How Animals Got Their Spots and Stripes—According to Math
From the peacock tail and the eyespots of a butterfly, to the evolving camouflage of the chameleon, nature loves patterns
By Thomas Woolley, The Conversation US on October 4, 2017
The natural world presents a palette of beautiful complexity. From the peacock tail and the eyespots of a butterfly, to the evolving camouflage of the chameleon, nature loves patterns.
Biologists may be able to tell you why an animal has a certain pattern. For example, it may have evolved its skin pattern for mating purposes, as a warning sign, or for defence purposes. However, we are still in the dark when it comes to how the patterns are produced.
Although we currently lack the experimental insight, mathematicians have been playing around with pattern formation equations since 1952, when the great Alan Turing published the seminal paper, The Chemical Basis of Morphogenesis. In this paper, he presented a theory that said patterns could spontaneously appear using nothing more than a protein’s natural tendency to move randomly through tissue and interact with other cells and proteins.
The theory is incredibly counter-intuitive, and we can only wonder how Turing discovered it. Patterns, as Turing saw them, depend on two components: interacting agents and agent diffusion. Each component on its own does not create a pattern. In fact, diffusion is a well-known pattern destroyer: if you put milk in water (and don’t stir), the milk will diffuse—or spread—out across the cup. You don’t end up with spots, or stripes of milk. You just have a cup of uniform milky water.
Turing’s genius saw through this and he demonstrated that if you combine these two components in just the right way, diffusion could actually drive the system to form spots and stripes. This idea was so far ahead of its time that we are still working on unravelling its complexity 65 years later.
Light and dark
Unfortunately, biology refuses to be so simple. Diffusion assumes that the agents which create a pattern—for example, chemicals, proteins or cells—are dumb, in that they move around space randomly. However, in 2014, the experimental lab of Shigeru Kondo demonstrated that cells in particular are more cunning than we thought.
Kondo’s lab works on understanding the black and white stripes presented on zebrafish, a tropical freshwater fish, which is native to the Himalayan region. They discovered that zebrafish skin patterns are made up of a light type of cell (xanthophore) and a dark type of cell (melanophore) that interact with each other. Specifically, the light cells spread out tendrils to investigate their environment.