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Genomic selection (GS) is now practiced successfully across many species. However, many questions remain, such as long-term effects, estimations of genomic parameters, robustness of genome-wide association study (GWAS) with small and large datasets, and stability of genomic predictions. This study summarizes presentations from the authors at the 2020 American Society of Animal Science (ASAS) symposium. The focus of many studies until now is on linkage disequilibrium between two loci. Ignoring higher-level equilibrium may lead to phantom dominance and epistasis. The Bulmer effect leads to a reduction of the additive variance; however, the selection for increased recombination rate can release anew genetic variance. With genomic information, estimates of genetic parameters may be biased by genomic preselection, but costs of estimation can increase drastically due to the dense form of the genomic information. To make the computation of estimates feasible, genotypes could be retained only for the most important animals, and methods of estimation should use algorithms that can recognize dense blocks in sparse matrices. GWASs using small genomic datasets frequently find many marker-trait associations, whereas studies using much bigger datasets find only a few. Most of the current tools use very simple models for GWAS, possibly causing artifacts. These models are adequate for large datasets where pseudo-phenotypes such as deregressed proofs indirectly account for important effects for traits of interest. Artifacts arising in GWAS with small datasets can be minimized by using data from all animals (whether genotyped or not), realistic models, and methods that account for population structure. Recent developments permit the computation of P-values from genomic best linear unbiased prediction (GBLUP), where models can be arbitrarily complex but restricted to genotyped animals only, and single-step GBLUP that also uses phenotypes from ungenotyped animals. Stability was an important part of nongenomic evaluations, where genetic predictions were stable in the absence of new data even with low prediction accuracies. Unfortunately, genomic evaluations for such animals change because all animals with genotypes are connected. A top-ranked animal can easily drop in the next evaluation, causing a crisis of confidence in genomic evaluations. While correlations between consecutive genomic evaluations are high, outliers can have differences as high as 1 SD. A solution to fluctuating genomic evaluations is to base selection decisions on groups of animals. Although many issues in GS have been solved, many new issues that require additional research continue to surface.

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 F1 (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 F1 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.

The availability of dense panels of common single-nucleotide polymorphisms and sequence variants has facilitated the study of statistical features of the genetic architecture of complex traits and diseases via whole-genome regressions (WGRs). At the onset, traits were analyzed trait by trait, but recently, WGRs have been extended for analysis of several traits jointly. The expectation is that such an approach would offer insight into mechanisms that cause trait associations, such as pleiotropy. We demonstrate that correlation parameters inferred using markers can give a distorted picture of the genetic correlation between traits. In the absence of knowledge of linkage disequilibrium relationships between quantitative or disease trait loci and markers, speculating about genetic correlation and its causes (e.g., pleiotropy) using genomic data is conjectural.

Current aquaculture breeding programs aimed at improving resistance to diseases are based on challenge tests, where performance is recorded on sibs of candidates to selection, and on selection between families. Genome-wide evaluation (GWE) of breeding values offers new opportunities for using variation within families when dealing with such traits. However, up-to-date studies on GWE in aquaculture programs have only considered continuous traits. The objectives of this study were to extend GWE methodology, in particular the Bayes B method, to analyze dichotomous traits such as resistance to disease, and to quantify, through computer simulation, the accuracy of GWE for disease resistance in aquaculture sib-based programs, using the methodology developed. Two heritabilities (0.1 and 0.3) and 2 disease prevalences (0.1 and 0.5) were assumed in the simulations. We followed the threshold liability model, which assumes that there is an underlying variable (liability) with a continuous distribution and assumed a BayesB model for the liabilities. It was shown that the threshold liability model used fits very well with the BayesB model of GWE. The advantage of using the threshold model was clear when dealing with disease resistance dichotomous phenotypes, particularly under the conditions where linear models are less appropriate (low heritability and disease prevalence). In the testing set (where individuals are genotyped but not measured), the increase in accuracy for the simulated schemes when using the threshold model ranged from 4 (for heritability equal to 0.3 and prevalence equal to 0.5) to 16% (for heritability and prevalence equal to 0.1) when compared with the linear model.

This study investigated, through stochastic computer simulation, the extra gains expected from marker-assisted selection (MAS) in an infinitesimal model with linkage. The trait under selection was assumed to be controlled by 2,000 loci of additive small effect and evenly distributed in c chromosomes of one Morgan each (and c = 5, 10, 20, or 30). This approach differs from previous studies on the benefits of MAS that have considered mixed inheritance models. Marker information was used together with pedigree information to compute the relationship matrix used in BLUP genetic evaluations. The MAS schemes were compared with schemes where genetic evaluations were performed using standard BLUP (i.e., the relationship matrix is obtained using pedigree information only). When the number of markers was large enough (approximately one marker every 10 cM), there were increases in the accuracy of selection with MAS, and this led to extra gains compared with standard BLUP for all genome sizes considered. The benefit from MAS increased over generations. At the last generation of selection (Generation 10), the response from MAS was 11, 9, 7, and 5% greater than with standard BLUP for genomes with 5, 10, 20, and 30 chromosomes, respectively. Thus, although small, gains from MAS were nonetheless detectable for genome sizes typical of livestock populations.

