A population has two times heterozygotes as homozygous dominant What is the frequency of the dominant
allele ?
a)0.2
b)0.5
c)0.3
d)0.1
please explain with steps...
Answers
Given : heterozygotes is twice the homozygous dominant
To Find : frequency of the dominant allele
Solution:
- Let the alleles of homozygous dominant is =AA
Let the alleles of homozygous recessive is = aa
and, Let the alleles of heterozyotes is
= Aa
- The basic formula is in equation as follow:
p^2 + 2pq + q^2 = 1
where, p = frequency of dominant allele .
q = frequency of recessive allele
p^2 = percentage of homozygous dominant individuals
q^2 = percentage of homozygous recessive individuals
2pq = percentage of heterozyotes individuals.
- Given that, Heterozyotes individuals is twice the homozygous individuals.
So, q^2 (aa) = 2 × Frequency of Aa
Thus, q^2 = 2(2pq)
q^2 = 4pq
- The basic formula is given as
p + q = 1
that may also be written as
p = 1 - q...(i)
- By substituting 1 - q for p
so, q^2 = 4 (1-q)a
- If by multiplying everything on the right side by q
we get, q^2 = 4q - 4q^2...(ii)
- Divide (ii) equation by q
q = 4 - 4q...(iii)
- Subtract equation (iii) by 4
-4q = -5q
q = -5/-4
= 0.8 q
- So, Again by formula,
p+q = 1
p = 1 - 0.8
p = 0.2
- So, The frequency of dominant allele is 0.2
- The correct option is (A).