Estimation of Recombination Rate and Maternal Linkage Disequilibrium in Half-Sibs

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.

Male recombination map of the autosomal genome in German Holstein

Background

Recombination is a process by which chromosomes are broken and recombine to generate new combinations of alleles, therefore playing a major role in shaping genome variation. Recombination frequencies (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\theta$$\end{document}θ) between markers are used to construct genetic maps, which have important implications in genomic studies. Here, we report a recombination map for 44,696 autosomal single nucleotide polymorphisms (SNPs) according to the coordinates of the most recent bovine reference assembly. The recombination frequencies were estimated across 876 half-sib families with a minimum number of 39 and maximum number of 4236 progeny, comprising over 367 K genotyped German Holstein animals.

Results

Genome-wide, over 8.9 million paternal recombination events were identified by investigating adjacent markers. The recombination map spans 24.43 Morgan (M) for a chromosomal length of 2486 Mbp and an average of ~ 0.98 cM/Mbp, which concords with the available pedigree-based linkage maps. Furthermore, we identified 971 putative recombination hotspot intervals (defined as \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\theta$$\end{document}θ > 2.5 standard deviations greater than the mean). The hotspot regions were non-uniformly distributed as sharp and narrow peaks, corresponding to ~ 5.8% of the recombination that has taken place in only ~ 2.4% of the genome. We verified genetic map length by applying a likelihood-based approach for the estimation of recombination rate between all intra-chromosomal marker pairs. This resulted in a longer autosomal genetic length for male cattle (25.35 cM) and in the localization of 51 putatively misplaced SNPs in the genome assembly.

Conclusions

Given the fact that this map is built on the coordinates of the ARS-UCD1.2 assembly, our results provide the most updated genetic map yet available for the cattle genome.

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.