routine genetic evaluations possible, which has triggered a considerable interest in animal and plant breeding fields. Here, we investigated whether complete or partial sequence data can improve upon existing SNP (single nucleotide polymorphism) array-based selection strategies by simulation using a mixed coalescence - gene-dropping approach., Results: We simulated 20 or 100 causal mutations (quantitative trait nucleotides, QTN) within 65 predefined 'gene' regions, each 10 kb long, within a genome composed of ten 3-Mb chromosomes. We compared prediction accuracy by cross-validation using a medium-density chip (7.5 k SNPs), a high-density (HD, 17 k) and sequence data (335 k). Genetic evaluation was based on a GBLUP method. The simulations showed: (1) a law of diminishing returns with increasing number of SNPs; (2) a modest effect of SNP ascertainment bias in arrays; (3) a small advantage of using whole-genome sequence data vs. HD arrays i.e. ~4%; (4) a minor effect of NGS errors except when imputation error rates are high (≥20%); and (5) if QTN were known, prediction accuracy approached 1. Since this is obviously unrealistic, we explored milder assumptions. We showed that, if all SNPs within causal genes were included in the prediction model, accuracy could also dramatically increase by ~40%. However, this criterion was highly sensitive to either misspecification (including wrong genes) or to the use of an incomplete gene list; in these cases, accuracy fell rapidly towards that reached when all SNPs from sequence data were blindly included in the model., Conclusions: Our study shows that, unless an accurate prior estimate on the functionality of SNPs can be included in the predictor, there is a law of diminishing returns with increasing SNP density. As a result, use of whole-genome sequence data may not result in a highly increased selection response over high-density genotyping.

Background: Estimates of dominance variance in dairy cattle based on pedigree data vary considerably across traits and amount to up to 50% of the total genetic variance for conformation traits and up to 43% for milk production traits. Using bovine SNP (single nucleotide polymorphism) genotypes, dominance variance can be estimated both at the marker level and at the animal level using genomic dominance effect relationship matrices. Yield deviations of high-density genotyped Fleckvieh cows were used to assess cross-validation accuracy of genomic predictions with additive and dominance models. The potential use of dominance variance in planned matings was also investigated., Results: Variance components of nine milk production and conformation traits were estimated with additive and dominance models using yield deviations of 1996 Fleckvieh cows and ranged from 3.3% to 50.5% of the total genetic variance. REML and Gibbs sampling estimates showed good concordance. Although standard errors of estimates of dominance variance were rather large, estimates of dominance variance for milk, fat and protein yields, somatic cell score and milkability were significantly different from 0. Cross-validation accuracy of predicted breeding values was higher with genomic models than with the pedigree model. Inclusion of dominance effects did not increase the accuracy of the predicted breeding and total genetic values. Additive and dominance SNP effects for milk yield and protein yield were estimated with a BLUP (best linear unbiased prediction) model and used to calculate expectations of breeding values and total genetic values for putative offspring. Selection on total genetic value instead of breeding value would result in a larger expected total genetic superiority in progeny, i.e. 14.8% for milk yield and 27.8% for protein yield and reduce the expected additive genetic gain only by 4.5% for milk yield and 2.6% for protein yield., Conclusions: Estimated dominance variance was substantial for most of the analyzed traits. Due to small dominance effect relationships between cows, predictions of individual dominance deviations were very inaccurate and including dominance in the model did not improve prediction accuracy in the cross-validation study. Exploitation of dominance variance in assortative matings was promising and did not appear to severely compromise additive genetic gain.

Genome-wide association studies have proven successful but they remain underpowered for detecting variants of weaker effect. Alternative methods propose to test for association by using an aggregate score that combines the effects of the most associated variants. The set of variants that are to be aggregated may come from either of two modeling approaches: single-marker or multi-marker. The goal of this paper is to evaluate this alternative strategy by using sets of single-nucleotide polymorphisms identified by the two modeling approaches in the simulated pedigree data set provided for the Genetic Analysis Workshop 18. We focused on quantitative traits association analysis of diastolic blood pressure and of Q1, which served to control the statistical significance of our results. We carried out all analyses with knowledge of the underlying simulation model. We found that the probability to replicate association with the aggregate score depends on the single-nucleotide polymorphism set size and, for smaller sets (≤100), on the modeling approach. Nonetheless, assessing the statistical significance of these results in this data set was challenging, likely because of linkage because we are analyzing pedigree data, and also because the genotypes were the same across the replicates. Further methods need to be developed to facilitate the application of this alternative strategy in pedigree data.

