Question

In a certain population of birds, 16 percent of the population have grey feathers and 84 percent have red feathers. If grey feathers is a recessive trait, what percentage of the population is heterozygous for this trait?
a. 20%
b. 32%
c. 48%
d. 64%

Answer 1

If grey feathers is a recessive trait, then 72.8% of the population is heterozygous for this trait.

Explanation:

The concept used here is of Hardy Weinberg principle, $p^{2} + q^{2}$ +2pq =1

The homozygous dominant genotypeis represented as $p^{2}$ = 84

Red = dominant

The homozygous recessive genotype trait is represented as $q^{2}$ = 16

grey = recessive

2pq = heterozygous individual

Thus for dominant homozygous the alleles are given as

p= $\sqrt{84}$

  = 9.1

q = $\sqrt{16}$

  = 4

for heterozygous individual 2pq

2 x 9.1 x 4

= 72.8

72.8% population is heterozygous for the trait.