Parent‑offspring regression.

If failure of ear‑row breeding for yield is established but not fully explained, and if hybrids of second cycle lines are scarcely more productive than those of first cycle lines, explanations may be sought in peculiarities of the parent‑offspring regression. It may be that both reputed failures will have the same explanation.

The present purpose is to propose the essentials of a variation of experimental approach. Practical details are omitted mostly.

Grow 1000 individuals of a common crossbred variety in such manner as to minimize environmental variations. Record an appropriate measure of vigor for each plant and sort into a frequency distribution of 10 groups or more. Breed within groups to obtain 10 progenies. Record the same measure of vigor for progenies as for parents. Plot means of parent groups against means of progeny groups to obtain the regression curve.

It will be of interest to learn if the curve has a positive slope throughout or if it may bend down at the right end as our present evidence might lead us to suspect. If this suspicion is verified, it will follow that the most elite individuals are not the best parents. It would then be of further interest to note the optimal parent grade ‑ the highest point on the curve. It would also be desirable to determine variances of individuals within groups of progenies to learn if variance of those from the top parent group is greater than of those from the optimal parent group as we might expect if elite individuals have above‑average heterozygosity.

The foregoing has been general so it may apply also with small animals which may be better suited than corn for such an experiment.

With corn, cross breeding may be done within parent groups or parents my be selfed. Both might well be done. Cross breeding should provide results of more general application. Further, the selection processas may be continued by choosing elite individuals again from the top group and "optimal" from the indicated optimal group, thus to compare effects of selecting from different sections of the range. Selfing may accentuate curvature of regression, and thus make experimental verification more certain, particularly of any downward trend at the right. Results from selfing would also bear more directly on the problem of which grade of parent plants may produce the stronger inbred lines.

Earlier regression studies with yield or vigor have not been designed to detect much more than that the general trend was positive. From this it was concluded that elite individuals mst be the best parents.

It may seem that a generally positive regression of offspring on parent for yield or vigor of corn ‑ an appreciable heritability ‑ is contradictory to a theory of overdominance. We may note that zero heritability and regression are expceted only when there is an equilibrium of selection or vice versa. If the number of progeny left by every individual is proportional to its phenotype, the population should theoretically reach an equilibrium where heritability is zero. This condition may be met by "survival value" in nature. It is hardly to be expected with prized characters of varieties and breeds, which have been developed by culling less desirable individuals. From data of the above experiment, estimates may be made of progress from saving any proportion or any part of the population.

Where there is considerable extra advantage of heterozygosity, strong selection, saving the top one per cent or less may degrade gene frequency; selection may have a negative effect on the mean, even though initial gene frequency is below equilibrium. Paradoxically, weak selection, culling only 30 to 40 per cent, may improve gene frequency and the population mean. These considerations have suggested the above experimental approach and the hope that it may be effected with various characters of more than the one species.

Fred H. Hull