Master Naturalists: Taking a Levy walk to find cheese

Whether it's a bee, a coyote, a hummingbird, a teenager in a mall or a guy in a hardware store, each hunts, searching for prey. If they know where prey is, each will go there straightaway.

It's a species survival skill called efficient foraging or getting a high return for low energy use. Bees even share where food is, dancing for other workers, indicating direction and how far to fly for known nectar and pollen.

What is an efficient foraging strategy if food can be pretty much anywhere and is plentiful? Randomly moving about will get to the cheese. Physics has a name for this. It's called Brownian movement.

It describes how dust motes move around in a liquid or dissolving sugar molecules disperse in water. Biologists once thought this was how predators hunted.

When food is scarce and found in clumps - think about patches of flowers in a field - how does the first bee find the flowers? How does the first teenager find its prey - a new shoe style in a mall?

In 1982, at Yale University, Benoit Mandelbrot described another movement pattern he named Levy flight or walk. Biologists in the 1990s identified it as the efficient foraging model for scarce food.

They argued that predators hunt in a straight line for a considerable distance then stop and do intensive searching for prey, making random sharp turns and moving short distances before turning again. If they are unsuccessful, they will take another straight walk (or flight) followed by extensive random searching.

Without doing the math behind this - it's pretty hairy - it turns out that the Levy hypothesis works. Species survival favors animals that hunt this way. It is exhibited by all kinds of critters - from ants to sharks and even humans.

In October, the National Academy of Sciences of the United States of America published a study describing a tribe of African aboriginal hunter-gatherers tracked via GPS. Their hunters use a Levy walk strategy. Who else does?

At amusement parks like Disney World, watch first-timers enter then hunt for fun, excitement and food. They'll use Levy walk strategy.

Paul has been wondering, why do stores put merchandise where they do then reorganize the aisles and shelves for no apparent reason? And why do they move stuff around in the stores so often?

If he knows where the milk is, like a bee, he'll make a beeline to it then zip to the bananas if they are needed, too. Stores seem to place those oft-purchased items at the end of paths that take him by lots of other prey.

And, if they move stuff or add new items he wants, he goes into hunt mode - long, straight walks with potentially attractive prey along the path (prey that merchants hope he'll buy) - followed by intensive search for what he wanted to start with.

Do people doing store layouts/merchandising use knowledge of his innate tendency to Levy walk when shopping?

Our suspicion is that smart ones do. If we're like our aboriginal cousins, the store's expense of moving the cheese around may yield more profits.

Sources: Mandelbrot, Benoit B., The Fractal Geometry of Nature.

2013, Raichlen, David A., et. al., "Evidence of LEvy walk foraging patterns in human hunter-gatherers", Proceedings of the National Academy of Sciences of the USA (PNAS), doi:10.1073/pnas.1318616111.

2008, Reynolds, A. M., "Adaptive LEvy walks can outperform composite Brownian walks in non-destructive random searching scenarios", Physica A, Volume 388, Issue 5, p. 561-564.

1996, Viswanathan G. M, et. al., "LEvy flight search patterns of wandering albatrosses", Nature, 381, 413-415.

Paul and Mary Meredith are master naturalists. Contact them at