← Mathematical compendium

Published equation contexts

u(p)=1−e−4Nsp1−e−4Nsu(p) = \frac{1-e^{-4Nsp}}{1-e^{-4Ns}}

Why this formula appears here

That machinery pays off in the cleanest result in the theory of drift. Kimura’s 1962 formula for the probability that a gene with selective advantage s eventually fixes, starting from frequency p in a population of effective size N , is u(p)=1−e−4Nsp1−e−4Nsu(p) = \frac{1-e^{-4Nsp}}{1-e^{-4Ns}}. as verified directly from his derivation [ 7 ] . Let the selective advantage vanish — the allele is neutral, indistinguishable from its alternatives in its effect on survival or reproduction — and the exponentials cancel term by term, leaving

Read the full article-specific guide →

Read the representative guide

e−4Nspe^{-4Nsp}

Symbol e^-4Nsp

e−e^-4Nsp occurs above the fraction bar. The numerator is divided by the entire denominator below it.

Read this term in its guide →
e−4Nse^{-4Ns}

Symbol e^-4Ns

e−e^-4Ns 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 →
1−e−4Ns1-e^{-4Ns}

Denominator: 1-e^-4Ns

The complete quantity below the fraction bar; it must be nonzero for this division.

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

Learn the mathematics behind it

Published contexts (1)

A symbol can carry a different meaning in another article. Each occurrence keeps its own guide and term definitions.

u(p)=1−e−4Nsp1−e−4Nsu(p) = \frac{1-e^{-4Nsp}}{1-e^{-4Ns}}

Equation 28 · Einstein & Evolution

Einstein's Random Walk and the Mathematics of Genetic Drift

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

That machinery pays off in the cleanest result in the theory of drift. Kimura’s 1962 formula for the probability that a gene with selective advantage s eventually fixes, starting from frequency p in a population of effective size N , is u(p)=1−e−4Nsp1−e−4Nsu(p) = \frac{1-e^{-4Nsp}}{1-e^{-4Ns}}. as verified directly from his derivation [ 7 ] . Let the selective advantage vanish — the allele is neutral, indistinguishable from its alternatives in its effect on survival or reproduction — and the exponentials cancel term by term, leaving

Meanings in this article

  • pp: the starting from frequency.
Equation guide → · Article →