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Equation 2 · Part 4 · Hominin Evolution and Deep Prehistory: A First-Principles Introduction

Symbol P_1

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))}
P1P_1

What this part means

P1P_1 is one of the signed contributions combined to compute the quantity on the left.

Its job in the formula

P1P_1 is one of the signed contributions combined to compute the quantity on the left.

The passage around this formula

…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 logic: if population P2P_2 has interbred with the archaic lineage P4P_4 and P3P_3 has not,…

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