Biting fly vision and zebra stripes

Abstract

The function of the zebra's striped coat has been debated since Darwin and Wallace. A growing body of comparative and experimental evidence supports the hypothesis that the stripes act primarily as a defence against visually orienting biting Diptera - in particular tabanids (horse flies), glossinids (tsetse flies) and culicids (mosquitoes). The mechanisms proposed for this protection range from polarotactic disruption and silhouette break-up to motion-based illusions arising in the Reichardt-type motion detectors of the insect visual system. In this work we focus on a complementary, purely optical mechanism: the Moir\'e interference that arises when a periodic striped stimulus is sampled by the periodic ommatidial lattice of an insect compound eye. We develop a linear, shift-invariant Fourier model of the diptera compound eye, parameterised from published optical data on diurnal Culicidae, and apply it to images of zebra coats observed at biologically relevant viewing. The model predicts that, in a band of approach distances of approximately 1-5 m, the interaction of the stripe pattern with ommatidial sampling generates parasitic spatial frequencies that are absent from the physical stimulus and that fall within the spatial-frequency window most relevant to host fixation and landing control. A post-retinal motion-detector stage demonstrates that these parasitic frequencies translate into spurious local motion vectors, consistent with the empirical observation that tabanid and glossinid flies fail to land cleanly on striped surfaces. Our results are therefore consistent with the biting-fly hypothesis of zebra striping.