Suppose that a beneficial mutant in the Lenski experiment in

Suppose that a beneficial mutant in the Lenski experiment increased in frequency from 0.001 to 0.01 in about 47 days. (“Frequency” means the proportion of cells that have the mutation. To do this problem, you will need to convert the frequencies to ratios of mutant to ancestral).

A) Approximately how long would it take to increase in frequency from 0.09 to 0.5?

B) The selection coefficient s in favor of a beneficial mutation is defined by w = 1 + s, where w is its fitness relative to the ancestor. What is the approximate value of s for this example? Choose one and show your work: i) 0.5 ii) 0.1 iii) 0.05 iv) 0.01 v) 0.005 vi) 0.001

Solution

A)

Mutation frequency is commonly referred to as mutation rate per generation or per cell generation

If the mutation frequency has changed from 0.001 to 0.01 in 47 days

Then the ten times increase of frequency seems to have happened in 47 days.

If the frequency of mutation changed from 0.09 to 0.9, then it takes 47 days. But, the frequency has changed to 0.5 instead of to 0.9. So, another 0.4 of the difference can be obtained by multiplying 0.9 with 2/3.6 which again is 1/1.8.

If the mutation frequency has changed 10 times, the time taken is 47 days while the change is 2/3.6 times then the time taken will be (47*3.6/2)*10.

=470*1.8 = 846 days

So, the total time taken from 0.09 to 0.5 is 47+846 = 893 days.

B)

Selection alters the frequency of the germ line mutation

W=1+s where w is the fitness of the mutant relative to the ancestor

Here, the frequency of mutants has increased from 0.09 to 0.5 and it can be considered as the fitness rate of the mutants. So, selection coefficient can be calculated by subtracting “w” or mutant frequency from 1. So, 1-0.5 will give 0.5 as the selection coefficient. Selection coefficient is the measure of the relative fitness of the phenotype.

The answer is i) 0.5