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 ˉt1(p) is:
ˉt1(p)=−4N(1−pp)ln(1−p)
similarly they showed that the mean time to loss ˉt0(p) is
ˉt0(p)=−4N(p1−p)ln(p)
Combining the two, they found that the mean persistence time of an allele ˉt(p) is given by ˉt(p)=(1−p)ˉt0(p)+pˉt1(p) which equals
ˉt(p)=−4N⋅((1−p)⋅ln(1−p)+p⋅ln(p))
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?
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