Estimation of genetic parameters in the square lattice analysis

Abstract

This paper shows how to obtain unbiased estimates of genetic parameters of base populations, e.g., genotypic variance among families, heritability on a family mean basis, genotypic correlation and direct and indirect expected genetic gains, when the sampled families were evaluated in square lattice experiment. The theoretical part presents the variance and covariance components of the intra-block analysis of square lattice and the estimators of the components associated to treatment effect, considering the ordinary least squares method. In the analysis with treatments not corrected for blocks/replications, the estimator of the component due to treatment effect is equal to that of the analysis considering the complete block model. Experimental data from a breeding program of Eucalyptus pyrocarpa were used for genetic analysis. The high estimates of narrow sense heritabilities and additive genetic correlation, related to height and diameter, indicate that selection of the superior families will be effective in changing the means of the base population.