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Is broad-sense heritability just the slope of the line that passes through the coordinates:

  1. (1, The phenotypic correlation among monozygotic twins)
  2. (0.5, The phenotypic correlation among dizygotic twins
  3. [Optionally] (0, The phenotypic correlation among unrelated individuals)?

Here, the X axis is the relatedness (0 for unrelated, 0.5 for dizygotic, and 1 for monozygotic) and the Y axis is the correlation coefficient r. Is this the same as twin-based broad-sense heritability?

(This would also mean you can estimate heritability by taking the slope of the line through only dizygotic siblings, as they don't always share 50/50 of their DNA and there will be some spread in the X dimension.)

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    $\begingroup$ Context here is important, slope of what? Wht kind of plot are you looking at. $\endgroup$
    – John
    Jul 13 at 15:12
  • $\begingroup$ @John Slope of the line which passes through dizygotic twin correlation and monozygotic twin correlation, where the x-axis is relatedness (0 to 1) and the y-axis is correlation (0 to 1). $\endgroup$
    – BigMistake
    Jul 13 at 22:13
  • $\begingroup$ typo: bounty should not say "twin A," it should just say "A." $\endgroup$
    – BigMistake
    Jul 18 at 6:57
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    $\begingroup$ In a population without genetic variation, the slope would be 0 while the offsprings are essential clones. Wording a meaningful definition of what it is, that you are calculating is not so easy. Maybe it would be easier the other way round: You start with a definition of what you want to calculate. $\endgroup$
    – KaPy3141
    Jul 18 at 13:02
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    $\begingroup$ The broad-sense heritability is the ratio of total genetic variance to total phenotypic variance. H2 = VG/VP (as defined here), so no, unless in a very limited sense of one trait with binary values for phenotype. $\endgroup$
    – bob1
    Jul 19 at 3:56

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The original question's guess happened to be exactly how heritability is defined in the Falconer's formula.

Given genetic relatedness (1 for mz identical twin, 0.5 for dz fraternal twin) on the $x$ axis and twin correlation for the phenotype on the $y$ axis, we can define these two points: $$\begin{align} (x_1, y_1) &= (0.5, r_{dz})\\ (x_2, y_2) &= (1, r_{mz}) \end{align} $$

Then, we can write the line between them in the two-point form: $$(y - y_1) = \frac{y_2 - y_1}{x_2 - x_1} (x - x_1)$$ $$(y - r_{dz}) = \frac{r_{mz} - r_{dz}}{1 - 0.5} (x - 0.5)$$ Therefore, the slope is $\frac{r_{mz} - r_{dz}}{1 - 0.5} = 2(r_{mz}-r_{dz})$, which is equal to the broad-sense heritability.

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  • $\begingroup$ See also the pages leading up to page 185 in INTRODUCTION TO QUANTITATIVE GENETICS by D. S. FALCONER, University of Edinburgh. It seems he arrived at this in a similar way (by looking at genetic relatedness), though he maybe didn't make an explicit connection to slope. $\endgroup$
    – BigMistake
    Jul 25 at 3:05

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