Background: Haemonchosis is a parasitic disease that causes severe economic losses in sheep industry. In recent years, the increasing resistance of the parasite to anthelmintics has raised the need for alternative control strategies. Genetic selection is a promising alternative but its efficacy depends on the availability of genetic variation and on the occurrence of favourable genetic correlations between the traits included in the breeding goal. The objective of this study was twofold. First, to estimate both the heritability of and the genetic correlations between growth traits and parasite resistance traits, using bivariate linear mixed animal models, from the phenotypes and genotypes of 1004 backcross lambs (considered as a single population), which underwent two subsequent experimental infestations protocols with Haemonchus contortus. Second, to compare the precision of the estimates when using two different relationship matrices: including pedigree information only or including also SNP (single nucleotide polymorphism) information., Results: Heritabilities were low for average daily gain before infestation (0.10 to 0.15) and average daily gain during the first infestation (0.11 to 0.16), moderate for faecal egg counts during the first infestation (0.21 to 0.38) and faecal egg counts during the second infestation (0.48 to 0.55). Genetic correlations between both growth traits and faecal egg count during the naïve infestation were equal to zero but the genetic correlation between faecal egg count during the second infestation and growth was positive in a Haemonchus contortus free environment and negative in a contaminated environment. The standard errors of the estimates obtained by including SNP information were smaller than those obtained by including pedigree information only., Conclusions: The genetic parameters estimates suggest that growth performance can be selected for independently of selection on resistance to naïve infestation. Selection for increased growth in a non-contaminated environment could lead to more susceptible animals with long-term exposure to the infestation but it could be possible to select for increased growth in a contaminated environment while also increasing resistance to the long-term exposure to the parasite. The use of molecular information increases the precision of the estimates.

Genomic evaluation models so far do not allow for accounting of newly generated genetic variation due to mutation. The main target of this research was to extend current genomic BLUP models with mutational relationships (model AM), and compare them against standard genomic BLUP models (model A) by analyzing simulated data. Model performance and precision of the predicted breeding values were evaluated under different population structures and heritabilities. The deviance information criterion (DIC) clearly favored the mutational relationship model under large heritabilities or populations with moderate-to-deep pedigrees contributing phenotypic data (i.e., differences equal or larger than 10 DIC units); this model provided slightly higher correlation coefficients between simulated and predicted genomic breeding values. On the other hand, null DIC differences, or even relevant advantages for the standard genomic BLUP model, were reported under small heritabilities and shallow pedigrees, although precision of the genomic breeding values did not differ across models at a significant level. This method allows for slightly more accurate genomic predictions and handling of newly created variation; moreover, this approach does not require additional genotyping or phenotyping efforts, but a more accurate handing of available data., (Copyright © 2013 American Dairy Science Association. Published by Elsevier Inc. All rights reserved.)

Background: Using a multi-breed reference population might be a way of increasing the accuracy of genomic breeding values in small breeds. Models involving mixed-breed data do not take into account the fact that marker effects may differ among breeds. This study was aimed at investigating the impact on accuracy of increasing the number of genotyped candidates in the training set by using a multi-breed reference population, in contrast to single-breed genomic evaluations., Methods: Three traits (milk production, fat content and female fertility) were analyzed by genomic mixed linear models and Bayesian methodology. Three breeds of French dairy cattle were used: Holstein, Montbéliarde and Normande with 2976, 950 and 970 bulls in the training population, respectively and 964, 222 and 248 bulls in the validation population, respectively. All animals were genotyped with the Illumina Bovine SNP50 array. Accuracy of genomic breeding values was evaluated under three scenarios for the correlation of genomic breeding values between breeds (r(g)): uncorrelated (1), r(g) = 0; estimated r(g) (2); high, r(g) = 0.95 (3). Accuracy and bias of predictions obtained in the validation population with the multi-breed training set were assessed by the coefficient of determination (R(2)) and by the regression coefficient of daughter yield deviations of validation bulls on their predicted genomic breeding values, respectively., Results: The genetic variation captured by the markers for each trait was similar to that estimated for routine pedigree-based genetic evaluation. Posterior means for rg ranged from -0.01 for fertility between Montbéliarde and Normande to 0.79 for milk yield between Montbéliarde and Holstein. Differences in R(2) between the three scenarios were notable only for fat content in the Montbéliarde breed: from 0.27 in scenario (1) to 0.33 in scenarios (2) and (3). Accuracies for fertility were lower than for other traits., Conclusions: Using a multi-breed reference population resulted in small or no increases in accuracy. Only the breed with a small data set and large genetic correlation with the breed with a large data set showed increased accuracy for the traits with moderate (milk) to high (fat content) heritability. No benefit was observed for fertility, a lowly heritable trait.

