Question

Fraggles are mythical, mouselike creatures that live underground beneath a large vegetable garden. Of the 100 Fraggles in this population, 84 have green fur and 16 have gray fur. A dominant allele F confers green fur, and a recessive allele f confers gray fur. Assuming Hardy–Weinberg equilibrium is operating, answer the following questions. (a) What is the frequency of the gray allele f? (b) What is the frequency of the green allele F? (c) How many Fraggles are heterozygotes (Ff)? (d) How many Fraggles are homozygous recessive (ff)? (e) How many Fraggles are homozygous dominant (FF)?

Answer 1

Answer:

a) $0.4$

b) $0.6$

c) $0.48$

d) $0.16$

e) $0.36$

Explanation:

It is given that  alleles for confers green fur (F) are dominant over allele for confers gray fur (f)

Given , out of $100$ fraggles, $16$ have gray furs.

Gray fur allele is recessive. Thus,  genotype for a recessive fraggle would be "ff", hence its frequency would be

$\frac{16}{100} \\= 0.16$

$q^{2} = 0.16$

a)

Thus, allele for recessive fraggle would be represented by "q" and it is equal to $\sqrt{0.16} \\= 0.4$

b)

Allele for dominant allele would be represented by "p" and it is equal to

$p= 1-q\\p= 1-0.4\\p=0.6$

c) As per Hardy Weinberg's equation,

$p^2+q^2+2pq = 1\\0.4^2 + 0.6^2 + 2pq = 1\\2pq = 1-0.16-0.36\\2pq = 0.48$

d) Fraggles are homozygous recessive (ff) $= 0.16$

e) Fraggles are homozygous dominant (FF) $= 0.36$