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) 



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 (1) gives : 



^P^J^S 30 -" 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 80 i\«° /i.o48575\2o 



* = ("SS-j = (iSS^s) = lo S9-9999957 - 0.999998. 



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

 „pure homozygotes. 



