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Equation 1 · Part 3 · Fitness Landscapes and the Limits of the Metaphor

Symbol R

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

What this part means

The real numbers: all values on the continuous number line, including negative and fractional values.

Its job in the formula

R is part of the quantity the equation computes from the expression on the right.

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

A variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.

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Sources cited in the surrounding passage

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