Recently, a Haley-Knott-type regression method using combined linkage disequilibrium and linkage analyses (LDLA) was proposed to map quantitative trait loci (QTLs). Chromosome of 5 and 25 cM with 0·25 and 0·05 cM, respectively, between markers were simulated. The differences between the LDLA approaches with regard to QTL position accuracy were very limited, with a significantly better mean square error (MSE) with the LDLA regression (LDLA_reg) in sparse map cases; the contrary was observed, but not significantly, in dense map situations. The computing time required for the LDLA variance components (LDLA_vc) model was much higher than the LDLA_reg model. The precision of QTL position estimation was compared for four numbers of half-sib families, four different family sizes and two experimental designs (half-sibs, and full- and half-sibs). Regarding the number of families, MSE values were lowest for 15 or 50 half-sib families, differences not being significant. We observed that the greater the number of progenies per sire, the more accurate the QTL position. However, for a fixed population size, reducing the number of families (e.g. using a small number of large full-sib families) could lead to less accuracy of estimated QTL position.

For genomic selection methods, the statistical challenge is to estimate the effect of each of the available single-nucleotide polymorphism (SNP). In a context where the number of SNPs (p) is much higher than the number of bulls (n), this task may lead to a poor estimation of these SNP effects if, as for genomic BLUP (gBLUP), all SNPs have a non-null effect. An alternative is to use approaches that have been developed specifically to solve the 'p >> n' problem. This is the case of variable selection methods and among them, we focus on the Elastic-Net (EN) algorithm that is a penalized regression approach. Performances of EN, gBLUP and pedigree-based BLUP were compared with data from three French dairy cattle breeds, giving very encouraging results for EN. We tried to push further the idea of improving SNP effect estimates by considering fewer of them. This variable selection strategy was considered both in the case of gBLUP and EN by adding an SNP pre-selection step based on quantitative trait locus (QTL) detection. Similar results were observed with or without a pre-selection step, in terms of correlations between direct genomic value (DGV) and observed daughter yield deviation in a validation data set. However, when applied to the EN algorithm, this strategy led to a substantial reduction of the number of SNPs included in the prediction equation. In a context where the number of genotyped animals and the number of SNPs gets larger and larger, SNP pre-selection strongly alleviates computing requirements and ensures that national evaluations can be completed within a reasonable time frame.

Background: Genetic relatedness or similarity between individuals is a key concept in population, quantitative and conservation genetics. When the pedigree of a population is available and assuming a founder population from which the genealogical records start, genetic relatedness between individuals can be estimated by the coancestry coefficient. If pedigree data is lacking or incomplete, estimation of the genetic similarity between individuals relies on molecular markers, using either molecular coancestry or molecular covariance. Some relationships between genealogical and molecular coancestries and covariances have already been described in the literature., Methods: We show how the expected values of the empirical measures of similarity based on molecular marker data are functions of the genealogical coancestry. From these formulas, it is easy to derive estimators of genealogical coancestry from molecular data. We include variation of allelic frequencies in the estimators., Results: The estimators are illustrated with simulated examples and with a real dataset from dairy cattle. In general, estimators are accurate and only slightly biased. From the real data set, estimators based on covariances are more compatible with genealogical coancestries than those based on molecular coancestries. A frequently used estimator based on the average of estimated coancestries produced inflated coancestries and numerical instability. The consequences of unknown gene frequencies in the founder population are briefly discussed, along with alternatives to overcome this limitation., Conclusions: Estimators of genealogical coancestry based on molecular data are easy to derive. Estimators based on molecular covariance are more accurate than those based on identity by state. A correction considering the random distribution of allelic frequencies improves accuracy of these estimators, especially for populations with very strong drift.

