#note Population Genetics A Concise Guide (10)

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Problem 2.1 What is the probability that a particular allele has at least one copy in the next generation? The surprising answer quickly becomes independent of the population size as N increases.

Note:

The probability that a particular allele has at least one copy in the next generation is equal to one minus the probability that the allele has no copies in the next generation:

   

As 2N -> infinity,

   

Proof: https://www.quora.com/Why-is-the-displaystyle-lim_-n-to-infty-1-frac-1-n-n-equal-to-frac-1-e