Confidence interval estimators for heritability for several mating and experiment designs

Abstract

Confidence interval estimators have not been described for several heritability (H) estimators relevant to recurrent family selection. Previously described H interval estimators do not apply to onefactor mating designs in split-plot in time experiment designs in one or more locations, one-factor mating designs for several experiment designs in two or more locations and years, and two-factor mating designs for several experiment designs in two or more locations or years. Our objective was to derive H interval estimators for these cases. H reduced to a function of constants and a single expected mean square ratio in every case; H=1−E(M′)/E(M″) where E(M′) is a linear function of expected mean squares and E(M″) is a single expected mean square. It was shown that F′=[M″/E(M″)]/[M′/E(M′)] has an approximate F-distribution with df″ and df′ degrees of freedom, respectively, where M′ and M″ are mean squares corresponding to E(M′) and E(M″), respectively. H is a function of F′, therefore, we used F′ to define an approximate (1−α) interval estimator for H.