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Equation 28 · Part 3 · Einstein's Random Walk and the Mathematics of Genetic Drift

Symbol e^-4Nsp

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

What this part means

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

Its job in the formula

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

The passage around this formula

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

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An exponent tells how a base is used in multiplication. In x³, x is the base and 3 is the exponent: x³ = x × x × x.

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Sources cited in the surrounding passage

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