Deep Sea Math Hunting

Every now and then an article pops up which highlights a link between mathematics and the animal kingdom, and I've been able to discuss several such links on this blog.  The latest entry into this category concerns the movement of sharks (and other ocean creatures) as they hunt for food.  A recent article in Nature has spawned a great deal of interest, and the topic has been discussed on the websites of Wired, Discovery, and Physics World.

What does the motion of sharks have to do with mathematics?  Well, suppose you are a shark.  Unfortunately, there are not yet any In-N-Out's under water, so when it comes to food you are on your own.  What would be the best way to forage for your food?  With your heightened senses, you would undoubtedly be a formidable opponent in an area rich with prey, but what if you are in a more sparsely populated area?  What's the best way for you to search for nutrition?  As it turns out, the best thing for you to do may be to follow a type of random motion known as a Lévy flight.

The following is from the aforementioned Wired article: "Computer models suggest Lévy flight is the optimal search pattern for predators in low-prey areas, and maximizes the chance of a random encounter."  Visually speaking, a Lévy flight is characterized by short movements in random directions, interspersed with occasional longer trips in a particular direction.  Here is a sample from the Wikipedia article on the subject:

I bet little kids are awesome at drawing Lévy flights.

Suggestions of Lévy flight patterns in animals goes back to at least 1996, but a recent study led by David Sims of the Marine Biological Association Laboratory is the first to reach these conclusions on the basis of such a vast amount of data.  Indeed, by tagging marine animals with GPS locators, they were able to track the movement of 14 different predator species over a period of 5,700 days!  With some rare exceptions (such as the great white shark), they found that animals in areas with less food were more likely to move in a Lévy flight pattern.

Several articles (jokingly, I assume) point out that this should make us even warier of sharks, since they can use math to optimize their behavior.  As is often the case with these articles, the headline rarely reflects the reality.  Whether this behavior is learned or evolved, the fact that sharks may follow this pattern says as much about their mathematical ability as the resemblance of trees to fractal patterns says about their mathematical ability.  Mathematics is a language that we can use to describe nature, so the fact that we can use mathematics to describe this natural phenomenon shouldn't necessarily be that surprising.  If a shark gets a 5 on the calculus AP, that's when I'll be surprised.

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