There is a striking correlation between terrestrial species’ pupil shape and ecological niche (that is, foraging mode and time of day they are active). Species with vertically elongated pupils are very likely to be ambush predators and active day and night. Species with horizontally elongated pupils are very likely to be prey and to have laterally placed eyes. Vertically elongated pupils create astigmatic depth of field such that images of vertical contours nearer or farther than the distance to which the eye is focused are sharp, whereas images of horizontal contours at different distances are blurred. This is advantageous for ambush predators to use stereopsis to estimate distances of vertical contours and defocus blur to estimate distances of horizontal contours. Horizontally elongated pupils create sharp images of horizontal contours ahead and behind, creating a horizontally panoramic view that facilitates detection of predators from various directions and forward locomotion across uneven terrain.

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Even if the proposed benefit for image quality does in fact occur with slit pupils, this hypothesis applies only to species with multifocal lenses and, more importantly, does not explain why slit pupils are elongated vertically in some species and horizontally in others.

Simple lenses focus different wavelengths at different distances: for example, blue at nearer distance than red. This chromatic aberration produces noteworthy blur in images containing a wide range of wavelengths. Kröger and colleagues ( 9 , 10 ) proposed that some animal eyes minimize blur due to chromatic aberration with a multifocal lens. This lens has concentric zones of different focal lengths, with each zone focusing a different wavelength band onto the retina. They argued that the multifocal arrangement is useful because it allows reasonable image sharpness across a range of wavelengths at the expense of some contrast: “dividing the lens into three zones of equal aperture areas and focusing a specific wavelength improves the functionality of the lens in comparison to a monofocal lens” [( 10 ), p. 1792]. When a circular pupil constricts, the peripheral zones of a multifocal lens are no longer involved in image formation, thus preventing the suggested improvement in image quality. Malmström and Kröger ( 11 ) hypothesized that the slit pupil is an adaptation for maintaining image quality because when the pupil constricts to a slit, the peripheral zones of the lens remain involved in image formation.

Brischoux and colleagues ( 7 ) and Heath and colleagues ( 8 ) discussed the utility of vertical-slit pupils in some reptiles. They claimed that the image formed by a vertical pupil has a greater depth of field for horizontal contours and thereby ensures sharp focus of horizontals across a range of distances [Fig. 8 in ( 8 )]. This claim is unfortunately false. The depth of field for horizontal contours is determined by the vertical extent of the pupil; thus, with a vertical slit, the depth of field will be greater for vertical contours, not horizontal. Even if the proponents of this hypothesis corrected the error concerning depth of field, it does not explain why vertical elongation is functionally adaptive for some species and horizontal elongation is for others.

This hypothesis is persuasive. It explains why pupils are elongated in species that require more light regulation than other species. However, the hypothesis only explains why some species evolved elongated pupils, not why they are vertical in some species and horizontal in others.

Retinal illumination is the product of pupil area and incident light intensity. Thus, pupil dilation and constriction respectively increases and decreases retinal illumination affording rudimentary adaptation to different light environments. Constriction of circular pupils is achieved by ring-shaped muscles, whereas closure of slit pupils involves two additional muscles that laterally compress the opening, allowing much greater change in area ( 1 , 2 ). For example, the vertical-slit pupils of the domestic cat and gecko undergo area changes of 135- and 300-fold ( 3 – 5 ), respectively, whereas humans’ circular pupil changes by ~15-fold ( 6 ). Species that are active in night and day need to dilate sufficiently under dim conditions while constricting enough to prevent dazzle in daylight. A slit pupil provides the required dynamic range.

