Comparison of computing methods for inverse of an additive genetic relationship matrix in non-overlapped pedigree data on generation in a closed herd of swine.

The estimation of heritability has been an important question in statistical genetics. Due to the clear mathematical properties, the modified Haseman–Elston regression has been found a bridge that connects and develops various parallel heritability estimation methods. With the increasing sample size, estimating heritability for biobank-scale data poses a challenge for statistical computation, in particular that the calculation of the genetic relationship matrix is a huge challenge in statistical computation. Using the Haseman–Elston framework, in this study we explicitly analyzed the mathematical structure of the key term tr(KTK), the trace of high-order term of the genetic relationship matrix, a component involved in the estimation procedure. In this study, we proposed two estimators, which can estimate tr(KTK) with greatly reduced sampling variance compared to the existing method under the same computational complexity. We applied this method to 81 traits in UK Biobank data and compared the chromosome-wise partition heritability with the whole-genome heritability, also as an approach for testing polygenicity.

Download Full-text

The use of a genetic relationship matrix biases the best linear unbiased prediction

Journal of Genetics ◽

10.1007/s12041-020-01220-y ◽

2020 ◽

Vol 99 (1) ◽

Cited By ~ 1

Author(s):

Bongsong Kim

Keyword(s):

Genetic Relationship ◽

Best Linear Unbiased Prediction ◽

Relationship Matrix ◽

Linear Unbiased Prediction ◽

Best Linear Unbiased ◽

Genetic Relationship Matrix ◽

Unbiased Prediction

Download Full-text

Mixed Model with Correction for Case-Control Ascertainment Increases Association Power

10.1101/008755 ◽

2014 ◽

Author(s):

tristan hayeck ◽

Noah Zaitlen ◽

Po-Ru Loh ◽

Bjarni Vilhjalmsson ◽

Samuela Pollack ◽

...

Keyword(s):

Genetic Relationship ◽

Mixed Model ◽

Threshold Model ◽

False Positive Rate ◽

Case Control ◽

Relationship Matrix ◽

Case Control Studies ◽

Chi Square ◽

Data Set ◽

Genetic Relationship Matrix

We introduce a Liability Threshold Mixed Linear Model (LTMLM) association statistic for ascertained case-control studies that increases power vs. existing mixed model methods, with a well-controlled false-positive rate. Recent work has shown that existing mixed model methods suffer a loss in power under case-control ascertainment, but no solution has been proposed. Here, we solve this problem using a chi-square score statistic computed from posterior mean liabilities (PML) under the liability threshold model. Each individual’s PML is conditional not only on that individual’s case-control status, but also on every individual’s case-control status and on the genetic relationship matrix obtained from the data. The PML are estimated using a multivariate Gibbs sampler, with the liability-scale phenotypic covariance matrix based on the genetic relationship matrix (GRM) and a heritability parameter estimated via Haseman-Elston regression on case-control phenotypes followed by transformation to liability scale. In simulations of unrelated individuals, the LTMLM statistic was correctly calibrated and achieved higher power than existing mixed model methods in all scenarios tested, with the magnitude of the improvement depending on sample size and severity of case-control ascertainment. In a WTCCC2 multiple sclerosis data set with >10,000 samples, LTMLM was correctly calibrated and attained a 4.1% improvement (P=0.007) in chi-square statistics (vs. existing mixed model methods) at 75 known associated SNPs, consistent with simulations. Larger increases in power are expected at larger sample sizes. In conclusion, an increase in power over existing mixed model methods is available for ascertained case-control studies of diseases with low prevalence.

Download Full-text

Accuracy of genomic selection predictions for hip height in Brahman cattle using different relationship matrices

Pesquisa Agropecuária Brasileira ◽

10.1590/s0100-204x2018000600008 ◽

2018 ◽

Vol 53 (6) ◽

pp. 717-726 ◽

Cited By ~ 1

Author(s):

Michel Marques Farah ◽

Marina Rufino Salinas Fortes ◽

Matthew Kelly ◽

Laercio Ribeiro Porto-Neto ◽

Camila Tangari Meira ◽

...

Keyword(s):

Allele Frequency ◽

High Density ◽

Genomic Relationship Matrix ◽

Relationship Matrix ◽

Genomic Relationship ◽

Genomic Information ◽

Pedigree Data ◽

Snp Chip ◽

Numerator Relationship Matrix ◽

Brahman Cattle

Abstract: The objective of this work was to evaluate the effects of genomic information on the genetic evaluation of hip height in Brahman cattle using different matrices built from genomic and pedigree data. Hip height measurements from 1,695 animals, genotyped with high-density SNP chip or imputed from 50 K high-density SNP chip, were used. The numerator relationship matrix (NRM) was compared with the H matrix, which incorporated the NRM and genomic relationship (G) matrix simultaneously. The genotypes were used to estimate three versions of G: observed allele frequency (HGOF), average minor allele frequency (HGMF), and frequency of 0.5 for all markers (HG50). For matrix comparisons, animal data were either used in full or divided into calibration (80% older animals) and validation (20% younger animals) datasets. The accuracy values for the NRM, HGOF, and HG50 were 0.776, 0.813, and 0.594, respectively. The NRM and HGOF showed similar minor variances for diagonal and off-diagonal elements, as well as for estimated breeding values. The use of genomic information resulted in relationship estimates similar to those obtained based on pedigree; however, HGOF is the best option for estimating the genomic relationship matrix and results in a higher prediction accuracy. The ranking of the top 20% animals was very similar for all matrices, but the ranking within them varies depending on the method used.

