Thursday, February 28, 2008

Levy Walks in the Ocean

A paper published this week in Nature about Levy Walks among marine predators.

Reference info, title, and abstract follow:


Nature 451, 1098-1102 (28 February 2008) | doi:10.1038/nature06518; Received 17 October 2007; Accepted 29 November 2007

Scaling laws of marine predator search behaviour

David W. Sims, Emily J. Southall, Nicolas E. Humphries, Graeme C. Hays, Corey J. A. Bradshaw, Jonathan W. Pitchford, Alex James, Mohammed Z. Ahmed, Andrew S. Brierley, Mark A. Hindell, David Morritt, Michael K. Musyl, David Righton, Emily L. C. Shepard, Victoria J. Wearmouth, Rory P. Wilson, Matthew J. Witt & Julian D. Metcalfe

Many free-ranging predators have to make foraging decisions with little, if any, knowledge of present resource distribution and availability1. The optimal search strategy they should use to maximize encounter rates with prey in heterogeneous natural environments remains a largely unresolved issue in ecology1, 2, 3. Lévy walks4 are specialized random walks giving rise to fractal movement trajectories that may represent an optimal solution for searching complex landscapes5. However, the adaptive significance of this putative strategy in response to natural prey distributions remains untested6, 7. Here we analyse over a million movement displacements recorded from animal-attached electronic tags to show that diverse marine predators—sharks, bony fishes, sea turtles and penguins—exhibit Lévy-walk-like behaviour close to a theoretical optimum2. Prey density distributions also display Lévy-like fractal patterns, suggesting response movements by predators to prey distributions. Simulations show that predators have higher encounter rates when adopting Lévy-type foraging in natural-like prey fields compared with purely random landscapes. This is consistent with the hypothesis that observed search patterns are adapted to observed statistical patterns of the landscape. This may explain why Lévy-like behaviour seems to be widespread among diverse organisms3, from microbes8 to humans9, as a 'rule' that evolved in response to patchy resource distributions.


So there has been a lot of attention to this Levy Walk stuff in recent years. Do animal movements form power law distributions in terms of the length of each 'flight' they take? If you track an animal as it moves, it goes in a straight line for a while and then turns. These straight line lengths between turns are called paths or flights. A Levy Flight distribution is one where the histogram of these flights has a really long tail toward long flights and the probability of finding a flight of any given length is a power law distribution with an exponent between about 1 and 3 (around 2 being typical). This means there are a lot of small lengths and a few really long ones and that as length increases by some factor the probability decreases by a constant factor (the exponent). Some folks think the importance of these Levy Flights is way overblown and some people think its a big deal. If its a big deal its because we are learning something fundamental about how foraging behavior is organized and presumably how that organization reflects something about the underlying ecology or prey distribution. Are these things adaptive? To get a visual, imagine taking 'flights' while foraging that were all the same length. You might deplete all the resources in your immediate surroundings efficiently but what happens when you have to move a long way? So lots of small steps and a few long ones might be the way to go to efficiently search in your foraging habitat - and that is more or less what the Levy Flight is about.

Here they argue that Levy Flights are optimal foraging strategies that reflect the underlying distribution of prey. Hopefully we'll know more about the mechanistic links between path length distributions and prey distributions in the future. Also note that the book on Foraging that I have been blogging about does not cover this new work on Levy Flights even though this would certainly be a hot topic to some. Of course I don't blame the editors of the book as you can't fit in everything.

Anyway, its an interesting paper that is worth checking out.


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