Improved models for the prediction of breeding values in trees

This thesis develops a number of tools and strategies for the adaptation to forest trees of the individual additive genetic model for the prediction of breeding values. Eucalyptus globulus ssp. globulus and central Victorian E. nitens are the most important temperate hardwood plantation species in Australia. The geographic patterns of variation in these species were examined using multivariate analysis of open pollinated base population progeny trials. Race classifications were developed from these patterns. New divisions were identified and previously separated provenances were amalgamated. Prediction of breeding values for a variety of traits for E globulus showed that the inclusion of races improved the model and increased selection gains by up to 20%. One problem in the prediction of breeding values in open pollinated base population progeny trials of many genera, including Eucalyptus, is that the parents and their offspring do not conform to the assumptions usually made about relatedness in the construction of the additive relationship matrix. An algorithm was developed to modify the additive relationship matrix, and generate its inverse, using simple rules, where parental inbreeding and partial selfing occurs. In simulated data sets, use of the modified relationship matrix lead to unbiased heritability and breeding value estimates. If the correct variance components were used with an incorrect relationship matrix, then the correlation between breeding values was high, but the offspring breeding values were deflated and parental breeding values were inflated. Breeding value prediction can be further improved by better modelling of environmental variations within trials. The spatial analysis of forest genetic trials using separable autoregressive processes of residuals was adapted from agricultural variety yield trial analysis following the comparison of a number of approaches for five selected forest genetic trials. Augmenting the design model with a spatially auto-correlated component was found to be a good general model which lead to large reductions in design feature effects. The spatial component was found to be relatively small, but with high auto-correlations indicating features spread over relatively large areas. Models without an independent error term were poorer and lead to inflation of estimates of additive variance. The spatial model increased selection gain by up to 6%. Modelling other features identified by the spatial model was not always successful and resulted in only marginal increases in selection gain. Applying the model to 216 variables from 55 forestry trials resulted in selection gains of more than 10% in around one tenth of cases, although in general the gains were more modest. For growth data, the auto-correlations were generally high, indicating a smooth environmental surface, but they were lower for other traits such a pest and disease damage, indicating more patchiness. Auto-correlations less than zero, indicating competition was dominant, occurred for some large diameter trials, but a bimodal likelihood surface indicated competition was present in more cases. Traits such as stem counts, and form and branching scores, did not respond as often to spatial analysis. The race classifications, modified relationship matrix, and better environmental modelling developed in the thesis will allow better application of the individual tree additive genetic model to tree breeding programs.