Some Investigations on Sampling Variance of Genetic Correlation

The present investigation is an attempt to compare the estimated, predicted, empirical and bootstrap Standard Errors (SE) for different combinations of population heritability, genetic and phenotypic correlations for different family sizes and structures under half-sib mating design. The data under half-sib model are simulated by taking sire effects following normal as well as gamma distribution. It is observed that the empirical SE of genetic correlation, when sire effects are from gamma distribution, are invariably higher as compared to the data with sire effects following normal distribution irrespective of the sample size, heritability and genetic correlation of the traits. The empirical SE of estimates of genetic correlation are very high for lowly heritable traits for whole range of genetic correlation. The large sample approximation of SE given by Tallis is always underestimating the SE even for large family size of 30 to 50 and should not be used in practice. Barring small sample size, the bootstrap estimates of SE are very close to predicted SE and can be used as an estimate of SE of genetic correlation. The bootstrap estimates of SE of genetic correlation are found to be very close to the predicted SE for sample size 500 and above in case of lowly heritable traits for whole range of genetic correlation. In case of moderately and highly heritable traits, the bootstrap estimates of SE are found very close to predicted SE for all values of genetic correlation and for all the sample sizes and family structures except for small sample size with moderately heritable traits. Hence, it can be concluded that the bootstrap estimates of SE which are very close to predicted values can be used to estimate the SE instead of approximate formula given in literature. It is also found that in case of non-normal datasets with sire effects following gamma distribution the bootstrap estimates of SE of genetic correlation are always underestimated