Vector space algebra for scaling and centering relationship matrices under non-Hardy–Weinberg equilibrium conditions

Abstract Background Scales are linear combinations of variables with coefficients that add up to zero and have a similar meaning to “contrast” in the analysis of variance. Scales are necessary in order to incorporate genomic information into relationship matrices for genomic selection. Statistical and biological parameterizations using scales under different assumptions have been proposed to construct alternative genomic relationship matrices. Except for the natural and orthogonal interactions approach (NOIA) method, current methods to construct relationship matrices assume Hardy–Weinberg equilibrium (HWE). The objective of this paper is to apply vector algebra to center and scale relationship matrices under non-HWE conditions, including orthogonalization by the Gram-Schmidt process. Theory and methods Vector space algebra provides an evaluation of current orthogonality between additive and dominance vectors of additive and dominance scales for each marker. Three alternative methods to center and scale additive and dominance relationship matrices based on the Gram-Schmidt process (GSP-A, GSP-D, and GSP-N) are proposed. GSP-A removes additive-dominance co-variation by first fitting the additive and then the dominance scales. GSP-D fits scales in the opposite order. We show that GSP-A is algebraically the same as the NOIA model. GSP-N orthonormalizes the additive and dominance scales that result from GSP-A. An example with genotype information on 32,645 single nucleotide polymorphisms from 903 Large-White × Landrace crossbred pigs is used to construct existing and newly proposed additive and dominance relationship matrices. Results An exact test for departures from HWE showed that a majority of loci were not in HWE in crossbred pigs. All methods, except the one that assumes HWE, performed well to attain an average of diagonal elements equal to one and an average of off diagonal elements equal to zero. Variance component estimation for a recorded quantitative phenotype showed that orthogonal methods (NOIA, GSP-A, GSP-N) can adjust for the additive-dominance co-variation when estimating the additive genetic variance, whereas GSP-D does it when estimating dominance components. However, different methods to orthogonalize relationship matrices resulted in different proportions of additive and dominance components of variance. Conclusions Vector space methodology can be applied to measure orthogonality between vectors of additive and dominance scales and to construct alternative orthogonal models such as GSP-A, GSP-D and an orthonormal model such as GSP-N. Under non-HWE conditions, GSP-A is algebraically the same as the previously developed NOIA model.

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Robust, flexible, and scalable tests for Hardy–Weinberg equilibrium across diverse ancestries

Genetics ◽

10.1093/genetics/iyab044 ◽

2021 ◽

Author(s):

Alan M Kwong ◽

Thomas W Blackwell ◽

Jonathon LeFaive ◽

Mariza de Andrade ◽

John Barnard ◽

...

Keyword(s):

Population Structure ◽

Statistical Power ◽

Sequence Data ◽

Population Heterogeneity ◽

Alternative Methods ◽

Data Sets ◽

Real Sequence ◽

Weinberg Equilibrium ◽

Hardy Weinberg Equilibrium ◽

The Impact

Abstract Traditional Hardy–Weinberg equilibrium (HWE) tests (the χ2 test and the exact test) have long been used as a metric for evaluating genotype quality, as technical artifacts leading to incorrect genotype calls often can be identified as deviations from HWE. However, in data sets composed of individuals from diverse ancestries, HWE can be violated even without genotyping error, complicating the use of HWE testing to assess genotype data quality. In this manuscript, we present the Robust Unified Test for HWE (RUTH) to test for HWE while accounting for population structure and genotype uncertainty, and to evaluate the impact of population heterogeneity and genotype uncertainty on the standard HWE tests and alternative methods using simulated and real sequence data sets. Our results demonstrate that ignoring population structure or genotype uncertainty in HWE tests can inflate false-positive rates by many orders of magnitude. Our evaluations demonstrate different tradeoffs between false positives and statistical power across the methods, with RUTH consistently among the best across all evaluations. RUTH is implemented as a practical and scalable software tool to rapidly perform HWE tests across millions of markers and hundreds of thousands of individuals while supporting standard VCF/BCF formats. RUTH is publicly available at https://www.github.com/statgen/ruth.

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Robust, flexible, and scalable tests for Hardy-Weinberg Equilibrium across diverse ancestries

10.1101/2020.06.23.167759 ◽

2020 ◽

Author(s):

Alan M. Kwong ◽

Thomas W. Blackwell ◽

Jonathon LeFaive ◽

Mariza de Andrade ◽

John Barnard ◽

...

