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Equation 21 · Part 2 · Evolutionary Biology and Ecology in Practice: An Advanced Technical Guide

Symbol hatr^2

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

What this part means

the mean squared correlation of allele frequencies across pairs of loci observed in the sample.

Its job in the formula

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

Where the article explains it

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 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…

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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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