However, that's going by the scientific meaning of the word 'rodent'. In everyday speech, I've heard the term applied to a even wider range of animals, including such things as shrews, but, most commonly, rabbits. Yet rabbits, along with hares and pikas, are not rodents. On close examination, it doesn't take much to demonstrate that, despite their size and shape, shrews aren't rodents, but rabbits... well, rabbits are pretty rodent-like. So what's the difference?
If you looked at pictures of every single species of rodent, it wouldn't take you long to conclude that most of them are basically mice or rats. Indeed, around two thirds of all rodent species belong to the mouse family, and a high proportion of the ones that don't look, on visual examination, as if they really ought to. Take this, for example, which actually belongs to the hamster family. In general, rodents are small mammals with compact bodies, long narrow tails and short limbs, and that walk on the soles of their feet.
Well, you'd never mistake a rabbit for a mouse, but the fact is, not all rodents do look like that. Some rodents, such as beavers and porcupines, are much larger than rabbits, or, in some cases, even hares. Others are at least at good at hopping as rabbits are (kangaroo rats, for example), and there's at least one species that does, aside from the long tail, look really rather rabbit-like. We aren't going to decide that rabbits aren't rodents just because they have short tails, or apes wouldn't be primates, so how do we define them?
It turns out that the defining feature of rodents is also the source of their remarkable success: the shape of their teeth.
One of the key features that distinguished the first mammals from reptiles was their development of four distinct kinds of teeth. At the front of the mouth are small, clipping, incisors for snipping off food. The first placental mammals had three pairs of these in each jaw, although we primates have lost a pair, presumably because of our short snouts. Behind those are the stabbing canine teeth, then the grinding cheek teeth for chewing up food - the lack of these latter teeth means that reptiles can't chew in the way that we do. The cheek teeth are, in turn, divided into premolars and molars; in young placental mammals, premolars are, like canines and incisors, preceded by a set of milk teeth, while molars are only present in older animals, as the jaw elongates to fit them in.
At least, that's the original pattern, from which the various kinds of placental mammal evolved: each half of each jaw has, in the adult, three incisors, one canine, four premolars, and three molars. Different groups of mammal have evolved and adapted these teeth to suit their diets, or even for other purposes, such as fighting or digging. Carnivorans, for example, are defined by the presence of large, slicing, carnassial teeth.
Although there are some exceptions, most rodents are herbivores. It's worth noting, though, that this doesn't necessarily mean they eat nothing but plant matter. In reality, most animals are neither pure carnivores nor pure herbivores, and there's usually some blurring. Rodents, for example, will often eat insects or spiders, if that's what's around, and some of them feed on carrion or eggs. Indeed, some gnaw on bones, presumably to get a supply of calcium, and a few are genuinely carnivorous. But, in general, the vast majority of their nutrition comes from plants, and their teeth are ideally suited to a herbivorous diet.
Probably the first thing that you notice on looking at a rodent skull, and, for that matter, one of the first things you'll notice on looking at live rodents, is the size of their incisors. They're huge, and, in fact, they're even bigger than they look, because the roots extend way back into the jaw. There's only one pair in each jaw, instead of the usual three, because that pair is so useful that they just don't need any of the others.
Once they are finished growing, the teeth of most mammals close off at the base, leaving only a narrow channel for nerves and blood vessels to enter the central pulp cavity. That's because, aside from staying put, teeth don't really need to do much once they're grown, and so don't require a substantial blood supply. The incisors of rodents, however, are 'rootless'; that is, the base of the tooth remains wide open, allowing the tooth to continue growing. And, indeed, the incisors do continue growing, throughout life, and the only reason they don't just continue getting longer forever, until the animal can no longer open its mouth, is because of the teeth growing in the opposite direction from the other jaw.
Unlike normal teeth, rodent incisors have a layer of hard enamel only on their front surfaces. The back of the tooth, on the inside of the mouth, is covered only by a layer of dentine, the softer material that, in other teeth, lines the pulp cavity and is surrounded by the enamel on all sides. The fact that the enamel is only found on one side of the tooth allows them to be perpetually honed against each other, like a knife on a sharpening stone, creating a sharp chisel-like shape.
That chisel shape is the crucial element in the success of rodents. It gives them an incredible ability to gnaw away at material, and is ideally suited to eating tough plant material, such as seeds, nuts, thick roots, and stems. The very word 'rodent' comes from the Latin word rodere, 'to gnaw', and its because of the wear produced by the constant gnawing that the teeth have to grow perpetually in the first place.
