The wiki doesn't seem to mention this, but I've noticed an automatically self-imposed population cap on my animals. My embark group of 3 dogs + 1 pet dog quickly shot up to a population of around 50 dogs in just a few years . . . and then stopped. Same with my sheep, although those take longer to reproduce. After my sheep-dog population stabilized, I decided to try out this "Nest Box" thing and give my peacock & peahen (both pets, incidentally) a nice, locked paddock in which to raise their young. Mrs. Peacock hasn't budged from her nest in over a year, and she's laid 2 clutches of eggs, but so far, there's nary a peep.
Then I bought mating pair of Grizzly bears. As there was no longer any need to even pretend to be raising War Dogs, I decided to get rid of them. And as soon as my Butcher started striking them down, they began having puppies again. I thought I could kill them gradually, a few every season, culling just the weakest ones from the herd, but now that they're reproducing almost as fast as my Butcher can handle them, I have to go on Full Auto extermination. So, now I have a few bear cubs, the ewes are producing lambs again (I did slaughter a couple of sheep as well) . . . but there are still no peachicks.
So . . . is there an actual population cap on livestock? Might it be based on caps on the different individual species, a different cap on each grazing zone, or total number of animals over the entire map? Has any Science been done on this?