Math

QuestionBIOL 0300
2. Assume that a new beneficial mutant allele appeared in a population. i. In which population would the frequency of the beneficial allele increase more quickly, a small population or a large population? Explain. ii. After how many generations would the frequency of the beneficial allele show the greatest increase, four generations or 400 generations? Explain.

Studdy Solution

STEP 1

1. We are considering a new beneficial mutant allele in a population.
2. We need to compare the rate of increase in allele frequency in small versus large populations.
3. We need to compare the increase in allele frequency over four generations versus 400 generations.

STEP 2

1. Analyze the effect of population size on allele frequency increase.
2. Analyze the effect of the number of generations on allele frequency increase.

STEP 3

In a small population, genetic drift has a stronger effect, which can lead to faster changes in allele frequencies, including beneficial alleles. However, this can also lead to random loss of the allele.
In a large population, genetic drift has a weaker effect, and natural selection is more efficient at increasing the frequency of a beneficial allele.
Therefore, in a large population, the frequency of the beneficial allele is more likely to increase steadily and predictably due to natural selection.

STEP 4

Over a short period, such as four generations, there may be some increase in the frequency of the beneficial allele, but it is limited by the number of generations.
Over a long period, such as 400 generations, there is more time for natural selection to act, leading to a greater increase in the frequency of the beneficial allele.
Therefore, the frequency of the beneficial allele would show the greatest increase after 400 generations.
Conclusion: i. The frequency of the beneficial allele would increase more quickly in a large population due to the stronger effect of natural selection. ii. The frequency of the beneficial allele would show the greatest increase after 400 generations due to the extended time for selection to act.

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