We use laboratory populations of flour beetles to study the influence of selecti
ID: 3170789 • Letter: W
Question
We use laboratory populations of flour beetles to study the influence of selection and genetic drift on the probability of fixation of a mutant allele. The wild type allele is called bwt. The mutant allele is called bmut. The genotype fitnesses are :
Fitness of bwt/bwt = 1
Fitness of bwt/bmut = 1 + s
Fitness of bmut/bmut = 1 + 2s
where s is the selection coefficient of the mutant allele. The effective population size is denoted by Ne. Different populations can be subject to different environmental conditions, resulting in different values if s; and they can have different effective size, Ne.
a) Rank the following five populations according to the fixation probability of the mutant allele, from lowest probability to highest probability. Explain briefly how you obtain this ranking. (Note: we are not asking that you compute the fixation probability.)
1. In Population 1, s = 0.01 and Ne = 200.
2. In Population 2, s = 0.01 and Ne = 10.
3. In Population 3, s = 0.1 and Ne = 100.
4. In Population 4, s = - 0.01 and Ne = 200.
5. In Population 5, s = - 0.01 and Ne = 10.
6. In Population 6, s = - 0.1 and Ne = 10.
b) Use your results to comment briefly on the efficacy of selection to promote beneficial alleles or impede deleterious ones.
Explanation / Answer
(a) The fixation probability is given by the below equation.
U = (1-exp(-2s)) / (1-exp(-4Ns))
where N is the population size, and s is the selection coefficient.
Using the above formula, calculation of the fixation probability for the given 6 poulations are
1. In Population 1, s = 0.01 and Ne = 200 ; fixation probability = 0.0198
2. In Population 2, s = 0.01 and Ne = 10 ; fixation probability = 0.0600
3. In Population 3, s = 0.1 and Ne = 100 ; fixation probability = 0.1812
4. In Population 4, s = - 0.01 and Ne = 200 ; fixation probability = 0.000006
5. In Population 5, s = - 0.01 and Ne = 10 ; fixation probability = 0.041
6. In Population 6, s = - 0.1 and Ne = 10 ; fixation probability = 0.00413
So, the ranking of 6 populations according to the fixation probability of the mutant allele, from lowest probability to highest probability is
1. Population 4, s = - 0.01 and Ne = 200 ; fixation probability = 0.000006
2. Population 6, s = - 0.1 and Ne = 10 ; fixation probability = 0.00413
3. Population 1, s = 0.01 and Ne = 200 ; fixation probability = 0.0198
4. Population 5, s = - 0.01 and Ne = 10 ; fixation probability = 0.041
5. Population 2, s = 0.01 and Ne = 10 ; fixation probability = 0.0600
6. Population 3, s = 0.1 and Ne = 100 ; fixation probability = 0.1812
(b) The efficacy of selection to promote beneficial alleles or impede deleterious ones depends both on the population size and the selection coefficient. For population size of 100, selection coefficient should be greater around 0.1. Results shows that for population size greater than 100 with low selection coefficient (0.01, -0.01) , the fixation probability of mutant alleles is low.
For population size of 10, selection coefficient can be around 0.1. Results shows that for population size around 10 with low selection coefficient (0.01, -0.01) , the fixation probability of mutant alleles is significant.
For any poulation size, if the selection coefficient is very low (around -0.1), then fixation probability of mutant alleles is low as can be seen in the poulation rankings.