( A ) Different pupil shapes. From top to bottom: vertical-slit pupil of the domestic cat, vertically elongated (subcircular) pupil of the lynx, circular pupil of man, and horizontal pupil of the domestic sheep. ( B ) Pupil shape as a function of foraging mode and diel activity. The axes are pupil shape [vertically elongated, subcircular (but elongated vertically), circular, or horizontally elongated] and foraging mode (herbivorous prey, active predator, or ambush predator). Each dot represents a species. Colors represent diel activity: yellow, red, and blue for diurnal, polyphasic, and nocturnal, respectively. The dots in each bin have been randomly offset to avoid overlap. ( C ) Results of statistical tests on the relationship between foraging, activity, and pupil shape. Multinomial logistic regression tests were conducted with foraging mode, activity time, and pupil shape as factors and genus as a covariate. Relative-risk ratios were computed for having a circular, subcircular, or vertical-slit pupil relative to having a horizontal pupil as a function of foraging mode or diel activity. Activity time proceeded from diurnal to polyphasic to nocturnal. Foraging mode proceeded from herbivorous prey to active predator to ambush predator. When the relative-risk ratio is greater than 1, the directional change in the independent variable (foraging or activity) was associated with a greater probability of having the specified pupil shape than a horizontal pupil.

Pupils come in a variety of shapes. Why do some animals have vertical pupils, whereas others have round or horizontal? We examined the optical consequences of terrestrial animals’ pupil shape in the context of their ecological niche. We found a striking correlation between pupil shape and ecological niche ( Fig. 1 ). Consider three previous hypotheses about the function of elongated pupils.

RESULTS

Figure 1A provides examples from top to bottom of vertical-slit, subcircular, circular, and horizontal pupils. The vertically elongated pupils in the first category can be adequately described as slits, but the horizontally elongated pupils in the fourth category cannot; horizontally elongated pupils are roughly rectangular and their aspect ratio changes with dilation and constriction (1). Interestingly, there were no terrestrial species for which we could obtain the relevant data that had diagonally elongated pupils.

Figure 1B plots pupil shape as a function of foraging mode and diel activity for our database. There is a clear relationship between ecological niche and the shape of the pupil. For example, herbivorous (prey) animals are very likely to have horizontal pupils, and most diurnal predators have circular pupils. Additionally, nocturnal and polyphasic ambush predators generally have vertical-slit pupils, which was previously documented for snakes (7) and described somewhat informally for other species (1). Figure S1 is an interactive version of Fig. 1B, table S1 is a list of the species.

Figure 1C shows the results of a multinomial logistic regression using foraging mode and diel activity to predict pupil shape. (More detailed tables and descriptions are provided in tables S2 and S3.) The relative-risk ratios in Fig. 1C indicate the increase in the likelihood of having the specified pupil shape, relative to horizontal, when the indicated niche parameter was incremented from the lowest to the highest value and the other niche parameter was held constant. There was a highly significant increase in the probability of vertical-slit pupils as animals moved from being herbivorous (prey) to ambush predators. There were also very significant increases in the probability of subcircular and circular pupils going from prey to ambush predator. Additionally, there were significant increases in the probability of vertical-slit and subcircular pupils when animals moved from diurnal to nocturnal. The overall effect of foraging mode and diel activity in predicting pupil shape was highly significant: χ2 = 219.9; P < 1 × 10−15.

Nearly half the animals in our database are snakes. We asked if the relationship between niche and pupil shape persists when snakes are removed. Indeed, it does: The same trends were statistically reliable, and the overall relationship between foraging mode, diel activity, and pupil shape remained highly significant: χ2 = 102.5; P < 1 × 10−15.

The strong relationship between foraging mode and activity time on the one hand and pupil shape on the other suggests that there are functional advantages for particular pupil types in certain ecological niches. Our goal is to determine what those advantages are. That is, why would a horizontally elongated pupil be advantageous for prey and a vertically elongated pupil be advantageous for ambush predators who are active at night and day? To answer these questions, we analyzed the optical properties of these eyes and visual requirements in different niches.

We describe new hypotheses for the functional advantages of elongated pupils: one for vertical elongation first and then one for horizontal.

