Question

A locus that affects susceptibility to a degenerative brain disease has two alleles, V and v. In a population, 16 people have genotype VV, 92 have genotype Vv, and 12 have genotype vv. Is this population evolving? Explain.

Short answer

The total number of people is 120. Therefore, the number of alleles present in the population is 240. The total number ‘V’ allele in the population is 124. Thus, the frequency of V is 052. The frequency of ‘v’ alleles in the population is 0.48.

If the population is not evolving, the expected population number matches with the observed population number. In the given case, it is not exactly matching with the population. Therefore, the population is evolving as it is not in equilibrium with Hardy-Weinberg law.

Step-by-step solution

Hardy-Weinberg Equation

The genetic variation is determined by using the Hardy-Weinberg equation. It is represented by the formula \({p^2} + 2pq + {q^2}\). The basic principle of genetics is explained by the scientists G.H Hardy and Wilhelm Weinberg.

The law states that the genetic variation in a large population is constant in every generation without disturbing factors.

Frequency of allele ‘V’ and ‘v’

The total number of alleles is 240.

Therefore, the frequency of ‘V’ is equal to the total number of ‘V’ alleles divided by the total number of alleles.

\(\frac{{124}}{{240}} = 0.52\)

Thus, the frequency of ‘v’ is 0.48 because

\(\begin{aligned}{l}p + q &= 1\\0.52 + q &= 1\\q &= 1 - 0.52\\q &= 0.48\end{aligned}\)

Frequency of genotype ‘VV’, Vv. And vv’

The frequency of ‘VV’ is \({p^2} = {\left( {0.52} \right)^2} = 0.27\)

The frequency of ‘Vv’ is \(2pq = 2\left( {0.52 \times 0.48} \right) = 0.5\)

The frequency of ‘vv’ is \({q^2} = {\left( {0.48} \right)^2} = 0.23\)

Prediction of the evolution of the population

The expected number of people in the genotype ‘VV’ is

\({p^2} \times n\)(n equals the number of people in a population)

\(0.27 \times 120 = 32.4\)

Thus, around 32 people have ‘VV’ genotype in the population.

However, in the given case ‘VV’ genotype is observed in 16 people.

The expected number of people in the genotype ‘Vv’ is

\(\begin{aligned}{l}2pq \times n\\2 \times \left( {0.52 \times 0.48} \right) \times 120 &= 59.904\end{aligned}\)

Thus, around 60 people have ‘Vv’ genotype in the population.

However, in the given case ‘Vv’ genotype is observed in 92 people.

The expected number of people in genotype ‘vv’ is

\(\begin{aligned}{l}{q^2} \times n\\0.23 \times 120 &= 27.6\end{aligned}\)

Thus, around 28 people have ‘vv’ genotype in the population.

However, in the given case ‘vv’ genotype is observed in 12 people.

Therefore, the actual number of populations deviates from the expected number of populations. It indicates that the population is evolving. The population is not exhibiting equilibrium with the Hardy-Weinberg equation.