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. / Thesis (PhD)--University of Pretoria, 2013. / gm2014 / Genetics / unrestricted
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:up/oai:repository.up.ac.za:2263/40245 |
| Date | January 2013 |
| Creators | Eatwell, Karen Anne |
| Contributors | Roux, Carl Z., karen.eatwell@gmail.com, Verryn, Stephen David |
| Publisher | University of Pretoria |
| Source Sets | South African National ETD Portal |
| Language | English |
| Detected Language | English |
| Type | Thesis |
| 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. |
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