434 INTRODUCTION TO EVOLUTION 



calculating the nature of the gene pool from the proportion of individuals 

 exhibiting (and therefore homozygous for) a recessive characteristic. The 

 procedure is only valid insofar as conditions of random mating actually 

 prevail in the population and insofar as the recessive characteristic in ques- 

 tion does not affect fertility and viability. Obviously if gray hamsters were 

 less viable than black ones calculations based on the number of gray ham- 

 sters which managed to survive would give an incorrect idea concerning 

 the nature of the gene pool. 



So far we have confined attention to situations in which an equilibrium is 

 already present. We have seen that an equilibrium tends to persist genera- 

 tion after generation. But such an equilibrium is the antithesis of evolu- 

 tion; "evolution means change," to quote the statement with which this 

 book opens. When changes occur what effect will the tendencies embod- 

 ied in the Hardy-Weinberg formula have upon them? 



Suppose we imagine the formation of an artificial and arbitrary popula- 

 tion of hamsters: A thousand black hamsters, half of them homozygous, 

 half heterozygous, become isolated in some way — marooned on an island, 

 perhaps. What may be expected in future generations of such a popula- 

 tion? 



The original population has the frequency 50 percent MM, 50 percent 

 Mm. All the genes contributed by the MM individuals are M, but only 

 half the genes contributed by the Mm individuals are M. Thus the fre- 

 quency of M in the gene pool will consist of 50 percent of the total num- 

 ber of genes, contributed by the MM parents, plus one-half the genes con- 

 tributed by the Mm parents. The latter contribute 50 percent of the total 

 number of genes; one half of this 50 percent, or 25 percent, are M genes. 



Thus, p = 50% + 25% = 75% or .75 

 q - 25% or .25 



(P + qy = P' + 2p(7 + q^ 



= (.75)2 + 2- (.75)(.25) + (.25)^ 



= .5625 + .375 + .0625 



56.25%, MM + 37.5% Mm + 6.25% mm 



We note immediately that a change has occurred in the population. 

 There is a somewhat larger proportion of homozygous, black hamsters 

 than there was among the parents, and the proportion of heterozygous ani- 

 mals has been somewhat reduced. In addition, a small group of gray ham- 

 sters has appeared, although none of the parents were gray. Since this 

 change from the parental generation has occurred it is evident that the 

 original population was not in a state of genetic equilibrium. What is the 

 situation among the offspring? 



