Note 48 — Chapter VIII

Let us suppose that we are dealing with the inheritance of a character which depends upon the presence of the genetic factor X; and let us also suppose that the heterozygous form () is indistinguishable from the homozygous form () 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 containing 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 individuals and r xx individuals, the population will be in stable equilibrium with regard to the relative proportions of these three classes so long as the equation pr = q2 is satisfied[48].