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GENETICS AND EVOLUTION 



Table 14. THE OFFSPRING OF THE RANDOM MATING OF A POPULATION 

 COMPOSED OF 14 AA, 1/2 Aa AND 14 aa INDIVIDUALS 



as people with brown eyes, successive generations will have the same 

 proportion of blue- and brown-eyed people as the present one. 



A brief excursion in mathematics is needed to illustrate this point. 

 If we consider the distribution of a single pair of genes, A and a, in a 

 population (of men, animals or plants), any member of the population 

 will have one of these three genotypes: AA, Aa or aa. Let us suppose 

 that these genotypes are present in the population in the ratio of 

 ^AA:%Aa:^aa. (The point of the argument, that there is no change 

 in the proportion in successive generations, will be the same no matter 

 what particular initial ratio we assume.) If all the members of the 

 population select their mates at random, without regard as to whether 

 they are genotypically AA, Aa or aa, and if all the pairs produce com- 

 parable numbers of offspring, the succeeding generation will also have 

 genotypes in the ratio of Y^AA-.Y^^o-Vioa. This can be demonstrated 

 by setting down all the possible types of matings, the frequency of their 

 random occurrence, and the kinds and proportions of offspring which 

 result from each type of mating, and finally adding up all the kinds of 

 offspring (Table 14). 



Hardy, a mathematician, and Weinberg, a physician, independently 

 concluded in 1908 that the frequencies of the members of a pair of allelic 

 genes are described by the expansion of a binomial equation. The gen- 

 eral relationship can be stated if we let p be the proportion of A genes 

 in the population and let q be the proportion of a genes in the popula- 

 tion. Since any gene must be either A or a (there is, by definition, no 

 other possibility), then p -f q = 1. Thus, if we know either p or q we 

 can calculate the other. 



When we consider all the possible matings of any generation, a p 

 number of A-containing eggs and a q number of a-containing eggs are 

 fertilized by a p number of A-containing sperm and a q number of 

 a-containing sperm: (pA + qa) X (pA -f qa), or (pA + qaF. The 

 proportion of the types of offspring of all of the possible matings is 

 described by the algebraic product: p^AA + 2pqAa + q-aa. This 

 formulation, and its implication of genetic stability in a population in 

 the absence of selection, is known as the Hardy-Weinberg Law. 



In studies of human genetics, in which test matings are impossible 