An experimental F2 cross between Iberian and Landrace pig strains was performed to map quantitative trait loci (QTL) for diverse productive traits. Here we report results for meat quality traits from 369 F2 animals with records for pH 24 h postmortem (pH 24 h), muscle color Minolta measurements L* (lightness), a* (redness), and b* (yellowness), H* (hue angle), C* (chroma), intramuscular fat (IMF) and haematin pigment content measured in the longissimus thoracis. Pigs were genotyped for 92 markers covering the 18 porcine autosomes (SSC). Results of the genome scan show evidence for QTL for IMF (SSC6; F = 27.16), pH 24 h (SSC3; F = 7.73), haematin pigments (SSC4 and SSC7; F = 8.68 and 9.47 respectively) and Minolta color measurements L* (SSC4 and SSC7; F =16.42 and 7.17 respectively), and a* (SSC4 and SSC8; F = 8.05 and 7.36 respectively). No QTL were observed for the color measurements b*, H*, and C*. Alternative models fitting epistasis between QTL were also tested, but detected epistatic interactions were not significant at a genome-wise level. In this work we identify genomic regions related with meat quality traits. Improvement by traditional selection methods is complicated, and finer mapping would be required for their application in introgression programs.

The use of population genetic variability in present-day selection schemes can be improved to reduce inbreeding rate and inbreeding depression without impairing genetic progress. We performed an experiment with Drosophila melanogaster to test mate selection, an optimizing method that uses linear programming to maximize the selection differential applied while at the same time respecting a restriction on the increase in inbreeding expected in the next generation. Previous studies about mate selection used computer simulation on simple additive genetic models, and no experiment with a real character in a real population had been carried out. After six selection generations, the optimized lines showed an increase in cumulated phenotypic selection differential of 10.76%, and at the same time, a reduction of 19.91 and 60.47% in inbreeding coefficient mean and variance, respectively. The increased selection pressure would bring greater selection response, and in fact, the observed change in the selected trait was on average 31.03% greater in the optimized lines. These improvements in the selection scheme were not made at the expense of the long-term expectations of genetic variability in the population, as these expectations were very similar for both mate selection and conventionally selected lines in our experiment.

A comparison of three family indices to increase number of pupas from 3-d lay in Drosophila melanogaster is reported. The three indices were Id, based exclusively on dam's information; Ihd, based additionally on dam's full-sibs' and half-sibs' information; and Ihs, which also included the sire's full-sibs' and half-sibs' records. Three lines, D, HD, and HS, were selected, each according to one of the three indices: Id, Ihd, or Ihs. Each line consisted of 10 sires and 60 dams. Each dam contributed one male offspring and three female offspring. Seven generations of selection were performed in a two-replicate experiment. The expected advance of Ihs and Ihd over Id in the seventh generation was .38 and .15 phenotypic standard deviations, respectively. The experiment was analyzed in terms of both classical ordinary least squares (OLS) and mixed-model methodology (MMM). The phenotypic trends in the first replicate were 4.06 +/- 1.74, 1.42 +/- 1.76, and .26 +/- 1.94 pupas per generation for Lines D, HD, and HS, respectively, and in the second replicate 8.52 +/- 2.40, 6.16 +/- 3.21, and 4.21 +/- 2.60, respectively. The genetic trends in the first replicate were 2.18 +/- .61, 1.08 +/- .67, and .24 +/- .68 pupas per generation and, in the second replicate, 2.51 +/- .60, .16 +/- .61, and .05 +/- .64 for Lines D, HD, and HS, respectively. Despite theoretical expectations, the Id index was consistently better than the more complex indices. Several explanations for these results are possible: 1) smaller than expected selection differential, 2) inbreeding depression, and 3) incorrect heritability used to construct the indices.(ABSTRACT TRUNCATED AT 250 WORDS)

Twenty generations of divergent selection for abdominal bristle number were carried out starting from a completely homozygous population of Drosophila melanogaster. All lines were selected with the same proportion (20%) but at two different numbers of selected parents of each sex (5 or 25). A significant response to selection was detected in eight lines (out of 40) and, in most cases, it could be wholly attributed to a single mutation of relatively large effect (0.5-2 phenotypic standard deviations). The ratio of new mutational variance to environmental variance was estimated to be (0.33 +/- 0.11) X 10(-3). The distribution of mutant effects was asymmetrical, both with respect to bristle number (85% of it was negative) and to fitness (most detected bristle mutations were lethal or semilethal). Moreover, this distribution was leptokurtic, due to the presence of major genes. Gene action on bristles ranged from additive to completely recessive, no epistatic interactions being found. In agreement with theory, larger responses in each direction were achieved by those lines selected at greater effective population sizes. Furthermore, the observed divergence between lines selected in opposite directions was proportional to their effective size, as predicted for mutations of large effect.