Quantitative genetics: directional selection on a heritable trait
R = h² × S Breeders' equation: response = heritability × selection differential
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Generation
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Mean trait (z̄)
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Selection diff. S
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Response R
Narrow-sense heritability h² = Vg/(Vg+Ve) determines how much of trait variation is transmitted to offspring.
Truncation selection: only the top fraction breeds. Selection differential S = mean of selected − mean of all.
Response per generation R = h²S. With h²=0.5 and S=2, R=1 per generation — the trait mean shifts by 1 unit.
Mutation adds variance, preventing fixation; finite population causes genetic drift.