Falconer's formula

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Falconer's formula is used in twin studies to determine the genetic heritability of a trait based on the difference between twin correlations.

The formula is Hb2 = 2(rmz - rdz), where Hb2 is the broad sense heritability, rmz is the (monozygotic, MZ) identical twin correlation, and rdz is the (dizygotic, DZ) fraternal twin correlation. The correlation of same sex MZ twins is always higher than the DZ twin correlation with various sexes and thus all gender differences are evaluated as heritable. To avoid this error, only genetic studies comparing MZ twins with the same sex DZ twins are valid. Or correlation between A = hb2 (additive genetics) and C (common environment) must be included in derivation

rmz = A + C + 2 Corr(A,C)
rdz = ½A + C + 2 Corr(½A,C)

and can not be neglected (also as covariance in the statistical model).

It is also possible to do narrow-sense heritability estimates by using sibling/adoptee correlations:

hn2 = rsib - rad, where hn2 is the narrow sense heritability, rsib is the sibling correlation, and rad is the adoptee correlation.


  • Falconer, DS, MacKay TFC. Introduction to Quantitative Genetics, 4th Ed. 1996. Longmans Green, Harlow, Essex, UK.

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