1 18 REDUCTION OF VARIABILITY. 



total potential variability in mixed populations, and we saw 

 that there also is a very pronounced tendency in every compon- 

 ent species toward reduction and speedy loss of the potential 

 variabilit}', wholly irrespective of selection. Selection will 

 hasten the process somewhat, but we have seen, how it is the 

 limitation of the number of individuals pro-creating, which is 

 the active principle in selection. Selection is only one kind of 

 the several kinds of isolation. 



The next case, which we have to examine, is that of the allog- 

 amous organisms. We want to know, whether in such organ- 

 isms there is anything comparable to the automatic reduction 

 of variability we met in self- fertilized and asexually propagated 

 plants and animals. 



However much crossing there is in an animal population, 

 or in a group of beets or other allogamous plants, we know 

 that for every gene respect to which the whole group is not 

 pure, not every individual will be heterozygous in every gener- 

 ation. Heterozygous animals will produce homozygotes. And 

 as soon as there are homozygotes (with and without) and 

 heterozygotes for some gene in a group, the potential variabil- 

 ity is bound to diminish. Let us take a few examples. 



Let us first examine a simple case of inbreeding, a succession 

 of brother to sister matings, in which the number of couples 

 in every generation is one. If the original couple are impure, 

 heterozygous for some gene, A, they will produce three kinds 

 of off-spring, A A 's, Aa's and aa's, in proportions of i : 2 : 1, 

 And we can see how great the chances are, that a couple of the 

 children will be homozygous for the gene for which the parents 

 were still heterozygous. There is one chance in two that one of 

 the young pair is homozygous, and one in four that both will 

 be homozygous, but as one may be pure for the presence and 

 the other for the absence of the gene, there is one chance in 

 eight that the new couple will be alike and pure in respect to 

 a gene for which both parents were impure. 



However, from this generation on there will be other possi 

 bilities; the new couple may consist of two heterozygotes, or 