Vertical-slit pupils Consider a viewer fixating and focusing on a point at distance z 0 . Another point at a distance z 1 creates a blurred image. The diameter of the blur circle on the retina for that point is: (1)where A is the diameter of the pupillary aperture and s 0 is the distance from the aperture to the retina (12). Using the small-angle approximation, the eye-length term s 0 drops out, yielding blur-circle diameter in radians: (2)where ΔD is the difference between distances z 0 and z 1 in diopters (12). Thus, blur is proportional to aperture diameter and to the difference in diopters between the eye’s focal distance and the point of interest. These equations incorporate geometric blur due to defocus and not blur due to the eye’s aberrations including diffraction (13). Incorporating aberrations yields more blur, but only for object distances at or very close to the focal distance: that is, where ΔD ≈ 0 (14). We are most interested in blur caused by significant defocus, so we will ignore aberrations henceforth. Now consider an elongated pupil with vertical extent A v and horizontal extent A h . With the eye focused at z 0 , the retinal images of contours at z 1 are blurred differently, depending on their orientation. For example, the blur of the vertical and horizontal limbs of a cross (Fig. 2B) is determined by A h and A v , respectively: (3) (4)Thus, eyes with vertical-slit pupils have astigmatic depth of field: larger (that is, less blur due to defocus) for vertical than for horizontal contours. Objects in front of and behind the eye’s focal distance are differently blurred such that the retinal images of horizontal contours are more blurred than the images of verticals (Fig. 2A). Figure 2B shows that the equations provide a good approximation of image blur for different pupil orientations and defocus (meaning that diffraction and other aberrations make small contributions to image quality when the eye is defocused). Figure 2C shows astigmatic depth of field for a natural scene (see movie S1 for more details; note that this phenomenon is not the same as astigmatism, a common source of defocus in eyes). Fig. 2 Image quality for different amounts of defocus and pupil shapes. (A) Astigmatic depth of field with vertical-slit pupil (12 × 1.5 mm). Three crosses are presented at different distances (0D, 0.4D, and 0.8D). The camera is focused on the nearest cross, so the other two are farther than the focal plane. The vertical limbs of all three crosses are relatively sharp, whereas the horizontal limbs of the two farther crosses are quite blurred. (B) Horizontal and vertical cross sections of point spread functions (PSFs) as a function of focal distance for an eye with a vertical-slit pupil (12 × 1.5 mm). The object was white. The PSFs incorporate diffraction and chromatic aberration. Log intensity in the PSF is represented by brightness (brighter corresponding to higher amplitude). Intensities lower than 10−3 of the peak amplitude have been clipped. The upper panel shows horizontal cross sections (relevant for imaging vertical contours). The icon in the lower middle of the panel represents the cross sections by a nominal PSF with a horizontal cut through it. The lower panel shows vertical cross sections (for imaging horizontals). The icon in the lower middle of the panel represents those cross sections. The dashed white lines are from Eqs. 3 and 4 and show that the equations are a good approximation to the PSF cross sections. (C) Photograph of a depth-varying scene taken with a camera with a vertical-slit aperture. The camera was focused on the toy bird, so objects nearer and farther are blurred, but more vertically than horizontally because of the aperture elongation. Movie S2 shows PSF cross sections and the scene as the aperture rotates from vertical to horizontal and back to vertical. From Fig. 1, we observe that vertically elongated pupils are much more common in ambush predators than in other species. These animals must estimate the distance to potential prey accurately. Three depth cues, all based on triangulation, can in principle provide the required metric distance estimate: (i) stereopsis (binocular disparity created by two vantage points), (ii) motion parallax (image differences created by moving the vantage point), and (iii) defocus blur (differences created by projecting through different parts of the pupil) (12, 15). Ambush predators cannot use motion parallax because head movements would reveal their position to potential prey. They must rely on stereopsis and defocus blur. Horizontal disparity, the primary depth signal in stereopsis, is proportional to the interocular separation (I) and the difference in dioptric distance between the fixation point and a point of interest (ΔD): (5)where the disparity δ is in radians (12). From Eq. 2, blur is also proportional to the dioptric difference in distance between the fixated (and presumably focused) point and a point