We know from the derivations above that and . For unrelated individuals sampled from the same population, , we therefore get(10)This was also tested by simulations (Text S1) and the approximated standard errors were highly consistent with those observed from simulations, especially when sample size was large (Table 1). When , i.e. two traits are completely independent, for traits measured on the same sample, and for traits measured on different samples. Therefore, for independent traits, the ratio of sampling variance of genetic correlation between the two traits measured on the same sample to that on different samples is simply .
