Comparisons of unweighted with weighted least squares methods of fitting a genetic model to a diallel cross

Abstract

Data on mean seed weight from the F1 of a complete 6 by 6 diallel cross with flax (Linum usitatissimum), grown in a randomized block design, were used to evaluate the benefits of weighted compared with unweighted least squares fitting of a genetical model for this type of cross. The model examines combining abilities and reciprocal differences. Matrix methods were employed in this study for weighted and unweighted least squares solutions. These methods accommodate rapid modification of appropriate models through changes in the corresponding design matrices, the use of various types of weight, the handling of missing data, the construction of orthogonal sets of parameters, the calculation of sums of squares accounted for by one or more of the parameters in the model, and the analysis of variance of the data. Weights used here were reciprocals of variances of diallel cell means, i.e., a variance reflecting variation among replicate mean values for a given cell. Weighted fitting with sequential elimination of redundant parameters in the original model extracted the minimum adequate model. Predicted values, generated from significant parameters in weighted or unweighted fittings of the model to overall F1 and parental means, were compared. Deliberate, increasing distortion of data in one replicate of the randomized block design showed that weighted fitting of the model distinguished consistent diallel data from distorted, giving predicted values reflecting the more reliable observations.Key words: diallels, weighted versus unweighted fitting.