Symbol hatf
hatf is part of the quantity the equation computes from the expression on the right.
Read this term in its guide →Published equation contexts
Why this formula appears here
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: . where through 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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Symbol i
i appears in the bound of this sum. The bound states where the repeated operation starts, ends, or which values it includes.
Read this term in its guide →Symbol P_2
occurs above the fraction bar. The numerator is divided by the entire denominator below it.
Read this term in its guide →Symbol P_1
is one of the signed contributions combined to compute the quantity on the left.
Read this term in its guide →Symbol P_4
is one of the signed contributions combined to compute the quantity on the left.
Read this term in its guide →Symbol P_3
occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.
Read this term in its guide →Numerator: sum_i (P_2(i) - P_1(i))(P_4(i) - P_1(i))
The complete quantity above the fraction bar.
Read this term in its guide →Denominator: sum_i (P_3(i) - P_1(i))(P_4(i) - P_1(i))
The complete quantity below the fraction bar; it must be nonzero for this division.
Read this term in its guide →Starting index or lower bound: i
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.
Read this term in its guide →Starting index or lower bound: i
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.
Read this term in its guide →How to interpret it
With a fixed numerator, increasing a nonzero denominator reduces the fraction. Read it with the definitions, units, and assumptions supplied by the article.
Research cited beside this formula
Published contexts (1)
A symbol can carry a different meaning in another article. Each occurrence keeps its own guide and term definitions.
Equation 2 · Human Evolution
Hominin Evolution and Deep Prehistory: A First-Principles Introduction
This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.
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: . where through 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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