Editing Twin study (section)

=== Classical twin method ===
Like all behavior genetic research, the '''classical twin study''' begins by assessing the variance of behavior (called a [[phenotype]] by geneticists) in a large group, and attempts to estimate how much of this is due to:
* genetic effects ([[heritability]])
* shared environment – events that happen to both twins, affecting them in the same way
* unshared, or unique, or nonshared environment – events that occur to one twin but not the other, or events that affect either twin in a different way.
Typically these three components are called '''A''' (additive genetics) '''C''' (common environment) and '''E''' (unique environment); hence the acronym ''ACE''. It is also possible to examine non-additive genetics effects (often denoted '''D''' for dominance ([[ADE model]]); see below for more complex twin designs).

The [[ACE model]] indicates what proportion of variance in a trait is heritable, versus the proportion due to a shared environment or unshared environment. Research is typically carried out using [[Structural equation modeling]] (SEM) programs such as  [[OpenMx]] capable in principle of handling all sorts of complex pedigrees. However the core logic underlying such programs is the same as the one underlying the twin design described here.

Monozygotic (identical – MZ) twins raised in a family share 100% of their genes, and all of their shared environment. Any differences arising between them in these circumstances are random (i.e. due to environmental effects unique to each twin). The correlation between identical twins provides an estimate of ''A'' + ''C''. Dizygotic (DZ) twins also share C, but share, on average only 50% of their genes: so the correlation between fraternal twins is a direct estimate of ½''A''+''C''. If we denote with ''r'' the [[correlation]], we can define ''r''<sub>mz</sub> and ''r''<sub>dz</sub> as the correlations of a trait among identical and fraternal twins, respectively. For any particular trait, then:

:''r''<sub>mz</sub> = ''A'' + ''C''

:''r''<sub>dz</sub> = ½''A'' + ''C''

Stated again, the difference between these two sums then allows us to solve for ''A'' and ''C'' (and as a consequence, for ''E''). As the difference between the identical and fraternal correlations is due entirely to a halving of the genetic similarity, the additive genetic effect ''A'' is twice the difference between the identical and fraternal correlations:

:''A'' = 2&nbsp;(''r''<sub>mz</sub> − ''r''<sub>dz</sub>)

given the estimate for ''A'', the one for ''C'' can be derived, for instance, from the first equation:

:''C'' = ''r''<sub>mz</sub> − ''A''

Finally, since the trait correlation among identical twins reflects the full contribution of ''A'' and ''C'', the residual variation ''E'' can be estimated by subtracting this correlation from 1

:''E'' = 1 − ''r''<sub>mz</sub>.

To summarize therefore, the additive genetic factor ''A'' is twice the difference between MZ and DZ twin correlations (this is known as [[Falconer's formula]]), ''C'' is the MZ twin correlation minus this estimate of ''A'', and the random (unique) factor ''E'' is (1 - ''r''<sub>mz</sub>), i.e. MZ twins differ due to unique environments only (Jinks & Fulker, 1970; Plomin, DeFries, McClearn, & McGuffin, 2001).