One other bug that I noticed recently and reported, that you might want to watch out for (at least, I assume it's a bug, not a feature): If an animal has been tamed by a tamer and formed a bond with them, whenever that tamer comes into their pasture, they will run to join them. Even if they're SUPPOSED to be keeping their nest of eggs warm. (And in that case, if they do have eggs, they then bounce back and forth between the trainer and nest).
In Dwarf Fortress, if the mother leaves the nest even for a second, the eggs get cold and can't hatch. So obviously, this is undesirable behavior (to put it mildly) if you're trying to breed egg-layers that were once wild.
I got around it for my Emus by building walls around the nests with one door, so that it made a room of one tile. Then once the emu went in to lay her eggs, I made the door tightly closed (q), find the door, (o). Which keeps pets from pathing through it. I noticed that any re-training seemed to go on with the trainer a few tiles away anyhow, so they didn't go through the door and displace the mother/let them slip through the open door.
I suppose you could also maybe get around it by assigning a different trainer to each animal, but if the trainer comes in to train that one specific animal, they'd still probably leave the nest. :/