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Equation 21 · Part 10 · Evolutionary Biology and Ecology in Practice: An Advanced Technical Guide

Denominator: 3(hatr^2 - tfrac1S)

N^e≈13 (r^2−1S)\hat{N}_e \approx \frac{1}{3\,(\hat{r}^2 - \tfrac{1}{S})}
3 (r^2−1S)3\,(\hat{r}^2 - \tfrac{1}{S})

What this part means

The complete quantity below the fraction bar; it must be nonzero for this division.

Its job in the formula

3(hatr2r^2 - tfrac1S) occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.

The passage around this formula

The relationship Waples and Do build their estimator around, in the form most commonly used for the single-sample method: N^e≈13 (r^2−1S)\hat{N}_e \approx \frac{1}{3\,(\hat{r}^2 - \tfrac{1}{S})}. where r^2\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 r^2\hat{r}^2 even when the true population NeN_e is large. The practical consequence practitioners have to internalize: r^2\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…

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Learn the underlying idea

A fraction a/b means a divided by b. The top number is the numerator; the bottom number is the denominator, and it cannot be zero.

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Sources cited in the article section

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