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Vision in the midwater of the open ocean requires animals to perform visual tasks quite unlike those of any other environment. These tasks consist of detecting small, low contrast objects and point sources against a relatively dim and uniform background. Deep-sea animals have evolved many extraordinary visual adaptations to perform these tasks. Linking eye anatomy to specific selective pressures, however, is challenging, not least because of the many difficulties of studying deep-sea animals. Computational modelling of vision, based on detailed morphological reconstructions of animal eyes, along with underwater optics, offers a chance to understand the specific visual capabilities of individual visual systems. Prior to the work presented here, comprehensive models for apposition compound eyes in the mesopelagic, the dominant eye form of crustaceans, were lacking. We adapted a model developed for single-lens eyes and used it to examine how different parameters affect the model's ability to detect point sources and extended objects. This new model also allowed us to examine spatial summation as a means to improve visual performance. Our results identify a trade-off between increased depth range over which eyes function effectively and increased distance at which extended objects can be detected. This trade-off is driven by the size of the ommatidial acceptance angle. We also show that if neighbouring ommatidia have overlapping receptive fields, spatial summation helps with all detection tasks, including the detection of bioluminescent point sources. By applying our model to the apposition compound eyes of Phronima, a mesopelagic hyperiid amphipod, we show that the specialisations of the large medial eyes of Phronima improve both the detection of point sources and of extended objects. The medial eyes outperformed the lateral eyes at every modelled detection task. We suggest that the small visual field size of Phronima's medial eyes and the strong asymmetry between the medial and lateral eyes reflect Phronima's need for effective vision across a large depth range and its habit of living inside a barrel. The barrel's narrow aperture limits the usefulness of a large visual field and has allowed a strong asymmetry between the medial and lateral eyes. The model provides a useful tool for future investigations into the visual abilities of apposition compound eyes in the deep sea.
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