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by Krešo Josic
Foraging






The world around is unpredictable. Will the markets go up or down tomorrow? Is there a hurricane in store for us this fall? 



We simply cannot answer these questions with any certainty. Yet we have evolved to navigate this sea of randomness in a structured way. This may seem like a contradiction: Randomness and structure seem fundamentally at odds. To explain what I mean, let us look at something that all animals do: foraging for food. 



Animals need to forage efficiently. An alligator is in trouble if the energy she spends hunting is greater than the energy her catch provides. When a predator senses its meal, it is clear what it needs to do -- pounce! But, what if prey is too distant to be sensed?

For instance, in the ocean schools of fish swim from place to place.  A shark is constantly on the move to find its prey. How should the shark move to maximize its chances of eating? If prey is abundant, changing directions frequently, and thoroughly exploring its neighborhood seems like a reasonable approach. 

But when prey is sparse spending too much time near one spot may be futile. The shark may be better off by occasionally taking a long swim and trying its luck at another, distant spot. Physicists have shown that these are precisely the foraging patterns that work best: When there’s a lot of fish around, a shark should move around and change direction frequently. On the other hand, when fish are sparse, a shark should still look around, but it should also occasionally take a long trip in a fixed direction, something we call a Levy flight.


Levy Flight Example
Yet, there is no guarantee that animals will care for such reasoning. Or perhaps the assumptions that lead to such mathematically elegant solutions do not reflect the real world. It was therefore satisfying when a series of studies over the last 15 years has found evidence that different animals behave as theory predicts.  In the most recent study, scientists have attached tracking devices to sharks and tuna. These fish indeed seemed to engage in Levy flights in deeper waters where prey was scarcer.

Recently a similar study was performed on humans. Data from mobile phones was used to analyze the structure of our own movements.  We drive to work and to the grocery store, and frequently mill around our neighborhood. Somewhat less frequently, we take a plane to visit a relative in Boston. Our movements are far from random: we revisit a few spots very frequently and regularly. However when we account for this, our motion is still akin to that of sharks when prey is sparse: We engage in Levy flights.

These observations are not free of controversy. Levy flights are, by definition, rare. It is exactly because they are rare that they’re hard to study. Characterizing stock market crashes and earthquakes is similarly difficult, and leads to similar controversies. While the latest studies of animal foraging used millions of data points recorded from thousands of animals, some scientists are still not convinced.

The structures behind the movements of animals and humans only become apparent after vast amounts of data are collected and analyzed. The sensors and computers that make this possible have been available for no more than several decades. And these tools are only useful in the hands of operators
An Osprey Hunting
who understand mathematics and statistics. When they’re used properly they let us see the world in a new light: Yes, the world around us is random. But the randomness around us is structured. Understanding the patterns behind this randomness and the rules that govern them will drive scientific discoveries for decades to come.

So consider this, there was a time when the orderliness of crystals was no more within our comprehension than the foraging of predators. John Lienhard will ask us to look next at our struggle to understand the seemingly “transparent” crystal. 





Sources:

Here is a short account of the issue:
http://www.sciencenews.org/view/generic/id/60106/title/Sharks_use_math_to_hunt
see also            http://physicsworld.com/cws/article/news/42899

A review of the wandering albatross is here:
http://polymer.bu.edu/hes/articles/rp-peterson96albatross.pdf

The original analysis of data suggesting that albatross foraging follows a power law was called into question by the same team that originally found it:
http://www.sciencedaily.com/releases/2007/10/071024130445.htm

It has still not be conclusively shown that animals exhibit Levy flights. For a nice review you can look at the following article: Mark Buchanan, Ecological modeling: the mathematical mirror to animal nature. Nature vol. 453 (7196) pp. 714-6 (2008).

Here is a short press release on the structure of human mobility:
http://www.newswise.com/articles/view/541452/



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