Correlation used as explanatory device in ''The neuroscience of Intelligence' I am currently reading Dr. Richard Haier's book The Neuroscience of Intelligence. I have a base knowledge of statistics, but I am confused about the following extract from page 80 (chapter 2.4): 


  When correlations are computed in identical twins reared apart, the
  correlation is  also one way to estimate heritability, so a
  correlation of .70 indicates that 70% of the  variance in intelligence
  is due to genetic factors and 30% is not.


Is using correlation a valid way to estimate the heritability of a specific trait? I was under the impression that for a comparison of shared variance r² would have to be used, which would mean IQ is not 70% inherited, but only 49% (a huge difference!).
The author is simply not being explicit. The 


  correlation


is neither r or r2, it is simply the relation between x and y.

Pearson's correlation coefficient, or r is a measure of the linear correlation between two variables. It's value is between +1 and −1, 1 being a total positive linear correlation, 0 means no linear correlation, and −1 is total negative linear correlation.

The coefficient of determination, or r2 has a value between 0 and 1. A value near 1 indeed indicates that most of the variation of the response data is explained by the different input values, whereas a value of r2 near 0 indicates that little of the variation is explained by the different input values.   

Now to your book; 70% seems indeed like a lot. I thought it was approximately 40% and this is backed up by NIH and Scientific American that mention approximately 50%. However wikipedia mentions numbers up to 86% and back this statement up with influential articles. (Plomin &amp; Deary, 2015) indeed postulate that 


  The heritability of intelligence increases from about 20% in infancy to perhaps 80% in later adulthood.


Reference
- Plomin &amp; Deary, Molecular Psychiatry (2015); 20: 98–108