Haplotype phasing after joint estimation of recombination and linkage disequilibrium in breeding populations

Gomez‐Raya, Luis; Hulse, Amanda M.; Thain, David; Rauw, W. M.

doi:10.1186/2049-1891-4-30

Cited by 3 publications

(5 citation statements)

References 22 publications

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“…In this study, estimates were obtained by NM of the log-likelihood function. Alternatively, θ and D could be estimated by the expectation-maximization (EM) algorithm ( Gomez-Raya et al 2013 ). However, this iterative approach is more time consuming than the iterations required for NM.…”

Section: Discussionmentioning

confidence: 99%

“…The covariance matrix

is set up with the following elements:

The linkage phase of sire, the corresponding recombination rate (

), and the LD (

) of maternal gametes are assumed to be known. If they are not available, these population parameters may be estimated, such as using the maximum likelihood approach ( Gomez-Raya et al 2013 ). Now it is necessary to determine whether genomic evaluations can be improved by knowing this covariance structure.…”

Section: Methodsmentioning

confidence: 99%

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Covariance Between Genotypic Effects and its Use for Genomic Inference in Half-Sib Families

Wittenburg

Teuscher

Klosa

et al. 2016

G3 Genes|Genomes|Genetics

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In livestock, current statistical approaches utilize extensive molecular data, e.g., single nucleotide polymorphisms (SNPs), to improve the genetic evaluation of individuals. The number of model parameters increases with the number of SNPs, so the multicollinearity between covariates can affect the results obtained using whole genome regression methods. In this study, dependencies between SNPs due to linkage and linkage disequilibrium among the chromosome segments were explicitly considered in methods used to estimate the effects of SNPs. The population structure affects the extent of such dependencies, so the covariance among SNP genotypes was derived for half-sib families, which are typical in livestock populations. Conditional on the SNP haplotypes of the common parent (sire), the theoretical covariance was determined using the haplotype frequencies of the population from which the individual parent (dam) was derived. The resulting covariance matrix was included in a statistical model for a trait of interest, and this covariance matrix was then used to specify prior assumptions for SNP effects in a Bayesian framework. The approach was applied to one family in simulated scenarios (few and many quantitative trait loci) and using semireal data obtained from dairy cattle to identify genome segments that affect performance traits, as well as to investigate the impact on predictive ability. Compared with a method that does not explicitly consider any of the relationship among predictor variables, the accuracy of genetic value prediction was improved by 10–22%. The results show that the inclusion of dependence is particularly important for genomic inference based on small sample sizes.

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Section: Discussionmentioning

confidence: 99%

“…The covariance matrix

is set up with the following elements:

The linkage phase of sire, the corresponding recombination rate (

), and the LD (

Section: Methodsmentioning

confidence: 99%

Covariance Between Genotypic Effects and its Use for Genomic Inference in Half-Sib Families

Wittenburg

Teuscher

Klosa

et al. 2016

G3 Genes|Genomes|Genetics

View full text Add to dashboard Cite

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“…Although the form of log LF is elementary, computing the maximum-likelihood (ML) estimation is not straightforward, see e.g., Hill ( 1974 ) and File S1 . Gomez-Raya ( 2012 ) and Gomez-Raya et al ( 2013 ) proposed an EM algorithm to estimate θ and maternal haplotype frequencies based on the log LF . For an EM algorithm, and for other commonly used optimization methods, it is known that it may converge to a local maximum if the underlying distribution is bimodal (Dempster et al, 1977 ).…”

Section: Methodsmentioning

confidence: 99%

“…It is obvious to select the estimates of parameter values constituting the higher value of log LF . Because log LF can be rather flat (e.g., Figure 1 and Figure 2 in Gomez-Raya et al, 2013 ), sometimes the height of the two modes cannot be differentiated even when p 1 ≠0.5 or p 2 ≠0.5. Hence we introduce the interval [0.48, 0.52] for allele frequencies; this is denoted as the critical range.…”

Section: Methodsmentioning

confidence: 99%

“…Previous studies (Gomez-Raya, 2012 ; Gomez-Raya et al, 2013 ) explicitly exploited the family structure of paternal half-sibs and proposed a likelihood approach for the estimation of θ and D dam which was based on an expectation maximization (EM) algorithm. However, a special characteristic of the underlying likelihood function (LF) is its bimodality (Figure 2 in Gomez-Raya et al, 2013 ) and thus the possibility of having two maxima. Depending on the maternal allele frequencies at the two loci, the modes can have equal height.…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2018

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A livestock population can be characterized by different population genetic parameters, such as linkage disequilibrium and recombination rate between pairs of genetic markers. The population structure, which may be caused by family stratification, has an influence on the estimates of these parameters. An expectation maximization algorithm has been proposed for estimating these parameters in half-sibs without phasing the progeny. It, however, overlooks the fact that the underlying likelihood function may have two maxima. The magnitudes of the maxima depend on the maternal allele frequencies at the investigated marker pair. Which maximum the algorithm converges to depends on the chosen start values. We present a stepwise procedure in which the relationship between the two modes is exploited. The expectation maximization algorithm for the parameter estimation is applied twice using different start values, followed by a decision process to assess the most likely estimate. This approach was validated using simulated genotypes of half-sibs. It was also applied to a dairy cattle dataset consisting of multiple half-sib families and 39,780 marker genotypes, leading to estimates for 12,759,713 intrachromosomal marker pairs. Furthermore, the proper order of markers was verified by studying the mean of estimated recombination rates in a window adjacent to the investigated locus as well as in a window at its most distant chromosome end. Putatively misplaced markers or marker clusters were detected by comparing the results with the revised bovine genome assembly UMD 3.1.1. In total, 40 markers were identified as candidates of misplacement. This outcome may help improving the physical order of markers which is also required for refining the bovine genetic map.

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Male recombination map of the autosomal genome in German Holstein

Qanbari

Wittenburg

2020

Genet Sel Evol

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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 ($$\theta$$ 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 $$\theta$$ 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.

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Haplotype phasing after joint estimation of recombination and linkage disequilibrium in breeding populations

Cited by 3 publications

References 22 publications

Covariance Between Genotypic Effects and its Use for Genomic Inference in Half-Sib Families

Covariance Between Genotypic Effects and its Use for Genomic Inference in Half-Sib Families

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

Male recombination map of the autosomal genome in German Holstein

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