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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).)

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.

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 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.

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: 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.