Doing the Levy walk

What's the best way to locate your next meal, if you can't see or smell it?

Animals throughout the world, including some human tribes, all use a similar foraging technique called the 'Lévy walk', which seems to be the best way to find a randomly scattered resource.

But when did this evolve? Well, for the first time evidence of this Lévy walk has been found in the fossil record, showing this technique is at least 50 million years old.

David Sims at the University of Southampton told Kat Arney more about how various animals walk the walk...

David - We carried out some research a few years ago on living animals, sharks and penguins, and tunas and found that they move, they search for resources, in a very characteristic way. So, we're interested to know, where did this pattern arise? Could it have arisen many millions of years ago? I teamed up with a palaeontologist called Richard Twichett and together, we searched for fossils to investigate it and we found some in northern Spain.

Kat - So, how on Earth do you tell from fossils that are in the rocks how they were moving?

David - The fossils themselves obviously are just the fossilised trail that the animal moved through. So in our case, we were looking at worm-like animals and sea urchins from the Eocene era; about 50 million years ago. And so, what's preserved is their movement trail. As they displaced sediment, you get this sort of trail etched. And so in our lab, we study the movement ecology of marine predators. We use statistical methods to extract patterns from electronic tag data. And so, what we did was use that technique and analyse the trail that was fossilised from these extinct animals.

Kat - So, tell me about what you found.  How were these prehistoric extinct animals wiggling about through the sand?

David - Well, we found that the animals wiggled about as you put it in different ways. Some of the worm-like animals moved around with what's called a self-avoiding random walk. So, they avoid their own path and move into areas that could be good for feeding opportunities. What we found from the worm-like animals is that they tended to do spirals. But the interesting thing was that for the extinct sea urchins, they had patterns of movement that were clustered across 3 or 4 different scales. So imagine in the context of humans, we exhibit a search in our office, but then we don't find it so we then exhibit a search in our institution or our house. And if we don't find it then, we then do a search let's say, in our town. So, at each scale, the pattern looked the same. And so, that's why it's interesting because that is what's called theoretically at least a Lévy walk.

Kat - And that's what sea creatures today are doing when they're searching for food too.

David - That's right, yes. We've shown previously a few years ago in a few papers in Nature and proceedings in the National Academy that birds like wondering albatrosses, basking sharks, big eye tunas, and penguins, all have movement patterns that are very well approximated by this optimal model, this Lévy walk. And of course, Lévy walks are interesting because we showed that animals, living animals were using them. That's interesting because the Lévy walk is a theoretically optimal pattern of movement if you want to find resources that are sparsely distributed. So, imagine that you don't know where the resources are and you don't have a good mental map of where to find things, you don't know your environment that well. And so, this would be the best pattern in which to move. In fact, there are humans that have been shown to demonstrate this pattern of movement as well. So, just recently, there was a study on hunter gatherers in Northern Tanzania and they also adopt this Lévy walk pattern of movement. So, it seems that this is - when you don't know where things are, a Lévy walk is a very good approximation to what you should do to find the resources quickly.

Kat - The way that humans find food, the way that albatrosses and penguins find food, and the way that these tiny marine creatures millions and millions of years ago are all doing it in the same way. That tells us that this is a very old way of looking for stuff, doesn't it?

David - That's right. The evidence is pointing towards it being a very old pattern. I mean obviously, we only looked - I say 'only - we only looked at animals 50 million years old. But in fact, some of the patterns we saw, I mean, we had one fossil from the cretaceous which was 70, 80 to 140 million years ago. So, it's put it back a bit further. So, it could be that if this pattern of movement, if that has some sort of intrinsic pattern, one which is sort of innate to the animal, then of course, that could mean that it has a very long origin.

Kat - So, if I'm looking for chocolates or my lost keys, I can thank hundreds of millions of years of evolution for helping me.

David - That's right, exactly. It's the best way of searching for something and we imagine that this is a problem that was solved many, many tens of millions, if not, hundreds of millions of years ago.