RECURRENT SELECTION AND OVERDOMINANCE 467 



In familiar theory, selective advantage of a heterozygote leads to an 

 equilibrium gene frequency in natural selection, where every individual 

 leaves progeny (no culling) in proportion to fitness or where fitness is in fact 

 fertility or more specifically, number of offspring surviving to breed. We 

 must distinguish now between k for a physical trait, kna for natural selection 

 of the same trait, and k, for artificial selection. Since there is little apparent 

 difference between bushels per acre and potential number of offspring surviv- 

 ing to breed, it may be supposed that k and kns are about the same for yield 

 factors in corn. But if ^ > 1, artificial selection including strong culling may 

 make k^ appreciably greater than k, and (1 + ks)/2ks appreciably less than 

 (1 + k)/2k. The expected effect of any single cycle of artificial selection is 

 to shift gene frequency towards (1 + k^/2ks, '\i k > 1. The operator's suc- 

 cess (measured by k^) in culling out homozygotes will improve as gene fre- 

 quency approaches § and frequency of aA approaches maximum. The limit 

 is reached when ks is infinite, and gene frequency is (1 + oo)/2co or |; e.g., 

 as when saving only roan Shorthorns for breeding stock. The roans then have 

 infinitely more progeny than whites or reds, which have none. 



It does not seem likely that the limit equilibrium oi q = \ can be reached 

 or maintained with multigenic complexes such as corn yield, because of ina- 

 bility to cull absolutely all homozygotes. On this theory, strong selection 

 will seem to degrade vigor. Relaxation of selection may allow vigor of the 

 corn variety to improve. But there may be important loci where overdomi- 

 nance does not obtain, which tend to obscure the overdominance effect. 



If artificial control should maintain fertility continually proportional to 

 the physical trait where k > 1, gene frequency should progress to equilibrium 

 at (1 + k)/2k; cf. recurrent selection for general combinability for corn 

 yield. The population mean is maximum for the physical trait when q = 

 (1 -f k)/2k. 



If overdominance should be important in vigor of cattle at a number of un- 

 fixed loci and a herd is close to (1 + k)/2k for those loci, mild culling of fe- 

 males would tend to raise gene frequencies above (1 + k)/2k. Strong culling 

 of males might have the opposite effect. Founding an elite herd with choice 

 females from many herds and an expensive bull might be more likely to de- 

 grade gene frequency below optimum in the event of overdominance. The 

 offspring of the choice animals might be disappointing aside from expected 

 regression towards the mean of the breed. 



EFFECTIVENESS OF RECURRENT SELECTION 

 Most of the selection practiced with plants and animals is recurrent. Ex- 

 ceptions are selection among homozygous lines or among clones. Inbreeding 

 may curtail the efficiency of recurrent selection by lengthening the cycle. 

 Selection within inbred lines during the process of inbreeding is recurrent but 

 inefficient to the extent that freedom of recombination is curtailed. I have 



