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Equation 1 · Part 5 · Fitness Landscapes and the Limits of the Metaphor

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

What this part means

The expressions on both sides represent the same quantity under the stated assumptions.

Its job in the formula

The equals sign connects the complete expression on the left with the complete expression on the right. Both sides must have compatible units.

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 equals sign says that the expression on its left and the expression on its right have the same value under the stated definitions and assumptions.

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Sources cited in the surrounding passage

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