A natural estimate of is the least squares estimate from the univariate linear regression of on . Then is asymptotically normally distributed with sampling mean and variance since is standardised by definition. Assuming that genetic effects are small, it is henceforth conservatively taken that as previously suggested by Daetwyler et al [23]. The total variance of this estimator over markers and samples is , and its correlation with the effects on iswhere are the sampling errors. Immediate power and accuracy calculations are then available by substituting and into equations 2–5. When , as when the same trait is considered in both samples, equation 2 gives the formula previously derived by Daetwyler et al [23], modified to allow for prediction of the phenotype rather than the genetic value. In the present notation,corresponds to equation 1 of those authors, with the additional factor being the genetic variance of the phenotype. This shows that the key determinants of the predictive accuracy are the variance explained by the markers and the ratio of the sample size to the number of markers.
