REMARKS ON EXPLANATION OF HETEROSIS 423 



or the type of each of the parent, these ratios will persist in all the successive 

 generations if the ma tings of the individuals are left to chance, and do not 

 differ systematically as regards fertility. 



If, instead, the matings were not left to chance, naturally the results 

 would be different. In the above example, according to the way in which 

 couples are mated, proportions of heterozygous varying between 75 and 25 

 per cent can be obtained in the third generation, it being always understood 

 that the different matings do not differ systematically as to fertility. In the 

 case of self-fertilization, just the lowest proportion of 25 per cent of heterozy- 

 gous would be obtained in the third generation, and the percentages in the 

 successive generations would diminish, in that case, in geometrical progres- 

 sion at the ratio 1:2, exactly as it is admitted in the above illustration of the 

 theory of East and Jones. 3 



It is scarcely necessary to point out that the hypothesis of self-fertiliza- 

 tion can materialize only in a limited number of cases (bisexual species which 

 are not self -sterile). On the other hand, the point of particular interest to 

 explain is the progressive diminution of heterosis when hybrids reproduce by 

 chance mating to which natural conditions approach. 



We are therefore forced to the conclusion that the above stated theory, 

 while affording an excellent explanation of the heterosis of the first genera- 

 tion of hybrids, and leading us to expect a 50 per cent reduction from the 

 first to the second generation, would lead us to expect that, by chance mat- 

 ing, there would be no further reduction in the following generations. Then, 

 granted that on the contrary this reduction does occur, we must conclude 

 that the above explanation is insufficient, and that it must either be com- 

 pleted by an additional explanation or replaced by another more in keeping 

 with the facts. 



It would appear also, that a 50 per cent reduction of heterosis from the 

 first to the second generation of hybrids is not always in keeping with ex- 

 perience, so that also from this side, the theory is not always confirmed by 

 facts. 



In order to explain the discrepancies referred to, between theory and ex- 

 perience, one might turn to the hypothesis of multiple factors. In that 

 connection it should be clearly distinguished, between the hypothesis of 



3 It is possible that, in the illustration of their theory, East and Jones had just this 

 particular case in mind as regards the reproduction of the generations following the second 

 one, whereas, concerning the second generation (for which it makes no difference whether 

 it be obtained by self-fertilization or by chance mating), they considered that it was ob- 

 tained "by selfing or by interbreeding individuals of the first generation." 



