(Biology) Human pop genetics question

Question

I think I did both of these wrong. Should I have gotten only a 1 or 0 for answer a? and for part b, what formula should I be using? Do you have to use log rhythms to find t or did I do more work than necessary? (It's frustrating that I can't post a picture of my work).

The mutation rate for an allele that codes for a particular trait is estimated to be 4.1x10^-4 (or 0.00041 ). Assume there is no back mutation. Furthermore, assume no selection, an infinite population, random mating, and so forth. (a) What is the equilibrium allele frequency? (b) How many generations will it take a population to go from an allele frequency of ( p= 0.8 to p=0.4?

a)

b)

Answer 1

A)

Since there is no back mutation rate, the answer should be 0 or 1. Due to the wording of the problem and how question B asks how long it will take the allele to go from .8 to .4, I think it should be 0 since the allele is being removed from the population and will eventually not exist anymore.

B)

Assuming the mutation rate is per generation. You would need to find how many generations it would take to “lose” .4. So 4.1x10^-4 x X = .4. So your answer should be .4/(4.1x10^-4).

Let me know if that makes sense or does not work!

Answer 2

To solve these problems, we can use the concepts from population genetics.

(a) Equilibrium Allele Frequency

The equilibrium allele frequency ppp can be calculated using the formula:

p=μμ+(selection coefficient)p = \frac{\mu}{\mu + \text{(selection coefficient)}}p=μ+(selection coefficient)μ​

In this case, since we are assuming no selection (selection coefficient s=0s = 0s=0), the equation simplifies to:

p=μp = \mup=μ

Given the mutation rate (μ\muμ) is 4.1×10−44.1 \times 10^{-4}4.1×10−4, the equilibrium allele frequency is:

p=4.1×10−4p = 4.1 \times 10^{-4}p=4.1×10−4

(b) Generations to Change Allele Frequency

To determine how many generations it will take for the allele frequency to change from p=0.8p = 0.8p=0.8 to p=0.4p = 0.4p=0.4 in a population under mutation, we can use the following formula:

pt=p0⋅(1−μ)tp_t = p_0 \cdot (1 - \mu)^tpt​=p0​⋅(1−μ)t

Where:

1. ptp_tpt​ is the allele frequency after ttt generations
2. p0p_0p0​ is the initial allele frequency
3. μ\muμ is the mutation rate
4. ttt is the number of generations

Rearranging the formula to solve for ttt:

t=log⁡(ptp0)log⁡(1−μ)t = \frac{\log\left(\frac{p_t}{p_0}\right)}{\log(1 - \mu)}t=log(1−μ)log(p0​pt​​)​

Plugging in the values:

1. p0=0.8p_0 = 0.8p0​=0.8
2. pt=0.4p_t = 0.4pt​=0.4
3. μ=4.1×10−4\mu = 4.1 \times 10^{-4}μ=4.1×10−4

Let's calculate the number of generations required.

Summary of Results

(a) The equilibrium allele frequency is p=4.1×10−4p = 4.1 \times 10^{-4}p=4.1×10−4.

(b) It will take approximately 1690 generations for the population to change the allele frequency from p=0.8p = 0.8p=0.8 to p=0.4p = 0.4p=0.4. ​​