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The delicate veins that adorn the wings of dragonflies and other insects are like fingerprints: each wing has a distinct pattern. A new study reveals that a randomized mathematical process can explain how some thin filaments, called secondary veins, form these complex patterns.
The insect wings consist of two types of veins, both of which provide structural support (SN: 6/24/17, p. 5). The primary veins, which tend to be long and relatively straight, are found in the same places on the wings of each member of a species. But the smaller secondary veins appear in slightly different places on each wing.
Together, these two types of veins cut the wing into a multitude of tiny pieces, such as stained glass fragments. Scientists characterized 468 wings of 232 species by calculating the area of each small section and quantifying whether it was circular or elongated.
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In a mathematical simulation, scientists recreated the shapes of the dragonfly wing sections formed by primary veins (black lines) and secondary veins (red). The shapes of the sections in a simulated wing (on the right) corresponded for the most part to a real one (on the left).
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A special series of steps recreated wing patterns, scientists report on September 17 Proceedings of the National Academy of Sciences. The team started by simulating a reduced kite in order to mimic the processes taking place during the development of the insect. First, the layout of the primary veins divided the wing into large areas. Then, the researchers randomly selected regularly spaced locations, called "inhibitory centers," in each wing region. In a real insect, these inhibitory centers could correspond to places where a chemical signal prevents the formation of veins.
The researchers then selected locations for the secondary veins via a mathematical mechanism called Voronoi tessellation. It cuts a region around each selected inhibitory center so that each point within a section is closer to its inhibitory center than any other. Finally, the wing develops, stretching the sections and making some areas more elongated.
Grow
A four-step process can explain the sections seen on the insect wings. 1. Primary veins divide sections of a wing into distinct regions (indicated by different colors). 2. Form "inhibition centers" regularly spaced (gray dots). 3. Secondary veins form around these centers. 4. The sections stretch as the wings grow.
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This technique produced simulated dragonfly wings with sections that corresponded most to the actual wings in terms of length and size. The technique has also worked for distant insects with wings of different shapes, such as grasshoppers.
Researchers do not make assumptions about a molecular mechanism that causes vein development, only showing that the mathematical procedure can replicate the models. Similar explanations based on mathematics have been postulated to explain how other patterns are formed in biology, from zebrafish stripes (SN: 22/02/14, p. 9) with lizard stains (SN: 5/13/17, p. 32).
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