Australia as a Triumph of Reversion to the Mean

Not many people really understand the idea of reversion to the mean in the context of genetics. If it’s discussed at all, it’s usually in terms of the rich smart guy having an idiot son who ruins the family business. But there’s more to it than that.

The first part you need to realise is that it’s often unhelpful to think of your genes as a deterministic set of instructions that will be replicated over and over in your children unless mutations.

Instead, one crude metaphorical way to think of the process of Mendelian Inheritance is that your genetic outcomes are the process of a random variable that is drawn from the joint distribution of your mother’s family and your father’s family. Combined, you can think of this as your family genetic distribution.

Your particular genes contain information both about you (i.e. the one particular realization of that variable) and the overall distribution of traits in your family (the possible range of other realizations of you and your siblings). When you have children, each child is a realization of the joint distribution of your family traits and your husband or wife’s family traits. If you have enough children, you’ll start to see the outlines of the whole distribution of possible traits – ranges of height, ranges of facial features, ranges of hair colors, etc.

So what this means is that when it comes to whether your children will be smart, the question is not just whether you and your wife are smart. The question is whether you and your wife come from families that are generally smart. If you and your wife are both smarter than the rest of your families, unfortunately your children will probably be less smart than either of you. They’ll be closer to the average of the joint distributions, whereas you two are closer to your respective maximums.

So what’s this got to do with Australia?

Australia was a society settled from the dregs of British society. Not the absolute dregs, mind you – it didn’t take too much to get the gallows in those days, but mid-level crime like larceny or burglary might get you transported. But it’s fair to say that the convicts getting transported were likely below average for Britain at the time, like most convicts in most societies.

Suppose you take a cross-section of people from the lower end of the genetic distribution and put them in an environment with British laws and institutions. What happens next?

 The crucial part is that we’ve got people who are probably below their familial averages. But these cases get the benefit of mean reversion – if you’re dumber or more aggressively antisocial than your family average, your children will be on average smarter and less anti-social than you.

Run this forward a few generations, and you’re basically back to where you started. The convict starting point still lingers a little in terms of anti-authoritarian cultural attitudes, but that’s about it. You can take the dregs of society, but the next generation won’t be the same dregs. Thankfully. Mean reversion taketh away, but mean reversion giveth as well. So while the British who were sending convicts to Australia probably thought they were going to create a permanent colony of antisocial idiots, what they actually ended up creating was Britain #2, but with much better weather. The joke’s on them, really.

The practical punch line, of course, is that if you’re worried about how your children might turn out, pay close attention to the extended family, not just your partner. A son or daughter who’s not too bright but who has lots of doctors and lawyers and scientists in the family is still a pretty good bet.