Equation 21 · Part 5 · Einstein's Random Walk and the Mathematics of Genetic Drift

Symbol V

\frac{\partial \phi(p,t)}{\partial t} = \frac{1}{2}\,\frac{\partial^{2}}{\partial p^{2}}\Big[V(p)\,\phi(p,t)\Big], \quad V(p) = \frac{p(1-p)}{2N} \qquad \text{(Kimura, 1955/1962)}

V

What this part means

V is one of the signed contributions combined to compute the quantity on the left.

Its job in the formula

V is one of the signed contributions combined to compute the quantity on the left.

Full expressionSymbol VArticle meaning

The passage around this formula

…only the variable and the coefficient it multiplies have changed. One honest difference is worth stating rather than smoothing over: Einstein’s D is a constant, fixed once by temperature and viscosity, while Kimura’s V(p) depends on the frequency itself, so the spread is fastest near p=0.5 and vanishes at the boundaries — an allele already fixed or already lost has nothing left to drift into [ 7 ] . The operator is identical; the coefficient it acts on has learned something about the biology.

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Learn the underlying idea

A function assigns an output to each allowed input. The expression f(x) means “apply f to x”.

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Sources cited in the surrounding passage

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