scholarly journals Perils of Parsimony: Properties of Reduced-Rank Estimates of Genetic Covariance Matrices

Genetics ◽  
2008 ◽  
Vol 180 (2) ◽  
pp. 1153-1166 ◽  
Author(s):  
Karin Meyer ◽  
Mark Kirkpatrick
Keyword(s):  
Covariance Matrices ◽  
Genetic Covariance ◽  
Reduced Rank ◽  
Rank Estimates

Genetic principal components for live ultrasound scan traits of Angus cattle

2005 ◽  
Vol 81 (3) ◽  
pp. 337-345 ◽  
Author(s):  
K. Meyer
Keyword(s):  
Genetic Variation ◽  
Maximum Likelihood ◽  
Principal Components ◽  
Muscle Area ◽  
Genetic Covariance ◽  
Eye Muscle ◽  
Rank Estimation ◽  
Reduced Rank ◽  
Angus Cattle ◽  
Rank Estimates

AbstractMultivariate restricted maximum likelihood analyses were carried out for a large data set comprising records for eye-muscle area, fat depth at the 12/13th rib and the rump P8 site, and percentage intramuscular fat, recorded via live ultrasound scanning of Australian Angus cattle. Records on heifers or steers were treated as separate traits from those on bulls. Reduced rank estimates of the genetic covariance matrix were obtained by restricted maximum likelihood, estimating the leading three, four, five, six, seven and all eight principal components and these were contrasted with estimates from pooled bivariate analyses.Results from analyses fitting five or six genetic principal components agreed closely with estimates from bivariate and eight-variate analyses and literature results. Heritabilities and variances for ‘fatness’ traits measured on heifers or steers were higher than those recorded for bulls, and genetic correlations were less than unity for the same trait measured in different sexes. Eye-muscle area showed little association with the other traits.Reduced rank estimation decreased computational requirements of multivariate analyses dramatically, in essence corresponding to those of an m-variate analysis for m principal components considered. Five or six principal components appeared to be necessary to model genetic covariances adequately. The first three of these components then explained about 97% of the genetic variation among the eight traits.A simulation study showed that errors in reduced rank estimates of the genetic covariance matrix were small, once three or more principal components from analyses fitting five or more components were used in constructing the estimates. Similarly, accuracy of genetic evaluation for the eight traits using the first four components was only slightly less than that using all principal components.Results suggest that reduced rank estimation and prediction is applicable for the eight scan traits considered. The leading three to four principal components sufficed to describe the bulk of genetic variation between animals. However, five or more principal components needed to be considered in estimating covariance matrices and the ‘loadings’ of the original traits to the principal components.

Estimates of the complete genetic covariance matrix for traits in multi-trait genetic evaluation of Australian Hereford cattle

2004 ◽  
Vol 55 (2) ◽  
pp. 195 ◽  
Author(s):  
Karin Meyer ◽  
David J. Johnston ◽  
Hans-Ulrich Graser
Keyword(s):  
Genetic Parameters ◽  
Carcass Traits ◽  
Early Growth ◽  
Genetic Evaluation ◽  
Covariance Matrices ◽  
Ultrasound Scanning ◽  
Genetic Covariance ◽  
Individual Traits ◽  
Hereford Cattle ◽  
Covariance Components

Estimates of covariance components among all 22 traits considered in the current multi-trait genetic evaluation of Australian Hereford cattle were obtained. Traits included 5 weight traits, 8 traits measured through live ultrasound scanning, 3 traits related to reproductive performance, and 6 carcass traits. Estimates were obtained by restricted maximum likelihood, carrying out a series of bivariate analyses. Data for each analysis were selected attempting to maximise the number of animals or animal–parent pairs that had both traits recorded. Estimates were pooled using a weighted 'iterative summing of expanded part matrices' procedure, which ensured positive semi-definite covariance matrices. Models of analyses for individual traits closely resembled those used in genetic evaluation. Results generally agreed with literature results, although estimates of genetic parameters for carcass traits that had few records available tended to fluctuate. Except for 'days to calving', heritability estimates were moderate to high for all traits. Genetic parameters for early growth were different to those for other breeds, with maternal effects for weaning weight being considerably more important and the heritability somewhat lower.

scholarly journals Integration of genomic information into beef cattle and sheep genetic evaluations in Australia

2012 ◽  
Vol 52 (3) ◽  
pp. 126 ◽  
Author(s):  
Andrew A. Swan ◽  
David J. Johnston ◽  
Daniel J. Brown ◽  
Bruce Tier ◽  
Hans-U. Graser
Keyword(s):  
Beef Cattle ◽  
Covariance Matrices ◽  
Relationship Matrix ◽  
Genomic Information ◽  
Genetic Covariance ◽  
Breeding Values ◽  
Snp Panels ◽  
Genetic Evaluations ◽  
Genomic Predictions ◽  
Cattle And Sheep

Genomic information has the potential to change the way beef cattle and sheep are selected and to substantially increase genetic gains. Ideally, genomic data will be used in combination with pedigree and phenotypic data to increase the accuracy of estimated breeding values (EBVs) and selection indexes. The first example of this in Australia was the integration of four markers for tenderness into beef cattle breeding values. Subsequently, the availability of high-density single nucleotide polymorphism (SNP) panels has made selection using genomic information possible, while at the same time creating significant challenges for genetic evaluation with regard to both data management and statistical modelling. Reference populations have been established in both the beef cattle and sheep industries, in which an extensive range of phenotypes have been collected and animals genotyped mainly using 50K SNP panels. From this information, genomic predictions of breeding value have been developed, albeit with varying levels of accuracy. These predictions have been incorporated into routine genetic evaluations using three approaches and trial results are now available to breeders. In the first, genomic predictions have been included in genetic evaluation models as additional traits. The challenges with this method have been the construction of consistent genetic covariance matrices, and a significant increase in computing time. The second approach has been to use a selection index procedure to blend genomic predictions with existing EBVs. This method has been shown to produce very similar results, and has the advantage of being simple to implement and fast to operate, although consistent genetic covariance matrices are still required. Third, in sheep a single-step analysis combining a genomic relationship matrix with a standard pedigree-based relationship matrix has been used to estimate breeding values for carcass and eating-quality traits. It is likely that this procedure or one similar will be incorporated into routine evaluations in the near future. While significant progress has been made in implementing methods of integrating genomic information in both beef and sheep evaluations in Australia, the major challenges for the future will be to continue to collect the phenotypes needed to derive accurate genomic predictions, and in managing much larger volumes of genomic data as the number of animals genotyped and the density of markers increase.

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