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Published in Crop Sci 14:6-8 (1974)
© 1974 Crop Science Society of America
677 S. Segoe Rd., Madison, WI 53711 USA
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Modification of the Variety Cross Diallel Model for Evaluating Cycles of Selection1

J. J. Hammond and C. O. Gardner2

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.

Key Words: Diallel analysis • Quantative genetic models • Recurrent selection • Population improvement • Heterosis • Inbreeding • Gene fixation

1 Contribution from the Department of Agronomy, University of Nebraska. Published with the approval of the Director as Paper No. 3547 Journal Series, Nebraska Agricultural Experiment Station. Financial support was provided by the Atomic Energy Commission under Contract AT(ll-1)-lS12. Research reported was conducted under Project No. 12-49.

2 Associate Professor of Agronomy, North Dakota State University, and Meyer Katzman Professor of Agronomy, University of Nebraska, respectively.

Received for publication February 5, 1973.




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