Monday, May 15, 2006

Hamilton's Rulers   posted by DavidB @ 5/15/2006 04:07:00 AM

In today's London Times Anjana Ahuja reports on a recent study by anthropologist Kathleen Heath on the bloodthirsty habits of the medieval English kings. (I think I've also seen this reported somewhere else, but I can't remember where.) The gist of it is that although they killed a lot of their relatives, it was consistent with their own genetic interests to do so: they never killed their own direct descendants, and their aggregate genetic relatedness to their victims was always much less than that of their direct descendants. So if by killing collateral relatives they protected themselves and their direct descendants they were promoting their own inclusive fitness.

Well, maybe. The problem is that genetic relatedness 'decays' so quickly with distance that you would have to kill an awful lot of distant relatives - e.g. five nephews or nine first-cousins - to outweigh the benefit of saving yourself or two offspring. So a monarch would have to be very bloodthirsty (or paranoid) indeed to fail the test. Interestingly, Heath suggests that the Ottoman Empire would show a similar result. If it does, I would be more impressed. If I recall correctly, the first act of every new Sultan was to have all his brothers strangled with a bowstring. These would usually be only half-brothers, so it would be necessary to kill at least five of them to break Hamilton's Rule, but on the other hand, there were so many concubines in the Seraglio that there might well be sufficient potential victims to put the hypothesis to a real test. [Added: having just written this, it strikes me that Sultans would also potentially have a very large number of offspring, so they would have to kill an even larger number of brothers to fail Heath's test.] [Added #2: but then again, if your brother becomes Sultan he also potentially has a large number of offspring, so his genetic value to you is proportionately greater. It all gets quite intricate...] [Added #3: the other report that I vaguely recalled was at Steve Sailer's blog. The study was also discussed at Razib's Science Blog. Returning to the point in Added #2, I think the (approximately) correct analysis is as follows. Suppose that a non-Sultan has on average A surviving offspring (where A is usually about 2). Suppose also that a Sultan who eliminates his rivals has A + K surviving offspring, where K is a substantial but not huge number (say around 20). Suppose finally that a Sultan has N half-brothers, all of whom have an equal chance 1/N of displacing him if he does not kill them first. The genetic value of a new Sultan to himself can be expressed as 1 x (A + K). The average genetic value to him of each of his half-brothers, if they are allowed to survive, can be expressed as 1/4 x [A + K/N]. The point of 'K/N' is that a brother who takes over as Sultan will have an extra K offspring, but each brother has only a 1/N chance of doing so. Given these assumptions, it will pay a new Sultan to kill his brothers unless N>X, where X = 4[(A + K)/(A + K/N). However, this is still only a superficial analysis. The Sultan would really need to know whether or not the custom of killing brothers will continue, as this affects the value to him of all his brothers. It is possible that there are two different Evolutionarily Stable Strategies: maybe if the custom of killing brothers is expected to continue, it pays the Sultan to kill his brothers no matter how many there are, whereas if the custom were likely to be abolished, it would pay him to let them live.]