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Modification of the Variety Cross Diallel Model for Evaluating Cycles of Selection 1
Author(s) -
Hammond J. J.,
Gardner C. O.
Publication year - 1974
Publication title -
crop science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.76
H-Index - 147
eISSN - 1435-0653
pISSN - 0011-183X
DOI - 10.2135/cropsci1974.0011183x001400010002x
Subject(s) - diallel cross , biology , genetics , allele frequency , statistics , population , additive genetic effects , selection (genetic algorithm) , regression , linear regression , mathematics , regression analysis , gene , allele , heritability , computer science , artificial intelligence , sociology , botany , demography , hybrid
A general model for the analysis of variety cross diallels was modified for use when the populations represent different cycles of selection from one parent variety. The a and d parameters in the improved populations are functions of a and d in the parent variety assuming negligible mutation effects. The modified model permits the simultaneous estimation of a polynomial regression in a and in d . The regression equation in homozygous effects ( a ) is a direct measure of weighted average change in gene frequency, and the equation in heterozygous effects ( d ) is a measure of the approach to fixation of the favorable alleles. If favorable genes are dominant, the first derivative of the equation in heterozygous effects evaluated at zero gives the cycle at which the weighted average gene frequency will be 0.5. A parent population and selected cycles of selection were generated on an IBM 360 computer to illustrate the theory. Crosses and related populations were generated according to the Gardner‐Eberhart model and estimates obtained were compared to known parametric values. From the idealized diallel and related populations, change in gene frequency was determined as well as time to fixation and expected response at the endpoint of selection, when gene frequencies are changing at a linear rate.