The Gene Pool in Cross-Fertilizing Populations 



225 



will the gene pool be in their gametes? The 

 4% of BB individuals will furnish 4% of all 

 gametes and these will be 5, and the 32% of 

 Bb individuals will furnish 32% of all 

 gametes of which half, or 16%,, will be B 

 and half, or 16%, b. So, in the total gene 

 pool there will be 20%, or .2, gametes with 

 B. The b gametes comprise 80%, or .8, of 

 the gene pool (16^o from the 32% Bb het- 

 erozygotes and 64% from the 64% of bb 

 individuals). Note that the gene pool of the 

 Fi is identical to that of the Pi. It follows 

 that in the F2 and all subsequent generations 

 the same genotypic and phenotypic ratios 

 will be found, because the frequencies of B 

 and b in the gene pool will remain constant 

 in every subsequent generation. 



What would be the consequence if, instead 

 of starting the Martian colony with 80% b 

 and 20% B, some other proportion had ob- 

 tained? We can generalize the analysis by 

 letting p equal the fraction of male and of 

 female gametes in the population which car- 

 ries B, and q equal the fraction of male and 

 of female gametes which carries b. Natu- 

 rally, for eggs, p + q = 1, as is true also for 

 sperm. These sex cells will combine at ran- 

 dom to produce the result shown in Figure 

 26-2. The resultant offspring population 

 will be, then, p'^ BB + 2pq Bb + q- bb. The 

 fraction of individuals who are brown-eyed 

 will be p- + 2pq, while q- will be the blue- 

 eyed fraction. The frequency of B and b 

 among the gametes produced by the offspring 

 population will be: 



5 = p2 + pq = p(p + q) = p 



6 = q- 4- pq = q(q + p) = q. 



SPERMS 



Thus the gene frequencies will remain the 

 same as they were in the gametes of the pre- 

 vious generation, and all future generations 

 will have the same gene pool and the 

 same relative frequencies of genotypes. The 

 formula 



p- BB + 2pq Bb + q- bb 



describes the genotypic equilibrium produced 

 by a static gene pool.^ 



It should be noted that this equilibrium 

 principle is not dependent upon either the 

 presence or the absence of dominance. 

 Moreover, the B and b in the formula can 

 represent any two alleles whose frequency 

 in the gene pool is known, even if the sum 

 of their frequencies is less than 1. 



If this equilibrium principle applied indefi- 

 nitely, gene frequencies would remain un- 

 changed, and the evolution of different 

 genotypes (and accordingly of new pheno- 

 types) would not occur. In the Martian 

 model described, however, certain condi- 

 tions had to be fulfilled in order to maintain 

 genie equilibrium. One condition was met 

 by barring mutation. \{ mutation is permitted 

 to occur, to allelic states other than B and 6, 

 it is clear that the frequency of these two 

 alleles in the population will become reduced, 

 upsetting the equilibrium. Moreover, the 

 frequency of any allele will be changed if 



^ This is called the Hardy-Weinbeii^ equilibrium prin- 

 ciple (see references at the end of this Chapter). 



EGGS 



p B (Brown) q b (Blue) 



FIGURE 26-2. The types and fre- 

 quencies of genotypes produced by a 

 gene pool composed of p B and q b. 



pB 

 (Brown) 



qb 

 (Blue) 



