On Methods for Detecting Linkage from Analysis of Genetic Covariance
One of the critical issues in designing crop improvement programs is whether or not linkage is important m quantitative traits. This thesis is concerned with evaluating methods for detecting and estimating linkage among genes controlling a quantitative trait. Gates' test for linkage was evaluated by theoretical analysis and computer simulation. A general express10n for variances and covariances between relatives in selfed generations derived from a cross of two inbred lines was developed for a two-locus model with both linkage and epistasis. From analysis of this general expression, epistasis was found to mimic the effects of repulsion linkage. Furthermore, the use of an approximate expectation for variances and covariances m Gates' test caused an upward bias in both additive and dominance effects involving linkage. Twenty genetic models were simulated with eight values of both coupling and repulsion linkages to determine under which genetic situations Gates' test is a valid test for linkage. Coefficients of determination ( R2), calculated as the proportion of total variability among 30 variances and covariances in Gates' test explained by additive and dominance effects only, were close to unity for most combinations of models and linkage values. R2 values in repulsion linkages showed greater departure from unity than those in coupling linkages in both the presence and absence of epistasis. Although Gates' test generally fails to detect linkage because of high R2 values, it is more sensitive to repulsion linkages than coupling linkages. Numbers of families in hierarchical mating designs were the single most important factor in determining precision of the estimated variances and covariances used m Gates' test for linkage. This number must be at least several hundred to give suitably precise estimates of variances and covariances for traits with low heritability. Numbers of sub-families and numbers of replications can be of minimum size (about two). Weighted least squares and maximum likelihood methods were used to fit linkage, epistasis or genotype-environmental interaction models to data from a two-year field evaluation of hierarchical progenies in two spring wheat crosses, Potam x Ingal and RL4137 x Ingal. The genotype-environmental interaction model, which allows for heterogeneous error variances, was most satisfactory. The environmental variation between the two years may be due to the different climatological patterns. Among components of genetic variance, additive variance was of principal importance for all eight traits measured in both Potam x Ingal and RL4137 x Ingal.