In a population size of 100 haploid individuals, there are two alleles: allele A

Question

In a population size of 100 haploid individuals, there are two alleles: allele A has a selection coefficient of -0.001 and allele B has a selection coefficient of 0.05.

a. Are alleles A and B advantageous or deleterious?

b. Assuming the population size changes to 10, which evolutionary process is more likely to be important to the evolution of A and B: selection or genetic drift? Explain using maths to justify your answer (Hint: calculate Ns for each allele. We do not expect any exact probabilities just qualitative answers. Sometimes you will see N written as Ne; they are the same.) PS: How to use the Ne value to justify whether selection or genetic drift is more important to the evolution ?

c. What if the population size suddenly changed to 1000? (How to use new Ne values to determine whether selection or genetic drift is more important in this case ? )

d. Which selection coefficient and population size combination described above is most likely to result in an allele reaching 100% frequency in the population?

Explanation / Answer

Importance of random genetic drift and selection depends on absolute value of the product of effective population size Ne and selection co-efficient s.

a. Here population size Ne = 100

Selection co-efficient (s) of allele A is -0.001.

Selection co-efficient (s) of allele B is 0.05.

For allele A – I Nes I= I 100 * -0.001I = 0.1

For allele B – Nes = 100 * 0.05 = 5

We know that if Nes >1 , beneficial mutations are more likely to become fixed in the population, while deleterious mutations are efficiently eliminated.

According to this allele A is deleterious and allele B advantageous.

b. In this case population size (Ne) = 10

Selection co-efficient (s) of allele A is -0.001.

Selection co-efficient (s) of allele B is 0.05.

For allele A – Nes= I 10 * -0.001I = 0.01

For allele B – Nes = 10 * 0.05 = 0.5

We know that if Nes >1, selection dominates over genetic drift.

According to this, genetic drift is more likely to be important to the evolution of A and B as here Nes value for both allele A and B is less than 1.

c. In this case population size (Ne) = 1000

Selection co-efficient (s) of allele A is -0.001.

Selection co-efficient (s) of allele B is 0.05.

For allele A – Nes= I 1000 * -0.001 I = 1

For allele B – Nes = 1000 * 0.05 = 50

We know that if Nes >1, selection dominates over genetic drift.

According to this, selection is more likely to be important to the evolution of B as here Nes value for allele B is greater than 1 but in case of allele A both selection and genetic drift plays an important role.

d. When an allele reaches a frequency of 100% it is said to be fixed in the population. Smaller populations achieve fixation faster, whereas in the large population, fixation is not achieved.

Thus, selection coefficient and population size combination described in condition b where population size is 10, is most likely to result in an allele reaching 100% frequency in the population.

To "fix" an allele means that the allele is present at a frequency of 1.0, so all individuals in the population have the same allele at a locus. So, fixation is occurred in small population. Large effective population sizes and an even distribution in allele frequencies tend to decrease the probability that an allele will become fixed. That means the probability of fixation is very low in a large population.

So, the correct answer is population size 10.

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