Empirical experience with genomic selection in dairy cattle suggests that the distribution of the effects of single nucleotide polymorphisms (SNPs) might be far from normality for some traits. An alternative, avoiding the use of arbitrary prior information, is the Bayesian Lasso (BL). Regular BL uses a common variance parameter for residual and SNP effects (BL1Var). We propose here a BL with different residual and SNP effect variances (BL2Var), equivalent to the original Lasso formulation. The λ parameter in Lasso is related to genetic variation in the population. We also suggest precomputing individual variances of SNP effects by BL2Var, to be later used in a linear mixed model (HetVar-GBLUP). Models were tested in a cross-validation design including 1756 Holstein and 678 Montbéliarde French bulls, with 1216 and 451 bulls used as training data; 51 325 and 49 625 polymorphic SNP were used. Milk production traits were tested. Other methods tested included linear mixed models using variances inferred from pedigree estimates or integrated out from the data. Estimates of genetic variation in the population were close to pedigree estimates in BL2Var but not in BL1Var. BL1Var shrank breeding values too little because of the common variance. BL2Var was the most accurate method for prediction and accommodated well major genes, in particular for fat percentage. BL1Var was the least accurate. HetVar-GBLUP was almost as accurate as BL2Var and allows for simple computations and extensions.

Background: Since 2001, the use of more and more dense maps has made researchers aware that combining linkage and linkage disequilibrium enhances the feasibility of fine-mapping genes of interest. So, various method types have been derived to include concepts of population genetics in the analyses. One major drawback of many of these methods is their computational cost, which is very significant when many markers are considered. Recent advances in technology, such as SNP genotyping, have made it possible to deal with huge amount of data. Thus the challenge that remains is to find accurate and efficient methods that are not too time consuming. The study reported here specifically focuses on the half-sib family animal design. Our objective was to determine whether modelling of linkage disequilibrium evolution improved the mapping accuracy of a quantitative trait locus of agricultural interest in these populations. We compared two methods of fine-mapping. The first one was an association analysis. In this method, we did not model linkage disequilibrium evolution. Therefore, the modelling of the evolution of linkage disequilibrium was a deterministic process; it was complete at time 0 and remained complete during the following generations. In the second method, the modelling of the evolution of population allele frequencies was derived from a Wright-Fisher model. We simulated a wide range of scenarios adapted to animal populations and compared these two methods for each scenario., Results: Our results indicated that the improvement produced by probabilistic modelling of linkage disequilibrium evolution was not significant. Both methods led to similar results concerning the location accuracy of quantitative trait loci which appeared to be mainly improved by using four flanking markers instead of two., Conclusions: Therefore, in animal half-sib designs, modelling linkage disequilibrium evolution using a Wright-Fisher model does not significantly improve the accuracy of the QTL location when compared to a simpler method assuming complete and constant linkage between the QTL and the marker alleles. Finally, given the high marker density available nowadays, the simpler method should be preferred as it gives accurate results in a reasonable computing time.

Background: Ranks have been used as phenotypes in the genetic evaluation of horses for a long time through the use of earnings, normal score or raw ranks. A model, ("underlying model" of an unobservable underlying variable responsible for ranks) exists. Recently, a full Bayesian analysis using this model was developed. In addition, in reality, competitions are structured into categories according to the technical level of difficulty linked to the technical ability of horses (horses considered to be the "best" meet their peers). The aim of this article was to validate the underlying model through simulations and to propose a more appropriate model with a mixture distribution of horses in the case of a structured competition. The simulations involved 1000 horses with 10 to 50 performances per horse and 4 to 20 horses per event with unstructured and structured competitions., Results: The underlying model responsible for ranks performed well with unstructured competitions by drawing liabilities in the Gibbs sampler according to the following rule: the liability of each horse must be drawn in the interval formed by the liabilities of horses ranked before and after the particular horse. The estimated repeatability was the simulated one (0.25) and regression between estimated competing ability of horses and true ability was close to 1. Underestimations of repeatability (0.07 to 0.22) were obtained with other traditional criteria (normal score or raw ranks), but in the case of a structured competition, repeatability was underestimated (0.18 to 0.22). Our results show that the effect of an event, or category of event, is irrelevant in such a situation because ranks are independent of such an effect. The proposed mixture model pools horses according to their participation in different categories of competition during the period observed. This last model gave better results (repeatability 0.25), in particular, it provided an improved estimation of average values of competing ability of the horses in the different categories of events., Conclusions: The underlying model was validated. A correct drawing of liabilities for the Gibbs sampler was provided. For a structured competition, the mixture model with a group effect assigned to horses gave the best results.

