Scientists tracking the flight of the bumblebee have been astonished by the power of the insects' tiny brains.

Let loose to find their way among five artificial flowers in a one kilometre-wide field, the bees quickly learned which routes were the most efficient.

In a surprisingly short time they drew up "flight plans" that allowed them to navigate around the flowers while using as little energy as possible.

"The speed at which they learn through trial and error is quite extraordinary for bumblebees, as this complex behaviour was thought to be one which only larger-brained animals were capable of," said lead scientist Professor Lars Chittka, from Queen Mary, University of London.

Tiny radar transponders mounted on the bees' backs were used to plot where the insects were flying.

The artificial flowers were fitted with motion-triggered webcams, as well as landing platforms containing a drop of sugar solution to simulate nectar.

To prompt the bumblebees to visit all five flowers, each sucrose drop was only big enough to fill one fifth of a bee's crop.

The flowers, arranged in a pentagon, were also far enough apart to be out of each other from a bee perspective.

"Using mathematical models, we dissected bees' learning process and identified how they may decipher this optimal solution without a map," said fellow Queen Mary's scientist Dr Mathieu Lihoreau, co-author of the study reported in the online journal Public Library of Science Biology.

"Initially, their routes were long and complex, revisiting empty flowers several times. But, as they gained experience, the bees gradually refined their routes through trial and error.

"Each time a bee tried a new route it increased its probability of re-using the new route if it was shorter than the shortest route it had tried before. Otherwise the new route was abandoned and another was tested.

"After an average of 26 times each bee went foraging, which meant they tried about 20 of the 120 possible routes, they were able to select the most efficient path to visit the flowers, without computing all the possibilities."

Previous research by the same group has shown how bees learn to navigate under laboratory conditions, but this was the first study observing such behaviour in a natural setting.

Prof Chittka said if a flower was removed, the bees continued to investigate the site where it had been for some time. "It seems bees don't easily forget a fruitful flower," he added.

The webcam recordings showed that the bees were highly individual, each favouring a different arrival and departure direction.

Professor Chris Rawlings, another member of the team from Rothamsted Research in Harpenden, Hertfordshire, said: "This is an exciting result because it shows that seemingly complex behaviours can be described by relatively simple rules which can be described mathematically.

"This means we can now use mathematics to inform us when bee behaviour might be affected by their environment and to assess, for example, the impact of changes in the landscape."