Zulma G. Vitezica

Bias in genomic predictions for populations under selection

Prediction of genetic merit or disease risk using genetic marker information is becoming a common practice for selection of livestock and plant species. For the successful application of genome-wide marker-assisted selection (GWMAS), genomic predictions should be accurate and unbiased. The effect of selection on bias and accuracy of genomic predictions was studied in two simulated animal populations under weak or strong selection and with several heritabilities. Prediction of genetic values was by best-linear unbiased prediction (BLUP) using data either from relatives summarized in pseudodata for genotyped individuals (multiple-step method) or using all available data jointly (single-step method). The single-step method combined genomic- and pedigree-based relationship matrices. Predictions by the multiple-step method were biased. Predictions by a single-step method were less biased and more accurate but under strong selection were less accurate. When genomic relationships were shifted by a constant, the single-step method was unbiased and the most accurate. The value of that constant, which adjusts for non-random selection of genotyped individuals, can be derived analytically.

On the Additive and Dominant Variance and Covariance of Individuals Within the Genomic Selection Scope

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.

Genome-wide association mapping including phenotypes from relatives without genotypes in a single-step (ssGWAS) for 6-week body weight in broiler chickens

The purpose of this study was to compare results obtained from various methodologies for genome-wide association studies, when applied to real data, in terms of number and commonality of regions identified and their genetic variance explained, computational speed, and possible pitfalls in interpretations of results. Methodologies include: two iteratively reweighted single-step genomic BLUP procedures (ssGWAS1 and ssGWAS2), a single-marker model (CGWAS), and BayesB. The ssGWAS methods utilize genomic breeding values (GEBVs) based on combined pedigree, genomic and phenotypic information, while CGWAS and BayesB only utilize phenotypes from genotyped animals or pseudo-phenotypes. In this study, ssGWAS was performed by converting GEBVs to SNP marker effects. Unequal variances for markers were incorporated for calculating weights into a new genomic relationship matrix. SNP weights were refined iteratively. The data was body weight at 6 weeks on 274,776 broiler chickens, of which 4553 were genotyped using a 60 k SNP chip. Comparison of genomic regions was based on genetic variances explained by local SNP regions (20 SNPs). After 3 iterations, the noise was greatly reduced for ssGWAS1 and results are similar to that of CGWAS, with 4 out of the top 10 regions in common. In contrast, for BayesB, the plot was dominated by a single region explaining 23.1% of the genetic variance. This same region was found by ssGWAS1 with the same rank, but the amount of genetic variation attributed to the region was only 3%. These findings emphasize the need for caution when comparing and interpreting results from various methods, and highlight that detected associations, and strength of association, strongly depends on methodologies and details of implementations. BayesB appears to overly shrink regions to zero, while overestimating the amount of genetic variation attributed to the remaining SNP effects. The real world is most likely a compromise between methods and remains to be determined.

Genomic analysis of dominance effects on milk production and conformation traits in Fleckvieh cattle

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.

Unknown-parent groups in single-step genomic evaluation

In single-step genomic evaluation using best linear unbiased prediction (ssGBLUP), genomic predictions are calculated with a relationship matrix that combines pedigree and genomic information. For missing pedigrees, unknown selection processes, or inclusion of several populations, a BLUP model can include unknown-parent groups (UPG) in the animal effect. For ssGBLUP, UPG equations also involve contributions from genomic relationships. When those contributions are ignored, UPG solutions and genetic predictions can be biased. Options to eliminate or reduce such bias are presented. First, mixed model equations can be modified to include contributions to UPG elements from genomic relationships (greater software complexity). Second, UPG can be implemented as separate effects (higher cost of computing and data processing). Third, contributions can be ignored when they are relatively small, but they may be small only after refinements to UPG definitions. Fourth, contributions may approximately cancel out when genomic and pedigree relationships are constructed for compatibility; however, different construction steps are required for unknown parents from the same or different populations. Finally, an additional polygenic effect that also includes UPG can be added to the model.

Evaluation of a multi-line broiler chicken population using a single-step genomic evaluation procedure

Effects on prediction of analysing a multi-line chicken population as one line were evaluated. Body weight records were provided by Cobb-Vantress for two lines of broiler chickens. Phenotypic records for 183 695 and 164 149 broilers and genotypic records for 3195 and 3001 broilers were available for each line. Lines were combined to create a multi-line population and analysed using a single-step procedure combining the additive relationship matrix and the genomic relationship matrix (G). G was scaled using allele frequencies from each line, the multi-line population, or 0.5. When allele frequencies were calculated from each line, distributions of diagonal elements were bimodal. When allele frequencies were calculated from the multi-line population, the distribution of diagonal elements had one peak. When allele frequency 0.5 was used, the distribution was bimodal. Genomic estimated breeding values (GEBVs) were predicted using each allele frequency. GEBVs differed with allele frequency but had ≥ 0.99 correlations with GEBVs predicted with correct allele frequencies. Means of each line and differences in mean between the lines differed based on allele frequencies. Assumed allele frequencies have little impact on ranking within line but larger impact on ranking across lines. G may be used to evaluate multiple populations simultaneously but must be adjusted to obtain properly scaled estimates when population structure is unknown.

