Mathematical predictability may explain why some animals – like tigers or zebras – have vertical stripes.
In the study – published in the journal Cell Systems – researchers analyse the reason why the stripes of different species form the patterns they do. A possible explanation has to do with what substance is generated while the baby animal is still in the womb.
The new research is based on previous studies conducted by the famous British pioneering computer scientist and mathematician Alan Turing, who also had an interest in mathematical biology.
One of Dr. Turing’s theories states that zebra stripes grow in a certain direction due to an unstable diffusion that takes place during a chemical reaction.
Although the Turing model has a mathematical explanation for different patterns, it does not explain why some animals have horizontal stripes (okapis) and others have vertical stripes (tigers). Researchers now want to answer that exact question in the new research.
Tom Hiscock, lead author of the study and a PhD student at Harvard Medical School, said that they needed a simple model to include all of those various explanations. They looked into mechanical, molecular, and cellular hypotheses to see what causes living creatures to orient their stripes in a specific way, Hiscock added.
For the study, the researchers developed a model that analysed all the physical changes that lead to stripe orientation. These included: parameter gradient, a substance that modifies the parameters of stripe development; production gradient, a substance that increases the density of stripe pattern; and different changes that have to do with the mechanical, cellular, and molecular origin of stripes.
The new model is based on a simple equation that has also been previously used to analyse stripe formation. Local pattern density and the idea that the patterns recur over a larger area is what the question rests on.
According to Hiscock, this mathematical equation describes what happens in stripe formation. The model successfully predicted more complex patterns, but was not reliable for models with a lot of instabilities.
Previous research suggested that zebras have developed their stripes as a defence mechanism against flies. Now the study from Hiscock offers an explanation as to why that happens.
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