Light levels are considered a major physical factor in the evolution of eye shape [29, 45–47]. Diel activity patterns are the main mechanism controlling ambient light levels of teleost reef fish. If light levels do indeed impact the evolution of eye morphology in reef fish, then nocturnal and diurnal species are expected to differ in eye size and shape. We also postulated that stabilizing selection for traits that improve light-sensitivity limits morphological and functional diversity in nocturnal species. Our results confirm all hypotheses, even though shape differences are more subtle than what is observed in terrestrial amniotes , which may be due to constraints of aquatic vision. The observed patterns for relative eye size and optical ratios indicate that differences between nocturnal and diurnal eye morphology become less pronounced for absolutely larger eyes. This may indicate that neural summation by pooling of photoreceptor signals becomes more important in larger eyes, where the negative effects of decreased acuity by summation could be at least partially mitigated by the increase of focal length with eye size.
The optical system of diurnal reef species, which are active in mostly bright light environments, is characterized by photopic image formation. Some diurnal fish on reefs may experience lower light levels depending on microhabitats that locally reduce light availability, such as crevices, reef overhangs, or other three-dimensionally complex reef structures. Light levels exponentially decrease with water depth, yet light levels equivalent to star-lit night conditions on land are not reached until a depth of approximately 600-700 m in clear ocean waters that characterize most coral reef environments . As far as currently known, none of the species in our dataset are active at such depths. Even if one assumes coastal visibility conditions for reefs, diurnal species do not experience the dim ambient light levels of their nocturnal counterparts during their diel activity period. Several species in our dataset are known to enter water with large amounts of suspended sediment and lower ambient light levels. One of these species, the mullet Mugil cephalus, appears to show characteristics of scotopic vision, but all in all it is diel activity pattern that defines the ambient light levels experienced by the species we sampled. Nocturnal fish need to rely on scotopic image formation and there is a clear perception of how the optical system of nocturnal species should be shaped in order to meet the requirements of scotopic vision .
Differences between nocturnal and diurnal eye size and morphology
Our results confirm the predictions from physiological optics. Nocturnal teleost reef fish have much larger eyes for given body mass than diurnal species, as shown by the regression of eye diameter on body mass (Figure 1a). On average, eye diameter of nocturnal species is about 1.4 times larger than that of diurnal reef teleosts for given body mass. We assessed differences in eye shape by means of morphological proxies of the optical ratio (Figures 2b-d) and also multivariate analyses (PCA, Figures 3a-c, and DA). The eyes of nocturnal reef teleosts differ from their diurnal counterparts in that they have relatively large lens diameters and large, rounded pupils. These characteristics should increase the amount of light transmitted compared to a smaller lens and smaller or asymmetric pupils. More light transmission should enhance the brightness of the retinal image, which will translate into better scotopic vision for a given retinal structure and neurological processing. Interestingly, the differences in relative eye size and eye shape fade to some degree for larger species. The negative allometry observed in the scaling of eye diameter with body mass is in the range previously reported for fish [18, 22, 49], although elasmobranchs seem to have much stronger negative allometry .
The characteristics of a nocturnal eye seem to be present in nocturnal species independent of phylogeny, indicating convergent morphological evolution. We sampled nocturnal species from 12 different families across Elopomorpha and the acanthomorph clades Holocentridae and Percomorpha, and most species show nocturnal characteristics. It is not clear at this point how many independent nocturnal lineages are included in our dataset, because the phylogenetic relationships of these clades are not well studied. In particular the phylogenetic relationships among families of acanthomorphs, a group containing more than 16, 000 extant species, is currently poorly understood  and is one of the most challenging problems in vertebrate phylogenetics. On the basis of the current understanding of teleost phylogeny [51–53] and a conservative approach, there are at least seven independent origins of nocturnality represented in the data. There is at least one origin of nocturnality within elopomorphs (Congridae, Muraenidae, Ophichthidae) and one within holocentrids. Within percomorphs, there are probably more than five independent origins: apogonids+pempherids (Apogonoidei) as possible sister group to the diurnal Gobioidei , one each within the largely diurnal Serranidae (e.g., Alphestes) and Tetraodontiformes (e.g., Diodon), and all other sampled nocturnal families, i.e., Priacanthidae, Haemulidae, Sciaenidae, Lutjanidae, which conservatively, even though unlikely, may represent a single nocturnal radiation.
