twin data math, clarify Rijsdijk & Sham

Analytic approaches to twin data using structural equation models.
Rijsdijk & Sham, 2002

http://bib.oxfordjournals.org/content/3/2/119.long

It's good that I found an authentic source, but I'm very confused.

The 1st confusion arises from Falconer's formula.

Why are the equations set equal to the square of h, c, or e? For example:

[math]h^{2} = 2(r_{MZ} - r_{DZ})[/math]

I understand that the difference between the covariance of the mono- and di- zygotes equals the heritability estimate x0.5. What I don't get is why h is squared. This seems to recur later in the paper: "the heritability is given by a² / (a²+c²+e²)."

The 2nd and 3rd confusions arise from Path analysis and structural equations, two topics I know nothing about.

Why is D (dominant or non-additive genetic influences) 0.25 for dizygotic twins rather than 0.5?

The genetic covariance between twin 1 and twin 2 is the product of the paths linking the trait scores via A (for MZ: a * 1 * a = a² ; for DZ: a * ½ * a = ½ a² ). The covariance due to C and D can be similarly derived by 'path tracing rules'.

This quote just doesn't make any sense to me. What are paths, and why does A occur twice along its path?

Edited November 13, 201411 yr by MonDie