74 THE EVOLUTION OF LIVING BEINGS. 



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

 fertilizations, and that we are dealing with 10 pairs 

 ,,of characters. 



,,What proportion x of the organisms will be ho- 

 ,,mozygotic with respect to all the 10 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 10 characters, by 

 ,,formula (i) 



,,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 : 



* = P?^ 25! = '" 609375 ' 

 ,,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 : 



(2 to I\w /i. 048575X2 . 



- I = I 0^5) =1 S 9-9999957 = 0.999998. 



,,That is, of a million individuals, all but two would be 

 ,,pure homozygotes. 



