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Equation 3 · Ecological Rationality: When Biases Are Adaptations

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cfac_{fa}

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the fitness cost of a false alarm. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.

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cfac_{fa}

Symbol c_fa

the fitness cost of a false alarm.

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subscript

subscript

The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.

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What the article says around this equation

This is a rule about optimal thresholds, not merely an intuition, and it has a compact formal statement. A decision-maker observes ambiguous evidence D bearing on whether a state H holds — a predator is present, a partner is unfaithful, an approach signals romantic interest — against the alternative that it does not. Where cfac_{fa} is the fitness cost of a false alarm and cmissc_{miss} is the fitness cost of a miss, the threshold that minimizes total expected fitness cost is to infer H whenever:

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