Joint modelling of spatial variability and interplot competition to improve the efficiency of plant improvement.

Australian sugarcane breeding trials, many varieties are tested in the early stages of selection. Small single-drill plots are typically used because of the limitations on seedcane and space. Such trials may he subject to variation arising from spatial variability and interplot competition, which could seriously bias varietal estimates and reduce genetic progress. Test varieties in early stage sugarcane trials are routinely selected using an index calculated from cane yield and sucrose content relative to commercial varieties. This selection index is based on the paradigm of positive dependence between neighbouring plots but this may not hold in the presence of interplot competition. Although this selection index may be useful in detecting broad trends in the field, variation often occurs on a much smaller scale. Methods such as spatial analysis adjust a plot for variability by using information from immediate neighbours. These techniques are routinely used to analyse cereal data in Australia and have resulted in increased accuracy and precision in the estimates of variety effects. Spatial analysis methods were applied to 28 early generation sugarcane trials. These analyses showed large global trend (fixed linear column and random row effects) and extraneous variation for cane yield and sucrose content. Removal of this variability through appropriate modelling techniques resulted in large differences in varieties ranked in the top 10% for the spatial and routine methods. Most trials also showed substantial interplot competition for cane yield, but not for sucrose content. Given the presence of significant spatial variability and interplot competition in early stage sugarcane trials, the challenge was to effectively model both spatial variability and interplot competition and hence improve genetic gain by improving the accuracy of prediction of genetic effects. The immediate consequence of not modelling interplot competition would be that Australian sugarcane breeders may select varieties that perform well in mixed, rather than pure stands. In this thesis, an approach to the simultaneous modelling of spatial variability and interplot competition is presented. This approach allows for competition at the phenotypic and genotypic (or treatment) levels and models global trend and extraneous variation. Variety effects were considered random and both adjusted profile likelihood and residual maximum likelihood based on a transformation of the data were used for parameter estimation. A simulation study was undertaken to determine the level of bias in parameter estimates for the two different methods of estimation. As previous approaches to joint modelling of spatial variability and interplot competition by Durbgn Reguera (1998), Durban et al. (2001) and Matassa (2003) had considered varieties fixed it was important to determine if the level of bias in parameters of interest changed for random varieties. It was found that adjusted profile likelihood had a low relative bias regardless of fixed or random variety effects. However, restricted maximum likelihood based on a transformation of the data can only be used when varieties are random. It was also found that the variance structure for the residuals may be complex and can be modelled using stationary conditional autoregressive processes and two special simultaneous autoregressive models. An equal roots second order autoregressive model was proposed for trials where competition was dominant, while an equal roots third order autoregressive model allowed for a mixture of competition and trend. The joint modelling approach developed in this thesis was applied to cane yield data from 22 datasets. In the majority of these, modelling competition at the genotypic level was the superior method. To determine the effect of simultaneously adjusting for spatial variability and interplot competition on selection, the percentages of superior varieties in common in the top 10% for the joint model and classical approaches were compared. Agreement between the two approaches varied from 38% to 90%. Hence, for some trials there are large differences in the varieties selected to advance to the next stage of selection. To confirm the impact on selection of adjusting for spatial variability and interplot competition, trials have now been planted which directly compare cane yield and sucrose content in varieties selected using the current and new techniques