Genomic evaluation models can fit additive and dominant SNP effects. Under quantitative genetics theory, additive or "breeding" values of individuals are generated by substitution effects, which involve both "biological" additive and dominant effects of the markers. Dominance deviations include only a portion of the biological dominant effects of the markers. Additive variance includes variation due to the additive and dominant effects of the markers. We describe a matrix of dominant genomic relationships across individuals, D, which is similar to the G matrix used in genomic best linear unbiased prediction. This matrix can be used in a mixed-model context for genomic evaluations or to estimate dominant and additive variances in the population. From the "genotypic" value of individuals, an alternative parameterization defines additive and dominance as the parts attributable to the additive and dominant effect of the markers. This approach underestimates the additive genetic variance and overestimates the dominance variance. Transforming the variances from one model into the other is trivial if the distribution of allelic frequencies is known. We illustrate these results with mouse data (four traits, 1884 mice, and 10,946 markers) and simulated data (2100 individuals and 10,000 markers). Variance components were estimated correctly in the model, considering breeding values and dominance deviations. For the model considering genotypic values, the inclusion of dominant effects biased the estimate of additive variance. Genomic models were more accurate for the estimation of variance components than their pedigree-based counterparts.

BackgroundThe current availability of genotypes for very large numbers of single nucleotide polymorphisms (SNPs) is leading to more accurate estimates of inbreeding coefficients and more detailed approaches for detecting inbreeding depression. In the present study, genome-wide information was used to detect inbreeding depression for two reproductive traits (total number of piglets born and number of piglets born alive) in an ancient strain of Iberian pigs (the Guadyerbas strain) that is currently under serious danger of extinction.MethodsA total of 109 sows with phenotypic records were genotyped with the PorcineSNP60 BeadChip v1. Inbreeding depression was estimated using a bivariate animal model in which the inbreeding coefficient was included as a covariate. We used two different measures of genomic inbreeding to perform the analyses: inbreeding estimated on a SNP-by-SNP basis and inbreeding estimated from runs of homozygosity. We also performed the analyses using pedigree-based inbreeding.ResultsSignificant inbreeding depression was detected for both traits using all three measures of inbreeding. Genome-wide information allowed us to identify one region on chromosome 13 associated with inbreeding depression. This region spans from 27 to 54 Mb and overlaps with a previously detected quantitative trait locus and includes the inter-alpha-trypsin inhibitor gene cluster that is involved with embryo implantation.ConclusionsOur results highlight the value of high-density SNP genotyping for providing new insights on where genes causing inbreeding depression are located in the genome. Genomic measures of inbreeding obtained on a SNP-by-SNP basis or those based on the presence/absence of runs of homozygosity represent a suitable alternative to pedigree-based measures to detect inbreeding depression, and a useful tool for mapping studies. To our knowledge, this is the first study in domesticated animals using the SNP-by-SNP inbreeding coefficient to map specific regions within chromosomes associated with inbreeding depression.Electronic supplementary materialThe online version of this article (doi:10.1186/s12711-014-0081-5) contains supplementary material, which is available to authorized users.

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 (, 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 (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 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.

Estimation of non-additive genetic effects in animal breeding is important because it increases the accuracy of breeding value prediction and the value of mate allocation procedures. With the advent of genomic selection these ideas should be revisited. The objective of this study was to quantify the efficiency of including dominance effects and practising mating allocation under a whole-genome evaluation scenario. Four strategies of selection, carried out during five generations, were compared by simulation techniques. In the first scenario (MS), individuals were selected based on their own phenotypic information. In the second (GSA), they were selected based on the prediction generated by the Bayes A method of whole-genome evaluation under an additive model. In the third (GSD), the model was expanded to include dominance effects. These three scenarios used random mating to construct future generations, whereas in the fourth one (GSD + MA), matings were optimized by simulated annealing. The advantage of GSD over GSA ranges from 9 to 14% of the expected response and, in addition, using mate allocation (GSD + MA) provides an additional response ranging from 6% to 22%. However, mate selection can improve the expected genetic response over random mating only in the first generation of selection. Furthermore, the efficiency of genomic selection is eroded after a few generations of selection, thus, a continued collection of phenotypic data and re-evaluation will be required.

