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Equation 30 · Part 1 · Evolutionary Biology and Ecology in Practice: An Advanced Technical Guide

Symbol hatr^2

r^2\hat{r}^2
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 is squared: multiply the underlying quantity by itself. The square is a mathematical operation, not a second independent variable.

Where the article explains it

The relationship Waples and Do build their estimator around, in the form most commonly used for the single-sample method: N^e\hat{N}_e ≈\approx 13 (r^2−1S)\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 passage around this formula

What this means for study design , working backward from the estimator: r^2\hat{r}^2. The genetic estimate and the demographic estimate from workflow one are not redundant. A mark-recapture study can show a stable or growing census count while an LD-based NeN_e estimate reveals a much smaller effective size — a mismatch that is itself diagnostic, typically pointing to high variance in reproductive success (a few individuals contributing disproportionately to the next generation) or a historical bottleneck whose genetic signature outlasts the demographic recovery.

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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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