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SOME ASPECTS OF GENERAL AND SPEFIC COMBINING ABILITY,
NEW YORK STATE COLL OF AGRICULTURE ITHACA
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For the diallel crossing system involving pp-12 possible crosses among p lines, the linear yield equation, the estimated effects, the sums of squares in the analysis of variance, and the expected values for the various sums of squares under different models are described. A number of different definitions or models are given for both fixed and random genetic effects. Under these descriptions, it is shown how to obtain the several published forms of the ex pectations for the sums of squares among the estimated combining ability effects for the ith line. Thus, all published forms are correct, but different models or definitions were utilized to obtain each form. The specific combining ability variance for the ith line is redefined in such a manner as to make the genotypic variance in the absence of epistatic effects, equal to twice the sum of the general combining ability variance additive variance the square of sigma sub alpha and the specific combining ability vari ance non-additive variance the square of sigma sub alpha. The currently used definition of specific combining ability variance requires that the genotypic variance be 2 the square of sigma sub alpha the square of sigma sub alpha rather than the redefined form of 2the square of sigma sub alpha the square of sigma sub alpha as suggested herein. Author
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