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. 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). 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.

中文翻译：

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鳞翅目证明了墨累定律与潮汐流循环系统的相关性


墨累定律描述了分叉管的分支结构，预测了许多羊膜动物和植物的血管形态。在这里，我们利用昆虫来探索墨累定律的普遍性，并评估其对鳞翅目（最多样化的昆虫目之一）翅膀脉络的预测能力。鳞翅目动物与墨累定律的普遍性特别相关，因为它们的翅脉具有潮汐或振荡的空气和血淋巴流动。我们检查了代表 667 种鳞翅目昆虫的 1000 多个翅膀。我们发现，直径大于约 50 微米的静脉符合默里定律，直径小于 50 微米的静脉随着变窄，越来越不可能符合默里定律。最有可能偏离墨累定律的微小静脉也最有可能萎缩，无论分支结构如何，这都会阻碍有效的液体输送。然而，许多类群的静脉继续向远端分支到它们萎缩的区域，并且这些在较大直径下也符合墨累定律（例如，Sesiidae）。这一发现表明，在较大的类群中遵循墨累定律可能反映了对结构支持和液体运输的要求，或者可能表明在蛹阶段（在静脉萎缩之前的翅膀发育期间），液体运输的选择压力比成虫更强阶段。我们的结果扩大了默里定律的分类范围，并更清楚地说明了体型的相关性。