Iowa State University
Information from Castle-Wright experiment --Simic, D, Hallauer AR Plant breeders have made limited use of the Castle-Wright formula because of the underlying assumptions. Main assumptions of this method are 1) with respect to all relevant loci, one parent is fixed with the alleles increasing the trait of interest and the other parent is fixed with alleles decreasing the trait of interest; 2) additive gene effects; 3) unlinked loci; and 4) equal allelic effects at all loci. When these assumptions are violated the method substantially underestimates the true number of loci (Zeng, Houle, and Cockerham, 1990). Using selected lines and choosing properly examined traits (Hallauer and Miranda, 1988) our experiment does not violate assumptions 1 and 2. Biased estimates, however, occur largely due to linkage and unequal effects at alleles (Zeng, 1992). We estimated the number of effective genes of an F2 population that was not in linkage equilibrium and in the F2 population (Syn 10) after 10 generations of intermating which is an approximate linkage equilibrium. Results are summarized in Table 1.

Three versions of estimates of the effective number of loci are given without their standard errors. nE1, nE2, and nE3 for the silking date are similar for F2 and more different for F2 Syn. 10. While nE1 and nE2, for plant height are similar for F2 and F2 Syn. 10, nE3 (33.97 and 35.45) almost reached a recombination index of about 36 (Darlington, 1937 in Lande, 1981).

According to Zeng (1992) only at ear height were all three favorable conditions met: 1) the two parental populations are "many" (approx. 10) phenotypic standard deviations apart. In this experiment three deviations for silk date, plant height and ear height are 5.66, 4.91, and 17.21, respectively; 2) no linkage; and 3) large sample size (>200). Estimates of the number of genes for ear height, however, seem underestimated. Linkage did not affect the estimates because the number of estimated genes are similar for F2 and F2 Syn. 10 populations. Consequently, unequal effects of alleles seem to be important. There is no reliable procedure for correcting the bias from unequal effects of alleles. Zeng (1992) suggests use of parameter z, composite measure of variability of allelic effects and frequencies among loci. There are difficulties, though, in estimating the parameter z. Linkage effects, however, summarized by the mean recombination frequency is estimable, and can be corrected (Zeng, 1992). Hence, efforts of intermating are not necessary. Additionally, random intermating plants within F2 populations did not increase the genetic variability. Similar results were reported by Covarrubias-Prieto, Hallauer and Lamkey (1889) and Han and Hallauer (1989). Linkage was, probably, primarily in repulsion phase (Cavalli, 1952). On the basis of the estimates obtained for the F2 and F2 Syn. 5 populations, however, it does not seem that repulsion phase linkages had a large affect on the estimates of s2A (Han and Hallauer, 1989). We could not obtain estimates of the dominance parameter in our experiment because no backcross data were available.

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