Classification of diel activity patterns
We distinguished between two main diel activity patterns: nocturnal (night-active) and diurnal (day-active). We classified all fish that are mainly active at night as nocturnal, and all fish with main activity during the day as diurnal, on the basis of literature surveys [1, 3–6, 14, 30–33] and personal observations (P.C. Wainwright). A finer distinction of diel activity patterns is currently impossible because of the lack of more quantitative behavioural data for most reef fishes (although see [14] and [34] for examples). There is some indication that some fish species, in particular within Serranidae, Scorpaenidae, and Haemulidae, are active both day and night (cathemeral), or twilight-active (crepuscular). As the evidence for this is often anecdotal we refrain from a formal classification for the purpose of this analysis until more data are available.
Specimens, measurements, and procedures
We sampled 265 species of teleost reef fish in 43 families with a total number of 849 specimens (1-30 individuals per species) for eye morphometrics (Additional file 1). Most species in our sample are mainly reef inhabitants and live in clear marine environments, but a few species also enter murkier brackish and muddy coastal waters, e.g., the silverside Atherinomorus stipes, the mojarra Gerres cinereus, the haemulids Plectorhinchus chaetodonoides and Orthopristis chrysoptera, the kyphosid Microcanthus strigatus, and the mullet Mugil cephalus. The size range across individuals was 44-638 mm standard length. We sampled adults whenever possible, but some specimens were relatively small juveniles. There were 211 diurnal species in the dataset, and 54 nocturnal species. The nocturnal species are from the following 12 families: Apogonidae (9 species), Congridae (1), Diodontidae (1), Haemulidae (13), Holocentridae (10), Lutjanidae (5), Muraenidae (7), Ophichthidae (2), Pempheridae (1), Priacanthidae (2), Sciaenidae (1), Serranidae (2).
We dissected all specimens shortly after euthanizing them with an overdose of MS-222. We excised the left eyeball first, removed attached ocular muscles, and cut the optic nerve close to the sclera. We measured eyeball diameter, axial length, the largest and smallest pupil diameter, and lens diameter (Figure 1) with an optical micrometer on a Wild binocular stereomicroscope. It should be noted here that the pupil of teleosts is generally considered static, i.e., there is no pupillary response to changes in ambient light, with a few notable exceptions [35]. Then, we cut away iris and cornea, removed the lens from the eye, and measured the equatorial diameter of the lens, again using the optical micrometer. We repeated this procedure for the right eye. All research was carried out in accordance with the UC Davis animal use and care protocols.
Physiological optics
Optics provides models for light sensitivity on the basis of morphological and physiological features of the eye. Schmitz and Motani [27] introduced the optical ratio (OPT) as a descriptor of light sensitivity, on the basis of earlier work by Hughes and Land [36, 37]. OPT is the product of the ratio between the optical aperture (A) and the posterior nodal distance (PND), i.e., the inverse of f-number, and the ratio between optical aperture and the diameter of the retina (RD):
OPT is a useful discriminator between the three main types of ocular image formation in terrestrial amniotes: photopic (image formation in bright light), mesopic (intermediate light), and scotopic (dim light). The form-function relation of OPT and ocular image formation has been tested empirically and found valid by approximating the optical variables with morphological features [27, 28, 38].
Absolute eye size may also influence light sensitivity under certain conditions. As both OPT and f-number are ratios, they are independent of size unless there are deviations from the optically expected isometry. Nevertheless, a bigger eye may still have better light sensitivity to extended light sources because of a higher degree of neural summation by pooling of photoreceptor signals. The negative effect of signal-pooling on visual acuity could be offset by the increase of the focal length of the eye. Bigger eyes may also have better sensitivity to point light sources such as bioluminescent flashes, because of their absolutely larger apertures. In contrast to sensitivity to extended light sources, point light detection is independent from retinal area and focal length [8, 9]. However, the importance of point light detection for reef fish is unclear.
Hypotheses and data analysis
We tested for differences between nocturnal and diurnal eye morphology with several different techniques. All calculations were performed on the statistical platform 'R' (version 2.13.1) [39]. We calculated species means of the individual averages obtained from measurements of left and right eyes prior to all analyses. Then, we log10-transformed the data and rounded to four significant figures. Ratios were calculated directly from the original, untransformed species averages.
Differences between nocturnal and diurnal eye size
We tested whether nocturnal fish have larger eyes than diurnal species by Standardised Major Axis regression of eye diameter and body mass, performed with the R package smatr (as for all other regression analyses) [40]. We first calculated the slope for all species in order to understand the scaling of eye and body size among all reef fish. We then tested for differences in slope to determine if the slopes were equal. Finally, we compared intercepts between nocturnal and diurnal species. We chose body mass as the independent variable because it may better account for variability in body shape (e.g. long and slender versus deep-bodied and short) than the other commonly used size proxy, standard length. Anguilliforms, with their extremely elongated bodies and large mass but relatively small heads were not included in this part of the analysis.
