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Equation 8 · The Peacock Problem: Darwin's Second Theory and Its Hard Tests

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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 tˉ\bar t be the population mean of a male display trait and pˉ\bar p 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 tˉ\bar t be the population mean of a male display trait and pˉ\bar p the population mean of the corresponding 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:

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