POPULATION GENETICS AND EVOLUTIONARY CHANGE 441 



Original parents MM X Mm 



/ \ 

 1st frencration MM X Mm Mm X MM 



In the case of each of these first-generation matings the chances with re- 

 gard to two offspring are the same as they were for the original parents. 

 Both may be MM (the m gene being lost as far as that mating is con- 

 cerned); both may be Mm (the frequency of the m gene being doubled); 

 one may be MM, the other Mm (the frequency of the m gene remaining 

 unchanged). 



For the sake of illustration, let us suppose that the second possibility ma- 

 terializes in both cases, that the offspring from each mating are both Mm. 



On this supposition we see that the frequency of the m gene has doubled 

 again. Two individuals possessed it in the first generation; four possess it 

 in the second generation. 



We might continue on into a third generation, following the matings of 

 the four second-generation individuals. But the principle involved should 

 be evident without more extensive illustration. In small populations, pro- 

 ducing small numbers of offspring per mating, the frequencies of mutant 

 genes may fluctuate either up or down according to chance. This chance 

 fluctuation in gene frequencies has been termed genetic "drift" by Sewall 

 Wright, who has emphasized its role in evolution. Owing to chance, gene 

 frequencies may "drift" either up or down. In our illustration, the fre- 

 quency of gene m might continue to increase generation after generation; 

 if so, actual gray hamsters (mm) would soon appear, and their breeding 

 would accelerate the spread of the m gene. If this trend continued to its 

 culmination, the m gene might reach a frequency of 100 percent; i.e., a 

 population entirely composed of gray hamsters might result. Or the trend 

 in the other direction might set in at any time: matings in which offspring 

 possessing the m gene were possible but not inevitable might fail to pro- 

 duce such offspring. As a result the frequency of the /;; gene would de- 

 cline. If the decline were of sufficient magnitude, the m gene might be 

 lost entirely from the population, all the hamsters being homozygous for 

 black coloration. In the former case we should say that the recessive gene 

 had become fixed, by chance; in the latter case that the dominant gene 



