Don't put breeders in cages, as critters don't breed at all while caged (they may still give birth if impregnated prior to being caged).
As Albedo otherwise said, pigs are suitable for being kept in a reasonably small room. Breeding for all real creatures (i.e. excluding vermin) is now based on being in adjacent tiles. The room has to be large enough for the creatures not to feel cramped, or they'll start fighting. I THINK one tile per creature (which includes the eventual offspring) is enough, but don't relay on that. A two tile room with a nest box caused the parent birds to kill at least one chick, while I seem to get things to work with three tiles, but I remove the chicks from the breeding chamber as soon as they are hatched.
I keep my non grazing breeders mixed up in room that's about 10*4 (you wouldn't expect it to work, but tigers go along just fine with gorillas, chicken, boa constrictors, and dogs. Rutherers fit right in as well).
Apart from physical proximity, animals (as well as dwarves) have to have a suitable sexual leaning, i.e. being bi- or hetero-sexual. Dwarf Therapist shows this orientation for dwarves and animals alike. However, I've been told "no desire to have children" is shown as asexual, at least for animals (although I struggle with the concept of animals having heterosexual relations while still somehow blocking impregnation).