Quantitative Aspects of Genetics and Environment in the Determination of Behavior

With the definitions of hB2 and hW2 given, one can recover the relationship between hB2 and hW2 derived by DeFries (10).

“In SI Appendix, section S1.2, we show that with these definitions, one can recover the relationship between hB² and hW² derived by DeFries (10).”

In the absence of environmental controls, it is impossible to estimate r, the proportion of the variance in the genetic component of the trait accounted for by group membership.

“An immediate problem with application of Eq. 2 is that in the absence of environmental controls, it is impossible to estimate r, the proportion of the variance in the genetic component of the trait accounted for by group membership, a point that DeFries conveyed (10).”

Between-group heritability hB2 is mathematically related to within-group heritability hW2 as hB2≈hW2((1−t)r)/((1−r)t), if groups are large.

“With some algebra, he showed that the between-group heritability is mathematically related to the within-group heritability, hW². Specifically, defining r and t as in the previous paragraph, he showed that[2] hB²≈hW²((1−t)r)/((1−r)t),”