432 INTRODUCTION TO EVOLUTION 



a gene pool in which the numbers of dominant and recessive genes are 

 equal. In such a situation 



p = the frequency of gene M = }i 

 q = the frequency of gene m = 3^^ 



(Note that p + q = I or unity, standing for the total number of genes. 

 This must always be so since the number of dominant genes plus the 

 number of recessive genes must equal the total number of genes.) 



Substituting the numerical values in our formula we obtain 



(p + qf = p2 + 2pq + q^ 



= CAY + 2 ■ M • H + 0^)2 



= K + M + 3-^ 



= HMM + y^Mm + Umm 



(Recall that p represents gene M in this case, hence p- means M^ or 

 MM. Similarly pq means Mm, and q'-^ means nr or mm.) 



Thus the Hardy-Weinberg formula affords a means of calculating ex- 

 pectation with regard to offspring without recourse to the checkerboard 

 diagrams previously employed. 



So far in our discussion we have confined attention to a situation in 

 which the number of dominant genes equals the number of recessive genes 

 — in which p = q. It will be recalled that this situation arose in an ex- 

 periment in which homozygous, black hamsters were mated to gray ones. 

 The first-generation (Fi) individuals were all black but heterozygous. 

 When these F^ individuals were interbred, their offspring (Fo) fell into the 

 following groupings: ^4 homozygous black: % heterozygous black: y^ 

 gray (Fig. 17.1, p. 377). Then when the Fo individuals were allowed to 

 mate at random we discovered that the 1 :2:1 ratio appeared again in the 

 next (Fs) generation and continued through subsequent generations. That 

 is, an equilibrium had been reached. 



While situations in which the number of dominant genes equals the 

 number of corresponding recessive genes are common enough in genetics 

 laboratories, they are seldom encountered in a state of nature. There it 

 is much more common for one gene to preponderate in frequency, the 

 other gene being much rarer. Are the principles we have been discussing 

 applicable to such situations? 



Suppose we have a population of hamsters in which the gene pool con- 

 sists of 90 percent M genes and 10 percent m genes. If random mating oc- 

 curs, what proportion of the offspring may we expect to be black, what 

 proportion gray? The Hardy-Weinberg formula permits easy solution of 

 the problem. 



