A model of depth-dependent responses from neural superposition in fly compound eyes

Fly compound eyes pool signals from photoreceptors that sample the same region of visual space through neural superposition in the lamina. The optical axes of photoreceptors projecting to a single lamina cartridge are not perfectly parallel, but instead converge at a point a few millimeters in front of the eye. At short viewing distances (1-10 mm) this leads to distance-dependent differences in receptive field overlap. We explored whether it was possible that flies could sense depth in this "personal space" purely from the geometry of neural superposition. To this end, we combined a computational model of fly eye optics with a disparity-tuned lamina model originally developed for stereoscopic prey capture in praying mantises, and simulated the responses of lamina monopolar cells to moving stimuli at different distances. Across variations in stimulus parameters and lamina models, we found that lamina neuron responses indeed contain a distance-dependent component, which can overall be summarised as an enhanced response due to temporally overlapping receptor responses at a critical distance of 3-4 mm, the convergence distance of photoreceptor axes. Depending on the lamina model and stimulus size, either response amplitude or onset gradient, or both, exhibited this peak. We further show that changes in eye size systematically shift this preferred distance, such that larger flies had a peak response at a greater distance. Our results demonstrate that lamina cell responses may contain a robust, geometry-derived component that is specific to object distance and invariant to other stimulus properties. This suggests that neural superposition, beyond improving sensitivity, may function analogously to a light-field camera system that is effectively "focused" on a behaviorally relevant distance. Author summaryIn this study, we explored how neural superposition in fly compound eyes may lead to an enhanced response to objects at a behaviorally relevant distance. The optical axis of neurally pooled photoreceptors, from neighbouring ommatidia, are not parallel, but converge at a point a few millimeters in front of the eye, which should lead to the strongest correlation of their signals at that distance. This idea was tested by combining a geometric model of the fly eye optics with a computational model of how the lamina cells process the responses of photoreceptors, and evaluating the output for a moving bright dot at different distances. We found that the simulated lamina cell has its fastest response, as measured by the onset gradient, to a stimulus at the distance where the photoreceptors converge (3-4 mm). This distance scales with the simulated eye size and corresponds to behaviorally relevant distances for fly behavior. This suggests that neural superposition may act to enhance the response to objects at a critical distance in the early visual processing of flies.