A method of estimating broad-sense heritability for quantitative traits in the type 2 modified augmented design

Heritability is a basic genetic parameter for quantitative traits that may determine their selection generation and intensity as well as predict their selection response and efficiency in plant breeding. Estimation of heritability varies based on experimental design. The type 2 modified augmented design (MAD2) as an unbalanced experimental design, has been proposed for evaluating numerous unreplicated test genotypes with several replicated control genotypes to adjust for soil heterogeneity. Here, we define an inter-environment correlation (r_E), that is, the mean Pearson’s correlation coefficient of trait performance for test genotypes between all pairs of environments, to approximate broad-sense heritability (H^2). Computer simulation and empirical results demonstrated that r_E was consistent with H^2 estimates on a plot basis by ANOVA for non-missing data sets, and similar to those by the restricted maximum likelihood (REML)-based method for missing data sets. The r_E  method was shown to generally outperform the ANOVA- and REML-based methods.    Key words: Broad-sense heritability, analysis of variance, inter-environment correlation, modified augmented design, restricted maximum likelihood, flax.