202 



CHAPTER 15 



EGGS 

 p B (Brown) q b (Blue) 



SPERMS 



P B 



(Brown) 



qb 

 (Blue) 



p BB 

 (Brown Eyes) 



p q Bb 



(Brown Eyes) 



p q Bb 



(Brown Eyes) 



q 2 bb 

 (Blue Eyes) 



FIG1 ki 15-2. The types and frequencies of 

 genotypes produced by a gene pool composed 

 oj p B nnd q b. 



the analysis by letting p equal the fraction 

 of male and female gametes in the popula- 

 tion which carries B. and q equal the frac- 

 tion which carries /). Naturally, for eggs, 

 p -+- q = 1, as is also true for sperm. These 

 sex cells combine at random to produce the 

 result shown in Figure 15-2. The offspring 

 population, then, is 



p- BB + 2 pq Bb + q 2 bb 



The fraction of brown-eyed individuals is 

 p- + 2 pq, whereas q- is the blue-eyed frac- 

 tion. The frequency of B and b among the 

 gametes produced by the offspring popula- 

 tion is: 



B = p- + pq = p(p + q) = p 



b = q 2 + pq = q(q + p) = q 



Thus the gene frequencies have remained 

 the same as they were in the gametes of the 

 previous generation, and all future genera- 

 tions will have the same gene pool and the 

 same relative frequencies of diploid geno- 

 types. The formula 



p- BB + 2 pq Bb + q- bb 



describes the genotypic equilibrium produced 

 by a static gene pool. 1 



1 This is called the Hardy-Weinberg equilibrium 

 principle. 



It should be noted that this equilibrium 

 principle is independent oi the occurrence 

 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 one, as in cases of multiple allelism. 



If this equilibrium principle applied in- 

 definitely, gene frequencies would remain 

 unchanged, and the evolution of different 

 genotypes and their resultant new pheno- 

 types would not occur. In the Martian 

 model described, certain conditions had to 

 be fulfilled in order to maintain a genetic 

 equilibrium. One condition was met by 

 barring mutation, for if it were permitted, 

 obviously the frequency of the two alleles, 

 B and b, in the population would have 

 been reduced, and the equilibrium upset. 

 The frequency of any allele would also 

 have been changed if the mutation rates to 

 and from it were different. In either or both 

 types of events, the genetic equilibrium is 

 shifted until a new one is attained. There- 

 after, the new equilibrium is maintained 

 until some new factor acts on mutation rate 

 in a directional way. 



Our model also assumed that the repro- 

 ductive potential ( biological fitness, or adap- 

 tive value) was the same regardless of the 

 genotype for eye color. But it is possible, 

 under certain conditions, that persons with 

 blue (or with brown) eyes are preferred as 

 mates, in which case the reproductive po- 

 tential of an individual is not independent 

 of the alleles under consideration. Accord- 

 ingly, if individuals with a certain genetic 

 endowment produce more surviving off- 

 spring than those produced by a different 

 genetic endowment, the genes which transfer 

 this higher biological fitness tend to increase 

 their frequency in the population, whereas 

 those genes with lower fitness tend to de- 

 crease it. In this way selection, by operat- 

 ing on genotypes of different adaptive value. 



