For a bivariate analysis where the two traits are measured on the same individuals, the mixed linear model can be written as [6] (6)where y 1 and y 2 are N×1 vector of phenotypes, g 1 and g 2 are N×1 vectors of genetic effects with and , e 1 and e 2 are N×1 vectors of residuals with and , and N is the sample size. The variance covariance matrix iswhere is the genetic covariance between the two traits and is the residual covariance. The genetic variance and covariance components can also be estimated using REML [6]. The genetic correlation is estimated as . Since is a non-linear function of , and , there is no explicit derivation for . Reeve (1955) and Robertson (1959) provided an approximation of in the context of balanced pedigree design as [23], [24] and Koots and Gibson (1996) proposed a modified version as [25], where is the phenotypic correlation between the traits. However, both approximations have an unsatisfying property that will approach 0 if or is close to 1. We derived an approximation,