Another feature you'll probably notice about rodent incisors is that they are commonly orange, or at least yellowish. To human eyes, that looks like a stain, or perhaps plaque, but, in fact, the teeth are supposed to look like that, and do so even when they are clean and polished. The colour is actually produced by iron salts deposited in the sheet of enamel, although it's not (so far as I can tell) entirely clear why rodents do this. Perhaps it makes the enamel even tougher than it already is.
To fully understand how rodents eat, however, it is also necessary to look further back in the mouth. Immediately behind the incisor teeth there is a lengthy gap, where the jaws have no teeth at all. This is called the 'diastema', and its a common feature in herbivorous mammals, allowing them to hold food in place with their cheeks and lips before chewing it. The gap is formed, in part, because rodents have no canine teeth, only a single pair of incisors in each jaw, and also a reduced number of cheek teeth.
Many rodents have just one premolar tooth on the side of each jaw, and that is usually modified to look somewhat like the powerful chewing molars. Many, including all the members of the mouse family, don't even have that, relying on molars alone. In many rodents, the cheek teeth are, like the incisors, permanently growing, being constantly worn down by chewing against each other. Even when this is not the case, the constant wear as the teeth chew up tough food rapidly produces sharp ridges of enamel on the surface as the animal ages, which further increase their ability to grind up things like seeds and tough fibre.
In fact, it may well be slightly more complicated than that, because studies on rodent embryos suggest that some of the adult teeth actually are milk teeth that just never fall out and get replaced. This is often true of the premolars, when there are any, but it also seems to be true of the great incisors. Although they look like they should be the first pair of adult incisors - the ones that meet at the front of the mouth - they may actually be the second pair of milk incisors, with the real first pair, along with the 'true' adult incisors, never developing.
All of which allows us to turn to our original question: why aren't rabbits rodents? Open the mouth of a rabbit, and you'll see a large pair of chiselling incisors, apparently just like those of a rodent. There are other similarities, too, since both rodents and rabbits (and their relatives, the hares and pikas) have an enlarged caecum, a part of the intestine that helps ferment vegetable matter. Some rodents even eat their own faeces, as rabbits do, allowing them to digest their food twice and extract the maximum nutrition from it.
One answer would be simply to say that rabbits, hares, and pikas, form their own evolutionary line, distinct from the rodents, and that they therefore constitute a separate order of mammals. That's true, but actually not very relevant, since there is no biological definition of what an 'order' of animals is. So long as all the members of an order are more closely related to each other than to anything else, we can basically define it however we like. But the thing is - rabbits and their kin are more closely related to rodents than to anything else. There is absolutely nothing in the rules of biological naming to stop us defining a group of animals that includes both rodents and rabbits, and saying that they're all the same thing.
Rodents Rabbits, etc. Primates, etc.
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In fact, we have. But that group is called 'Glires', and rodents and lagomorphs (rabbits, hares, and pikas) are considered to be two different orders within it. So, clearly, there is some difference between the two that's large enough for us to say 'yeah, rabbits might look similar to rodents, but they're not actually the same'. That difference is, of course, in the teeth.
Like rodents, lagomorphs have a single pair of large, ever-growing, chisel-shaped incisors at the front of their jaw, separated by a wide diastema from the cheek teeth further back. But, unlike rodents, their incisors are fully encased in enamel on both sides, and so never hone to quite so sharp an edge. The incisors also aren't orange, lacking the hard iron salts, although, to be fair, there are a few rodents of which that is also true.
Further back in the mouth, the cheek teeth of lagomorphs are somewhat similar to those of rodents in shape, because they are, if anything, even more purely herbivorous. But, with three pairs of premolars in the upper jaw, and two in the lower, there are more of them. Admittedly, some of them are quite small, but, still, lagomorphs do not quite have the extreme reduction in dentition that rodents do.
It's not just the cheek teeth that's true of, however. As you can see from the image above, lagomorphs also have, in the upper jaw only, a second pair of incisors. (In fact, young animals have a third pair, too, but this is shed before they reach adulthood). These second incisors are small, and they are tucked behind the much larger main set of teeth, so that they actually aren't visible from the front at all. Nonetheless, they are there, and there is nothing like them in any rodent species.
[Beaver skull by "Lord Mountbatten" from Wikimedia Commons. Jackrabbit skull from the Smithsonian Museum of Natural History].