Look up the word “fractal” in the Merriam-Webster Dictionary and you get the definition shown at right. Accurate, but not terribly enlightening. In more layman’s terms, think of fractals in this way: a fern frond is a long stem with lots of smaller “leaves” on it. The large frond is somewhat elliptical in shape, with the mid-section of the frond being much wider than the base or tip. Now, if we look even closer at the frond, we see that those small “leaves” that run along either side of the frond are, in essence, much smaller fronds. They look the same as the larger whole. This is one example of fractal geometry at play in nature. The small parts that make up the whole are the same shape and proportion as the whole itself.
How does this relate to sharks and other open-water predators? For many years, scientists have been trying to see whether such fractal geometry occurs in the actions of living organisms — the so-called Lévy-flight foraging hypothesis. This hypothesis suggests that a foraging pattern is composed of long trajectories, followed by short, random movements that when looked at on a large scale over time resemble the smaller patterns. Studies have been conducted on birds such as albatross, on deer and other foraging animals and have shown that such fractal patterns exist. Unfortunately, discrepancies in the data collection have cast much of this research into question. That is, until now.
In June 9th’s issue of Nature, Humphries et al. show that the Lévy-flights are adopted by fourteen separate fish species when food resources are scarce and irregularly dispersed. Rather than following a random Brownian movement pattern, when food resources were significantly reduced, the sharks and other fishes in the study resorted to following more deliberate search patterns. They would swim long distances in one direction, then stop and make a series of shorter, random movements looking for food. In areas where food resources were abundant, the fishes resorted back to the random Brownian movements.
The research, which you can read in full here, shows that environmental circumstances more than any other factor determine foraging behavior of these specific fish species. Further research will need to be conducted to see if these “animals evolved such that they exploit Lévy flights as an optimal search strategy for life in complex, highly changeable landscapes.”
For more on mathematics in nature, read Visionlearning’s Wave Mathematics module.
Written by Heather Falconer
Heather Falconer holds undergraduate degrees in Graphic Arts and Environmental Science, as well as an MFA in Writing and an MLitt in Literature. She is currently completing her PhD in Rhetoric and Composition, with an emphasis on rhetoric in/and/of science. Heather has worked internationally in academic publishing as both an author and editor, and has taught a wide range of topics from research writing to marine biology in the public and private educational sectors.