106 1 The Process of Evolution 



9o+i = 9i 

 qi + i = 92 



90 



90/(1 + 90) 



1 + 90 



90/(1 + 90) 



1 + 90/(1 + 90) (l + 9o)/(l + 9o)+9o/(l + 9o) 



9o/(l + 9o) _ 90 



92+1 = 93 



(l + 29o)/(l + 9o) 

 1 + 390 



1 + 290 



These successive 9's (gene-frequency values) fall into a harmonic 

 series, i.e., one whose terms are the reciprocals of those in an 

 arithmetic series. When the initial gene frequency is known, the gene 

 frequency for any succeeding generation may be found by substi- 

 tuting in the equation 9,, = 90/(1 + n9o). The change in gene fre- 

 quency per generation is again symbolized by A9 and is given by 

 the following equation: 



A9 



1 + 9 



_ -r 



1 + 7 



Note that the rate of change of gene frequency is itself a function 

 of the gene frequency. When the gene frequency is high, the gene 

 is removed from the population rapidly. A few representative values 

 are given in Table 6.7. 



Table 6.6 { Complete Elimination of Recessives 



* p- + 2pq represents the total after the aa (q-) genotypes are removed. To 

 find the frequencies of the two remaining genotypes they must be expressed as 

 proportions of the total. These two frequencies are obtained simply as follows: 



_ pip) 



1-9 



- 1-9 



p^ + 2pq p{p + 2q) 1 - q + 2q l + q 



