The present investigation was conducted to study the effect of sample size for estimating the precision of heritability by regression of the offspring on the parent and to decide the optimum number of bootstrap replications required for precision of heritability. This Optimum Sample Size for Estimating the Precision of Heritability by Parent-Offspring Regression was achieved empirically by using the simulated data for different values of population parameters. The bootstrap technique, which is an analytical and highly computer oriented method, was used to obtain the estimate of heritability, bias and standard error. The results were obtained from the data simulated by the parent-offspring model by selecting different master samples of 200, 500, 1,000 and 1,500 pairs of observations from the population with different heritability levels for different bootstrap replication numbers. The optimum number of bootstrap replications required to obtain a stable estimate of standard error of heritability for all the three cases considered was about 100, except for small samples for which at least 200 bootstrap replications were required. The optimum sample size required to get precise estimate of the standard error for both low and moderate heritability values was about 1,000, but the sample size of 500 was sufficient for high heritability value.

The basic prerequisite for planning a plant or animal-breeding program is the total variability existing in the population and how much of it is caused by differences in the genetic makeup of the individuals. A quantitative measure of this genetic variability is provided by the genetic parameter `heritability'. The precise and accurate knowledge of heritability is very important as it expresses the reliability of the phenotypic values as a guide to the breeding value. Although a number of estimators of heritability are available in the literature, only very few have an exact sampling variance expression. Thus, the reliability, accuracy and trustworthiness of estimates of heritability need to be examined for different sample sizes. To overcome the difficulties arising from the mathematical complexities of the exact formulae for variance, it is desirable that the precision of these estimators is determined by using the analytical methods. Efron (1979 and 1982) has shown that the bootstrap method correctly estimates the variance of a sample median, a case where jackknife is known to fail. He showed that in many complex situations, where statistics are awkward to compute, they might be approximated by Monte-Carlo `re-sampling'. Further, it needs no prior assumption about the distribution of the observations as well as estimators. Singh et al. (2001) obtained an optimum size of the sample by the parent-offspring regression method for independent bootstrap master samples. Also, the optimum family size, structure and number of bootstrap replications were studied by half-sib method (Singh et al., 2003). As master samples are much concerned to get accurate estimates in bootstrap technique, an in-depth study is required to know the vital role of bootstrap master sample in the process. Thus, the present investigation is conducted by considering a single bootstrap master sample for a particular sample size to get the optimum number of bootstrap replications and sample size for estimating the standard error of heritability.

The important simulation model for regression or correlation as given by Ronningen (1974) has been used. To describe this model, the phenotypic values of a particular trait has to be assumed in both the parent and the offspring (or the relations) and the coefficient of inbreeding is assumed to be zero.

Parent-Offspring Regression, Standard error, Heritability, Bootstrap technique, Simulation, Parent-offspring, Phenotypic values, Mathematical Complexities, Acta Agriculturae Scandinavica, Statistical Biological Models.