Biologists have long wondered how animals find food. In times of plenty, when food is easy to find, wandering around at random should do the trick. And indeed, there is plenty of evidence that Brownian-like motion can serve many creatures well.

But what happens when the food is distributed unpredictably? What strategy should an animal adopt to find more?

It turns out there is a mathematical answer to this problem. The most effective way to comb an area is to search it at random using jumps that vary in length according to a power law. This type of movement is called Levy flight and the idea that animals use this method to search for food is called the Levy flight foraging hypothesis.

In the last ten years or so, a great deal of evidence has come to light that animals do indeed use Levy flight patterns to hunt for food. Last year, one team tracked the movement 14 different species of open-ocean predatory fish such as sharks and tuna for over 5700 days using electronic tags. The result was a data set with over 12 million steps.

This team said their analysis of the data fits the foraging hypothesis well. So it looks as if these creatures do use Levy behaviour.

But today, Friedrich Lenz at Queen Mary University of London and a couple of friends say that many creatures are likely to behave in more complex ways, even if a mathematical analysis of their movements indicates that it is Levy-like.

To prove this idea, Lenz and co monitored the way that bees visited an array of artificial flowers doped with nectar. Sure enough, their foraging behaviour appeared Levy-like.

But when Lenz and co put toy spiders on some of the flowers to scare the bees away, the bees’ naturally began to avoid these predators. That changed the statistical pattern of the bee flights in important but subtle ways.

But here’s the thing: the foraging still obeys Levy-like behaviour. In other words, bees still make random jumps from one flower to another over distances that follow a power law. So their spatial behaviour is seemingly identical.

What changes, however, is their behaviour over time. In avoiding the predators, the bees make detours that change their time of flight. So an analysis of the directions they take over time shows all kinds of new correlations.

“This means that the bumblebees adjust their flight patterns spatially to the environment and temporally to the predation risk,” say Lenz and pals.

And that’s something that a standard spatial analysis would miss.

So the moral of their story is that biologists need to collect more data about the foraging behaviour over time and how it changes in response to environmental factors such as the presence of predators.

That may not take long. It may be that they already have this data and have simply not analysed it in a way that reveals predaotr avoiding patterns.

It’d be interesting to see whether the huge dataset on predatory fish contains the kind of detail that Lenz and co could use to spot these extra aspects of behaviour.

Clearly the statistical study of animal behaviour is at an early stage, given that it’s only recently become possible to collect the huge datasets necessary to make it possible.

But that also means there’ll be no shortage of data to play with in the very near future.

Ref: arxiv.org/abs/1108.1278: Spatio-Temporal Dynamics Of Bumblebees Foraging Under Predation Risk