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Equation 17 · Part 2 · Einstein's Random Walk and the Mathematics of Genetic Drift

Symbol p

u(p,t)u(p,t)
pp

What this part means

the starting from frequency.

Its job in the formula

p is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

Where the article explains it

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−4Ns\frac{1-e^{-4Nsp}}{1-e^{-4Ns}} as verified directly from his derivation [ 7 ] .

The passage around this formula

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…

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Sources cited in the surrounding passage

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