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Using likelihood to test for Levy flight search patterns and for general power-law distributions in nature

Now where is that TV remote control? - under those magazines, behind the cushion, under my nose?! It's frustrating to waste time and effort searching for things, but sometimes it can be a matter of life and death. For air-sea rescue, every second counts. For animals, ineffective foraging for food leads to starvation and death. So what is the best way to search for things? Given the dire consequences of inefficient foraging, it is likely that the study of animal movements in their search for food will provide important clues.

A popular idea has been that animals forage in a random walk known as a Lévy flight. Mathematically, this is a sequence of movements of random length taken from a power law probability distribution, and an inverse square power law is thought to be optimal. In other words, this means that if we count up all the move lengths then for any length there are always four times more moves that are half as long and four times less moves that are twice as long. Numerous studies have counted up move lengths of various animal species and concluded that they do indeed obey a similar power law.

In this paper, Andy Edwards of the BAS Natural Complexity programme (but now at Fisheries and Oceans, Canada) has shown that Lévy flights might not be as common in animals as previously thought because the most common method used to test for a power law is flawed in several ways. Instead Edwards advocates an alternative method and, as an example, shows that this changes the conclusion that grey seal movements demonstrate Lévy flight behaviour.

Furthermore, the problem is not just confined to analysing Lévy flights but to power law investigations in general, ranging from other areas of ecology to physics or finance.

Find link to the full paper in the NERC Open Research Archive

Authors

Edwards, A. M., (2008)

Publication

Journal of Animal Ecology, doi: 10.1111/j.1365-2656.2008. 01428.x, 2008.