Monday, 31 March 2014

One in a billion

I've recently joined a history website about William Marshall - the knight and sometime Regent of England after the death of King John. But it does seem to have a lot of Americans on it who keep on telling me that they are related to William Marshall, often in the 30th generation or so. Here's the thing about geneology; I enjoy it, but I'm dubious about how much it actually means. I think a lot of people try to read things into it that aren't supportable, probably because they have no real grasp of statistics. The following is a genuine quote:

"Hey that's great - you know I feel a great affinity for your country because I am actually descended from King Henry II."

And this irritates me. I shouldn't let it irritate me, but it does. Now I know that we all like to look for things that make us special, and there's no shame in that. But unfortunately being descended from Henry II doesn't make you that special or unique. It's you and everyone else, buddy - that's just maths (or 'math', if you insist).

Look - if you go back 800 years, and you assume a spacing of 25 years on average per generation (we have kids later now, but they tended to have them much earlier as you go back), then you are talking about 32 generations that separate you from King Henry. That means that as well as Henry II, you have 2^32 other ancestors in that generation, and like the apocryphal Chinese emperor who offered the inventor of chess twice as many grains of rice per square as for the previous one, once you start doubling and redoubling, you soon discover that that is a very large number indeed. How large? Well it's 2.1 billion, actually. Yes, that's right, Henry II (or William Marshall, who was part of Henry's retinue at one stage) may well be one of your ancestors in that generation, but he is only one of 2.1 billion ancestors in that same generation who you also share *exactly* the same amount of DNA with. You are also descended from Jane Johnson the merchant's daughter and Wat the serf and probably Vladislav the stable boy and Aisha the slave girl. In fact there weren't even 2 billion humans alive then - the figure was more like 400 million, according to recent estimates, so in theory it's just about possible that you are related to everyone who was alive on planet Earth back then, but actually it almost certainly doesn't work like that. We didn't travel much before the modern era and it is mathematically more likely that you are related to the same person several times over via various different routes and chains of descent - you may well have 50 different chains of ancestry linking you to back Jane Johnson and a dozen to Wat, maybe 4 or 5 to Vladislav and 2 to Aisha (and one to Henry II), but none at all to Warragul the Aboriginal hunter, Ahuatl the Aztec stone cutter or Xie Ming the potter. But Royals being what they are, it is likely that over 90% of people of English descent can manage to find at least one line of ancestry from Henry II.

So what does it mean to say you are related to Henry II? If he is everyone's ancestor, then maybe you shouldn't feel too proprietorial about just one two billionth of your DNA that you share with tens or perhaps hundreds of millions of others - that's not even a single gene, it's not even a single base pair. You know the genetic code of thymine, guanine, adenine and cytosine amino acid bases which form the rungs of the DNA ladder? AGTTTGCACGAGTACA? It goes on for 3 billion letters in each of us - longer than 1,000 Bibles - and you might have shared just one of those letters with Henry II. OK, I admit that actually you'll share 99.9% of them as you're both human beings rather than dolphins, oak trees or bacteria, but those are the meaningless ones - you also share all of those 99.9% with Warragul, Ahuatl and Xie Ming as well, and about 50% of them with your chicken dinner, for that matter. Of the small proportion of base pairs that make up the full range of human diversity, you'll share at most one, but statistically you'll probably share no ancestral DNA at all with Henry. His contribution to your genetic makeup was most likely edited out somewhere in the intervening 800 years, replaced by a strain from Wat or Aisha, of whom you know (and presumably care) nothing.

So yes, geneology is fun, and yes, once you hit a noble or royal chain of descent then it becomes trivially easy to pursue that one particular chain because some herald has already done the work for you centuries ago, but just remember that chain is only one of hundreds of millions, and that the phrase; "I am descended from Henry II" has no real meaning. Once you get beyond 200-300 years you have so many ancestors (325,000 after 300 years) that pursuing any one particular chain is essentially meaningless other than as an academic exercise in how you came to inherit your surname. Unless you are Boris Johnson, you do not have the blood of kings flowing through your veins.