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 Incoming links: Falconer's formula

Falconer's formula Created 2026-09-28 Updated 2026-11-05

h^{2} = 2 (r_{MZ} - r_{DZ}) .

It relies on equal relevant environments and a dizygotic additive-genetic correlation of one half.

The common marginal trait variance is

V_{Y} = V_{A} + V_{C} + V_{E} .

For monozygotic pairs, shared genes and shared environment give

Cov (Y_{i 1}, Y_{i 2}) = V_{A} + V_{C}, r_{MZ} = \frac{V _{A} + V _{C}}{V _{Y}} .

For dizygotic pairs, the genetic covariance is halved while the common environment is unchanged:

Cov (Y_{i 1}, Y_{i 2}) = \frac{1}{2} V_{A} + V_{C}, r_{DZ} = \frac{V _{A} /2 + V _{C}}{V _{Y}} .

Subtracting cancels the common-environment variance and proves Falconer's formula

2 (r_{MZ} - r_{DZ}) = \frac{V _{A}}{V _{Y}} = h^{2},