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: Picture the mutation as one chip in a big lottery drum.
The population is diploid with $N$ individuals, so at this one gene position there are $2N$ copies in total. Right after the new mutation appears, $2N-1$ copies are the old version and just $1$ copy is the new, neutral, mutant version.

Step 2: See this as a fair random walk between two end states.
Since the mutation is neutral, nothing pushes its frequency up or down on purpose, it only moves because of random sampling of parents each generation (genetic drift). This frequency can only end at one of two points: it disappears completely (frequency $0$) or it fixes and replaces every other copy (frequency $1$).

Step 3: Use the fair-game property of neutral drift.
For an unbiased random walk like this, a well known result from Kimura's diffusion theory of drift says the chance of ending at the "fixed" end equals the fraction you started with, no more, no less.

Step 4: Write down the starting fraction.
The mutation began as $1$ copy out of $2N$ total copies, so its starting share of the population is
\[ \frac{1}{2N} \]

Step 5: Conclude.
By the fair-game rule for neutral alleles, this starting share is exactly the probability that the mutation eventually becomes fixed.
\[ \boxed{\dfrac{1}{2N}} \]