Fig 1.
Scanning electron micrographs of hair-like structures on a Penthetria heteroptera wing.
(A) A side view of microtrichia. These microtrichia cover nearly the entire wing surface. (B) Each microtrichium displays three parallel grooves running along the length of the hair. Such grooves are hierarchical structures, which have been shown to enhance wetting abilities [13]. (C) A side view of setae, which run along the margin of the wings. (D) Each seta displays two sublevels in the structural hierarchy: cord-like structures that run along the length of the seta, and, superimposed on these cords, small grooves running at an angle to the cord.
Fig 2.
Microtrichia point predominantly upslope in sections of a male P. heteroptera wing.
(Top) Venation of a male P. heteroptera wing, based on Hardy [15], with dashed lines indicating the approximate location of cross-sections A-H shown below. The direction points proximally along the torsional axis. The wing lies in a plane formed by
and
. Microtrichial orientation is denoted by the vector
, whose angle relative to the
axis is given by ϕ. (A-H) The P. heteroptera wing forms a rugged surface characterized by peaks and valleys. In all sections, hairs point overall towards the nearest peak on the dorsal surface, or towards the peaks on the ventral surface if the wing were flipped upside down. The inset on the right of section F zooms in on the red rectangle to highlight this phenomenon, and shows upslope orientation on the dorsal surface away from the medial vein and reverse orientation on the ventral surface. The areas that are exceptions to the uphill-orientation bias are highlighted with solid black lines; ambiguous areas are highlighted with dashed black lines. The scale bar refers to cross-sections A-H.
Fig 3.
The functional rationale of upslope orientation.
A schematic rationalizing the function of upslope oriented hairs in keeping water raised above the surface of a corrugated wing. (A) A downslope orientation would allow deeper penetration of drops into grooves. With the interface pinning preferentially against the grain of the hairs, the drop would be difficult to remove in this configuration. (B) An upslope orientation reduces penetration of water drop into grooves between local maxima, easing the release of these drops from the wing.
Fig 4.
Optimization of weighting factors for the upslope bias (W1) and nearest-edge bias (W2).
Colours correspond to sum-squared-residuals (SSR, in degrees squared) of the predicted vs. observed microtrichia orientation for particular combinations of W1 and W2. The optimization procedure converges on a single optimum in W1 and W2 (marked with a white cross) indicating the minimum SSR between predicted and observed local microtrichial orientation.
Fig 5.
Modelled microtrichia orientation on the P. heteroptera wing.
Modelled local microtrichial orientation (blue arrows) qualitatively match the observed microtrichial orientation (black arrows). Microtrichia orientation was measured at random locations on the wing, chosen using a random number generator. Wing edges and ridge peaks are denoted with black and red lines, respectively. The regions bounded by the left and right green rectangles are examined in detail in Fig 6, and represent zones of robust and poor model agreement, respectively. The values of the three parameters used in the model, corresponding to the best agreement with observed orientations, are given at the top-left of the figure.
Fig 6.
Examples of both good agreement and problem areas for modelling microtrichia orientation.
(A) The model displays good qualitative agreement in most regions of the wing. In the region shown (leftmost green rectangle in Fig 5), the model correctly predicts hair divergence midway between two ridges, as well as convergence towards a ridge. Thus the model captures a high degree of local complexity with only three factors affecting orientation. (B) The model can generate artifacts near edges, when the edge-weighting term dominates the other terms in Eq (2). Shown is a portion of the anal region denoted by the rightmost green rectangle in Fig 5. The model predicts divergent orientation in this region, which was not observed. Also predicted is a bifurcating region that roughly follows a diagonal line, due to the sharp corner on the (offscreen) anal margin.
Fig 7.
Quantitative assessments of model agreement with observed orientations.
(A) Predicted vs. observed microtrichial orientation. Data points are scattered narrowly about a one-to-one line, exhibiting a coefficient of determination R2 = 0.64 and p = 0.001. ϕ is microtrichia orientation as defined in Fig 2. Error bars are twice the standard error of the mean orientation in each quadrat. (B) The median absolute difference between modelled and observed microtrichial orientation is 20°. The model predictions are never more than 46° different from observed values, and 75% of the model predictions display residuals less than 25° from observations. The red crosses denote two outlier data points farther than 1.5 times the interquartile range from the upper quartile.