Many non-scientists have a great interest in heritability, but lack the science education and/or cognitive ability to understand modern techniques like Genome-wide Complex Trait Analysis (GCTA), so this post is a quick attempt to explain it. Full Disclosure: I have virtually no formal science training beyond high school but this is just an oversimplified explanation.

GCTA gives a measure of the squared correlation between additive genotype and phenotype. The reason it’s so confusing is that you can’t directly correlate a phenotype with a genotype if you haven’t found the genes that code for that phenotype, and thus you can’t determine if someone is genetically high on a given trait.

So for example, you can’t determine if someone’s genetic IQ matches their actual IQ, if you don’t know if they have the genes for IQ. Since a correlation, by definition, is how close the rank order of two variables (i.e. genetic IQ and actual IQ) agree, it can’t be directly calculated if one of said variables (i.e. genetic IQ) can’t be ranked. It would be like trying to calculate the correlation between height and weight, but all the weights were reported in a language you didn’t speak.

To sidestep this problem, GCTA was invented by a scientist of East Asian heritage. In GCTA, instead of ranking everyone in your sample from highest to lowest on each trait, you simply randomly assign people to pairs, and for each pair, calculate the genetic distance and the phenotype distance. So for example, if the people who differ by 100 single nucleotide polymorphisms (SNPs), on average, differ by one standard deviation in IQ, and if people who differ by one standard deviation in IQ differ, on average, by 39 SNPs, then perhaps it can be inferred that (in this sample) the correlation between genetic IQ and actual IQ is whatever number when squared and multiplied by 100, equals 39.

That number is 0.62

This is because in a bivariate normal distribution, the slope of the standardized regression line equals the correlation between two variables, so if a genetic difference of 100 SNPs regresses to a one standard deviation difference in IQ, then one standard deviation must be only 62% as extreme as 100 SNPs and if a one standard deviation difference in IQ regresses to a 39 SNP difference, then 39 must be only 62% as extreme as one standard deviation.

Once we have the correlation of say 0.62 between additive genotype and phenotype , we square it to get the amount of variation explained which in this example would be 0.38 (the real number is probably much higher, and even higher still for broad-sense heritability).

Of course what very few people realize is that heritability is technically NOT the percentage of the phenotypic variation explained by genes, it’s the percentage explained by genes **when environment is held constant or allowed to vary randomly**.