Stability analyses for estimating relative durability of quantitative resistance

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Abstract
Experiments in which a series of host cultivars are inoculated in all combinations with a series of pathogen isolates have been used to detect specificity in the host resistance. A theoretical model of polygenic resistance involving both general and specific interactions with pathogen virulence was developed to test the abilities of statistical analyses to discriminate between host genotypes with different levels of general and specific resistance. Estimates of levels of specific resistance could be obtained in regressions of disease severity scores for each host cultivar X pathogen isolate combination vs. the virulence index of each isolate. If the virulence index was based on the mean disease severity induced by the isolate over all host cultivars, the slopes of the regression lines were correlated with the levels of specific resistance in host cultivars. If the virulence index was based on the disease severity induced by the isolate on a host cultivar with a minimum of specific resistance, the mean squares for deviations from the regression were correlated with the levels of specific resistance in host cultivars. A method was developed to consistently choose host cultivars with minimum specific resistance. The two regression analyses gave estimates of specificity in randomly generated, model genotypes of approximately equal accuracy, although the second method appeared to be more accurate when the numbers of loci controlling resistance and virulence were small. The best estimates of numbers of genes for specific resistance were obtained by calculating a rating based on mean disease severity, the mean square for deviation from the regression on the virulence index based on disease severity on the cultivar with minimum specific resistance and the slope of the regression on the virulence index based on the mean disease severity. The best estimates of proportions of resistance genes that were specific were obtained by calculating a rating based on the above deviation mean square and slope alone.