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Scaffold S7 — Breeder's equation, year by year

Five rounds, each a different year and species of Darwin's finches on Daphne Major. You are given the selection differential S (survivor mean − pre-selection mean, from Grant-lab cohort data) and the narrow-sense heritability h². Predict the response R — the shift in the population mean in the next generation. Then compare against the observed year-to-year change. R = h² · S.

Locked — answer the pretest above first.

Running tally — predicted R vs. observed R

What you just did has a name

You have now applied the breeder's equation R = h² · S five times. The predicted and observed values agreed closely in rounds where h² was well-known and S was large — the 1977 drought and the 2004 character-displacement year. They disagreed by small amounts in other years: heritability is not constant, and selection acts on many correlated traits at once.

The breeder's equation has three variables. Give it two and it predicts the third. This is a general rule: a formula with three slots can be rearranged to solve for any one. Students often remember R = h² · S but forget h² = R / S (the realized heritability, measured from response-to-selection experiments) and S = R / h² (back-calculating selection from observed change). These are the same equation.

A small residual between predicted and observed R is not a sign the model is broken. It is the norm. Real populations have selection on multiple correlated traits, changing h², and drift. The equation is a first-order tool, not a closed solution.