While most investigations into the relationship between heterozygosis and performance in maize did not reveal important deviations from a linear response, there is one early reported exception still lacking a satisfactory explanation. This refers to the findings of J. C. Sentz et al. (Agron. J. 46:514-520, 1954), who compared five genetic groups representing 0%, 25%, 50%, 75%, and 100% heterozygosis. Unexpected deviations from linearity were observed with "second backcrosses" (B11 and B22) and "double backcrosses" (B12 and B21), which formed the 25% and 75% heterozygosis groups, respectively. Almost consistently over crosses, places and years, these deviations were antagonistic in direction (namely, enhancing with second, but depressing with double backcrosses) and asymmetric in size (namely, relatively larger with second than with double backcrosses). Furthermore, this peculiar pattern of curvilinear response considerably varied in expressivity over environments.

In discussing their results, Sentz et al. were led to attribute them to epistasis and, of course, to genotype-environment interactions, but not to any form of selection during development of the segregating generations. Quoting the authors: "It is difficult to visualize any natural selection for either gametes or zygotes which would simultaneously depress expression in the double backcross generations and enhance it in the second backcross generations." Nevertheless, it would seem to the present writer that those antagonistic effects could well have been brought about by an unconscious selection of more vigorous plants of the first backcrosses (B1 and B2) in producing the seed of the second and double backcrosses. Such selection would change the means of the latter generations by amounts which in sign and size depend on the covariances of B1 and B2 with these generations. Table 1 specifies averages of the pertinent covariances in terms of the model of R. E. Comstock and H. F. Robinson (Biometrics 4:254-266, 1948), assuming linkage and epistasis to be absent. It appears therefore that the average covariance of first with second backcrosses will always be positive. But the average covariance of first with double backcrosses may be positive, zero, or negative according to whether the respective average degree of dominance is below, equal to, or above one. In practice, a negative value of this covariance may result not only from the prevailing of true overdominance, but also from pseudo-overdominance due to repulsion linkages. The latter situation seems to be not uncommon in corn, and has indeed been demonstrated for one of the two crosses used by Sentz et al. (R. H. Moll et al., Genetics 49:411-423, 1964).

Finally, besides genotype-environment interactions, the fact that the seed in part had been produced anew for successive testing years may account for the varying expressivity of the curvilinear response observed in the study in question.

Table 1. Average covariances between indicated generations.

F. W. Schnell
 
 

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