After estimation of e ects from a linear mixed model, it is often useful to form predicted values for certain factor/variate combinations. This process has been well-deÿned for linear models, but the introduction of random e ects means that a decision has to be made about the inclusion or exclusion of random model terms from the predictions, including the residual error. For spatially correlated data, kriging then becomes prediction from the ÿtted model. In many cases, the size of the matrices required to calculate predictions and their covariance matrix directly can be prohibitive. An e cient computational strategy for calculating predictions and their standard errors is given, which includes the ability to detect the invariance of predictions to the parameterisation used in the model.

The statistical analysis of late-stage variety evaluation trials using a mixed model is described, with one-or two-stage approaches to the analysis. Two sets of trials, from Australia and the UK, were used to provide realistic scenarios for a simulation study to evaluate the different methods of analysis. This study showed that a one-stage approach gave the most accurate predictions of variety performance overall or within each environment, across a range of models, as measured by mean squared error of prediction or realized genetic gain. A weighted two-stage approach performed adequately for variety predictions both overall and within environments, but a two-stage unweighted approach performed poorly in both cases. A generalized heritability measure was developed to compare methods.

The weekly nitrogen (N), phosphorus (P), and potassium (K) release from 17 polymer-coated controlled-release fertilizer (CRF) formulations of Nutricote, Apex Gold, Osmocote, and a 9-month Macrocote were measured at 30.6±0.8°C and 40.0±1.5°C. Five grams of each CRF were placed at a depth of 50 mm in 280x50 mm acid washed then rinsed silica sand columns which were leached with deionized water three times each week until nutrient recovery ceased. The volume of leachate was recorded each week and subsampled for ammonium-N, nitrate-N, phosphate-P, and K analyses. Each CRF treatment was replicated three times at each temperature. Nutrient release profiles were determined. Longevities, measured as weeks to 90% nutrient recovery, were considerably shorter than the nominated release periods for all formulations. Within each CRF product group, the longevity of 9 and 12 month formulations were similar with Apex Gold 12-14 month high nitrate having the longest (38 weeks for N at 30°C) and Osmocote 8-9 month the 959 960 HUETT AND GOGEL shortest (23 weeks for N at 30°C). There were consistent trends in the nutrient release periods across all CRFs with P>K>N and with differences of around 10% in duration between nutrients. The P:N release ratio exceeded 0.10 for most CRFs during the early release period indicating an adequate P supply for most plant species. The mean reduction in longevity for Nutricote, Apex Gold, and Osmocote formulations for an increase in incubation temperature from 30°C to 40°C was 19-21 % for N, 13-14% for P, and 14-15% for K. All CRFs released nutrients unevenly with the highest rate occurring during the early part of the release period. This pattern was accentuated at 40°C and by the shorter term release formulations. The nutrient release rates of all CRFs declined steadily after their maxima.

Following estimation of effects from a linear mixed model, it is often useful to form predicted values for certain factor/variate combinations. The process has been well defined for linear models, but the introduction of random effects into the model means that a decision has to be made about the inclusion or exclusion of random model terms from the predictions. This paper discusses the interpretation of predictions formed including or excluding random terms. Four datasets are used to illustrate circumstances where different prediction strategies may be appropriate: in an orthogonal design, an unbalanced nested structure, a model with cubic smoothing spline terms and for kriging after spatial analysis. The examples also show the need for different weighting schemes that recognize nesting and aliasing during prediction, and the necessity of being able to detect inestimable predictions.

No abstract