The wing pattern of Hydriomena Hübner, [1825] (Lepidoptera: Geometridae: Larentiinae) lacks a predictable relationship with venation

Lepidoptera demonstrate the relevance of Murray's Law to circulatory systems with tidal flow

BACKGROUND

Murray's Law, which describes the branching architecture of bifurcating tubes, predicts the morphology of vessels in many amniotes and plants. Here, we use insects to explore the universality of Murray's Law and to evaluate its predictive power for the wing venation of Lepidoptera, one of the most diverse insect orders. Lepidoptera are particularly relevant to the universality of Murray's Law because their wing veins have tidal, or oscillatory, flow of air and hemolymph. We examined over one thousand wings representing 667 species of Lepidoptera.

RESULTS

We found that veins with a diameter above approximately 50 microns conform to Murray's Law, with veins below 50 microns in diameter becoming less and less likely to conform to Murray's Law as they narrow. The minute veins that are most likely to deviate from Murray's Law are also the most likely to have atrophied, which prevents efficient fluid transport regardless of branching architecture. However, the veins of many taxa continue to branch distally to the areas where they atrophied, and these too conform to Murray's Law at larger diameters (e.g., Sesiidae).

CONCLUSIONS

This finding suggests that conformity to Murray's Law in larger taxa may reflect requirements for structural support as much as fluid transport, or may indicate that selective pressures for fluid transport are stronger during the pupal stage-during wing development prior to vein atrophy-than the adult stage. Our results increase the taxonomic scope of Murray's Law and provide greater clarity about the relevance of body size.

Symmetry systems on the wings of Dichromodes Guenée (Lepidoptera: Geometridae) are unconstrained by venation

The nymphalid groundplan, an idealized schematic illustrating the essential elements of butterfly wing patterns, predicts a consistent relationship between color pattern and wing venation. Moths in the family Geometridae have wing shapes and patterns that often resemble those of butterflies, and until recently, this family was believed to be among butterflies’ closest relatives. However, an examination of the geometrid genus Dichromodes Guenée, 1858 shows no consistent relationship between the central symmetry system and wing venation. Whereas the distal edge of the central symmetry system is predicted to reach the costal margin proximal to the Subcostal vein in butterflies and acronictine moths, it has no consistent relationship with the Subcostal, Radius, or Radial Sector 1 veins in Dichromodes. This finding highlights developmental diversity that was previously overlooked due to the overwhelming preference for butterflies in studies of lepidopteran wing patterns.