Question

In a diploid population of \(N\) individuals, the probability of fixation of a new neutral mutation (assuming no other mutation occurs) is _________.

• A. \(1/N\)
• B. \(2/N\)
• C. \(1/(2N)\)
• D. \(1/(4N)\)

Hint:

For a neutral allele, the probability of fixation equals its starting frequency in the gene pool.

Answer 1

The Correct Option is C

Step 1: Count the total number of gene copies.
Each individual in a diploid population carries two copies of every gene, one from each parent. So a population of \(N\) diploid individuals carries a total of
\[ 2N \]
copies of any given gene (alleles) in the whole population.

Step 2: Note how many copies the new mutation starts with.
A brand new neutral mutation first appears as a single altered copy, arising on one chromosome in one individual. So out of the \(2N\) total gene copies in the population, exactly
\[ 1 \]
copy carries the new mutation at the moment it appears.

Step 3: Apply the neutral theory result for fixation probability.
Under the neutral theory of molecular evolution (developed by Motoo Kimura), a mutation that has no effect on fitness changes in frequency purely by random genetic drift. For a neutral allele, the probability that it eventually becomes fixed (reaches a frequency of 1, replacing all other alleles) equals its initial frequency in the population, because drift has no bias toward any particular allele.

Step 4: Compute the initial frequency of the new mutation.
The initial frequency of the new mutant allele is its copy number divided by the total number of copies:
\[ p_0 = \frac{1}{2N} \]

Step 5: State the fixation probability.
Since fixation probability equals initial frequency for a neutral allele,
\[ P(\text{fixation}) = \frac{1}{2N} \]

Final Answer:
\[ \boxed{\dfrac{1}{2N}} \]