Equation 2 · Part 12 · Hominin Evolution and Deep Prehistory: A First-Principles Introduction

Denominator: sum_i (P_3(i) - P_1(i))(P_4(i) - P_1(i))

\hat{f} = \frac{\sum_{i} (P_2(i) - P_1(i))\,(P_4(i) - P_1(i))}{\sum_{i} (P_3(i) - P_1(i))\,(P_4(i) - P_1(i))}

\sum_{i} (P_3(i) - P_1(i))\,(P_4(i) - P_1(i))

What this part means

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

Its job in the formula

su $m_i$ ( $P_3(i)$ - $P_1(i)$ )( $P_4(i)$ - $P_1(i)$ ) occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.

Full expressionDenominator: sum_i (P_3(i) - P_1(i))(P_4(i) - P_1(i))Article meaning

The passage around this formula

The basic tool for estimating what fraction of a genome derives from an archaic population is comparative allele sharing: for a given modern population, count how much more genetic variation it shares with an archaic genome than a population known to lack that admixture does, and scale by how much variation the archaic and comparison genomes share with each other overall. A simplified version of the widely used D -statistic framework expresses this as: $\hat{f} = \frac{\sum_{i} (P_2(i) - P_1(i))\,(P_4(i) - P_1(i))}{\sum_{i} (P_3(i) - P_1(i))\,(P_4(i) - P_1(i))}$ . where $P_1$ through $P_4$ are allele frequencies at site i in an outgroup, a candidate-admixed population, a comparison population without the admixture, and the archaic source, respectively. The estimator exploits a simple…

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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.

Open the illustrated fractions: division written vertically guide →

Sources cited in the article section

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