180 PAUL C. MANGELSDORF 



evidence now at hand. That Olotillo and Tepecintle are both hybrid races 

 involving teosinte is even more difficult to prove, although data on chromo- 

 some knobs presented by Wellhausen et al. tend to substantiate such a con- 

 clusion. 



There is at least no doubt that interracial hybridization has been an im- 

 portant factor in the evolution of maize in Mexico. Has this hybridization 

 produced heterosis, or has it merely resulted in Mendelian recombination? 

 The extent to which the suspected hybrid races remain intermediate be- 

 tween the two putative parents suggests that natural selection (operating in 

 a man-made environment) has tended to preserve the heterozygote and to 

 eliminate the segregates which approach homozygosity. It is at least certain 

 that the hybrid races are intermediate between their putative parents in 

 their characteristics to a remarkable degree and that they are highly hetero- 

 zygous. Even in the absence of natural selection favoring the more heterozy- 

 gous individuals, there would seem to be a tendency for repeated interracial 

 hybridization to create an ever-increasing degree of heterosis. This is the 

 consequence of the fact that maize is a highly cross-pollinated plant, and 

 that heterozygosity does not diminish after the Fo in cross-fertilized popula- 

 tions in which mating is random. 



Wright (1922) has suggested that the vigor and productiveness of an Fo 

 population falls below that of the Fi by an amount equal to l/« of the dif- 

 ference between the production of the Fi and the average production of the 

 parental stock, where n is the number of inbred strains which enter into the 

 ancestry of a hybrid. The formula is also applicable to hybrids in which the 

 parental stocks are not inbred lines, but are stable open-pollinated varieties 

 in which random mating does not diminish vigor. It is, of course, not ap- 

 plicable to hybrids of single crosses which are themselves subject to dimin- 

 ished vigor as the result of random mating. 



Hybrid Vigor in Advanced Generations 



The rate at which hybrid vigor diminishes in a population after the F2 gen- 

 eration is related to the proportion of outcrossing. This is true whether hybrid 

 vigor depends upon heterozygosity or upon the cumulative action of dominant 

 genes, and irrespective of the number of genes involved and the degree of 

 linkage. With complete selffiig the amount of hybrid vigor retained is halved 

 in each succeeding generation. With complete outcrossing the amount of 

 hybrid vigor falls to one-half in the F2 and thereafter remains constant. With 

 a mixture of selfing and outcrossing an intermediate result is to be expected. 

 This can be calculated from the following formula presented by Stephens 



(1950): 



h = l[{\-k)h'-Vk]. 



In this formula h is the proportion of Fi vigor retained in the current gen- 

 eration, // is the proportion retained in the preceding generation, and k is 



