Cats, for example, go so far as burying their feces to make their presence less easy to detect, while mice in particular but also other rodents and lagomorphs all leave a trail of waste everywhere they go. Given the vulnerability of prey animals, why aren’t they more likely to try to avoid detection instead of far less likely? Is it just because prey isn’t as clever as predators are?
Some of it is due to sheer volume. Herbivores produce a lot more waste, especially with nutritionally poor forage. The relatively tiny, compact nature of carnivore feces makes it worth the comparatively small effort.
Carnivores, including cats, don’t generally bury their feces. In the wild, dominant individuals of both big and smaller cats mark their territories with prominent deposits of feces or make latrines. It’s subordinate individuals that bury their waste to make them less conspicuous to the dominant individuals. (Smaller species may bury waste to avoid attracting the attention of their own predators.)
Although it may not seem like it, domestic cats generally regard the humans they live with as dominant, and hence bury their waste.
As for herbivores, the sheer volume of waste produced precludes trying to hide it.
Lions like to roll in the waste of herbivores, presumably to disguise their own smell. Dogs notoriously like to roll in stinky stuff, presumably for the same reason.
Indeed - I’ve known a couple of cats over the years that were bizarrely secure in their dominant position in the hierarchy and would refuse to bury their poop. They’d just deposit it neatly on top of the litter and stroll away, happy as could be.
heh, one of my cats flips the litter out of the box and in the tub (the litter box is in a non-working bathtub) in a small pile and poops on that and looks at me defiantly as she does it …
Another reason could be that it’s distracting and noisy which can cause the prey animal to become lunch. Additionally prey animal poops such as rabbit, have basically no odor to us, and may not have much to other animals.
A mouse doesn’t have to worry that a bag of grain will see its poop and decide to go into hiding.
A mouse does have to worry that a cat will see its pile of poop and decide to follow the scent trail. Or at least hang around nearby for awhile, waiting & watching.
Perhaps the real difference is that predators have (relatively) keen sense of smell so that prey hiding poop is less effective. Whereas prey has (relatively) weak sense of smell so that predators hiding poop is more effective. An interesting trade-off if true.
Game theory: it’s everywhere.
I guess this means that ferrets consider themselves dominant over their owners. Ferrets use litter boxes like cats do, but I’ve never known any to bury their faeces.
Not really. Polecats, the wild ancestors of ferrets, don’t bury their feces. Unlike cats, evidently ferrets don’t bury their feces in any circumstances, even when they are subordinate.
Haha! Boss cat. 
I read somewhere that this isn’t true. What they’re doing is putting their own scent on whatever it is they’re rolling in to mark it as theirs. I’m not sure which is correct.
Why would a lion want to mark a pile of elephant dung as theirs?
I’m going to ask for a cite. That could make a little sense for marking a carcass, but predators also roll in dung and other inedible things there would be no reason to mark. They mark possession of things by depositing their waste on it, not by rolling in it.
Also consider that roving grazers typically don’t have nests, don’t have established places to go and sleep. So establishing an area away from the nest or burrow to do their business is not applicable. They just go where they are because they will move on.
Animals with a sleeping place will avoid fouling it. Hence, bear - woods. (I recall this as an explanation why some animals can be house trained, and others never can)
Perhaps another explanation revolves around volume. Predators seem to behave like humans and have occasional large dumps. When you do this once or twice a day, it’s not inefficient to cover it up. If like a mouse or rabbit you’re letting go a few every so often, stopping to dig holes and/or cover things up can start to take a significant amount of time. Relocating to a favourite spot to do their business is also inefficient.