of interest, and to the aperture size (A). The smallest depth intervals ΔD t that can be accurately assessed from disparity and blur are: (6)where δ crit and β crit are the smallest discriminable changes in disparity and blur, respectively (16). Thus, as the baseline for triangulation (I or A) increases, the accuracy of depth estimation should increase as well. Stereopsis was classically thought of as a relative distance cue, but is now understood to provide absolute distance information at all but long distances (17). Similarly, blur can provide absolute distance information provided that the fixation (and therefore accommodation) distance is known, which can be estimated from the eyes’ vergence (18). To use stereopsis, these animals must determine which feature in one eye should be matched with a given feature in the other eye. Horizontal displacements are more readily measured with vertical than with horizontal contours, so stereopsis is understandably most precise for contours that are approximately vertical (19, 20). This is probably why orientation preferences among binocular cortical neurons serving the central visual field tend toward vertical (21, 22). Blur reduces the precision of stereopsis (23). The vertical-slit pupil aligns the orientation of the larger depth of field (that is, less blur) with the vertical contours of potential prey. This is advantageous for frontal-eyed, ambush predators because it facilitates stereopsis while allowing large changes in pupil area and thereby effectively controlling the amount of light striking the retinas (1, 2). Horizontal contours are commonplace for terrestrial animals. With gaze along the ground, retinal images are foreshortened vertically, so the prevalence of horizontal or nearly horizontal contours in those images increases (24). A vertically elongated pupil provides a short depth of field for horizontals and thus aids the use of defocus blur for estimating distances of horizontal contours along the ground (Eq. 6), providing useful depth information for contour orientations that are problematic for stereopsis. We conclude that the vertically elongated pupil is a clever adaptation that facilitates stereopsis for estimating distances of objects perched on the ground while simultaneously enabling depth from blur to estimate distances along the ground. The horizontal baseline for depth from disparity is determined by the interocular separation and is unaffected by pupil orientation. The vertical-slit pupil enables a relatively large vertical baseline for depth from blur. Thus, this arrangement of horizontally separated eyes and vertically elongated pupils facilitates depth estimation for contours of any orientation. If instead the pupils were elongated horizontally, the ability to estimate distances of both vertical and horizontal contours would suffer. Thus, many frontal-eyed, ambush predators may use disparity and blur in complementary fashion to perceive three-dimensional layout, much as humans do (16). The vertical-slit hypothesis predicts that eye height among frontal-eyed, ambush predators might affect the probability of having a vertically elongated pupil. In Fig. 3A, two viewers with different eye heights fixate points along the ground. The eyes are focused at distance z 0 : nearer for cats than humans. Rays above and below the fixation axis intersect the ground at distances z 1+ and z 1− , respectively (red and green). The difference in distances (in diopters) between the fixation axis and the axes above and below fixation are plotted in Fig. 3B. Different curves correspond to different eye heights. Except close to the feet, there is essentially no effect of how far along the ground the viewer fixates. Thus, the major determinant of dioptric difference for an eye with fixed pupil size is the height of the eye above the ground. Fig. 3 Height and defocus. (A) Two viewers—human and domestic cat—with different eye heights, h 1 and h 2 , fixate the ground. Fixation direction relative to earth vertical is θ. Fixation distances along the ground are d 1 and d 2 , and distances along the lines of sight are z 0 . The eyes are focused at z 0 , so points above and below the fixation point are defocused. (B) Defocus (difference in dioptric distances: 1/z 0 − 1/z 1+ and 1/z 0 − 1/z 1− ) as a function of fixation distance along the ground. Red and green curves correspond to the defocus 5° above and below fixation, respectively (ϕ = ±5°). Different curves represent different eye heights. How does pupil size vary with eye height? In vertebrates, A ∝ M0.196, where A is axial length and M is body mass (26). In quadrapeds, L ∝ M0.40, where L is limb length, an excellent proxy for eye height (27). Combining those equations, A ∝ L0.49, which means that axial length is proportional to the square root of eye height. Under the assumption that pupil size is proportional to eye size, the analysis shows that the defocus signal is indeed weaker in taller