Figure 1

Modelling visual performance in relation to eye size. Calculations are made for a depth of 800 m in clear oceanic water where the lack of daylight makes visual performance independent of viewing direction. Performance is plotted against pupil diameter (approximately a third of the eye diameter). Calculations are made for detection of bioluminescent point sources (blue) and for extended luminous targets (red) of different sizes corresponding to prey animals, conspecifics and predators (sperm whales) [2]. For bioluminescent flash intensity (E) and nearest neighbour distance (x) we use the alternative values of Schmitz et al. [1]: E =10¹⁰ quanta/s, x = 55 cm. All calculations are made using the theory of Nilsson et al. [2], but for extended targets, the calculations were modified such that the number of point sources within the target pixel is calculated in 3 dimensions for the volume of water displaced by the moving target (a cylinder with target diameter and a length of 2.5 times that diameter). The density of luminous plankton (per unit volume) is 0.7/x³[3]. In the original calculations [1, 2], a 2-dimensional case was considered, where the density of luminous plankton in the target pixel was calculated as 1/4x²[4]. A. Performance plotted as maximum detection distance, revealing that objects the size of sperm whales can be detected at nearly 120 m distance, which is almost twice the maximum detection distance for any other visible objects. B. Performance plotted as the volume of water in which objects can be detected. Detection of sperm whales massively outperforms all other visual functions, and the slope of the predator curve indicates that it offers a superior return for increasing eye size throughout the unique size range of giant and colossal squid (yellow shading). Blue shading indicates the size range of eyes in other animals.