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Model for studying nature’s patterns.

Model for studying nature’s patterns.

Wings are like fingerprints for many insect species, with no two patterns being the same. These insects, like many other organisms ranging from leopards to zebrafish, benefit from nature’s seemingly limitless ability to generate a wide range of shapes and patterns. However, how do these patterns emerge?

Harvard University researchers have created a model that can recreate the wing patterns of a large group of insects using only a few parameters, shedding light on how these complex patterns form.

“We have developed a simple model, with only a few assumptions about how wings grow, that can recapitulate patterns that look close to life-like and can do so for species that are distantly related to each other, from grasshoppers to dragonflies, damselflies and lacewings,” said Christopher Rycroft. “This model could be useful for studying the evolution of wing structure and other patterned shapes.”

While the shape and design of insect wings vary greatly between species, virtually all contain veins – thick, strut-like structures implanted on the wing surface. Some insects, like the well-known fruit fly, have only a few big main veins. The position and form of these veins are shared by the left and right wings of the same person, as well as between individuals of the same species.

Modeling the secondary veins of distantly related species. (A) The evolutionary relationships among the insects considered in this study. (B and C) The model applied to a (B) lacewing (order: Neuroptera) and (C) grasshopper (order: Orthoptera). Gray vein domains in B are bounded on all sides by primary wing veins; these are not simulated in the model.

Dragonflies, for example, have a complicated network of secondary veins that crisscross the whole wing, dividing it into hundreds or thousands of little, basic forms. The form and location of these secondary veins vary infinitely, resulting in unique patterns on each individual wing. Image © Pixabay

Researchers gathered specimens from Harvard entomology classes, images from 20th-century reference books, and data from existing entomological databases. The wings were then removed from the bodies and photographed to create 2D pictures. After compiling the information, the researchers distinguished, or segmented, each unique polygonal shape formed by crossing veins.

“We wanted to take this complex shape and turn it into something simpler so we could ask specific questions and compare its geometry across species,” said Jordan Hoffmann, co-author of the paper and Ph.D. candidate at SEAS. “We looked at the geometric properties of these individual shapes, which we called domains. We looked at how elongated each domain was, how many sides it had, how it touched its neighbors.”

Hoffmann and his colleagues discovered that the size of the domain and its circularity may explain a large portion of the variance in geometry. They also discovered that, while each wing’s pattern is unique, the distribution of domain shapes across families and species is surprisingly similar. They developed a simpler model for the formation of wing veins after they had a decent technique to assess the similarity of wings based on how these forms are spread across numerous species.

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According to the researchers, an unknown inhibitory signal diffuses from several signaling centers in the areas between the major veins. These inhibitory zones appear at random and oppose one another, preventing additional veins from developing in certain locations. Those zones may produce the intricate geometries of the wing when the veins developed around them as the wing expanded and stretched throughout development.

A simple developmental model recapitulates complex insect wing venation patterns, Jordan Hoffmann, Seth Donoughe, Kathy Li, Mary K. Salcedo, Chris H. Rycroft

Published: Oct 2018, Proceedings of the National Academy of Sciences
DOI: 10.1073/pnas.1721248115

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