The apparently constraining requirements on eye shape in nocturnal teleost reef fish are similar to what has been observed in terrestrial amniotes, where the strongest correlation between structure (OPT) and function (ocular image formation) is found at Pagel's λ of 0.01 . Pagel's λ is a measure of phylogenetic signal in the data, and a value of nearly zero indicates minimal phylogenetic signal . It is possible that the phylogenetic bias in eye morphology of teleosts is somewhat larger, yet this cannot be evaluated until a reasonably well-resolved and time-calibrated phylogeny at the species level is available.
Phylogenetic bias may be part of the reason why the differences between eye shape of nocturnal and diurnal teleost reef fish appear not as distinct as in terrestrial amniotes. For example, a comparison of DA results for the same measurements in each dataset (eye diameter, axial length, lens diameter) shows that the misclassified proportion tends to be larger within reef teleosts (10.94%) than in terrestrial amniotes (4.92%, regularized DA, spherical eyes, ). A phylogenetically-informed DA  can potentially improve correct classification.
It is also necessary to consider differences between vision in air and in water. The cornea does not function as a refractive surface in water, leaving the lens to provide all the light refraction required to focus the image in an aquatic eye [56–58]. Thus, the lens alone performs two main functions of the optical system. First, the lens focuses light onto the retina (assuming emmetropia) and sets the focal length. In terrestrial eyes both cornea and lens provide this function, and there is some variation in the proportional contributions to the total refractive power of the eye  that leaves opportunity for morphological diversity. This variation is absent in aquatic eyes, which are more or less built according to Matthiessen's ratio . In order to keep the eye and focal length at a reasonable size, the refractive power of the lens needs to be strong [16, 58]. The increase in refractive power can be realized by shortening the radius of curvature, resulting in a nearly spherical, small lens [58–60]. Second, lens diameter is correlated with pupil diameter, i.e., the aperture of the optical system, ensuring that most incoming light is focused onto the retina and does not cause any blur and scattering. The dual function may be an inherent structural limitation that renders further improvement of scotopic image formation difficult. For example, if an eye had a larger lens for a larger aperture, the larger radius of curvature of the lens would also increase focal length, provided everything else stayed the same. However, there is some indication that the eyes of nocturnal reef fish have shorter focal lengths , which may help to at least partially overcome the structural limitation of having only one refractive element. More data are needed to better understand potential differences between optical qualities of the lens of nocturnal and diurnal species.
Further research is also needed for an improved understanding of diel activity patterns in reef teleosts. There is a pronounced nocturnal-diurnal turnover at dusk and dawn among reef fish [5, 62, 63], but it is likely that a dichotomous split into nocturnal and diurnal species does not fully capture the complexity of temporal resource and habitat partitioning. Indeed, there is evidence that some reef teleosts may be active day and night, but current data are insufficient to have a clear understanding of possible cathemeral (day- and night-active) or crepuscular (twilight-active) behaviour. Furthermore, some species may display plasticity in their diel activity pattern . A third category as used in the analysis of terrestrial amniotes [27, 28] may further improve the delineation between groups. Some of the nocturnal and diurnal species that overlap in discriminant space may in fact be cathemeral or crepuscular species, which are expected to be intermediate in shape and light-gathering power. Clearly, more behavioural data are needed to further investigate diel activity patterns in reef fish.
