The Mike Leigh mark-recapture experiment

While standing on the platform of King's Cross Underground station last week (Metropolitan/Circle/Hammersmith and City lines, westbound, since you ask). I spotted Mike Leigh, director of, among others, the films Naked and Secrets and Lies. This is the third time in about four or five years that I have spotted him about the centre of town — I saw him once at an exhibition at the Royal Academy (I can't remember if it was Japanese prints or Renaissance illuminated manuscripts), and once walking down Charing Cross Road.

Now, every Londoner likes talking about famous people they have spotted in the street, pub or wherever (I saw Björk in a restaurant once, and sat opposite David Byrne on the tube). But this set me thinking about something different. How often can I expect to bump into a randomly chosen Londoner? Do I pass the same people every couple of years or so, but don't know it because they're not famous?

This is a problem that ecologists encounter all the time. Perfect knowledge of wild animals and plants is impossible, so we need techniques to estimate things such as population size, movement patterns, and mortality rates. One way to do this is a technique called mark-recapture. You catch say, 1,000 monarch butterflies, or cod, or swallows, mark them, and set them free again. Later, you see how many of the marked ones you can catch again, when, where, what percentage they make up of the recaptured population and so on.

This is used to estimate, among other things, fishing mortality, and was used to demonstrate the action of natural selection acting on the peppered moth: moths were much more likely to be recaptured in their camouflaged environment. Census takers, epidemiologists and others use similar techniques to estimate the true sizes of the populations they are interested in.

But answering my question raises lots of questions about sampling strategy. Who you see depends on where you go, and when. If one commutes into the centre of town most everyone is aged 20-50. If you want to see the elderly or children, you need to go out in the day. If I drove to work every day and spent the weekend playing video games, or doing DIY, my chances of spotting Mike Leigh would be smaller. Although most Londoners probably pass down Charing Cross Road every so often. how often they do so will depend on where they live, income and occupation. So, unless we all start behaving in a standardized way, we will all have different bumping-into frequencies for different (fuzzy) categories of people.

To answer my question, though, Mike Leigh seems like a good bumping-into benchmark, and an ideal subject for mark and recapture. He is random yet recognizable. I am not stalking him. I do not know where he lives, and, apart from being in central London, little connects the three locations in which I have spotted him. Apart from liking Japanese prints (or was it Renaissance illuminated manuscripts?) I would guess that we have little in common. If I were clever at maths I would use the parameters of my encounter rate, movement patterns and the population size of London to draw a curve plotting the probability of seeing him against time. But I'm afraid this is quite beyond me. So as it is, if you're reading this, Mr Leigh, I'll see you in 2008.