Remediation of instability in Best Linear Unbiased Prediction

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dc.contributor.advisor Roux, Carl Z.
dc.contributor.coadvisor Verryn, Stephen David
dc.contributor.postgraduate Eatwell, Karen Anne
dc.date.accessioned 2014-06-17T13:05:46Z
dc.date.available 2014-06-17T13:05:46Z
dc.date.created 2014-04-09
dc.date.issued 2014 en_US
dc.description Thesis (PhD)--University of Pretoria, 2014. en_US
dc.description.abstract In most breeding programmes breeders use phenotypic data obtained in breeding trials to rank the performance of the parents or progeny on pre-selected performance criteria. Through this ranking the best candidates are identified and selected for breeding or production purposes. Best Linear Unbiased Prediction (BLUP), is an efficient selection method to use, combining information into a single index. Unbalanced or messy data is frequently found in tree breeding trial data. Trial individuals are related and a degree of correlation is expected between individuals over sites, which can lead to collinearity in the data which may lead to instability in certain selection models. A high degree of collinearity may cause problems and adversely affect the prediction of the breeding values in a BLUP selection index. Simulation studies have highlighted that instability is a concern and needs to be investigated in experimental data. The occurrence of instability, relating to collinearity, in BLUP of tree breeding data and possible methods to deal with it were investigated in this study. Case study data from 39 forestry breeding trials (three generations) of Eucalyptus grandis and 20 trials of Pinus patula (two generations) were used. A series of BLUP predictions (rankings) using three selection traits and 10 economic weighting sets were made. Backward and forward prediction models with three different matrix inversion techniques (singular value decomposition, Gaussian elimination - partial and full pivoting) and an adapted ridge regression technique were used in calculating BLUP indices. A Delphi and Clipper version of the same BLUP programme which run with different computational numerical precision were used and compared. Predicted breeding values (forward prediction) were determined in the F1 and F2 E. grandis trials and F1 P. patula trials and realised breeding performance (backward prediction) was determined in the F2 and F3 E. grandis trials and F2 P. patula trials. The accuracy (correlation between the predicted breeding values and realised breeding performance) was estimated in order to assess the efficiency of the predictions and evaluate the different matrix inversion methods. The magnitude of the accuracy (correlations) was found to mostly be of acceptable magnitude when compared to the heritability of the compound weighted trait in the F1F2 E. grandis scenarios. Realised genetic gains were also calculated for each method used. Instability was observed in both E. grandis and P. patula breeding data in the study, and this may cause a significant loss in realised genetic gains. Instability can be identified by examining the matrix calculated from the product of the phenotypic covariance matrix with its inverse, for deviations from the expected identity pattern. Results of this study indicate that it may not always be optimal to use a higher numerical precision programme when there is collinearity in the data and instability in the matrix calculations. In some cases, where there is a large amount of collinearity, the use of a higher precision programme for BLUP calculations can significantly increase or decrease the accuracy of the rankings. The different matrix inversion techniques particularly SVD and adapted ridge regression did not perform much better than the full pivoting technique. The study found that it is beneficial to use the full pivoting Gaussian elimination matrix inversion technique in preference to the partial pivoting Gaussian elimination matrix inversion technique for both high and lower numerical precision programmes. en_US
dc.description.availability unrestricted en_US
dc.description.department Genetics en_US
dc.description.librarian gm2014 en_US
dc.identifier.citation Eatwell, KA 2013, Lowies, GE 2012, 'The role of behavioural aspects in investment decision-making by listed property fund managers in South Africa', PhD thesis, University of Pretoria, Pretoria, viewed yymmdd <http://hdl.handle.net/2263/40245> en_US
dc.identifier.other D14/4/112/gm en_US
dc.identifier.uri http://hdl.handle.net/2263/40245
dc.language.iso en en_US
dc.publisher University of Pretoria en_ZA
dc.rights © 2013 University of Pretoria. All rights reserved. The copyright in this work vests in the University of Pretoria. No part of this work may be reproduced or transmitted in any form or by any means, without the prior written permission of the University of Pretoria. en_US
dc.subject Family component of variance en_US
dc.subject Phenotypic variance en_US
dc.subject Additive genetic variance en_US
dc.subject Narrow-sense heritability en_US
dc.subject Fourth generation of breeding en_US
dc.subject Third generation of breeding en_US
dc.subject Second generation of breeding en_US
dc.subject Parental or first generation of breeding en_US
dc.subject Randomized Complete Block experimental design en_US
dc.subject Diameter at Breast Height en_US
dc.subject Best Linear Unbiased Prediction en_US
dc.subject Best Linear Prediction en_US
dc.subject Analysis of variance en_US
dc.subject UCTD en_US
dc.title Remediation of instability in Best Linear Unbiased Prediction en_US
dc.type Thesis en_US


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