# Why is the variance of the Wright-Fisher model not equal p(1-p)/(2N)?

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 $$Prob\{X=i\}=\frac{n!}{i!(n-i)!}p^i(1-p)^{n-i}$$?

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 $$\text{Var}[p'] = \text{Var}[n'/(2N)] = \text{Var}[n']/(2N)^2 = p(1-p)/(2N).$$
• 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 – M. Beausoleil Aug 16 '19 at 14:02