74 THE EVOLUTION OF LIVING BEINGS. 



Examples : (i) Suppose that there have been 8 self- 

 „fertilizations, and that we are dealing with lo pairs 

 „of characters. 



„What proportion x of the organisms will be ho- 

 „mozygotic with respect to all the lo characters? 

 „What proportion will be homozygotic with respect 

 „to any given one character? To any given two or 

 „three? 



„Taking first the case for the entire lo characters, by 

 ..formula (i) 



X = (^-^ ) = {-^\ = log- 9.9830020 = 0.961617. 



„Thus, out of 100 individuals, somewhat above 96 

 „ would be pure homozygotes; or by formula (4), but 

 „one in 26 would be heterozygotic in any respect 

 „(v = 0.038383). 

 „With respect to any one character formula (i) gives : 



255 



'=(-^) = 



256 ^ °-996o9375. 



„so that all but 4 in 1000 would be homozygotes with 

 „respect to that character" 



„In the same way we find that with respect to any 

 „two characters the proportion of homozygotes 

 „would be 0.9922 ; with respect to three, 0.9883 ; with 

 „respect to four, 0.9845, etc. 

 (2) Suppose that there are 20 pairs of characters, 

 and that there have been 20 self fertilisations. Then : 



T»-) = (i^Si^) =l<^g9.9999957 = 0.999998. 

 „That is, of a miUion individuals, all but two would be 

 „pure homozygotes. 



