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Equation 11 · The Peacock Problem: Darwin's Second Theory and Its Hard Tests

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B βpB\,\beta_p

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BB

Symbol B

the when.

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βp\beta_p

Symbol beta_p

betapa_p is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

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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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Read the first line on its own and the trait looks stable: natural selection ( βt\beta_t ) pulls the ornament back down every generation. But the second term, B\,βp\beta_p , imports a push from the preference side through the genetic covariance the mating system itself has created. When B is large enough relative to the stabilising pull of βt\beta_t , the two equations no longer settle to a fixed point; they feed each other, and tˉ\bar t and pˉ\bar p escalate together until some external limit — a wing that can no longer lift the tail, a display that finally costs more than it wins — brings the pair to a halt. Nothing in the equations names where that limit falls. That absence of an internal stopping…
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Read the first line on its own and the trait looks stable: natural selection ( βt\beta_t ) pulls the ornament back down every generation. But the second term, B\,βp\beta_p , imports a push from the preference side through the genetic covariance the mating system itself has created. When B is large enough relative to the stabilising pull of βt\beta_t , the two equations no longer settle to a fixed point; they feed each other, and tˉ\bar t and pˉ\bar p escalate together until some external limit — a wing that can no longer lift the tail, a display that finally costs more than it wins — brings the pair to a halt. Nothing in the equations names where that limit falls. That absence of an internal stopping rule is the entire content of “runaway”: once the covariance term dominates, the direction is set and the magnitude is set by biomechanics, not by the selective logic that started the process.

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