# Is the fixation rate always equal to the mutation rate for neutral alleles?

Background

A classical result of population genetic is that the rate of fixation of netreual alleles is the mutation rate $\mu$. The reason is that each generation $PN_e\mu$ mutations enter the population, where $P$ is the ploidy number (e.g. 2 for diploids) and $N_e$ is the effective population size. The probability of each neutral mutation to reach fixation is simply its frequency $p$. When the mutation occur $p=\frac{1}{PN_e}$ and therefore the rate of fixation is:

$$\lambda = PN_e\mu \frac{1}{PN_e} = \mu$$

This result s typically very much used in phylogenetic, as assuming a constant mutation rate only, one can estimate the divergence time between two extant lineages.

The above is also explained on wiki>fixation_rate

Question

How robust is the result $\lambda = \mu$?

I understand that the result $\lambda=\mu$ is independent of the effective population size but is it also independent of..

• changes in population size?
• background selection?
• selective sweep?
• population structure?
• selfing rate?
• etc..
• It is special case of Wright-Fisher game right ? In that case how it is independent of population size? Sep 23, 2015 at 19:20
• What do you mean by Wright-Fisher game? It is independent of $N_e$ (at least for constant population size) as I showed in the background. It is also explained in this wiki article Sep 23, 2015 at 20:15
• See Write-Fisher model of genetic drift. And see introduction of these notes. Sep 24, 2015 at 4:28
• I know the Wright-Fisher model of genetic drift. We also talk about Wright-Fisher population but I've never heard of Wright-Fisher game. Sep 24, 2015 at 13:23

• Thank you for your answer +1. I suppose that your answer also suggest that population structure and selfing aren't modifying the result $\lambda=\mu$, right? Is there anything else that you can think about that might affect this result? Thank you! Sep 24, 2015 at 13:55