Keyword(s):

Population Structure ◽

Statistical Power ◽

Software Tool ◽

Population Heterogeneity ◽

Alternative Methods ◽

Real Sequence ◽

Exact Test ◽

Weinberg Equilibrium ◽

Hardy Weinberg Equilibrium ◽

The Impact

ABSTRACTTraditional Hardy-Weinberg equilibrium (HWE) tests (the χ2 test and the exact test) have long been used as a metric for evaluating genotype quality, as technical artifacts leading to incorrect genotype calls often can be identified as deviations from HWE. However, in datasets comprised of individuals from diverse ancestries, HWE can be violated even without genotyping error, complicating the use of HWE testing to assess genotype data quality. In this manuscript, we present the Robust Unified Test for HWE (RUTH) to test for HWE while accounting for population structure and genotype uncertainty, and evaluate the impact of population heterogeneity and genotype uncertainty on the standard HWE tests and alternative methods using simulated and real sequence datasets. Our results demonstrate that ignoring population structure or genotype uncertainty in HWE tests can inflate false positive rates by many orders of magnitude. Our evaluations demonstrate different tradeoffs between false positives and statistical power across the methods, with RUTH consistently amongst the best across all evaluations. RUTH is implemented as a practical and scalable software tool to rapidly perform HWE tests across millions of markers and hundreds of thousands of individuals while supporting standard VCF/BCF formats. RUTH is publicly available at https://www.github.com/statgen/ruth.

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GENETICS AND POPULATION PRACTICABILITY OF USING SNP (C. 232Т>А) OF LEPR GENE AS A MARKER FOR FURTHER SELECTION FOR LARGE WHITE AND MYRGOROD PIG BREEDS

Animal Breeding and Genetics ◽

10.31073/abg.52.23 ◽

2016 ◽

Vol 52 ◽

pp. 176-180 ◽

Cited By ~ 1

Author(s):

N. K. Sarantseva ◽

V. M. Balatsky ◽

V. Y. Nor ◽

Ye. K. Oliinychenko

Keyword(s):

Selection Pressure ◽

Leptin Receptor ◽

Receptor Gene ◽

Large White ◽

Weinberg Equilibrium ◽

Lepr Gene ◽

Large White Breed ◽

White Breed ◽

Hardy Weinberg Equilibrium ◽

Selection For

Leptin is an important regulator of energy metabolism and reproduction and is mainly synthesized in the adipocytes and then secreted into bloodstream. Leptin receptor is one of regulating components of organism energetic homeostasis. Receptor influences on leptin effects by regulating feed intake, body weight and fat deposition. Leptin receptor gene (LEPR) is located in the sixth chromosome in the region that correlates with content of intramuscular fat, thickness of back fat, growth rate and pig carcass parameters. Due to these correlations, LEPR is known to be gene candidate that controls quantitative traits. Leptin receptor gene consists of 20 exons; not less than 25 single nucleotide polymorphisms (SNPs) were found in gene structure in different gene sites (exons, introns, 5’ and 3’ regions). SNPs of LEPR gene can be chosen as useful markers for predicting breeding value in pigs. For the experiment SNP c.232T>A was chosen; it is located in the second exon of LEPR gene. The aim of work was to study spreading of SNP c.232Т>А in LEPR gene of breeds under Ukrainian selection; to estimate if marker selection for proving meat quality is possible using chosen SNP as a marker. Materials and methods. For genetic population analysis, DNA samples of Large White breed (bred in Stepne farm, Poltava region, Ukraine) and Mirgorod breed (bred in Dekabristy farm, Poltava region, Ukraine) were used; 50 samples of each breed were taken for the research. Samples were genotyped using PCR-RFLP method. Deviations from genetic equilibrium found using the Hardy-Weinberg coefficient were signified with chi-square criterium, the frequency of alleles, estimation of gene frequencies, determination of heterozygosity were counted using GenAlex 6.0. Results. Genetic researches showed polymorphism c. 232Т>А in LEPR gene to be spread in population of Large White breed and Mirgorod breed under Ukrainian selection. Polymorphism with AA genotype was shown to be spread the most. In studied Large White population highly probable deviation of the actual distribution of genotypes of the expected value for the Hardy-Weinberg equilibrium (χ2 = 15.759, p ≤ 0.001) was found. The deviation was caused by increasing homozygotes (АА = 0.680). Small amount of heterozygotes (АТ = 0.160) and alternative homozygotes (ТТ = 0.160) was found. Positive designation of Rayt index (0.561) and the advantage of expected heterozygosis (0.365) on the actual (0.160) also show existence of selection pressure of LEPR in this herd. In Myrgorod pig population big amount of animals turned out to be homozygotes АА (0,720), small amount of heterozygotes was found (АТ=0.280), alternative homozygotes TT were not found. Deviation from spreading of genotypes of the expected value for the Hardy-Weinberg equilibrium was not significant and did not have a significant nature (χ2 = 1.325); SNP variety (c. 232Т>А) in LEPR gene is not spread, so this SNP in Mirgorod breed wasn’t under selection pressure. The fact of low selection pressure of (c. 232Т>А) in LEPR gene in Mіrgord breed can also be proved of negative designation of Rayt index (-0,163) and domination of heterozygotes (0.280). Allele A is found to be dominative above allele T in both studied populations. Conclusions. After DNA analysis of two breeds under Ukrainian selection (Mirgorod and Large White breeds) polymorphism c. 232Т>А in LEPR gene SNP was found to be spread; chosen SNP can be used for further researches in association analysis for finding correlation between SNP and meat traits.

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