A Further Improved Method

Wright’s method of estimating the number of genes contributing to the difference in a quantitative character between two populations involves observing the means and variances of the two parental populations and their hybrid populations. Although simple, Wright’s method provides seriously biased estimates, largely due to linkage and unequal effects of alleles. A method is suggested to evaluate the bias of Wright’s estimate, which relies on estimation of the mean recombination frequency between a pair of loci and a composite parameter of variability of allelic effects and frequencies among loci. Assuming that the loci are uniformly distributed in the genome, the mean recombination frequency can be calculated for some organisms. Theoretical analysis and an analysis of the Drosophila data on distributions of effects of P element inserts on bristle numbers indicate that the value of the composite parameter is likely to be about three or larger for many quantitative characters. There are, however, some serious problems with the current method, such as the irregular behavior of the statistic and large sampling variances of estimates. Because of that, the method is generally not recommended for use unless several favorable conditions are met. These conditions are: the two parental populations are many phenotypic standard deviations apart, linkage is not tight, and the sample size is very large. An example is given on the fruit weight of tomato from a cross with parental populations differing in means by more than 14 phenotypic standard deviations. It is estimated that the number of loci which account for 95% of the genic variance in the F2 population is 16, with a 95% confidence interval of 7-28, and the effect of the leading locus is 13% of the parental difference, with 95% confidence interval 8.5-25.7%. C ORRECT estimates of the number of genes contributing to the genetic variation of quantitative characters within and between populations are of fundamental importance in quantitative genetics. The original method of WRIGHT (in CASTLE 1921), as elaborated by WRIGHT (1968), for estimating the number of genes is the simplest and most widely used method. The method relates the difference in the means of two inbred lines to the variance of their F2 and backcross populations and relies on a number of assumptions. It has been known for a long time that the estimator is seriously biased. Since it was initially proposed, many authors have devised modifications for relaxing the assumptions or otherwise extending the applicability of the method. SEREBROVSKY (1 928) suggested formulae utilizing backcross data for correction of dominance effects in simplified situations. DEMPSTER and SNYDER (1 950) suggested a simplified way for the correction of linkage effects. LANDE (1 98 1) pointed out that WRIGHT’S method could also be used with outbred populations and also suggested that the same method could be applied to artificially selected lines from a single base population. COCKERHAM (1986) suggested an unbiased estimator of the difference in parental lines and also a method for Genetics 131: 987-1001 (August, 1992) combining the data from parental, F1, FP, and backcrosses into a single least-squares estimate. All of these analyses, however, addressed only the effects of relaxing some assumptions of the method, and the modified estimates are still seriously biased. In a previous paper (ZENG, HOULE and COCKERHAM 1990, hereinafter referred to as ZHC), we explored the utility of selection lines for estimating the number of loci and the effect of selection, linkage and the distributions of allelic effects and frequencies in the base population on the estimation. We established that unequal effects of alleles and linkage are the most important factors which create bias in the estimator. In this paper a modification for correcting the bias from unequal effects of alleles and linkage is suggested. The modification relies on the estimation of two new parameters: the mean recombination frequency between a pair of l ci and a composite measure of variability of allelic effects and frequencies among loci. With the assumption that loci are uniformly ( i e . , randomly) distributed in the genome, the mean recombination frequency can be inferred for some organisms. However, the variability of allelic effects has to be estimated from specially designed experiments for which an example is given for the effects of P