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Rowe & Houle (1996) give two criteria for the selection of costly female choice:

  1. Condition dependence of sexually selected traits
  2. High genetic variance in condition

Regarding heritability, they wrote,

comparisons based on heritability are misleading, as Fisher's fundamental theorem of natural selection shows that the response of fitness to selection depends only on the additive genetic variance, and not on other components of variance.

However, the magnitude of environmental variance should matter for the selection of female choice for sexually selected traits, since the more environmental variance means the less likely offspring of fitter males will be fitter themselves and the less likely females should be to incur costs to mate with fitter males. Am I not correct? Is this an oversight on their part?

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  • $\begingroup$ I would suppose they talked about genetic variance for fitness while you are expecting them to refer to genetic variance for female choice. Fisher's fundamental Theorem stands right when talking about the genetic variance for fitness, not for another phenotypic trait such as female choice. Do you think you were mislead by this confusion? Note: I have not read the paper. $\endgroup$
    – Remi.b
    May 27, 2017 at 23:49
  • $\begingroup$ Their paper is intended to explain the evolution of female choice. $\endgroup$
    – sterid
    May 28, 2017 at 1:34
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    $\begingroup$ Possibly relevant: the breeder's equation can be written in two different ways. for a given selection differential (covariance of trait with fitness), response to selection is proportional to heritability. But for a given selection gradient (regression of trait with fitness - i.e. the covariance divided by the total trait variance), response to selection is proportional to additive genetic variance. Between the two versions, you're just shunting the V(P) denominator between the two right hand quantities. See biology.stackexchange.com/a/52250/26665 $\endgroup$
    – David Bahry
    May 31, 2017 at 21:29
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    $\begingroup$ But ya I see your point - if e.g. horn length is condition dependent, but condition has high environmental variance, then shouldn't horn length be less correlated with fit genes? So shouldn't the same amount of "horn-length preference", get you a smaller fitness benefit for your children? $\endgroup$
    – David Bahry
    May 31, 2017 at 21:37
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    $\begingroup$ Thank you, sir. These comments are helpful. They seem to be equating the benefit a female receives from choice with response of fitness to selection, which I do not understand. $\endgroup$
    – sterid
    May 31, 2017 at 23:16

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