There currently isn't any domestication in the game.
If you're talking about the wild populations, there's a bug right now that's preventing animals from respawning. It will be fixed in a future staging version.
Animals will only breed when the local plant population (or prey, in the case of wolves and foxes) can support additional animals. This includes wild and planted crops. Animals cannot magically appear where a population doesn't already exist (such that if you clear a forest of elks, no more will appear since they're all dead). Destroying the food that the animals eat will cause them to die due to starvation.
So in a future staging version they will eat farmed crops?