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Equation 28 · Part 9 · Einstein's Random Walk and the Mathematics of Genetic Drift

Denominator: 1-e^-4Ns

u(p)=1−e−4Nsp1−e−4Nsu(p) = \frac{1-e^{-4Nsp}}{1-e^{-4Ns}}
1−e−4Ns1-e^{-4Ns}

What this part means

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

Its job in the formula

1-e−e^-4Ns occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.

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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Learn the underlying idea

A fraction a/b means a divided by b. The top number is the numerator; the bottom number is the denominator, and it cannot be zero.

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Sources cited in the surrounding passage

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