Madrid, 28 (European Press)
The evolution of skin color patterns in the eyed lizard allows for many different locations of the green and black scales, but always results in an ideal survival pattern.
An interdisciplinary team from the University of Geneva (UNIGE) has demonstrated, thanks to a very simple mathematical equation, the complexity of the system that generates the maze patterns formed by the green or black scales in this species. Their results were published in the journal Physical Review Letters.
A complex system consists of several (sometimes only two) elements whose local interactions lead to global properties that are difficult to predict. The result of a complex system will not be the sum of these elements taken separately, since the interactions between them will generate unexpected behavior for the whole.
The group of Michael Milinkovic, Professor of the Department of Genetics and Evolution, and Stanislav Smirnov, Professor of the Department of Mathematics in the Faculty of Science at UNIGE, were interested in the complexity of the distribution of colored scales on the skin of ocular lizards.
The individual scales of the lizard (Timon lepidus) change color (from green to black and vice versa) throughout the animal’s life, gradually forming a complex labyrinth pattern as they reach adulthood.
UNIGE researchers had previously shown that labyrinths appear on the surface of the skin because the network of scales makes up the so-called “human cellular”. “This is a computer system invented in 1948 by the mathematician John von Neumann in which each element changes its state according to the state of the neighboring elements,” explains Stanislav Smirnov in a statement.
In the case of the lizard, the scales change their state – green or black – depending on the colors of their neighbors according to a precise mathematical rule. Milinkovitch showed that this cellular automation mechanism arises from the superposition of, on the one hand, the geometry of the skin (thicker within the scales and much thinner between the scales) and, on the other hand, from interactions between pigment cells. from the skin.
Szabolex Zacani, a theoretical physicist in Michael Milinkovic’s lab, collaborated with the two professors to determine whether this change in scale color might be subject to a simpler mathematical law. Therefore, researchers turned to the Lenz-Ising model developed in the 1920s to describe the behavior of magnetic particles that possess spontaneous magnetization. Particles can be in two different states (+1 or -1) and interact only with their first neighbours.
“The elegance of the Lenz-Ising model is that it describes these dynamics using a single equation with only two parameters: the energy of aligned or skewed neighbors, and the energy of the external magnetic field that tends to push all the particles toward a +1 or -1 state,” Zacani explains.
The three UNIGE scientists determined that this model could accurately describe the phenomenon of scale color change in the eye lizard. More precisely, they adapted the Lenz-Ising model, which is usually arranged in a square lattice, for the hexagonal lattice of skin scales.
At a given mean energy, the Lenz-Ising model favors the formation of all state configurations of magnetic particles corresponding to this same energy. In the case of the ringed lizard, the color change process favors the formation of all distributions of green and black scales that lead each time into a maze pattern (and not in lines, spots, circles, or areas of one color). …).
These labyrinth patterns, which provide lizards with optimal camouflage shape, were selected in the course of evolution. These patterns are generated by a complex system, which can still be simplified as a single equation, where it is not the exact location of the green and black scales, but the general appearance of the final patterns”, explains Michal Milinkovitch.
Each animal will have a different exact location of its green and black scales, but all of these alternate patterns will have a similar appearance (i.e. very similar ‘energy’ in the Lenz-Ising model) giving these different animals an equivalent chance of survival.
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