What is the approximate expected time to the most recent common ancestor for two neutral alleles in a diploid population?

• A. 2Ne generations
• B. 4Ne generations
• C. Ne generations
• D. Ne^2 generations

Answer: (B)

Think about tracing two neutral gene copies backward through time. In a diploid population with effective size Ne, there are 2Ne gene copies in the population. In the previous generation, the two lineages coalesce (come from the same parent copy) with probability 1/(2Ne). If they don’t coalesce in that generation, you go back one more generation and repeat. This makes the waiting time until coalescence mathematically a geometric random variable with success probability 1/(2Ne). The expected waiting time is 1 divided by that probability, which is 2Ne generations.

So the average time to the most recent common ancestor for two neutral alleles is about 2Ne generations (and in coalescent time units, that’s 1 unit, since one unit equals 2Ne generations). The other magnitudes don’t describe this same event: 4Ne is often cited for the time to fixation of a new neutral allele, not the coalescence of two lineages.