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Equation 2 · Part 1 · Fitness Landscapes and the Limits of the Metaphor

Symbol w

w(g0)<w(g1)<⋯<w(gL)w(g_0) < w(g_1) < \cdots < w(g_L)
ww

What this part means

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

Its job in the formula

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

The passage around this formula

The reason is an ordering constraint. Under the standard assumption that a population moves by fixing one beneficial mutation at a time, a mutational path is accessible only if fitness increases at every single step: w(g0)<w(g1)<⋯<w(gL)w(g_0) < w(g_1) < \cdots < w(g_L). A single step that violates this inequality closes the entire path, regardless of how high the endpoint is. Sign epistasis is exactly the mechanism that produces such steps, and reciprocal sign epistasis — where each of two mutations is deleterious without the other and beneficial with it — is what creates genuinely separated local optima.

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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 article section

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