Abstract: Nested design has been widely used in animal and plant breeding, but there still exist some problems in calculating the estimates of genetic parameters and the statistics of some hypothesis tests with unbalanced data. In this paper, both fixed and random linear models were applied to estimate the genetic parameters and to perform tests of corresponding hypotheses with unbalanced data from the nested experiment design. For the fixed-effect model, we applied the methods of restricted linear model to estimate the general combining abilities of parents and to calculate the statistics for testing whether or not the general combining abilities of any two parents are different. For the random effect model, we used the theory of variance component model to derive the formulae for computing the variance components, their standard errors, and the statistics for hypothesis tests. Furthermore, formulae for calculating the heritabilities and estimating their standard errors were also given. Based on these results, a Windows-based software was developed to implement the calculations of all the genetic parameter estimates and the statistics for various hypotheses, and it would be a useful tool for forest breeders.

Key words: nested design, general combining ability, variance components, heritability