Grouping of genomic markers in populations with family structure.

BACKGROUND: Linkage and linkage disequilibrium (LD) between genome regions cause dependencies among genomic markers. Due to family stratification in populations with non-random mating in livestock or crop, the standard measures of population LD such as [Formula: see text] may be biased. Grouping of markers according to their interdependence needs to account for the actual population structure in order to allow proper inference in genome-based evaluations. RESULTS: Given a matrix reflecting the strength of association between markers, groups are built successively using a greedy algorithm; largest groups are built at first. As an option, a representative marker is selected for each group. We provide an implementation of the grouping approach as a new function to the R package hscovar. This package enables the calculation of the theoretical covariance between biallelic markers for half- or full-sib families and the derivation of representative markers. In case studies, we have shown that the number of groups comprising dependent markers was smaller and representative SNPs were spread more uniformly over the investigated chromosome region when the family stratification was respected compared to a population-LD approach. In a simulation study, we observed that sensitivity and specificity of a genome-based association study improved if selection of representative markers took family structure into account. CONCLUSIONS: Chromosome segments which frequently recombine in the underlying population can be identified from the matrix of pairwise dependence between markers. Representative markers can be exploited, for instance, for dimension reduction prior to a genome-based association study or the grouping structure itself can be employed in a grouped penalization approach.

Application of multivariate single-step SNP best linear unbiased predictor model and revised SNP list for genomic evaluation of dairy cattle in Australia.

The objectives of this study were (1) to evaluate the computational feasibility of the multitrait test-day single-step SNP-BLUP (ssSNP-BLUP) model using phenotypic records of genotyped and nongenotyped animals, and (2) to compare accuracies (coefficient of determination; R2) and bias of genomic estimated breeding values (GEBV) and de-regressed proofs as response variables in 3 Australian dairy cattle breeds (i.e., Holstein, Jersey, and Red breeds). Additive genomic random regression coefficients for milk, fat, protein yield and somatic cell score were predicted in the first, second, and third lactation. The predicted coefficients were used to derive 305-d GEBV and were compared with the traditional parent averages obtained from a BLUP model without genomic information. Cow fertility traits were evaluated from the 5-trait repeatability model (i.e., calving interval, days from calving to first service, pregnancy diagnosis, first service nonreturn rate, and lactation length). The de-regressed proofs were only for calving interval. Our results showed that ssSNP-BLUP using multitrait test-day model increased reliability and reduced bias of breeding values of young animals when compared with parent average from traditional BLUP in Australian Holsten, Jersey, and Red breeds. The use of a custom selection of approximately 46,000 SNP (custom XT SNP list) increased the reliability of GEBV compared with the results obtained using the commercial Illumina 50K chip (Illumina, San Diego, CA). The use of the second preconditioner substantially improved the convergence rate of the preconditioned conjugate gradient method, but further work is needed to improve the efficiency of the computation of the Kronecker matrix product by vector. Application of ssSNP-BLUP to multitrait random regression models is computationally feasible.

Design of experiments for fine-mapping quantitative trait loci in livestock populations.

BACKGROUND: Single nucleotide polymorphisms (SNPs) which capture a significant impact on a trait can be identified with genome-wide association studies. High linkage disequilibrium (LD) among SNPs makes it difficult to identify causative variants correctly. Thus, often target regions instead of single SNPs are reported. Sample size has not only a crucial impact on the precision of parameter estimates, it also ensures that a desired level of statistical power can be reached. We study the design of experiments for fine-mapping of signals of a quantitative trait locus in such a target region. METHODS: A multi-locus model allows to identify causative variants simultaneously, to state their positions more precisely and to account for existing dependencies. Based on the commonly applied SNP-BLUP approach, we determine the z-score statistic for locally testing non-zero SNP effects and investigate its distribution under the alternative hypothesis. This quantity employs the theoretical instead of observed dependence between SNPs; it can be set up as a function of paternal and maternal LD for any given population structure. RESULTS: We simulated multiple paternal half-sib families and considered a target region of 1 Mbp. A bimodal distribution of estimated sample size was observed, particularly if more than two causative variants were assumed. The median of estimates constituted the final proposal of optimal sample size; it was consistently less than sample size estimated from single-SNP investigation which was used as a baseline approach. The second mode pointed to inflated sample sizes and could be explained by blocks of varying linkage phases leading to negative correlations between SNPs. Optimal sample size increased almost linearly with number of signals to be identified but depended much stronger on the assumption on heritability. For instance, three times as many samples were required if heritability was 0.1 compared to 0.3. An R package is provided that comprises all required tools. CONCLUSIONS: Our approach incorporates information about the population structure into the design of experiments. Compared to a conventional method, this leads to a reduced estimate of sample size enabling the resource-saving design of future experiments for fine-mapping of candidate variants.

