There’s a particular type of lizard that changes the color of its spots as it ages — and researchers have just discovered the mathematical rules that govern this peculiar metamorphosis.
Meet the ocellated lizard, a 30-to-35-inch reptile that lives in Europe. These lizards are born with unimpressive brown and white polka dots. But as they grow, they develop this beautiful, labyrinthine green-and-black pattern across their bodies. We don’t know exactly why this happens, but now, we know a little more about how. The lizard scales might be changing according to a particular mathematical model, reports a study published this week in Nature. The weird thing is, this model is somewhat different from the one that scientists have long believed to determine how animals get dots and stripes.
In fact, one overarching theory of how biological patterns form comes from an unlikely place: codebreaker Alan Turing. About 65 years ago, he proposed that stripes, spots, and even appendages like fingers may emerge from a series of chemical interactions between two hypothetical substances: an activator and an inhibitor. As both substances spread across a canvas like an animal’s skin at different paces, they compete with one another to give rise to patterns.
Watch this MinuteEarth video for an explanation of Turing’s model:
Scientists are still figuring out which specific dots and stripes develop from a Turing mechanism, and what the actual activators and inhibitors are in living creatures. But evolutionary biologist Michel Milinkovitch wanted to see if Turing’s model also applied to how ocellated lizards change the color of their scales.
Milinkovitch’s lab is interested in beauty and the rules that control it, he says. So he and his colleagues took 3D scans of three ocellated lizards over three years, starting when they first hatched, to track how their colors changed over the years. They discovered something peculiar: the scales continued to flip from green to black, or black to green, depending on the color of their neighbors. Generally the green scales were surrounded by four black and two green scales, while the black scales were surrounded by three black and three green scales. (The researchers ignored the lizard’s belly scales and the blue spots for this analysis.)
That reminded Milinkovitch of a mathematical model developed by John von Neumann in the 1940s, called a cellular automaton. This computing model is basically a grid of connected units, and the state of each unit is governed by the state of its neighbors. (This is fairly easy to understand if you play with a simulation, and sort of difficult to explain with words, so click this link to play with the most famous cellular automaton ever, Conway’s The Game of Life.) Milinkovitch wondered if this mathematical model could be showing up in a living creature: “What if each scale is changing color as a function of the state of its neighbor?”
When he and his colleagues crunched the numbers, he turned out to be right. “Each scale senses the color of its neighbors and then takes a decision on the basis of its neighborhood,” he says. Milinkovitch is still narrowing down exactly what biological signals govern this.
The Turing mechanism doesn’t get completely lost, however. In fact, when Milinkovitch and his colleagues tweaked their model to incorporate the thickness of the scales, and the thinness of the skin between them, suddenly Turing’s model worked: basically, with the right parameters, Turing’s model could create von Neumann’s cellular automaton — on a living creature’s skin.
This study reveals that “a cellular automaton is not just an abstract concept, but corresponds to a process generated by biological evolution,” Leah Edelstein-Keshet, a mathematician at the University of British Columbia, writes in a commentary published alongside Milinkovitch’s paper. So, why does that matter? “We just want to understand better the universe,” Milinkovitch says. “And in this case, our universe is this beautiful lizard.”