In the last decade, genomic selection has become a standard in the genetic evaluation of livestock populations. However, most procedures for the implementation of genomic selection only consider the additive effects associated with SNP (Single Nucleotide Polymorphism) markers used to calculate the prediction of the breeding values of candidates for selection. Nevertheless, the availability of estimates of non-additive effects is of interest because: (i) they contribute to an increase in the accuracy of the prediction of breeding values and the genetic response; (ii) they allow the definition of mate allocation procedures between candidates for selection; and (iii) they can be used to enhance non-additive genetic variation through the definition of appropriate crossbreeding or purebred breeding schemes. This study presents a review of methods for the incorporation of non-additive genetic effects into genomic selection procedures and their potential applications in the prediction of future performance, mate allocation, crossbreeding, and purebred selection. The work concludes with a brief outline of some ideas for future lines of that may help the standard inclusion of non-additive effects in genomic selection.

The leptin receptor gene (LEPR) is a candidate for traits related to growth and body composition, and is located on SSC6 in a region where fatness and meat composition quantitative trait loci (QTL) have previously been detected in several F2 experimental designs. The aims of this work were: (i) to fine map these QTL on a larger sample of animals and generations (F3 and backcross) of an Iberian x Landrace intercross and (ii) to examine the effects of LEPR alleles on body composition traits. Eleven single nucleotide polymorphisms (SNPs) were detected by sequencing LEPR coding regions in Iberian and Landrace pig samples. Three missense polymorphisms were genotyped by pyrosequencing in 33 F0, 70 F1, 418 F2, 86 F3 and 128 individuals coming from the backcross of four F2 males with 24 Landrace females. Thirteen microsatellites and one SNP were also genotyped. Traits analysed were: backfat thickness at different locations (BF(T)), intramuscular fat percentage (IMF(P)), eye muscle area (EM(A)), loin depth (LO(D)), weight of shoulder (SH(W)), weight of ribs (RIB(W)) and weight of belly bacon (BB(W)). Different statistical models were applied in order to evaluate the number and effects of QTL on chromosome 6 and the possible causality of the LEPR gene variants with respect to the QTL. The results support the presence of two QTL on SSC6. One, at position 60-100 cM, affects BF(T) and RIB(W). The other and more significant maps in a narrow region (130-132 cM) and affects BF(T), IMF(P), EM(A), LO(D), SH(W), RIB(W) and BB(W). Results also support the association between LEPR alleles and BF(T) traits. The possible functional implications of the analysed polymorphisms are considered.

BackgroundEstimates 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.ResultsVariance 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.ConclusionsEstimated 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.

-A fundamental issue in quantitative trait locus (QTL) mapping is to determine the plausibility of the presence of a QTL at a given genome location. Bayesian analysis offers an attractive way of testing alternative models (here, QTL vs. no-QTL) via the Bayes factor. There have been several numerical approaches to computing the Bayes factor, mostly based on Markov Chain Monte Carlo (MCMC), but these strategies are subject to numerical or stability problems. We propose a simple and stable approach to calculating the Bayes factor between nested models. The procedure is based on a reparameterization of a variance component model in terms of intra-class correlation. The Bayes factor can then be easily calculated from the output of a MCMC scheme by averaging conditional densities at the null intra-class correlation. We studied the performance of the method using simulation. We applied this approach to QTL analysis in an outbred population. We also compared it with the Likelihood Ratio Test and we analyzed its stability. Simulation results were very similar to the simulated parameters. The posterior probability of the QTL model increases as the QTL effect does. The location of the QTL was also correctly obtained. The use of meta-analysis is suggested from the properties of the Bayes factor. Bayes factor / Quantitative Trait Loci / hypothesis testing / Markov Chain Monte Carlo