A Speculative Explanation of the Missing Heritability Problem III

Quincunx heritability

OK, gotta get to the point.

Jonathan and my contribution to the vast (ie non-existent) scholarly field of quincunx studies was this: we wondered what would happen if some of the pins in the quincunx didn’t have a 50-50 chance of bouncing the balls right or left. Because that is what GWAS is about, isn’t it? Everyone is born with a whole lot of pins (SNPs) and each of them has some tendency to bounce us more in the direction of divorce or more in the direction of marital bliss. Then a single ball falls down our personal quincunx (we only get one life) and winds up in a bin (the phenotype). The goal of GWAS is to find correlations between which pins you have and your phenotype, and (the important part) to use those correlations to infer the causal properties of the pins, that is their tendency to bounce people toward or away from divorce.

There is plenty of reason to expect this to be a dicey process. Suppose I have an A (as in ACTG) pin in the third row of my personal quincunx, and it has a 52% chance of bouncing me left. It’s a left-bias pin, amirite? But now suppose that in the next row, just on the left, I happen have a G pin that is strongly, (say 80%) biased to bounce to the right. Is the first pin still left biased? Yes it bounces balls left, but the net effect is to move things to the right, because (in my personal quincunx genome) it interacts with the right-biased pin below it. There is no way to describe all this without sounding a bit silly, but I insist that all this talk about pins in quincunx is, if anything, a vast simplification of what must happen in terms of genetic influences on human behavioral development.

So in the second paper, linked here, we actually build simulated quincunx with biased pins, drop a single ball down each of them, and conduct a GWAS. The details are in the paper, but the conclusion is: quincunx-GWAS doesn’t work. Specifically, it detects SNP hits, ie correlations between which SNPs you have and where your ball ends up, but the magnitude, and even the sign, of those correlations has essentially 0 relationship with the actual bounce-biases of the pins. In regular GWAS language, one would say that the magnitude and sign of the SNP hits don’t correspond to the real causal consequences of the SNPs (which in real GWAS are unknown; inferring them is the point, or at least one point, of the exercise.)

OK, getting close. Even under these discouraging circumstances in terms of causation, heritability still happens. Two balls dropped down identical quincunx (MZ twins) are much more likely to wind up in the same bin than balls dropped down quincunx that only share half their pins (DZ twins or siblings). Less similar for “half-siblings,” “cousins” and so forth in quincunx extended families. This is how heritability is typically estimated in humans, as the slope of the line relating genotypic similarity on the X-axis and phenotypic similarity on the Y. I show in my book how this is the easiest way to derive the Falconer formula for twin heritability.

Here is the key insight for now, especially for strong heritability doubters like Jay Joseph and

Steve Pittelli

. Even though there is no straightforward causal relationship between individual SNPs and behavioral outcomes, it is nonetheless true that organisms with more similar SNPs in general wind up with more similar phenotypes in general. These two ideas are hard to hold in the head at the same time, but they are both true. There are no genes that predispose to divorce, but people with similar genomes are more likely to have similar marital status.

And finally, tomorrow, the kicker: the relationship between genotypic and phenotypic similarity isn’t linear. This is the explanation of missing heritability.