How many generations are required for a specific neutral mutation to reach fixation?
How many generations are required for a specific neutral mutation to reach fixation?


Kimura and Ohta (1968) showed that the expected time for a neutral allele to reach fixation is 

$$\bar t(p_0)=-4N\left(\frac{1-p_0}{p_0}\right)\ln(1-p_0),$$

where $p_0$ is the initial frequency and $N$ is the population size. The model assumes a Wright-Fisher population (panmixia, constant population size, exclusively sexually reproducing hermaphroditic individuals, ...) and negligible mutation rate at the locus of interest.


  how do i calculate po in terms of known quantities, such as mutation rate? 


You can compute the expected allele frequency at mutation - drift balance (e.g. see here or any decent intro textbook to population genetics). In short, let $\theta = 4N\mu$, where $\mu$ is the mutation rate, the expected heterozygosity is

$$H = \frac{\theta}{\theta + 1}$$

From that you can compute the allele frequencies $p$ and $q=1-p$ by solving $H = 2pq$.

If needed, you can get the entire distribution of allele frequency given $N$ and $\mu$ (and even $s$ and $h$ if needed) in Wright (1937).