The Lande equation

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The Lande equation
RZ response of trait Z to selection
additive genetic variance in Z
phenotypic variance in Z COVw.Z covariance
between relative fitness and trait Z
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From the Lande equation to the breeders equation
h2 -- heritability S -- selection differential
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Standardization 1 (traditional) by trait
standard deviation
ßs gives the change in fitness for a 1 S.D.
change in the trait
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Standardization 2 by trait mean
ßµ gives the proportional change in fitness for
a proportional change in the trait is the
trait mean IA(CVA)2 is a mean-standardized
measure of additive genetic variation
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What happens when additive variance changes?
ß0.1
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Mean standardization represents landscape well
VA 0.5 IA0.005 ß µ1
ß0.1
VA 1.5 IA0.015 ß µ1
Changing the additive variance changes IA, not ßµ
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Breeders form does not separate effect of
variation from effect of landscape
VA 0.5 h20.5 ßs0.1
ß0.1
VA 1.5 h20.75 ßs0.14
Changing the variance changes both h2 and ßs
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ßµ for fitness provides a benchmark for strong
selection
ß0.1 ß µ100.11
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Mean standardization represents landscape well
VA 0.5 ß0.1 IA0.005 ß µ1
VA 0.5 ß0.05 IA0.005 ß µ0.5
Changing the landscape changes ßµ, not IA
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Breeders form and the landscape
VA 0.5 h20.5 ßs0.1
VA 0.5 h20.5 ßs0.14
Changing the landscape only changes ßs
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Features of ß µ

• Strength of selection is only interpretable on
  true ratio scale -- zero means absence, value
  measures amount.
• Examples of traits that are not true ratio
• Dates
• Colors
• Some transformed values
• ßµ changes with trait mean

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Literature review

• References from Kingsolver et al. (2001), plus
  a few more journals and references through 2003.
• Only 38 studies included all the necessary
  statistics to estimate ßµ

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Selection is strong!
N340
Filled bars, ß significantlygt0
77 estimates
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Medians biased due to taking absolute values
Selection is still on average 30 as strong as
that on fitness!
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Why are estimates so large?

• Non-exclusive alternatives
• Researchers like to study strong selection
• Publication bias, plus low power
• Environmental covariance biases estimates
• Strong selection on a few dimensions
• Poor estimators of fitness
• Selection on the average trait is strong