Precise, unbiased estimates of genetic parameters, such as heritability and genetic covariance, are necessary to optimise breeding programs and to predict rates of change for various selection schemes. A classical method of estimation is to use high and low selection experiments. We consider two generation selection experiments when observations in the parental generation are only taken on one sex, resulting in half-sib family information. We consider cases of two standardised traits, with zero mean and unit variance, and assume that the traits are normally distributed. The genetic and phenotypic variance-covariance matrices for the traits are denoted by G and P respectively. The genetic variances and covariances of the standardised traits are then heritabilities and co-heritabilities.

The construction of other designs is examined, assuming the phenotypic correlation of rp between traits is known. For simplicity, comparisons of designs are developed by considering the variance of the genetic variances when the traits are uncorrelated both phenotypically and genetically.