Heritability and the mind....

Jake at Pure Pedantry has a lengthy post on heritability. It makes concrete (using real psychological illneses, etc.) some of my points in my previous post where I discuss the complexity of behavioral genetics.

Two issues of note. First, Jake used the example of Huntington's Disease as "100% heritable." I think this is going to confuse people. There is often a distinction between "broad sense" and "narrow sense" heritability, the latter includes dominance effects into the genetic variation component,¹ while the latter is focused on additive genetic variation.² In most genetic discourse "heritability" is actually narrow sense heritability in the context of quantitative traits, that is, those that are distributed along a rough normal distribution. This is because (as Jake notes) behavioral traits are polygenic, so the central limit theorem implies that the trait will be normally distributed along a graph of frequency vs. trait value. The main reason that I think the nitpick about Huntington's is relevant is that introducing a Mendelian trait into the picture takes the focus off the overwhelming importance of distributions and expectations within behavior genetics.

Second, Jakes points out the relative weakness of "shared environment" as a component of variation in many psychological traits. To some extent this was the central thesis of Judith Rich Harris' The Nurture Assumption. In No Two Alike Judith tackles the question of why people are different, because she explores the reality that it seems that on some traits fraternal and identical twins are equally different (e.g., the spouses of identical twins are nearly as likely to assert that they couldn't fall in love with the other twin as those of fraternal twins!). The latter book is review worthy, and I will be getting into that in the near future (though probably on my other weblog, though I'll post a link here). But, I would like to offer that Judith points out that on most personality traits it seems that the "interaction effects" between genes & environment are not very large and do not cancel out so as to obscure the effect of environment.

This is what we could see....

This is what we normally see in actually most of the time....

This is simply an elaboration on the norm of reaction, but it's complicated!

Finally, I want to make a trivial prediction, no quantitative trait (i.e., distributed normally) with a extremely negative "tail" distribution that is non-trivial in frequency will be highly heritable. By highly heritable, I mean 80% of the variation being due to genotype. My logic is simple: quantitative traits are often weak in their fitness implications because if they were extremely fitness relevant they would quickly become "genetic" traits which show no intrapopulational variation. Selection would squeeze out the variation in the population if fitness correlated strongly with that variation and the trait was extremely heritable. Therefore, if you find a quantitative trait which also has a significant deleterious tail, say 10% are so pathological that they can't breed, I suspect that there has to be an enormous non-genetic component of variation because this is likely immune to natural selection.

1 - Keep in mind this rough model, heritability = (genetic variation)/(phenotypic variation). The total variance of phenotype is often conceived of like so, V_phenotype = V_additive + V_dominance + V_{environmental} + V_epistatic + V_{gene-environment correlation} + V_{gene-environment interaction}. Often quantitative geneticists focus on the first component because this is proportional to parent-offspring regression and can be used in breeding.

2 - To make "additive genetic variance" complicated, imagine 10 genes, 1 through 10. Imagine the genes all come in two flavors, "on" and "off." If you have 2 copies on, your contribution is 2 for that locus, 1 copy on, and it is one for that locus, and zero copies on, it is zero. Each locus contributes a value between 0-2 to the trait contingent upon the number of on alleles at that locus. So, the theoretical maximum is 20, where all 10 loci have duplicate on copies. The minimum is 0, where all the loci have duplicate off copies. If you assume that each locus is independent, and that each value of each copy is independent, and that each locus makes an equal contribution (implicit in the way I framed this), and that each potential allele has a 50/50 shot of being on or off, the expectation value is going to be 10. If you sampled in this fashion many times you would find a trend where the expectation, 10, was the median & the mode, and the frequencies would drop off towad 0 and 20. This isn't a continuous function, so it isn't technically normal, but it is good enough for genetic work (this is a binomial distribution, so if you added enough draws or events to one sampling of the distribution it would start to converge upon the normal). But, here I've shown really quickly how concrete genetic possibilities, a number of loci with a fixed phenotypic contributive value, can translate themselves into a statistical construct.