People who think the idea of property rights is learned rather than innate haven't seen Margaret. She gets very possessive about things she considers hers.
One of these things is her pink bouncy seat. We got her a toddler armchair of her own, thinking that she wouldn't need the bouncy seat any more, especially since she's now big enough that the bouncy seat almost hits the floor when she gets in. When we started using the bouncy seat for Duncan, though, she got upset. She knows she's not big enough to prevent us from doing it, so her solution has been to try to take control - for example, telling us when Duncan should be put in the seat for a nap, rather than letting us do it without her. And when she actually wants a nap herself, she'll wait for Duncan to wake up or for us to move him so she can lie down in that bouncy seat to sleep.
This isn't just a matter of wanting the only bouncy seat available, either. When we got a new light blue bouncy seat a couple days ago, Margaret was quite excited about it. I'd been afraid that, as the older sibling, she might want the new seat for herself, but I needn't have worried: she walked right over to the box, before the seat was even unpacked, and said "Duncan, Duncan!"
To be fair, the picture on the side of the box does kind of look like Duncan.
Howard started asserting "Howuhd turn" and sometimes "mine" right around 21 months, as I remember, which was also when Dorothy starting doing something similar. I think that this is definitely the age when they start understanding the concepts of possession, sharing, and taking turns (although they can't do either of the latter two without a fair amount of adult coaching yet).
Was she still napping in the bouncy seat before Duncan started using it? Ours didn't last nearly that long. Howard prefers his own crib and his own blanket and sheets for napping, although his mat at daycare is also acceptable. He absolutely will not allow himself to fall asleep in the carseat, though.
Sharing requires some supervision for Margaret as well - not only to enforce it, but to define it. My mother put one of Margaret's fuzzies in Duncan's bouncy seat with Duncan today, and Margaret got upset but didn't take it - which she could have without objection, as Duncan was asleep. I guess Duncan needs more of his own fuzzies.
Taking turns hasn't really happened yet, though waiting one's turn in line for a slide has.
Margaret was very possessive about things she considered hers even before age 1, though; I remember the first time we took her to the children's museum, she played with a toy for a bit, then got upset later when someone else played with it instead of with the identical copy of it.
Margaret was indeed still napping in the bouncy seat before Duncan started using it. She likes bouncy seats. She will no doubt be in the market for an adult sized one when she goes to college.