Background: Populational linkage disequilibrium and within-family linkage are commonly used for QTL mapping and marker assisted selection. The combination of both results in more robust and accurate locations of the QTL, but models proposed so far have been either single marker, complex in practice or well fit to a particular family structure., Results: We herein present linear model theory to come up with additive effects of the QTL alleles in any member of a general pedigree, conditional to observed markers and pedigree, accounting for possible linkage disequilibrium among QTLs and markers. The model is based on association analysis in the founders; further, the additive effect of the QTLs transmitted to the descendants is a weighted (by the probabilities of transmission) average of the substitution effects of founders' haplotypes. The model allows for non-complete linkage disequilibrium QTL-markers in the founders. Two submodels are presented: a simple and easy to implement Haley-Knott type regression for half-sib families, and a general mixed (variance component) model for general pedigrees. The model can use information from all markers. The performance of the regression method is compared by simulation with a more complex IBD method by Meuwissen and Goddard. Numerical examples are provided., Conclusion: The linear model theory provides a useful framework for QTL mapping with dense marker maps. Results show similar accuracies but a bias of the IBD method towards the center of the region. Computations for the linear regression model are extremely simple, in contrast with IBD methods. Extensions of the model to genomic selection and multi-QTL mapping are straightforward.

The availability of genomewide dense markers brings opportunities and challenges to breeding programs. An important question concerns the ways in which dense markers and pedigrees, together with phenotypic records, should be used to arrive at predictions of genetic values for complex traits. If a large number of markers are included in a regression model, marker-specific shrinkage of regression coefficients may be needed. For this reason, the Bayesian least absolute shrinkage and selection operator (LASSO) (BL) appears to be an interesting approach for fitting marker effects in a regression model. This article adapts the BL to arrive at a regression model where markers, pedigrees, and covariates other than markers are considered jointly. Connections between BL and other marker-based regression models are discussed, and the sensitivity of BL with respect to the choice of prior distributions assigned to key parameters is evaluated using simulation. The proposed model was fitted to two data sets from wheat and mouse populations, and evaluated using cross-validation methods. Results indicate that inclusion of markers in the regression further improved the predictive ability of models. An R program that implements the proposed model is freely available.

Selection plans in plant and animal breeding are driven by genetic evaluation. Recent developments suggest using massive genetic marker information, known as "genomic selection." There is little evidence of its performance, though. We empirically compared three strategies for selection: (1) use of pedigree and phenotypic information, (2) use of genomewide markers and phenotypic information, and (3) the combination of both. We analyzed four traits from a heterogeneous mouse population (http://gscan.well.ox.ac.uk/), including 1884 individuals and 10,946 SNP markers. We used linear mixed models, using extensions of association analysis. Cross-validation techniques were used, providing assumption-free estimates of predictive ability. Sampling of validation and training data sets was carried out across and within families, which allows comparing across- and within-family information. Use of genomewide genetic markers increased predictive ability up to 0.22 across families and up to 0.03 within families. The latter is not statistically significant. These values are roughly comparable to increases of up to 0.57 (across family) and 0.14 (within family) in accuracy of prediction of genetic value. In this data set, within-family information was more accurate than across-family information, and populational linkage disequilibrium was not a completely accurate source of information for genetic evaluation. This fact questions some applications of genomic selection.

Breeding sheep populations for scrapie resistance could result in a loss of genetic variability. In this study, the effect on genetic variability of selection for increasing the ARR allele frequency was estimated in the Latxa breed. Two sources of information were used, pedigree and genetic polymorphisms (fifteen microsatellites). The results based on the genealogical information were conditioned by a low pedigree completeness level that revealed the interest of also using the information provided by the molecular markers. The overall results suggest that no great negative effect on genetic variability can be expected in the short time in the population analysed by selection of only ARR/ARR males. The estimated average relationship of ARR/ARR males with reproductive females was similar to that of all available males whatever its genotype: 0.010 vs. 0.012 for a genealogical relationship and 0.257 vs. 0.296 for molecular coancestry, respectively. However, selection of only ARR/ARR males implied important losses in founder animals (87 percent) and low frequency alleles (30 percent) in the ram population. The evaluation of mild selection strategies against scrapie susceptibility based on the use of some ARR heterozygous males was difficult because the genetic relationships estimated among animals differed when pedigree or molecular information was used, and the use of more molecular markers should be evaluated.