Equation 9 · The Peacock Problem: Darwin's Second Theory and Its Hard Tests
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Symbol Δ
Δ is part of the quantity the equation computes from the expression on the right.
Symbol bart
bart is part of the quantity the equation computes from the expression on the right.
Symbol h_t^2
is one of the signed contributions combined to compute the quantity on the left.
Symbol beta_p
bet is one of the signed contributions combined to compute the quantity on the left.
Symbol barp
barp is one of the signed contributions combined to compute the quantity on the left.
Symbol h_p^2
is one of the signed contributions combined to compute the quantity on the left.
=
The expressions on both sides represent the same quantity under the stated assumptions.
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Capital delta attached to a quantity marks a difference between two values of that quantity; the article’s sign convention determines the order.
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.
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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What the article says around this equation
Russell Lande’s 1981 paper gave this verbal logic its standard quantitative-genetic form, modelling the joint evolution of a female preference trait and a male display trait under stabilising natural selection on the display and showed that, “despite stabilizing natural selection on males, various types of mating preferences may create a runaway process in which the outcome of phenotypic evolution depends critically on the genetic variation parameters and initial conditions of a population” [ 4 ] . One compact way to see why sits in the coupling itself. Let be the population mean of a male display trait and the population mean of the corresponding female preference; write…
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Russell Lande’s 1981 paper gave this verbal logic its standard quantitative-genetic form, modelling the joint evolution of a female preference trait and a male display trait under stabilising natural selection on the display and showed that, “despite stabilizing natural selection on males, various types of mating preferences may create a runaway process in which the outcome of phenotypic evolution depends critically on the genetic variation parameters and initial conditions of a population” [ 4 ] . One compact way to see why sits in the coupling itself. Let be the population mean of a male display trait and the population mean of the corresponding female preference; write and for the direct selection gradients acting on each (natural selection pulling downward, since the ornament is costly), and 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: . Read the first line on its own and the trait looks stable: natural selection ( ) pulls the ornament back down every generation. But the second term, B\, , 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 , the two equations no longer settle to a fixed point; they feed each other, and and 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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