A simple, decades-old mathematical model developed by Alan Turing can predict how subtle colour patterns will develop in a lizard鈥檚 scaly skin.
Over seventy years ago, the computer scientist Alan Turing proposed a model for how a bunch of identical cells in a developing animal would come to form intricate colour patterns on its skin.
Historically, many biologists dismissed his model as too simple to capture all the intricate biological processes involved in such development. But at the University of Geneva in Switzerland and his colleagues have found that it does have predictive power when applied to ocellated lizards (Timon lepidus).
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Ocellated lizards have either green or black scales. 快猫短视频s can use mathematical equations in Turing鈥檚 model to predict how the cells within these scales affect their colour 鈥� and other scales鈥� colours 鈥� through chemical reactions. The researchers solved the equations on a computer.
They had previously used a similar approach to reveal that whether or not a scale changes colour as a lizard matures depends neighbouring scales鈥� hues. But using Turing鈥檚 calculations, they showed that the precise shade of green a scale develops also correlates with the colours of the neighbouring scales. For instance, a green scale with six green neighbours has decreased blackness and increased greenness compared to a green scale with only two green neighbours, which would have a colour closer to black.
These colour variations are so subtle that they are invisible to the naked eye. But Milinkovitch and his team could detect them with a camera that captures a very large number of shades. The researchers noticed that the predicted colour variation also corresponded to the actual pigment distribution in scales that they examined surgically.
鈥淲e have looked at these lizards for years and years and years. And we鈥檇 always say, 鈥楾hey have green and black scales鈥�, but actually we should have been talking about different levels of green,鈥� says Milinkovitch.
at Durham University in the UK says that Turing himself wrote about the model being an idealisation which does not account for all biological details, like the 鈥渉orrendous complexity of genetic signalling鈥�. So it is striking that the new calculations predicted patterns correlating to those seen in the actual lizard scales. He says the model could be made even less of a 鈥渢oy鈥� by adding some rules for how the cells in the scales interact with one another mechanically and not just chemically.
Milinkovitch says that Turing also discussed this as an important factor for pattern formation in animals, but his calculations were stymied by the lack of computing power at the time. Not hindered by such constraints, Milinkovitch鈥檚 team is already working on adding cell mechanics to their model.
Physical Review X