animals. (C) Defocus (difference in dioptric distances) for different vertical eccentricities. The viewer is fixating the ground. Different curves represent animals of different heights. The eccentricities corresponding to ϕ = ±5° are represented by dashed vertical lines. Because defocus in (B) is nearly independent of fixation distance, we represent the relationship between defocus and retinal eccentricity with one curve for each eye height. (D) Images of the ground for viewers of different heights. A virtual camera with a field of view of 30° and an aperture diameter of 4.5 mm was aimed toward a plane with θ = 56°. The camera was focused on the black cross at distance z 0 . From top to bottom, z 0 was 0.6, 0.2, and 0.1 m (1.7D, 5D, and 10D, respectively). Figure 3C shows how dioptric difference varies with vertical retinal eccentricity for different eye heights. Shorter animals with their eyes close to the ground will experience much greater change across the retina. Figure 3D illustrates this by showing that the blur gradient is much greater when the camera is close to the surface (bottom panel) than when it is farther away (top panel). If pupil size were proportional to eye height, the defocus signal would not vary from short to tall animals, and the analysis in Fig. 3 would be invalid. However, eye size (and therefore pupil size) is roughly proportional to the square root of eye height [see figure caption; (25, 26)], so the analysis remains viable. As we said, ambush predators with frontal eyes use stereopsis to gauge the distance of prey before striking. For precision, they require sufficiently sharp vertical contours (20, 23). Figure 3 suggests that the need to minimize the blur of vertical contours is greater in shorter animals, so selective pressure to restrict the pupil horizontally is greater. In addition, short animals’ viewpoint close to the ground creates a larger blur gradient across the retina, thereby making depth from blur a potentially more effective means for estimating distances along the ground than it is in tall animals. We predict, therefore, that shorter frontal-eyed, ambush predators will be more likely to have a vertical-slit pupil than taller animals in that niche. We evaluated this prediction by examining the relationship between eye height in these animals and the probability that they have a vertically elongated pupil. There is indeed a striking correlation among frontal-eyed, ambush predators between eye height and the probability of having such a pupil. Among the 65 frontal-eyed, ambush predators in our database, 44 have vertical pupils and 19 have circular. Of those with vertical pupils, 82% have shoulder heights less than 42 cm. Of those with circular pupils, only 17% are shorter than 42 cm. Nearly all birds have circular pupils (1). The relationship between height and pupil shape offers a potential explanation. A near and foreshortened ground plane is not a prominent part of birds’ visual environment. The only birds known to have a slit pupil (and it is vertically elongated) are skimmers [Rynchopidae; (27)]. The primary foraging method for the black skimmer is to fly close to the water surface with its lower beak in the water, snapping shut when it contacts prey. The black skimmer is crepuscular or nocturnal. This niche is visually somewhat similar to the ones encountered by short terrestrial predators, and they tend to have vertical-slit pupils. We hypothesize that vertically elongated pupils in frontal-eyed, ambush predators allow complementary use of disparity and blur to estimate the distances of vertical and horizontal contours, respectively. However, some ambush predators, such as crocodiles, alligators, and geckos, have lateral eyes and are therefore unlikely to have useful stereopsis. Their distance estimation presumably has to rely on defocus blur. Their slit pupils again allow more control of aperture area and therefore enable functional vision in dim and bright conditions (1, 2). But why is the elongation vertical? Again the slit pupil creates astigmatic depth of field such that vertical contours that are nearer and farther than the eye’s focal distance remain relatively sharp. This allows the animal to see objects standing on the ground sharply for identification while also facilitating distance estimation from the blur gradient associated with foreshortened horizontal contours in the retinal image of the ground or water surface. Vertical elongation is more advantageous than horizontal elongation because it aligns the axis of short depth of field with the ground or water surface, thereby enabling depth estimation from the accompanying blur gradient, and it aligns the axis of long depth of field with vertical contours that can be used for object identification. Many of these animals may use the blur gradient to adjust accommodation and then estimate distance from an extra-retinal signal associated with the accommodative response (1).