On anxious tits...

Of all the sciences, biology and mathematics appear at first sight to be the most unconnected. But even though theoretical biologists are more involved with mathematics and computer programs than with plants and animals, they are still real biologists...

Theoretical biologists try to find the answers to questions to which the solutions cannot be found in nature. For example, theoretical biologists at the University of Groningen tried to find out why animals can have different personalities. Research in the field has revealed that individual animals display behavioural differences. In the laboratory in Groningen they divided their study population of great tits into two categories: the cautious and the reckless. Although this study is interesting enough in itself, to understand why the tits have different personalities you have go further than merely observing the behaviour of a few individuals.

When the theoretical biologists studied the tits’ personalities, they discovered that a group of tits has the greatest chance of survival when different personalities are present. The reason is that different personalities can be advantageous in different situations, and so the group as a whole is the most resilient when more personality types are represented.

The combination of biology and mathematics has its origins back at the beginning of the last century. Having captured various physical phenomena in a number of general laws of science, it was thought that such formulas could also be applied to biology.

And so in 1927 the mathematicians Alfred J. Lotka and Vito Volterra developed a formula to account for peaks and dips in species populations throughout the course of a year. They divided the animal kingdom into plant eaters and meat eaters, and made the assumption that the number of plant eaters could increase without restriction. However, they asserted, if the numbers of plant eaters increased the meat eaters must increase as well. If the meat eaters increase, more plant eaters will be eaten, and so the numbers of plant eaters will decrease. From this point onwards the meat eaters gradually begin to die out of starvation. This allows the plant-eater populations to increase and so the whole cycle begins anew.

Although Lotka and Volterra’s formula (better known as the Lotka-Volterra model) sounds theoretically plausible, it proved difficult to apply in practice. Even the best known study that was supposed to prove the model turned out to be flawed.

In this study dating from 1937, a Canadian researcher compared the numbers of poached hare and lynx pelts that were traded. In these numbers he saw the same fluctuations as in the Lotka-Volterra model. However, upon closer examination it turned out that the meat eaters (the lynxes) sometimes increased in numbers earlier than the hares did. But how could this be if the lynxes were dependent on the hares for food? The reason why the data did not add up was simple: the pelts were obtained from two different regions in Canada. The lynxes were mistakenly deemed to be dependent on a population of hares in a completely different part of the country.

This example teaches us that not every plausible-sounding model is reliable. That’s why model builders these days test their work thoroughly, modify their methods if necessary, and test again.

Despite the above, we used the Lotka-Volterra model for our Deer Hunter game. A more complex and realistic model would have been too difficult for the player to influence, and that would have spoiled all the fun!

Links

• Kennislink: ‘Model predicts stability of ecosystem’
• Theoretical Biology research group
• Centre for Ecological and Evolutionary Study
• Biodiversity in the Netherlands
• Biodiversity theory

Acknowledgements

Special thanks to: Ynze van der Spek, Arjen Pilon, Elske van der Vaart and Prof. Franjo Weissing. Please contact Science LinX if you should have been included in the acknowledgements.

Author

Arjen Pilon