Equation 2 · Part 13 · Hominin Evolution and Deep Prehistory: A First-Principles Introduction

Starting index or lower bound: 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))}

i

What this part means

This label says where the repeated addition, multiplication, or accumulation starts. Read its value or condition together with the article’s description of the index.

Its job in the formula

i appears in the bound of this sum. The bound states where the repeated operation starts, ends, or which values it includes.

Full expressionStarting index or lower bound: iArticle meaning

The passage around this formula

…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 logic: if population $P_2$ has interbred with the archaic lineage $P_4$ and $P_3$ has not, $P_2$ should share systematically more rare…

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Σ adds a collection of terms. Π multiplies them. The lower and upper labels tell you which terms belong to the collection.

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