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Ocellated lizard camouflage explained by a simple equation

The changing patterns of differently colored scales on a lizard’s skin can be modeled mathematically. A multidisciplinary research team did just that in an attempt to better understand the evolution of skin patterns. 

The researchers looked at the changing green and black patterns of the ocellated lizard. The experts found that the patterns may change but they always facilitate the lizard’s survival. 

“The ocellated lizard (Timon lepidus) exhibits an intricate skin color pattern made of monochromatic black and green skin scales, whose dynamics of color flipping are known to be well modeled by a stochastic cellular automaton,” wrote the study authors.

The scientists discovered that scales change depending on the color of nearby scales based on a mathematical rule. The ocellated lizard scales can be explained by the Lenz-Ising model, an important model in modern condensed matter physics.

This model was initially used to elucidate the behavior of magnetic particles, which could be in one of two states and interact only with their immediate neighbor.    

“The elegance of the Lenz-Ising model is that it describes these dynamics using a single equation with only two parameters: the energy of the aligned or misaligned neighbors, and the energy of an external magnetic field that tends to push all particles toward the +1 or -1 state,” explained Szabolcs Zakany, an expert in the Department of Genetics and Evolution at the University of Geneva.

The scientists adapted the Lenz-Ising model to the ocellated lizard. While it originally used a square lattice, this was modified to a rectangular lattice for lizards. The experts found that the favored pattern with ocellated lizards was a labyrinthine one rather than one of lines, spots, etc. 

“These labyrinthine patterns, which provides ocellated lizards with an optimal camouflage, have been selected in the course of evolution,” explained Michel Milinkovitch.

“These patterns are generated by a complex system, that yet can be simplified as a single equation, where what matters is not the precise location of the green and black scales, but the general appearance of the final patterns.”

The study is published in the journal Physical Review Letters

By Zach Fitzner, Staff Writer

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