Discussion and news about the modern effort to understand the nature of life on Earth, finding planets around other stars, and the search for life elsewhere in the universe

Monday, October 25, 2010

Scale-free mobility

Some ideas feel like an itch that you can't quite scratch because it's hard to pin down, but you really want to. A recent paper by Young et al. in Nature Physics (and available here), along with a commentary by Brockmann feels a little bit like that - at least when seen through the soupy goggles of astrobiology. On the surface this paper appears pretty innocent. It studies the nature of human mobility. With the rise of data-logging; from global positioning, cell-phone records, and the colossal airline databases of 3 billion annual travelers there is unprecedented material for studying exactly how we move around the planet. Not surprisingly we exhibit particular statistical patterns. For both distances traveled and 'rest times' (how long we linger over a cup of coffee or beneath the umbrella of some tropical beach) the distributions are inverse power laws. In plain language this means that we are more likely to travel short distances and to spend little time in any one place during travel.

There's nothing that sounds particularly revolutionary about that. But it gets more interesting. As Young et al. discuss, the particular shape of the statistics appears to be modeled rather well with a form of 'preferential return'. In other words although we may explore - making new journeys - we are more likely to travel to locations that we already know.  Not only that but the more locations that we already know the less likely we are to explore new ones at all. This naturally produces a so-called scale-free distribution - if you go out to any particular pub then there will be another pub that you are twice as likely to visit, and another one that is half as likely to have your patronage. The Young et al. model boils down to assigning a probability for any given 'step' in an individual's travels that results in exploration (a new location). They give this as the number of prior travel steps to the inverse-power of....0.2.

Why 0.2 ? Nobody knows, but this describes the way human populations explore the world - individuals will deviate from this pattern, but en-masse this is what we do. It's a deceptively simple, but extremely provocative result. Does this same kind of probabilistic scaling apply to other species? Do other species have a different power law value than 0.2? What are the implications for the occupation of niches by organisms on a planetary scale and throughout the history of life? This implicit tendency for exploration to slow down in favor of re-visiting known locations makes me wonder about a recent discovery on the global East-West divide in marine microbial genetics. While environmental differences are the most obvious root bio-physical cause (particularly the differing soluble phosphorus amounts in the Atlantic vs. Pacific oceans), does this give rise to a similar 'preferential return' scaling?

Then, to return to a popular theme - is there something to be learnt from this model for the questions of life exploring the cosmos beyond a planetary homeworld? On the face of it the more you explore the more likely you are to slow down and just keep circulating amongst the places you know. Clearly the present data represents humans who are not, we presume, exploring for survival or vital resources - lattes don't count. Nonetheless it is reasonable to hypothesize that humans behave this way because there is some circumstantial evolutionary advantage to it. The hard-to-pin-down-itch is that one suspects there is something deeper - perhaps universal -  in all this, waiting to be ferreted out.


MarkeD said...

Ever since reading "Linked" I'm in love with looking out for scale free applications, and this is another great example. It would make sense of course - my understanding is that any system which is growing (we travel more) and has preferential attachment (certain places are travelled to more than others) a system should display scale free properties - I'll be interested in seeing if there is any physical explanation to the exponent.

In astrobiology I imagine this could show some predictive properties - signs of life all seem to have some kind of scale free aspect to them - from enzymes in the brain to social behaviour.

Eniac said...

I think it is clear that the balance between running all over the place and staying put in one place is a parameter of individual psychology.

It is also quite apparent (although I would not bet my life on it) that the observed scaling law depends on this psychological parameter in aggregate (i.e, if we all had more Wanderlust, the exponent would be different).

Thus the specific value of this constant must come from evolution, representing an optimal behavior in terms of propagating the species (as you hypothesize). Like with most evolutionary balances, many factors should be involved. If there is universality, it is probably not very deep and fundamental, but rather a complex compromise between many different competing effects.

Caleb Scharf said...

I guess the question is whether or not the exponent measured for human activity is typical or atypical and whether or not there is some range of exponent values that all living organisms (from bacteria to whales) land in. I'd also imagine that there is a similar law (but what exponent?) for something like internet search - indeed, the Google algorithm (page rank) effectively incorporates preferential return.

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