230 



CHAPTER 27 



Achondroplastic {chondroclyslrophic) dwarf- 

 ism is characterized by normal head and 

 trunk size, but shortened arms and legs, 

 making for disproportionate dwarfism. This 

 rare, fully penetrant (see p. 71) disease is 

 due to the presence of a gene in heterozygous 

 condition, which acts, therefore, as a domi- 

 nant detrimental mutant. Such dwarfs 

 {A\A-2) produce only 20 per cent as many 

 children as are produced by normal people. 

 This lower reproductive potential is expressed 

 by assigning the AiA-i genotype a selection 

 coefficient, s, of .8. 



The frequency of A^A-i in the population 

 was found to be 10 dwarf babies in 94,075 

 births. This frequency must be due to the 

 occurrence of dwarf children from normal 

 parents, who carry new mutations to At, in 

 addition to dwarf children, one of whose 

 parents was dwarf. The gene frequency, p, 

 o{ A-2 in the population must be 10 2(94,075), 

 or .000053. From the incidence of dwarfs 

 who were known to have normal parents, the 



GENOTYPE 



PHENOTYPE 



FREQUENCY AT 

 EQUILIBRIUM 



A,Ai A, a, ajOj 



Normal Normal Dies 



P^ 2pq q2 



u= Mutation rate from A, *" Oj 



q ="\l u/s Here s = 1, hence q = ^1] 



u= 10'^ = 0.000,01 Hence q ='^X 



.000,01 



mutation rate, u, to A^ was determined to be 

 .000042. If the value s = .8 is correct, 

 p = u/s, or .000042 .8, or .0000525, which 

 is in excellent agreement with the value of p 

 observed. Note that for a dominant lethal 

 p = u because s = 1. In the present case s 

 is less than 1, so that p is larger than u. The 

 fact that for dwarfism p is not very much 

 larger than u illustrates the efficiency of 

 natural selection in eliminating such mutants 

 from the gene pool. 



The gene for juvenile amaurotic idiocy (a-i) 

 has no apparent effect when heterozygous 

 (Aiao), but causes homozygotes to die as 

 children. It is, therefore, a recessive lethal 

 mutant. Affected individuals (a-ya-i) are found 

 with a frequency of 1/100,000, or .00001. 

 What is the frequency of a-^ in the gene pool? 

 As shown in Figure 27-1, the frequency at 

 equilibrium of aofifi individuals is equal to q^. 

 Accordingly, the frequency of 02 (q) must be 

 equal to Vq^, or V.OOOOT, or about .003, 

 while the frequency of ^1 must be 1 — .003, 

 or .997. Note that the heterozygous car- 

 riers are 600 times more frequent than af- 

 flicted individuals. What is the mutation 

 rate from Ai to (22? We have presumed that 

 the gene pool is at equilibrium, that is, the 

 rate at which ^2 enters the population by mu- 

 tation must be equal to the rate at which it 

 leaves the population in a2a2 homozygotes. 

 Accordingly, u to ^2 must be .00001. The 

 selection coefficient for normal individuals 

 {AiAi and Aia2) is and for fl2«2 is 1. We 

 see, therefore, that at equilibrium the fre- 

 quency in the gene pool of a recessive mutant 



0.003 