Genomic prediction ability for beef fatty acid profile in Nelore cattle using different pseudo-phenotypes.

The aim of the present study was to compare the predictive ability of SNP-BLUP model using different pseudo-phenotypes such as phenotype adjusted for fixed effects, estimated breeding value, and genomic estimated breeding value, using simulated and real data for beef FA profile of Nelore cattle finished in feedlot. A pedigree with phenotypes and genotypes of 10,000 animals were simulated, considering 50% of multiple sires in the pedigree. Regarding to phenotypes, two traits were simulated, one with high heritability (0.58), another with low heritability (0.13). Ten replicates were performed for each trait and results were averaged among replicates. A historical population was created from generation zero to 2020, with a constant size of 2000 animals (from generation zero to 1000) to produce different levels of linkage disequilibrium (LD). Therefore, there was a gradual reduction in the number of animals (from 2000 to 600), producing a "bottleneck effect" and consequently, genetic drift and LD starting in the generation 1001 to 2020. A total of 335,000 markers (with MAF greater or equal to 0.02) and 1000 QTL were randomly selected from the last generation of the historical population to generate genotypic data for the test population. The phenotypes were computed as the sum of the QTL effects and an error term sampled from a normal distribution with zero mean and variance equal to 0.88. For simulated data, 4000 animals of the generations 7, 8, and 9 (with genotype and phenotype) were used as training population, and 1000 animals of the last generation (10) were used as validation population. A total of 937 Nelore bulls with phenotype for fatty acid profiles (Sum of saturated, monounsaturated, omega 3, omega 6, ratio of polyunsaturated and saturated and polyunsaturated fatty acid profile) were genotyped using the Illumina BovineHD BeadChip (Illumina, San Diego, CA) with 777,962 SNP. To compare the accuracy and bias of direct genomic value (DGV) for different pseudo-phenotypes, the correlation between true breeding value (TBV) or DGV with pseudo-phenotypes and linear regression coefficient of the pseudo-phenotypes on TBV for simulated data or DGV for real data, respectively. For simulated data, the correlations between DGV and TBV for high heritability traits were higher than obtained with low heritability traits. For simulated and real data, the prediction ability was higher for GEBV than for Yc and EBV. For simulated data, the regression coefficient estimates (b(Yc,DGV)), were on average lower than 1 for high and low heritability traits, being inflated. The results were more biased for Yc and EBV than for GEBV. For real data, the GEBV displayed less biased results compared to Yc and EBV for SFA, MUFA, n-3, n-6, and PUFA/SFA. Despite the less biased results for PUFA using the EBV as pseudo-phenotype, the b(Yi,DGV estimates obtained for the different pseudo-phenotypes (Yc, EBV and GEBV) were very close. Genomic information can assist in improving beef fatty acid profile in Zebu cattle, since the use of genomic information yielded genomic values for fatty acid profile with accuracies ranging from low to moderate. Considering both simulated and real data, the ssGBLUP model is an appropriate alternative to obtain more reliable and less biased GEBVs as pseudo-phenotype in situations of missing pedigree, due to high proportion of multiple sires, being more adequate than EBV and Yc to predict direct genomic value for beef fatty acid profile.

Technical note: Equivalent genomic models with a residual polygenic effect.

Routine genomic evaluations in animal breeding are usually based on either a BLUP with genomic relationship matrix (GBLUP) or single nucleotide polymorphism (SNP) BLUP model. For a multi-step genomic evaluation, these 2 alternative genomic models were proven to give equivalent predictions for genomic reference animals. The model equivalence was verified also for young genotyped animals without phenotypes. Due to incomplete linkage disequilibrium of SNP markers to genes or causal mutations responsible for genetic inheritance of quantitative traits, SNP markers cannot explain all the genetic variance. A residual polygenic effect is normally fitted in the genomic model to account for the incomplete linkage disequilibrium. In this study, we start by showing the proof that the multi-step GBLUP and SNP BLUP models are equivalent for the reference animals, when they have a residual polygenic effect included. Second, the equivalence of both multi-step genomic models with a residual polygenic effect was also verified for young genotyped animals without phenotypes. Additionally, we derived formulas to convert genomic estimated breeding values of the GBLUP model to its components, direct genomic values and residual polygenic effect. Third, we made a proof that the equivalence of these 2 genomic models with a residual polygenic effect holds also for single-step genomic evaluation. Both the single-step GBLUP and SNP BLUP models lead to equal prediction for genotyped animals with phenotypes (e.g., reference animals), as well as for (young) genotyped animals without phenotypes. Finally, these 2 single-step genomic models with a residual polygenic effect were proven to be equivalent for estimation of SNP effects, too.