$$\hat{N}_e \approx \frac{1}{3\,(\hat{r}^2 - \tfrac{1}{S})}$$

Equation 21 · Biology

Evolutionary Biology and Ecology in Practice: An Advanced Technical Guide

This equation gives an approximation: it relates the quantities while allowing an approximation.

The relationship Waples and Do build their estimator around, in the form most commonly used for the single-sample method: $\hat{N}_e \approx \frac{1}{3\,(\hat{r}^2 - \tfrac{1}{S})}$. where $\hat{r}^2$ is the mean squared correlation of allele frequencies across pairs of loci observed in the sample, and S is the sample size, with the 1/S term correcting for the sampling bias that a finite number of genotyped individuals introduces into $\hat{r}^2$ even when the true population $N_e$ is large. The practical consequence practitioners have to internalize: $\hat{r}^2$ is estimated with noise from a finite sample, and that noise itself creates apparent linkage disequilibrium indistinguishable from drift-generated LD unless it is explicitly…

Meanings in this article

• $\hat{N}_e$: the not just the final.
• $\hat{r}^2$: the mean squared correlation of allele frequencies across pairs of loci observed in the sample.
• $S$: the sample size.

Equation guide → · Article →