Probability of Extinction under Genetic Drift
update

The answer is here!



Original comment/answer

Kimura and Ohta (1969) showed that assuming an initial frequency of $p$, the mean time to fixation $\bar t_1(p)$ is:

$$\bar t_1(p)=-4N\left(\frac{1-p}{p}\right)ln(1-p)$$

similarly they showed that the mean time to loss $\bar t_0(p)$ is

$$\bar t_0(p)=-4N\left(\frac{p}{1-p}\right)ln(p)$$

Combining the two, they found that the mean persistence time of an allele $\bar t(p)$ is given by $\bar t(p) = (1-p)\bar t_0(p) + p\bar t_1(p)$ which equals

$$\bar t(p)=-4N\cdot \left((1-p)\cdot ln(1-p)+p\cdot ln(p)\right)$$

This does not answer any of the two questions!

This answer gives...


the average persistence time


but not...


the probability of fixation rather than extinction if we wait an infinite amount of time


neither...


the probability that the allele get extinct over a period of say 120 generations.


Can someone improve this answer?