94 THE CASE OF PAPILIO POLYTES [ch. 



from the homozygous form {XX) in appearance. In 

 other words the character dependent upon X exhibits 

 complete dominance. With regard to X then all the 

 members of our population must belong to one or 

 other of three classes. They may be homozygous {XX) 

 for X, having received it from both parents, or they 

 may be heterozygous {Xx) because they have received 

 it from only one parent, or they may be devoid of X, 

 i.e. pure recessives {xx). An interesting question arises 

 as to the conditions under which a population con- 

 taining these three kinds of individuals remains stable. 

 By stability is meant that with the three kinds mating 

 freely among themselves and being all equally fertile, 

 there is no tendency for the relative proportions of 

 the three classes to be disturbed from generation to 

 generation. The question was looked into some years 

 ago by G. H. Hardy, who shewed that if the mixed 

 population consist of p XX individuals, 2q Xx in- 

 dividuals and r xx individuals, the population will be 

 in stable equilibrium with regard to the relative pro- 

 portions of these three classes so long as the equation 

 pr = q^ is satisfied^. 



Now let us suppose that in place of equality of 

 conditions selection is exercised in favour of those 

 individuals which exhibit the dominant character. It 

 has been shewn by Mr Norton that even if the selection 

 exercised were slight the result in the end would be 

 that the recessive form would entirely disappear. 

 The total time required for bringing this about would 



1 Science, July, 1908. 



