REDUCTION OF VARIABILITY. 119 



of one homozygote and one heterozygote, or even of two homo- 

 zygotes, one with and one without the factor. If we calculate 

 these chances, we have to take into account the chance each 

 pair has of producing in its turn a pair of Uke homozygotes. 

 And in this way, we find that taking together all the possible 

 cases of chance matings of children from heterozygotes, the 

 chance in every generation of one couple having a potential 

 variability of one gene to produce one pair of children pure in 

 respect to this gene is as nine to thirty-two. In other words, if 

 we have a pair of animals or plants with a potential variability 

 32, the potential variability of one pair of children will on the 

 average only be 32 minus 9, that is 23. 



In such a strictly inbred series, it is evident that, once a pair 

 is pure in respect to a gene, whether this means that both have 

 it, or both lack it, this gene has to be reckoned out, in consid- 

 ering the potential variability of the series. 



It is, we think, imnecessary to go into details to show how 

 selection hastens the process of purification, the main point 

 is to show that purity is automatically attained, even in the 

 absence of any selection. 



The last case which we have to consider, is that of amphi- 

 mixis, the case of the potential variabiUty in a group of freely 

 crossing organisms. Does the potential variability diminish 

 in such a group? Here we can very easily show mathematically 

 that, supposing every mating to result in an equally large 

 number of of f -spring, and assuming an uninterrupted steady 

 increase in numbers, the potential variabihty remains undi- 

 minished. Jennings and Pearl have worked out these calcula- 

 tions very thoroughly. However, how does it work out in 

 reaUty? Is it possible that there is an automatic reduction of 

 variability in freely crossing populations, of the same nature 

 as the very great reduction in self-fertilized organisms and in 

 inbred series, slower, but still appieciable? 



In the first place it is obvious, that the multipUcation of any, 

 group of organisms cannot proceed indefinitely. A few hetero- 

 zygotes in a mixture of organisms, of which the majority are 



