POPULATION GENETICS AND EVOLUTIONARY CHANGE 433 



p = frequency of M = .90 (writiiifi; the percentage as a 



decimal fraction) 

 q = frecjueiicy of m = .10 



(/> + qT- = p"- + ' 2pq + q' 



(.9r- + 2- (.9) • (.1) + (.IV'' 

 .81 .18 .01 



81% MM 18% Mm 1% mm 



99% black 1% gray 



We see, then, that under such conditions only 1 percent of the offspring 

 will be expected to be gray — only one hamster in 100. If random breeding 

 occurs in subsequent generations, the gene pool may be expected to re- 

 main the same (90 percent M genes, 10 percent m genes) generation after 

 generation, with the result that gray hamsters may be expected to appear 

 about once in 100 individuals indefinitely. The genetic bases for the occa- 

 sional appearance of albino individuals among normally pigmented ones, 

 of black sheep among white ones, of cinnamon bears among black ones, 

 of rufous screech owls anions gray ones, and so on, are doubtless of this 

 type. 



We noted earlier (p. 376) that black hamsters appear with varying fre- 

 quencies in various regions of Europe and Asia; in some places they are 

 rare, in some places common, even approaching 100 percent of the popula- 

 tion. Thoughtful students will readily appreciate that if, knowing the na- 

 ture of the gene pool, we can calculate the proportion of gray hamsters 

 that will appear, we can reverse the process and calculate the nature of 

 the gene pool if we know the number of gray hamsters occurring. For ex- 

 ample, in a certain region 16 percent of the hamsters are gray ones. In 

 what proportions do dominant and recessive genes occur in that gene pool? 



The gray hamsters are represented by the c/' of the Hardy-Weinberg 



formula. Accordingly q- = 16'^ or .16; q = \/.16 = .4 or 40%. Thus 40 

 percent of the genes are recessive (/?/); consequently the remaining 60 per- 

 cent must be dominant (M). 



Having determined the nature of the gene pool we can now do one other 

 thing not possible by direct observation — estimate the proportion of the 

 hamsters that are heterozygous. These are represented by the 2pq of the 

 Hardy-Weinberg formula. Substituting the values of p and q, we find: 

 2 • (.6) • (.4) = .48 or 48 /< . Thus, in such a population we may expect 

 that 48 percent of the hamsters are heterozygotes, "carriers" of the gene for 

 gray color. There is interest in obtaining this statistic in view of the role 

 which heterozygotes are observed to play in evolution (see pp. 457-468). 



One word of qualification must be added concerning the correctness of 



