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Equation 29 · Part 2 · Einstein's Random Walk and the Mathematics of Genetic Drift

Symbol p

u(p)=p(s→0).u(p) = p \qquad (s \to 0).
pp

What this part means

the starting from frequency.

Its job in the formula

p is an argument of the function-like quantity on the left; its role is set by that function’s stated inputs.

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

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 u(p)=p(s→0)u(p) = p \qquad (s \to 0). The probability that a neutral allele eventually takes over the population is exactly its own starting frequency, nothing more. No fitness calculation, no bookkeeping of selection coefficients, is needed to answer the single most consequential question about a new mutation’s fate; the diffusion equation alone answers it.

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A variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.

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Sources cited in the surrounding passage

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