Portland, Oregon, is one of the places in the USA that takes great pride in its self-conscious kookiness -- you see bumper stickers saying 'Keep Portland Weird', just like you do in Asheville, North Carolina and Austin, Texas, and probably another dozen cities who, if they were people, would go around saying "I'm mad, me!"
I don't live near any of those liberal islands in seas of conservatism. Instead, I live up the road from the Isle of Portland, Dorset, which has bumper stickers saying 'I survived the ASDA traffic lights'.
Now, I'm not saying Portland, Dorset is weird. I wouldn't dream of casting such aspersions without bumper stickers to guide me. But they do have a severe phobia of the word 'rabbit1'. And -- according to comedian Mark Steele, in 1900, of the 6,000 people on the island, 90% of them shared ten surnames.
There ain't nothing wrong in that, I once played cricket against a village team that had a line-up of Cooper, Littlewood, Littlewood, Cooper, Littlewood, Cooper, Cooper, Littlewood, Littlewood, Littlewood, Littlewood, Muralitharam -- but I suspect one of the Littlewoods might have been a ringer). But it did get me thinking about something I wondered about when I was about 10: why do some names become really common and others die out?
Well, here's how I'd model it. I'm going to treat Portland as a closed system, with nobody ever leaving and nobody ever arriving, except for tourists and convicts. And I'm going to assume that, if you have a surname, you'll pass it on -- on average -- to one person in the next generation. Now, I know that's not precisely accurate: the women of Portland generally have their surnames subsumed into their husbands' -- but as a first stab, it's an ok model. In fact, I'm going to go further and say that the number of people in the next generation you pass your surname onto is going to be a Poisson distribution with a mean of one.
That makes modelling surnames quite easy, because Poisson distributions have a nice property: if you add them together, you get bigger Poisson distributions. So -- if you have 20 Littlewoods on the island in one generation, the number of Littlewoods in the next generation modelled by a Poisson distribution with a mean of 20. The one thing to be careful of: if a surname's population ever drops to zero, it dies out.
So, let's imagine we start with 10,000 people on the island, all of whom have different surnames. After the next generation, you'd expect to see about 3,700 of the surnames die out, 3,700 have a population of one, 1,800 have a population of two and the remaining 800 or so have more representatives.
After that, it gets more complicated! I'm doing this on a train and can't be bothered coding anything up -- I'll leave that as an exercise for the interested reader -- but you'll see that the number of surnames shrinks slightly each generation. I'd be interested to learn how many generations of isolation it'd take for 90% of the population to share 10 surnames... have at it!
* Edited 14/12/2103 for formatting.