Download Full-text

Genetic contributions of Finnish Ayrshire bulls over four generations

Animal Science ◽

10.1017/s1357729800013709 ◽

1995 ◽

Vol 61 (2) ◽

pp. 177-187 ◽

Cited By ~ 29

Author(s):

J. A. Woolliams ◽

E. A. Mäntysaari

Keyword(s):

Gene Flow ◽

Genetic Relationship ◽

Artificial Insemination ◽

Pedigree Information ◽

Generation Interval ◽

New Information ◽

Genetic Contributions ◽

Additive Genetic Relationship

AbstractThe long-term genetic contributions were calculated for 219 Finnish Ayrshire bulls born between 1958 and 1964 to 707 Finnish Ayrshire bulls made available for artificial insemination and born between 1986 and 1988. Three strategies were employed:(i) using all known pedigree information; (ii) ignoring information on the dam of females; (iii) only using information on sires. Expected contributions were calculated using gene flow matrices.The contributions from strategies 1, 2 and 3 were only 0.6 (1 and 2) or 0.7 (strategy 3) of those expected. The causes of this shortfall for strategies 2 and 3 were identified as (i) the use of an imported sire and (ii) generation skipping. For strategy 1, 0.2 of the expected pathways remained unaccounted for and were ascribed to missing pedigree information.Of the 219 ancestors, only 86 made positive contributions to the descendants. Only 10 ancestors made contributions more than the average, and one bull accounted for 0.3 of all pathways traced on strategy 2. There was general agreement in the relative contributions of individual bulls when assessed using the three strategies.The rate of inbreeding (ΔF) estimated by regression from 1974 to 1988 and using known pedigrees was 0.0018 per year and the average coefficients of additive genetic relationship among cohorts was increasing by 0.0030 per year. AF was estimated using the contributions calculated by strategies 1, 2 and 3 to be 0.0147, 0.0151 and 0.0125 per generation respectively. These were converted into rates per year by assuming a generation interval of 6.5 years taken from both published and new information on generation intervals in the Finnish Ayrshire population. This gave annual rates of 0.0023, 0.0023 and 0.0019. The estimates from strategy 3 were obtained without the use of any pedigree information pertaining to dams.

Download Full-text

Some properties of using the additive genetic relationship in the mixed model technique

Zeitschrift für Tierzüchtung und Züchtungsbiologie ◽

10.1111/j.1439-0388.1983.tb00741.x ◽

2010 ◽

Vol 100 (1-5) ◽

pp. 361-374 ◽

Cited By ~ 7

Author(s):

E. Fimland

Keyword(s):

Genetic Relationship ◽

Mixed Model ◽

Additive Genetic Relationship ◽

Model Technique

Download Full-text

Computing the condensed conditional gametic QTL relationship matrix and its inverse

Archives Animal Breeding ◽

10.5194/aab-50-294-2007 ◽

2007 ◽

Vol 50 (3) ◽

pp. 294-308 ◽

Cited By ~ 1

Author(s):

C. Baes ◽

N. Reinsch

Keyword(s):

Sparse Matrix ◽

Relationship Matrix ◽

Computer Memory ◽

Pedigree Data ◽

Linear Unbiased Prediction ◽

Marker Data ◽

Covariance Between Relatives ◽

Best Linear Unbiased ◽

Fortran 90 ◽

Trait Locus

Abstract. The inverse of the conditional gametic relationship matrix (G-1) for a marked quantitative trait locus (MQTL) is required for estimation of gametic effects in best linear unbiased prediction (BLUP) of breeding values if marker data are available. Calculation of the "condensed" gametic relationship matrix G* – a version of G where linear dependencies have been removed – and its inverse G*-1 is described using a series of simplified equations following a known algorithm. The software program COBRA (covariance between relatives for a marked QTL) is introduced, and techniques for storing and computing the condensed gametic relationship matrix G* and the non-zero elements of its inverse are discussed. The program operates with both simple pedigrees and those augmented by transmission probabilities derived from marker data. Using sparse matrix storage techniques, G* and its inverse can be efficiently stored in computer memory. COBRA is written in FORTRAN 90/95 and runs on a variety of computers. Pedigree data and information for a single MQTL in the German Holstein population are used to test the efficiency of the program.

Download Full-text