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Equation 2 · Part 1 · Hominin Evolution and Deep Prehistory: A First-Principles Introduction

Symbol hatf

f^=∑i(P2(i)−P1(i)) (P4(i)−P1(i))∑i(P3(i)−P1(i)) (P4(i)−P1(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))}
f^\hat{f}

What this part means

hatf is part of the quantity the equation computes from the expression on the right.

Its job in the formula

hatf is part of the quantity the equation computes from the expression on the right.

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: f^=∑i(P2(i)−P1(i)) (P4(i)−P1(i))∑i(P3(i)−P1(i)) (P4(i)−P1(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))}. where P1P_1 through P4P_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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