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I was looking at the properties of the Binomial probability distribution and it says that the variance is np(1-p). In population genetics, n = 2N. So I would expect to see that the variance is 2Np(1-p).

But when looking at the Wright-Fisher model, I often see that the variance is $p(1-p)/(2N)$ (see this presentation page 6).

How to derive the variance of the Wright-Fisher model to get this variance from $Prob\{X=i\}=\frac{n!}{i!(n-i)!}p^i(1-p)^{n-i}$?

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The binomial variance $2N p (1-p)$ is for the number of individuals $n'$ carrying the allele in the next generation. The frequency of the allele in the next generation is $p'=n'/(2N)$, so its variance is $$\text{Var}[p'] = \text{Var}[n'/(2N)] = \text{Var}[n']/(2N)^2 = p(1-p)/(2N).$$

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  • $\begingroup$ This is because $Var[n'] = 2Npq$ which is the variance of the binomial model $(2Np(1-p))$ Right? Because $n'$ is also coming from a binomial sampling $\endgroup$
    – M. Beausoleil
    Commented Aug 16, 2019 at 14:02
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    $\begingroup$ @M.Beausoleil: yes, exactly. $\endgroup$
    – Daniel Weissman
    Commented Aug 17, 2019 at 17:43

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