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Equation 1 · Fitness Landscapes and the Limits of the Metaphor

What does this equation mean?

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

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Inputs and operationsk^L
Result or conditionw colon G to R, qquad |G|
How to read the two sides of this formula. Follow the article passage for the meaning of each quantity.

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.

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ww

Symbol w

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

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G\mathcal{G}

Symbol G

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

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R\mathbb{R}

Symbol R

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

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kLk^{L}

Symbol k^L

kLk^L is an input to the expression that computes the quantity on the left.

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=

=

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

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superscript

superscript

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.

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How to interpret it

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What the article says around this equation

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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Sources cited in the surrounding passage

These citations give research context. Read each source to check which claims it supports.

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