The Theory of Population Genetics 93 



locus studied, H are heterozygous (Aa), and R are homozygous for 

 the other allele (aa). Then D-\-H ^R = N, and there are three types 

 of individuals earrying two types of genes. The N individuals have 

 2N genes at this locus. Since each AA individual has two A genes 

 and each Ao individual has one A gene, the total number of A genes 

 in the population is 2D + H. The proportion p of A genes in the 

 population is 



_ 2D + H _ D + 1/.H 

 ^~ 2N ~ N 



The quantity p, the proportion of A genes in the population, is known 

 as the geiw frequency of A. By convention, the gene frequency of the 

 other allele (a) is q. Since these are the only two alleles at the locus, 

 p -h ^ = 1, and q = I — p. 



Hardy-Weinberg Law 



If there is random mating in a population and if the gametes pro- 

 duced by the mates combine at random, there is complete random 

 union of all the gametes produced in the population. As each gamete 

 contains only one of the alleles, the frequency of the two different 

 kinds of gametes (A and a) and the gene frequency are the same. 

 Combining the gametes at random to produce zygotes gives us 



[p (A sperms ) + f/ ( a qoerms ) ] )< [p (A ova ) -\- q (o oxa ) ] 



= (p-^ q)- = p- (AA individuals) -\-2pq (Aa individuals) + 9- 



(aa individuals) 



Populations with this distribution of genotype frequencies are in an 

 equilibrium condition. 



This equilibrium is described by the Hardy-W^einberg law, which 

 may be stated briefly as follows: 



If alternate forms of an autosomal gene are present in a large 

 panmictic population, then in the absence of mutation, selection, or 

 differential migration the original proportions (gene frequencies) 

 of these alleles (pu p^, p-A, • • • p„) will he retained from generation 

 to generation, and after one generation the proportion of genotypes 

 will also reach an equilibrium. The genotype equilibrium frequencies 

 are given by the terms of the expansion (pi + ;?2 + Pa + " • ' + P»)'~- 



Further discussion of population genetics will center around this 

 law, which is one of the fundamental concepts of biology. An alge- 

 braic demonstration of the maintenance of Hardy-Weinberg equi- 

 librium is given in Table 6.2. 