Differences between nocturnal and diurnal eye morphology: Optical ratio and pupil shape
We empirically tested OPT with two sets of morphological proxies for optical variables. First we followed Schmitz and Motani's [27] approach and chose lens diameter (LD) as a proxy for optical aperture and eye diameter (ED) and axial length (AL) as proxies for retina diameter and focal length (note that focal length substitutes for PND in aquatic eyes):
We then substituted lens diameter with the smallest pupil diameter PDmin, respectively) as another empirical test:
We did not use the largest diameter of the pupil because this trait has two major functions. One function is related to optical aperture, while the other concerns lens accommodation. The elongation of the long axis of the pupil may result in an aphakic ("lensless") gap, which is considered useful for lens accommodation [41].
Lens diameter also serves two major optical functions in the teleost eye, which may compromise the distinction between nocturnal and diurnal reef fish. The lens ensures that most light entering the eye chamber is brought into focus by matching the size of the optical aperture, but is also the only refractive element in the teleost eye and determines the focal length. This means that, if everything else stays the same, any enlargement of lens diameter for a larger optical aperture may also result in a longer focal length, with f-number and possibly OPT remaining constant. Variation may be limited in particular concerning lens diameter and axial length, with the latter also being a proxy for focal length.
In order to test whether OPTmorph1 and OPTmorph2 are useful discriminators of diel activity patterns in teleost reef fish we plotted the numerators (LD^2; PDmin^2) against the common denominator (ED × AL). This approach avoids introducing size-dependent bias to the ratio by accounting for possible allometric scaling of involved variables. We fitted SMA regression lines to pooled data and also to nocturnal and diurnal species separately, comparing slopes and intercepts.
Furthermore, the pupil of nocturnal fish is expected to approximate a circular shape in order to maximize the area of the optical aperture. We tested this prediction by SMA regression of smallest and largest pupil diameter, where the regression line of nocturnal species should have a higher intercept than that of diurnal fish.
Finally we derived a new ratio, that combines aspects of OPT and geometry of the optical aperture. We modified OPTmorph1 by cancelling out LD/AL because both traits are correlated with focal length and differences between nocturnal and diurnal groups may be limited, leaving LD/ED. Nocturnal species are expected to have larger LD (~optical aperture) for a given ED (~retina diameter) than diurnal species. Then, we combined LD/ED with the ratio describing pupil shape, PDmin/PDmax, where nocturnal species should have a large PDmin for a given PDmax, in order to maximize the pupil area. The combination of these ratios yields
Differences between nocturnal and diurnal eye morphology: Multivariate analyses
We applied principal component analysis (PCA, correlation matrix) to further explore the eye-morphospace of nocturnal and diurnal reef teleosts. We performed two different PCAs. The first PCA included three variables, namely eye diameter, axial length, and lens diameter. These are the same variables used in the discriminant analysis in previous studies on terrestrial eyes [27, 28, 38]. The second PCA included these three variables plus the largest and smallest pupil diameter, in order to have a more complete description of eye morphology. For both PCAs we performed a MANOVA to test for differences between nocturnal and diurnal taxa.
Third, we tested whether linear, quadratic, regularized, or flexible discriminant analysis (LDA, QDA, RDA, and FDA, respectively) can successfully distinguish between nocturnal and diurnal eyes. Similar to the PCA, we first began with a set of three variables (eye diameter, axial length, and lens diameter), before adding in the largest and smallest pupil diameter as fourth and fifth variable. To determine the minimal misclassified proportion with RDA, we varied the regularization-lambda between 0 and 1 at increments of 0.01. LDA and QDA were performed with the R package MASS [42], FDA with the mda-package [43], and RDA with the klaR-package [44]. For all discriminant analyses we used prior probabilities defined by the training dataset.
Diversity of nocturnal and diurnal eye morphology
For the comparison of the diversity of nocturnal and diurnal eye morphology we analyzed the pattern of morphospace occupation defined by the PCA (PC axes 2-5) on all five variables. We assessed morphological diversity by means of variance. There are more diurnal (n = 211) then nocturnal species (n = 54) in our dataset, and even though variance is considered largely independent of sample size, we accounted for a possible bias by a rarefaction analysis. We randomly re-sampled 54 diurnal species without replacement and calculated variance on PCs 2-5, and repeated this procedure 100, 000 times. This procedure resulted in 100, 000 PC analyses with the same number of diurnal and nocturnal species, with diurnal species randomly selected anew for each run. Then, we compared the distribution of nocturnal variances to the bootstrap distribution of diurnal variances.