Variance effective size

You may remember¹⁸ that the variance in allele frequency in an ideal population is

$$Var(p_{t+1}) = \frac{p_t(1-p_t)}{2N} \quad.$$

So one way we can make our actual population equivalent to an ideal population to make their allele frequency variances the same. We do this by calculating the variance in allele frequency for our actual population, figuring out what size of ideal population would produce the same variance, and pretending that our actual population is the same as an ideal population of the same size. To put that into an equation,¹⁹ let $\widehat{Var}(p)$ be the variance we calculate for our actual population. Then

$$N_e^{(v)} = \frac{p(1-p)}{2\widehat{Var}(p)}$$

is the variance effective population size, i.e., the size of an ideal population that has the same properties with respect to allele frequency variance as our actual population.