Symbol phi
phi occurs above the fraction bar. The numerator is divided by the entire denominator below it.
Read this term in its guide →Published equation contexts
Why this formula appears here
Motoo Kimura, at Japan’s National Institute of Genetics, made the borrowing exact rather than approximate. His 1955 paper in the Proceedings of the National Academy of Sciences solved the full time-dependent diffusion equation derived from the Wright-Fisher model, recovering not just the eventual resting distribution of an allele’s frequency but its whole transient shape as it evolves generation by generation [ 6 ] . His 1962 paper in Genetics then posed the general fixation problem as a diffusion boundary-value equation and named the lineage precisely: the question of a mutant gene’s ultimate fate was “first treated quantitatively by Fisher (1922),” with “equivalent results” reached…
Read the representative guide
Symbol t
t is an argument of the function-like quantity on the left; its role is set by that function’s stated inputs.
Read this term in its guide →Symbol V
V is one of the signed contributions combined to compute the quantity on the left.
Read this term in its guide →Symbol N
N 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: partial phi(p,t)
The complete quantity above the fraction bar.
Read this term in its guide →Denominator: partial t
The complete quantity below the fraction bar; it must be nonzero for this division.
Read this term in its guide →Denominator: 2
The complete quantity below the fraction bar; it must be nonzero for this division.
Read this term in its guide →Denominator: partial p^2
The complete quantity below the fraction bar; it must be nonzero for this division.
Read this term in its guide →Denominator: 2N
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
Published contexts (1)
A symbol can carry a different meaning in another article. Each occurrence keeps its own guide and term definitions.
Equation 21 · 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.
Motoo Kimura, at Japan’s National Institute of Genetics, made the borrowing exact rather than approximate. His 1955 paper in the Proceedings of the National Academy of Sciences solved the full time-dependent diffusion equation derived from the Wright-Fisher model, recovering not just the eventual resting distribution of an allele’s frequency but its whole transient shape as it evolves generation by generation [ 6 ] . His 1962 paper in Genetics then posed the general fixation problem as a diffusion boundary-value equation and named the lineage precisely: the question of a mutant gene’s ultimate fate was “first treated quantitatively by Fisher (1922),” with “equivalent results” reached…