If the relative fitness of genotypes MM,MN,and NN are 0.8,1.0,and 0.2 respectively,the expected equilibrium frequency of N is
A) 0.8
B) 1.0
C) 0.2
D) 1.25
E) 4.0

Question

Quizplus · Accepted Answer

The Hardy-Weinberg equation states that the sum of the frequencies of all genotypes in a population should equal 1. Using this equation, we can solve for the frequency of the NN genotype as follows:
p^2 + 2pq + q^2 = 1
where p = frequency of M allele and q = frequency of N allele
Since there are only two alleles, p + q = 1
We are given the relative fitness of each genotype. Let wMM, wMN, and wNN be the relative fitness of MM, MN, and NN genotypes, respectively. The frequency of each genotype can be calculated using the following equations:
fMM = p^2wMM
fMN = 2pqwMN
fNN = q^2wNN
where fMM, fMN, and fNN are the frequencies of the MM, MN, and NN genotypes, respectively.
We can solve for p and q using the following two equations:
fMM + fMN + fNN = 1
and
q = sqrt(fNN/wNN)
Substituting the expressions for the frequencies of the genotypes, we get:
p^2wMM + 2pqwMN + q^2wNN = 1
and
q = sqrt(q^2wNN/wNN)
Simplifying these equations, we get:
p^2(wMM + 2qpwMN) + q^2wNN - 1 = 0
and
q = sqrt(q^2/wNN)
Solving for q using the second equation, we get:
q = q/sqrt(wNN)
Substituting this into the first equation, we get a quadratic equation in terms of q:
p^2(wMM + 2pqwMN) + q^2wNN - 1 = 0
p^2(wMM + 2pqsqrt(wNN)wMN) + q^2wNN - 1 = 0
q^2 + p^2(2sqrt(wNN)wMN)q + p^2wMM - 1 = 0
Using the quadratic formula to solve for q, we get:
q = (1 - p^2wMM)/(2sqrt(wNN)wMN)
Plugging in the given values for the relative fitness, we get:
q = (1 - p^2*0.8)/(2sqrt(0.2)*1)
Solving for q using this equation and the fact that p + q = 1, we get:
q = 0.2
Therefore, the expected equilibrium frequency of N is 0.2.

If the Relative Fitness of Genotypes MM,MN,and NN Are 0