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Equation 1 · Part 6 · Fitness Landscapes and the Limits of the Metaphor

superscript

w ⁣:G→R,∣G∣=kLw \colon \mathcal{G} \to \mathbb{R}, \qquad |\mathcal{G}| = k^{L}
superscript

What this part means

A raised number can be a power. When it is a label or bound, it selects a case or the upper limit of a sum; the formula’s structure distinguishes these uses.

Its job in the formula

A raised mark can be a power or an index. Its position and the surrounding notation determine which.

The passage around this formula

Take the genotype-space reading, which is the one that empirical work now uses. A genotype is a sequence. The map is w ⁣:G→R,∣G∣=kLw \colon \mathcal{G} \to \mathbb{R}, \qquad |\mathcal{G}| = k^{L}. where the sequence has some length and each site takes one of a small number of states. Two genotypes are neighbours when they differ at a single site. This is the object Maynard Smith described as protein space, and his framing remains the cleanest statement of the constraint: evolution must move through the space one step at a time, and every intermediate must itself be viable, in the way that changing WORD to GENE one letter at a time requires each intervening string to be a real word [ 4 ] .

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Learn the underlying idea

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

These citations provide research context; check each source for the exact claim it supports.