Calculate A's Evolution Over 1000 Generations with Mutation Probability

In summary, a strand of length L begins with all A's and after 1000 generations with a probability of ##\mu## for each letter to mutate to either C, G, or T, the number of A's can be calculated as ##N_A = \mu^{999}L##. To find the function for ##\mu## in terms of ##N_A##, we just have to use the opposite probability, which is the probability of not mutating, and apply it successively for each generation.
  • #1
bowlbase
146
2

Homework Statement


A strand of length L begins life as all A's. Assume that each letter evolves independent of all the rest until today, 1000 generations later. Within each generation there is a ##\mu## probability that the letter mutates to either C, G, T. Finally, assume that once a letter mutates that it cannot mutate again.
Calculate the number of A's as a function of ##\mu##. Then equate this expectation to ##N_A## and write down a function for ##\mu## in terms of##N_A##.

Homework Equations

The Attempt at a Solution


So, I have 1000 generations where each A has the possibility to mutate to something else with probability ##\mu##. The first generation the total number of A's is ##N_A=L##. The second generation we must multiply each A by the mutation probability. Since there is L A's we will get: ##N_A=\mu L##. The third generation occurs and we have to multiply the current number of A's by ##\mu## again. Which gives us ##N_A=\mu \mu L##. Taking this to 1000 generations we'd have ##N_A= \mu^{1000-1} L## which doesn't really seem likely at all.

Any suggestions, or is this correct?
 
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  • #2
What your solution is working toward is the number of non-A's in a given generation. What you want is to apply the opposite probability, the probability of not mutating.

For example, think if the probability was 1% to mutate. After the 1st generation, you would expect .99L A genes and .01L non-A genes. if you just took NA = μL, you would effectively be saying that NA in the first generation is (.01)L which would actually be the Nnot-A

So, your concept of multiplying the probability successively is correct, but you just need to use the right probability.
 
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  • #3
You are right. I had a feeling that I was getting the opposite result that I was meaning to get. I should have realized I had them mixed up! Thanks!
 
  • #4
No problem!

And one more thing, if the second generation is P2L, and the third is P3L. Wouldn't the 1000th be P1000L? Just wondering since you put P1000-1L
(assuming P is the corrected probability)

Edit: nevermind, the first generation is just L, haha :oops:
 

Related to Calculate A's Evolution Over 1000 Generations with Mutation Probability

1. How do you calculate A's evolution over 1000 generations with mutation probability?

To calculate A's evolution over 1000 generations with mutation probability, you would need to use a mathematical model or simulation that takes into account the mutation probability and tracks changes in A over each generation.

2. What is mutation probability and how does it affect A's evolution?

Mutation probability is the likelihood that a genetic mutation will occur in a specific gene or DNA sequence. This can affect A's evolution by introducing new variations and potentially leading to changes in the gene pool over time.

3. Can you provide an example of how to calculate A's evolution over 1000 generations with mutation probability?

Sure, let's say we have a population of A with 100 individuals and a mutation probability of 0.01 (1%). We can use a formula such as A' = A + (A*mutation probability) to calculate the expected number of individuals with a mutation in each generation. Then, we can continue to track changes in A over 1000 generations to see how it evolves with the given mutation probability.

4. How accurate are these calculations in predicting A's evolution over 1000 generations with mutation probability?

The accuracy of these calculations depends on the assumptions and variables used in the mathematical model or simulation. It is important to take into account factors such as genetic drift, natural selection, and environmental influences in order to make more accurate predictions.

5. Can this method be applied to other organisms besides A?

Yes, this method can be applied to any organism with a known mutation probability. However, the specific calculations and assumptions may vary depending on the species and its genetic characteristics.

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