Monday, 10 March 2008

evolution - 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 ˉt1(p) is:



ˉt1(p)=4N(1pp)ln(1p)



similarly they showed that the mean time to loss ˉt0(p) is



ˉt0(p)=4N(p1p)ln(p)



Combining the two, they found that the mean persistence time of an allele ˉt(p) is given by ˉt(p)=(1p)ˉt0(p)+pˉt1(p) which equals



ˉt(p)=4N((1p)ln(1p)+pln(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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