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) 



(2 8 _ I\io 

 ~2~) = (256) = 10g ' 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 : 



,,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 : 



_ I'<> 1. 0457520 



* = - = - lo S9.9999957 - -999998. 



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

 ,,pure homozygotes. 



