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Linkage and the Synthesis of Better Genotypes in Self-fertilizing Species¹

The basic task of the breeder of self-fertilized species is the aggregation of superior alleles in a single pure line or cultivar. This study focused on the model problem of collecting into one line all the favorable alleles present in one or the other of any pair of pure lines. Background theory and simulation data are presented. The breeding procedure investigated involved intra-line selection during the formation of single seed descent lines from an F₂, followed by selection among the derived lines. We also considered recurrent use of the procedure; two selected lines from one cycle being crossed to provide the F₂ base for the next cycle. Simulation was used to investigate the effect of genetic linkage on response to selection as reflected by probabilities of fixation of favorable alleles. As was to be expected, our data show that those probabilities are decreased by repulsion but increased by coupling linkages among the superior alleles. It follows that the impact of linkage depends on the way in which the superior alleles present in one parent line but not in the other are distributed among and within linkage groups. Assuming this to be random, our results indicate that, when parent lines are about equal in genetic value, the balance between repulsion and coupling will be such that linkage will have little effect on the average probability of fixation. However when one parent line is substantially better than the other, there will be more coupling linkage and the average probability of fixation will be increased. Nevertheless the average genetic value of selected lines will be less than or, at best, little above the level of the superior parent line

We conclude that the full genetic potential of a two line gene pool is not likely to be achieved by the selection system described. Two systems believed superior to the one on which this study was focused are discussed. Both require increases in the proportion of seed produced by cross-pollination but this may be justified by the associated potential for genetic improvement.

Key Words: Fixation probability • Simulation • Recurrent selection • Superior alleles

² Assistant professor of statistics, Iowa State Univ., formerly NIH predoctoral trainee at Univ. of Minn., and Regents' professor of genetics, Univ. of Minnesota.

Received for publication August 27, 1975.