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It is because we determine things as more closely related if they share a more recent common ancestor. So orcas and moose shared a common ancestor more recently than orca and horse or moose and horse. DNA supports Perissodactyla and Artiodactyla (or Cetartiodactyla) as two separate groups. Within mammals, convergent evolution (traits that look similar but do not share a single origin), is pretty common. This makes determining relationships from morphology alone much more challenging! If you are interested in cetacean evolution and how they came about from the artiodacyls you could look into transitional fossils for this group. It's actually really cool (to me anyway) to see the mix of traits as the cetaceans adapted back into life in the water!

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I can expand on this and answer specifically the question in the title. Organisms are classified based on how closely related they are to one another, not based on a single morphological trait, but a morphological trait can be a convenient way to distinguish between two groups. Even when phylogenies are built from morphological data (not common in the age of molecular biology) they use dozens of traits, which can be as simple as number of toes, but more often are measurements of different body parts or ratios of those measurements. It might be just as correct to say that Perissodactyla and Artiodactyla are distinguishable by the ratio of femur length to pelvis width (just for example, not a real measurement they used), but number of toes is much more convenient.

The ungulates (hoofed mammals) often share a superficial resemblance to one another because they are all loosely related. Before the genetic era taxonomists attempted to classify them based on morphology alone. There was a fair amount of guesswork involved in deciding which morphological features were taxanomically relevant.

At some point it was realised that the ungulates fell into two broad groups. Those who's axis of their limb (ie the distribution of weight down the leg) passed through the middle digit, and those who's passed between two digits. The former condition was described as mesaxonic and the latter paraxonic. This formed the basis of the division of the ungulates into the"odd toed" Perissodactyla and the "even toed" Artiodactyla.

There were other morphological features that seemed to follow that same division, lending support to it being a taxonomically relevant grouping. These were things like the presence of horns, the number of dorsolumbar vertebrae, and the anatomy of the skull and femur.

It seems that the morphologists got it right in this case. The division of the odd and even toed ungulates has held up after being examined genetically.

The Cetaceans (including orcas) were moved into Artiodactyla based on genetic work, which showed them to be most closely related to Hippos. This relationship was not realised based on morphology.

Fascinating! Thank you

This will probably make more sense if you look at extinct ungulates. When comparing a horse and a deer or antelope, you are comparing animals that have converged on similar solutions to similar problems, while whales have gone off and done something totally different. But if you look at the ancestors you can better see what's going on.

Also important is the details of the anatomy of these species. Horses may look like moose in many ways, but how they get to that final result is rather different even if that isn't always visible at a causal glance.

Early whale ancestors like indohyus and pakicetus looked less like whales and more like early hippos (the closest living relatives of whales).

There doesn't need to be any particular reason why they were originally classified by even- vs odd-toed

The more interesting question is why did this classification held up? Why wouldn't the number of toes change, or why would it remain odd or even when it does? It really seems that it's such a random criterion that it should have been blown up by molecular phylogeny by now

I honestly don't know the answer, but it may have to do with the fact that all odd-toed ungulates will tend to have most of the load on their central digit, whereas even-toed ungulates have two central digits that they load more or less symmetrically. in turn that completely changes how the ankle is loaded. To go from one system to the other you need to change the whole alignment and mechanics of the leg, and that could be something evolution can't easily mess with

as for how weird orcas/cetaceans are compared to the rest... evolution isn't always stable. as they adapted to life in water a lot of things have obviously been tuned. though seeing how cetacea are related to hippos we at least understand how they might have spent time in the water in the first place. same thing goes for tetrapods, they're definitely very abnormal fish. some salamanders could pass as fish if you remove the legs, the rest not so much

This is the correct answer. Before Linnaeus, there were lots of different classification systems. (Genus and species goes back at least as far as Aristotle, but morphological comparisons really weren't a thing until the 1700s. So you could characterize humans as "featherless bipeds" or as "rational animals", but there wasn't a systematic method of characterizing all living things. And it's pretty obvious that limiting yourself to just genus and species is of extremely limited utility. Especially if you have a plucked chicken.) Linnaeus proposed a method of grouping similar to similar. The method was essentially "look at everything, and if it's mostly the same, they're closely related, and if it's almost entirely different, they're not related at all".

Even-toed and odd-toed just happened to be something that indicated all the other stuff really, really well. (Among ungulates.)

I thought pakicetus looked mostly like a kitty with a ringed tail and was electric type. No?