A study on associations between PrP genotypes and meat traits in French sheep breeds

In this study the potential association of PrP genotypes with meat traits has been investigated. The data included young rams from individual testing stations of three breeds: Ile de France, Prealpes du Sud and Blanc du Massif Central. These breeds were chosen due to their large number of available animals (with performance records and PrP genotypes) and their differential ARR haplotype frequency. Two analyses differing in the PrP genotype classes considered were carried out. Firstly, animals were categorized into three classes: ARR homozygous, ARR heterozygous, and animals without the ARR haplotype. The data for this analysis included 725, 534 and 832 animals for Ile de France, Prealpes du Sud and Blanc du Massif Central breeds, respectively. Secondly, as the two predominant haplotypes in these breeds are ARR and AR- (and AR- includes ARQ and ARH haplotypes), the effect of substituting 1 or 2 ARR haplotypes for AR- haplotypes was studied. These comparisons involved three genotype classes: ARR homozygous, ARR/AR-, and AR-homozygous. The data for this analysis included 532, 509 and 620 animals of Ile de France, Prealpes du Sud and Blanc du Massif Central breeds, respectively. Meat traits were analysed using an animal model (where the PrP genotype was included as a fixed effect) and they included growth rate, ultrasonic fat depth, and ultrasonic muscle depth. The results of this study indicate no evidence of association between PrP genotypes and the meat traits studied in these sheep breeds.

Genetic parameters of product quality and hepatic metabolism in fattened mule ducks.

Genetic parameters of traits related to hepatic lipid metabolism, carcass composition, and product quality of overfed mule ducks were estimated on both parental lines of this hybrid: the common duck line for the maternal side and the Muscovy line for the paternal side. The originality of the statistical model was to include simultaneously the additive genetic effect of the common ducks and that of the Muscovy ducks, revealing a greater genetic determinism in common than in Muscovy. Plasma metabolic indicators (glucose, triglyceride, and cholesterol contents) were heritable, in particular at the end of the overfeeding period, and heritabilities increased with the overfeeding stage. Carcass composition traits were highly heritable in the common line, with values ranging from 0.15 for liver weight, 0.21 for carcass weight, and 0.25 for abdominal fat weight to 0.32 for breast muscle weight. Heritabilities of technological outputs were greater for the fatty liver (0.19 and 0.08, respectively, on common and Muscovy sides for liver melting rate) than for the pectoralis major muscle (between 0.02 and 0.05 on both parental sides for cooking losses). Fortunately, the processing industry is mainly facing problems in liver quality, such as too high of a melting rate, than in meat quality. The meat quality appraisal criteria (such as texture and cooking losses), usually dependent on pH and the rate of decline of pH, were also very lowly heritable. This study demonstrated that genetic determinism of meat quality and ability of overfeeding is not similar in the common population and in the Muscovy population; traits related to fattening, muscle development, and BW have heritability values from 2 to 4 times greater on the common line than on the Muscovy line, which is relevant for considering different selection strategies.

Quantitative trait loci linked to PRNP gene controlling health and production traits in INRA 401 sheep

In this study, the potential association of PrP genotypes with health and productive traits was investigated. Data were recorded on animals of the INRA 401 breed from the Bourges-La Sapinière INRA experimental farm. The population consisted of 30 rams and 852 ewes, which produced 1310 lambs. The animals were categorized into three PrP genotype classes: ARR homozygous, ARR heterozygous, and animals without any ARR allele. Two analyses differing in the approach considered were carried out. Firstly, the potential association of the PrP genotype with disease (Salmonella resistance) and production (wool and carcass) traits was studied. The data used included 1042, 1043 and 1013 genotyped animals for the Salmonella resistance, wool and carcass traits, respectively. The different traits were analyzed using an animal model, where the PrP genotype effect was included as a fixed effect. Association analyses do not indicate any evidence of an effect of PrP genotypes on traits studied in this breed. Secondly, a quantitative trait loci (QTL) detection approach using the PRNP gene as a marker was applied on ovine chromosome 13. Interval mapping was used. Evidence for one QTL affecting mean fiber diameter was found at 25 cM from the PRNP gene. However, a linkage between PRNP and this QTL does not imply unfavorable linkage disequilibrium for PRNP selection purposes.

Ancestral Relationships Using Metafounders: Finite Ancestral Populations and Across Population Relationships

Recent use of genomic (marker-based) relationships shows that relationships exist within and across base population (breeds or lines). However, current treatment of pedigree relationships is unable to consider relationships within or across base populations, although such relationships must exist due to finite size of the ancestral population and connections between populations. This complicates the conciliation of both approaches and, in particular, combining pedigree with genomic relationships. We present a coherent theoretical framework to consider base population in pedigree relationships. We suggest a conceptual framework that considers each ancestral population as a finite-sized pool of gametes. This generates across-individual relationships and contrasts with the classical view which each population is considered as an infinite, unrelated pool. Several ancestral populations may be connected and therefore related. Each ancestral population can be represented as a “metafounder,” a pseudo-individual included as founder of the pedigree and similar to an “unknown parent group.” Metafounders have self- and across relationships according to a set of parameters, which measure ancestral relationships, i.e., homozygozities within populations and relationships across populations. These parameters can be estimated from existing pedigree and marker genotypes using maximum likelihood or a method based on summary statistics, for arbitrarily complex pedigrees. Equivalences of genetic variance and variance components between the classical and this new parameterization are shown. Segregation variance on crosses of populations is modeled. Efficient algorithms for computation of relationship matrices, their inverses, and inbreeding coefficients are presented. Use of metafounders leads to compatibility of genomic and pedigree relationship matrices and to simple computing algorithms. Examples and code are given.