High School

If a recessive lethal allele has an initial frequency of 0.67, what will its frequency be after:

- One generation?
- 100 generations?
- 1,000,000 generations?

Answer :

After one generation, the frequency of the recessive lethal allele will be 0.45. After 100 generations, its frequency will decrease to 0.002, and after 1,000,000 generations, it will reach almost zero.

The frequency of the recessive lethal allele can be calculated using the Hardy-Weinberg equation, which states that the frequency of the homozygous recessive genotype (q2) is equal to the frequency of the recessive allele squared. Initially, the frequency of the recessive allele (q) is 0.67, which means that the frequency of the dominant allele (p) is 0.33.

After one generation, some individuals will die due to the lethal recessive allele, and the frequency of the recessive allele will decrease. The new frequency of the recessive allele can be calculated by multiplying the frequency of the recessive allele in the previous generation (q) by the probability that an individual carrying the recessive allele will survive (1 - q). Therefore, the new frequency of the recessive allele will be q' = q(1 - q) + 0.33q = 0.45.

After 100 generations, the frequency of the recessive allele will continue to decrease due to the selection against it. The new frequency can be calculated using the same equation as before, and it will be q'' = [tex]\sqrt{x} (0.33q)^100 + q(1 - q)^100[/tex] = 0.002.

Finally, after 1,000,000 generations, the frequency of the recessive allele will approach zero, as it will be selected against for such a long time that it will no longer be present in the population.

Learn more about the Hardy-Weinberg equation here:

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