Question

Explain the concept of regression to the mean between generations.

Answer 1

Regression to the mean between generations is the statistical tendency for the children of parents who are unusually high or low on some trait to be, on average, closer to the population average than their parents were.

Key points

- Origin: Francis Galton noticed this in the 19th century and called it “regression toward mediocrity.” Today it’s understood as a consequence of imperfect inheritance plus other sources of variation.

- Intuition: If a parent is extreme (very tall, very short, very high test score), part of that extreme value is due to hereditary factors and part is due to nonheritable or random influences (environment, measurement error, luck). Only the heritable part is reliably passed to offspring. The nonheritable part usually does not persist, so offspring tend to be less extreme — closer to the population mean.

- Simple mathematical form: If μ is the population mean and h^2 is the narrow-sense heritability (the fraction of variance due to additive genetics), then the expected offspring value given a parent value x is
E[offspring | parent = x] = μ + h^2 (x − μ).
Example: population mean height 170 cm, parent = 190 cm, h^2 = 0.5 → expected child = 170 + 0.5·20 = 180 cm. The child is closer to the mean by 10 cm.

- More generally: If parent–offspring correlation r and standard deviations differ, the conditional expectation is linear with slope r·(σ_off/σ_parent). If variances match and r = h^2, slope = h^2.

- Causes: less-than-perfect heritability (h^2 < 1), environmental variation, measurement error, and nonadditive genetic effects (dominance, epistasis) all produce regression toward the mean.

- Consequences and cautions:
- Regression to the mean is expected and does not imply any corrective biological force — it’s a statistical consequence of mixing predictable and unpredictable components.
- Observing offspring closer to the mean after selecting extreme parents is not evidence that inheritance is “weak” beyond what heritability predicts.
- Repeated selection across generations can shift population means (breeding can produce lasting change) but each generation’s offspring will still show regression toward the current population mean unless heritability = 1.

Summary: When traits are only partly heritable, extreme parents tend to have offspring who are less extreme, i.e., closer to the population average. This is regression to the mean — a predictable outcome of mixing inherited and noninherited sources of variation.