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Equation 9 · Part 5 · The Peacock Problem: Darwin's Second Theory and Its Hard Tests

Symbol B

Δtˉ=ht2 βt+B βpΔpˉ=B βt+hp2 βp\begin{aligned} \Delta \bar{t} &= h_t^{2}\,\beta_t + B\,\beta_p \\ \Delta \bar{p} &= B\,\beta_t + h_p^{2}\,\beta_p \end{aligned}
BB

What this part means

the when.

Its job in the formula

B is one of the signed contributions combined to compute the quantity on the left.

Where the article explains it

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.

The passage around this formula

…female preference; write βt\beta_t and βp\beta_p for the direct selection gradients acting on each (natural selection pulling βt\beta_t downward, since the ornament is costly), ht2h_t^2 and hp2h_p^2 for their heritabilities, and B for the genetic covariance that non-random mating builds between the two traits. The standard Lande-Fisher formalisation of one generation’s change is then a coupled pair: Δtˉ=ht2 βt+B βpΔpˉ=B βt+hp2 βp\begin{aligned} \Delta \bar{t} &= h_t^{2}\,\beta_t + B\,\beta_p \\ \Delta \bar{p} &= B\,\beta_t + h_p^{2}\,\beta_p \end{aligned}. Read the first line on its own and the trait looks stable: natural selection ( βt\beta_t ) pulls the…

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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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