Variance of heritability ratios estimated from phenotypic variance components.

Heritability ratios are considered from observations on genotypes grown in a series of environments, sampling sites, and years. Two random models, appropriate to randomised complete block designs, are examined: one classifying the environments into sites and years, the other not distinguishing between these effects but considering both simply as environments. Full and restricted definitions of heritabilities are examined. The former include all appropriate variance components in the definition of the phenotypic variance, while the latter include only genotype, genotype X environment, and error variances in the phenotypic variance. Estimation of the variance of estimates of both forms of heritability, using either model, is considered. Reference is made also to similar heritabilities estimated from experiments sampling only either sites or years.