Estimation of broad sense heritability in plant populations: an improved method

Abstract

In the present paper an improved method for estimating broad sense heritability is developed by generalization and improvement of the method of Sakai and Mukaide (1967); this itself is a generalization and improvement of Sakai and Hatakeyama's (1963) modification of Shrikhande's (1957) method to separately estimate the genetic variance, competitional variance and environmental variance of a plant population. Some of the assumptions postulated by these former authors - especially the assumption that the covariance between the genetic and competitional effects equals zero - were omitted. If competitive effects are genetically caused and controlled - and numerous experimental results leave no doubt about this - then this assumption can not be right. Our proposed improvement and generalization avoids this difficulty by considering competition as a usual quantitative character (for each genotype we introduce two quantitative competition-characters: competitive ability and competitive influence). The expected values of the various terms in the variance of plot means (for plots of different sizes) were derived to give a system of simultaneous non-linear equations from which the unknown parameters, genetic variance resp. broad sense heritability, competitional variance, environmental variance etc., can be estimated using least squares methods or direct search methods. The estimates for broad sense heritability are probably more correct and realistic (because of the altered assumptions proposed in this method) than the results of the former authors. The application of the proposed estimation-procedure is demonstrated using Norway-spruce data from Slovakia: Norway-spruce stands (80-90 years old) were investigated for four characters: height, diameter, crown percentage and taper, measured for each single tree.