The eye shape of some nocturnal species does not match the evolutionary response to scotopic vision seen in other reef fish, even though their nocturnal behaviour generally seems to be well supported. The pufferfish Diodon holocanthus is nocturnal as an adult, but settles from a planktonic mode of life at a standard length of 100-120 mm [personal communication, D.A. Bellwood]. As the three specimens of D. holocanthus that we sampled are all around 105 mm, we cannot fully exclude that there is an ontogenetic effect biasing the characterization of the ocular morphology of this species. In addition, some nocturnal species with ocular morphology not matched to scotopic vision may rely on non-visual senses (e.g., olfaction, lateral line system). Alternatively, they may solve the problem of vision at low light levels by modifications of parts of the visual system other than ocular morphology, e.g., at the level of the retina. It will be important in the future to expand this study to include additional features related to optical sensitivity, for example the diameter and length of photoreceptors [9, 37].
Morphological and functional diversity of nocturnal and diurnal eyes
One of the main objectives of this paper was to characterize the pattern of eye morphospace occupation. We chose the morphospace of the PCA performed on all five measured variables (PC 2-5), representing the most complete representation of eye shape. The results show convincingly that nocturnal species are restricted to a small area of morphospace compared to diurnal species. Functionally, the area of nocturnal species is related to improved scotopic image formation. Diurnal species, which are released from the physical limitations of scotopic vision, have a much wider morphospace occupation. Diurnal fish occur within the area of good scotopic vision, but also explore other parts of morphospace such as areas that are characterized by small pupil area for given eye size. Intriguingly, there is a trade-off between scotopic image formation and depth of focus, because a large pupil is positively correlated with light sensitivity yet negatively linked with depth of focus . In addition, some diurnal species have strongly elliptical pupils with often rostrally placed aphakic gaps, which supposedly enable them to focus on close objects in the anterior field of view, and may also allow for binocular vision . An ability to focus on close objects in the anterior field of view may be helpful to select benthic prey items. The presence of other adaptive peaks, in combination with the release from physical limitations of scotopic image formation results in a larger morphospace occupation of diurnal species compared to that of nocturnal species.
It is unlikely that this pattern of morphospace occupation is strongly influenced by phylogenetic bias. There are two possible phylogenetic mechanisms that would result in low variance in nocturnal taxa. First, if all nocturnal species were from a monophyletic clade they would be expected to be similar morphologically simply because of their shared evolutionary history. As explained earlier, we sampled at least seven independent origins of nocturnality, which should reduce this possible phylogenetic bias. Second, if all nocturnal radiations are very young compared to diurnal clades and one assumes a Brownian model of evolution, then the nocturnal clades are expected to have low variance, simply because they had less time to diversify [64, 65]. Time-calibrated phylogenies are not available yet and it is difficult to estimate the basal node ages of nocturnal and diurnal clades. However, the fossil record indicates that most nocturnal groups are of approximately the same age as diurnal groups, as many extant reef teleost families appear in the Eocene [19, 66]. The appearance of a large number of clades in a geologically brief time interval is congruent with the difficulty to resolve phylogenetic relationships of the percomorph "bush". We also attempted to sample widely within a given clade, both in terms of geographic provinces and known phylogenetic relationships, in order to avoid sampling a geologically young sub-clade. All in all, the phylogenetic influence on morphospace occupation should be small, and the low variance seen in the morphology of nocturnal reef fish seems to be the result of stringent functional requirements.
It will be an interesting avenue of future research to analyze how the eyes of mesopelagic (150-1,000 mm depth) fish have met the functional requirements of scotopic vision. For example, the presence of circumlental aphakic gaps in some deep-water species has been interpreted as a mechanism to improve sensitivity to point light sources like bioluminescent flashes [67, 68]. Warrant and Lockett  have suggested that there are two main eye shapes among these deep-water fish: the familiar ellipsoidal eye shape of shallow-water reef fish, and a tubular eye shape reminiscent of the eyes of owls and nocturnal primates, with large, spherical lenses, large pupils but small eye diameter for given axial length. Tubular eyes apparently represent a different solution to the problem of scotopic vision. Our data suggest that nocturnal reef teleosts have not followed these evolutionary pathways.