A simple developmental model recapitualtes complex insect wing veination patterns (A wingkle in time)*

Geometric patterns in nature have long been a matter of fascination and intrigue. Veins bifurcate insect wings into a diverse and complicated menagerie of shapes. For many insect species, even the left and right wings from the same individual have veins with unique topological arrangements, and little is known about how these patterns form. We present a quantitative study of the fingerprint-like “secondary veins.” We compile a dataset of wings from 232 species and 17 families from the order Odonata (dragonflies and damselflies), a group with particularly elaborate vein patterns. We characterize the geometric arrangements of veins and develop a simple model of secondary vein patterning. Last, we show that our model is capable of recapitulating the vein geometries of species from other, distantly related winged insect clades.