Human eyes have round pupils, but there is considerable variation in the animal kingdom, from the vertical slit pupil of a cat, to the horizontal slot of a goat, as pictured above.

So Martin S. Banks and his colleagues asked the question “Why?” in an article published in Science Advances in August 2015.

They started by collecting data on 214 terrestrial species, classifying them on their foraging mode (herbivorous, active predator, ambush predator), their time of activity (diurnal, nocturnal or polyphasic) and pupil shape (vertical slit, sub-circular, circular or horizontal slot). Then they plotted the data on a chart, and observed something interesting:

Ambush predators were more likely to have vertical slit pupils than were herbivores, whereas herbivores were more likely to have horizontal slots. And nocturnal animals were more likely to have vertical slits or subcircular pupils (vertically orientated ellipses) than animals that operate in the daytime. When they did the statistics on this, they came up with a p-value that is the most statistically significant result I’ve ever seen in my life: p<10^-15. So there’s obviously something going on. And Banks et al. had a potential explanation to offer.

First, we need to think about depth of field, a concept familiar to anyone who has more than a passing interest in photography. When we focus our camera lens (or our eyes) on an object, objects in the foreground and background of that object appear blurred, because they’re out of focus. The range of distances over which this blurring is so slight as to be invisible is called the depth of field. This depth-of-field blurring is more pronounce if the camera aperture (or eye pupil) is wide—so narrow pupils will give a deep depth of field, while dilated pupils have a shallow depth of field. And depth of field also gets shallower as we focus on objects closer to us.

The blurring happens because each ray of light coming from an out-of-focus object is projected on to the camera sensor (or the retina of the eye) as a little image of the pupil. (Whereas light from an in-focus object is brought to a sharp point focus at the surface of the sensor/retina.) So eyes with circular pupils produce out-of-focus images that are, in effect, composed of lots and lots of little circular overlapping spots of light.

But a vertical slit pupil will project an out-of-focus version of itself on to the retina, producing an image that is much more blurred vertically than horizontally. Which means that vertical slit pupils have a greater depth of field for vertically orientated edges than for horizontal edges. Here’s a simulation of what an out-of-focus cross would appear like, to an animal with a vertical slit pupil:

For a given level of light, the pupil must dilate or constrict to control the amount of light reaching the retina. If we compare a slit pupil with a circular pupil of equal area (which therefore would admit an equal amount of light), we can see that the vertical slit pupil is much narrower in the horizontal direction, and longer in the vertical direction. So an animal with a vertical slit pupil trades off good depth of field for vertical structures with poor depth of field for horizontal structures.

Why would evolution come up with such a trade-off? Banks et al. think it helps with depth perception. One way in which we judge distance is by triangulating our gaze—the amount by which our eyes converge on a target tells us how far away it is. And because our eyes are set horizontally, we triangulate best on narrow vertical structures, for which we can confidently bring together and superimpose the images from each eye. A horizontal line is correspondingly harder to triangulate, because there’s ambiguity about the “correct” superposition.

And the increased depth-of-field blur for horizontal structures is also a potential aid to depth-perception, say Banks et al. It produces a shallow depth of field which allows the predator to focus its eyes very precisely on its target. So we have to imagine the predator converging its gaze rapidly on its target, using its deep vertical depth of field, and then fine-tuning its distance estimate using its shallow horizontal depth of field.

But is there any evidence that predators actually use these visual cues? Banks et al. point out that small predators have their eyes nearer the ground and focus on more nearby prey, which will give them a reduced depth-of-field compared to larger predators. The two hypothesized advantages for vertical slit pupils should therefore be more advantageous for smaller predators, driving evolution more strongly towards equipping smaller predators with slit pupils. And so it proves to be:

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.

But the most striking support evidence they advance is the fact that birds almost all have circular pupils, which might reflect the large heights from which they usually observe. The only birds known to have vertical slit pupils are the skimmers. These birds catch fish by flying fast and low just a few inches above a lake surface, with their lower jaws dipped into the water, ready to snap shut on any unsuspecting fish. An ability to precisely judge the distance of obstacles ahead might well be an advantage.

What about the horizontal pupils of herbivores? These will have the reverse properties of the vertical slits—good depth of field for horizontal structures, at the expense of poor depth of field for vertical structures.

How could that help a prey animal? Banks et al. point out that light rays entering our eyes from the peripheries tend to be poorly focussed—something called astigmatism of oblique incidence. We tend not to notice that, because our peripheral vision is more involved in detecting movement than in trying to resolve images. But prey animals generally have their eyes placed on the sides of their heads, so that they can observe a wide field of view. This means that they have a very limited field of binocular vision in front of their noses, and that’s all mediated by peripheral vision. By prioritizing deep depth of field for horizontal structures, their pupils reduce the effect of astigmatism of oblique incidence in important parts of the visual field—straight ahead, when galloping full-tilt to escape predators, and also at the “corner of the eye” looking backwards, so a slight shift of the head can assess where a pursuing predator is. Or, as the authors put it:

We conclude that the optimal pupil shape for terrestrial prey is horizontally elongated. Such a pupil improves image quality for horizontal contours in front of and behind the animal and thereby helps solve the fundamental problem of guiding rapid locomotion in a forward direction despite lateral eye placement.

And they have a test for this hypothesis, too. If horizontal slot pupils are to be advantageous in this way, they should stay horizontal, despite the animal’s head position, rotating to maintain their orientation as the animal bows and raises its head—something called cyclovergence. So Banks and his colleagues went off to farms and zoos and shot video footage of some prey animals raising and lowering their heads—sheep, goats, white-tailed deer, horses and moose—and they all exhibited strong cyclovergence. How cool is that? Rest assured that I will be closely observing the next sheep I encounter.

There’s a lot more to the paper, including analysis of other pupil shapes, like those of geckos and dolphins, which constrict to multiple small apertures in bright light, and an investigation of how often different pupil shapes have emerged during the evolution of cats and dogs. If I’ve whetted your appetite, head off to look at the original paper, accessible in full here.