For a diploid species, assume one set of 100 demes, each with a constant size of

Question

For a diploid species, assume one set of 100 demes, each with a constant size of 10 individuals, and another set of 100 demes, each with 100 individuals.

A) If in each deme the frequencies of neutral alleles A1 and A2 are 0.2 and 0.8, respectively, what fraction of demes in each set is likely to become fixed for allele A1 versus A2? Show your work below:

B) Assume that a neutral mutation arises in each deme. Calculate the probability that it will become fixed in a population of each size. In what fraction of demes do you expect it to become fixed?

C) If fixation occurs, how many generations do you expect it to take?

D)  Compare your results for the two sets of demes. What effect does population size have on the results? Explain any differences.

Explanation / Answer

A) Fixing of an allele refers to that particular allele being solely present in the population i.e. all other allelic forms of that gene have vanished. The fraction of demes being fixed for a particular allele depend on the its frequency.

Therefore, for both sets, the fraction of demes being fixed for A1 = frequency*total num of demes = 0.2 * 100 = 20 demes

the fraction being fixed for A2 = 0.8

B) The initial frequency of any mutation arising in a population = 1/(2N), where N is the population size

Hence frequency of the neutral mutation in set -1 = 1/(2*10)= 0.05

and frequency of the neutral mutation in set-2 = 1/(2*100) = 0.005

NOTE: probability of getting fixed in a population size = the initial frequency of the mutation

For set - 1, fraction of demes it would become fixed in = 0.05

For set - 2, fraction of demes it would become fixed in = 0.005

C) If fixation occurs, the number of generations it would take = 4 (Ne), where Ne is the effective population size

For set-1, no. of generations = 4(10) = 40

for set - 2, no. of generations = 4(100)=400

D) The population size has no effect on the number of demes having the allele/mutation fixed but it drastically affects the time taken (generations) for the process of fixation to be completed.

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