Question

Around 2005 it was reported in several scientific journals that toads were spontaneously exploding in a small pond in an upscale suburb of Hamburg, Germany (and no, I’m not making this up). Assume that scientists determine that the exploding phenotype was due to an acute fungal infection; only toads with the homozygous tt genotype are susceptible to infection by this fungus. If the initial frequency of allele t is 0.56, what is the frequency of this allele one generation after the introduction of this fungus (i.e. qn+1)? [Assume no mutation occurs and that exploding will reduce a toad’s fitness (W) to 0.]

Answer 1

Ans) qn+1=1

Solution:

Allele frequency of t allele before exploding=q=0.56

Genotype freq of tt=(0.56)²=0.31

Allele frequency of B allele before exploding=p=1-q=1-0.56=0.46

After exploding only tt homozygotes survive whose survival fitness is 1while survival fitness of TT and Tt is 0.

Wo=survival fitness of TT=0

W1=survival fitness of Tt=0

W2= survival fitness of tt=1

p2Wo +2pq W1+q2 W2=W*

W*= mean fitness=0+0+0.31=0.31

Allele frequency after one generation of fungal introduction=qn+1=q2xW2/W*+1/2(2pq xW1)=0.31x1/0.31=1

qn+1=1.