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Equation 21 · Part 8 · Evolutionary Biology and Ecology in Practice: An Advanced Technical Guide

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

A raised number can be a power. When it is a label or bound, it selects a case or the upper limit of a sum; the formula’s structure distinguishes these uses.

Its job in the formula

A raised mark can be a power or an index. Its position and the surrounding notation determine which.

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

An exponent tells how a base is used in multiplication. In x³, x is the base and 3 is the exponent: x³ = x × x × x.

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Sources cited in the article section

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