Equation 2 · Part 8 · Hominin Evolution and Deep Prehistory: A First-Principles Introduction

fraction

\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))}

fraction

What this part means

Divide the expression above the line by the one below it.

Its job in the formula

The expression above the fraction bar is divided by the complete expression below it. The denominator must not be zero.

Full expressionfractionArticle 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.

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Sources cited in the article section

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