A Mathematical Model to Capture Complex Microstructure Orientation on Insect Wings

Microstructures on insect wings can promote directional drop shedding, and the local orientation of these structures is expected to facilitate drop removal. However, microstructures may exhibit very different orientations at different locations on the wing. Using the march fly Penthetria heteroptera, we propose that local orientation of small hairs (microtrichia) reflects a balance of three nonexclusive strategies: (1) preventing water from becoming stuck in intervenous grooves (microtrichia point upslope), (2) shedding water off the wing as readily as possible (microtrichia point towards the nearest edge), and, (3) shedding water away from the body (microtrichia point distally). We present evidence for all three and show that local microtrichial orientation is seldom determined by any one factor. We develop a mathematical model that employs factor-specific weighting values determined via optimization. Our predictions are tested against the orientation of microtrichia randomly sampled from a P. heteroptera specimen. Using the best-fit weighting parameters, the model displays a median residual of 20°; no residual is greater than 46°. The model also reproduces qualitative aspects of microtrichial orientation, such as bifurcation midway between veins and convergence toward peaks. This strong correspondence between modelled and observed orientation supports the role of microtrichia as directional antiwetting devices and highlights the importance of considering both function and wing geometry to explain the organization of natural microstructure arrays.

昆虫翅面的微结构可促进液滴定向脱落，而这类结构的局部朝向被认为有助于提升液滴移除效率。然而，翅面不同区域的微结构朝向往往存在显著差异。本研究以黑毛菌蚊（Penthetria heteroptera）为研究对象，提出其翅面小型刚毛——微毛（microtrichia）的局部朝向，实则是三种非排他性策略共同权衡的结果：（1）防止积水滞留在翅脉间凹槽内（微毛指向斜坡上方）；（2）尽可能高效地将液滴从翅面排离（微毛指向最近的翅缘）；（3）将液滴向远离虫体的方向排离（微毛指向远端）。我们为这三种策略均提供了实验证据，并证实局部微毛的朝向极少由单一因素决定。随后我们构建了数学模型，该模型通过优化过程确定各影响因子的专属权重值。我们将模型预测结果与从P. heteroptera标本中随机采样得到的微毛朝向数据进行比对验证。采用最优拟合权重参数时，模型的残差中位数为20°，最大残差未超过46°。此外，该模型还能复现微毛朝向的若干定性特征，例如翅脉间中点处的朝向分叉以及朝向翅脉峰点的汇聚趋势。模型预测与观测结果间的高度一致性，证实了微毛作为定向抗润湿结构的功能，并凸显了同时考量功能与翅面几何形态，以解析自然微结构阵列排布规律的重要性。