Built a new Pasture and win one animal always...
Build a couple of the smallest possible pasture, transfer the animals to the larger pasture and then demolish the small one.
Yes, this gets bad in the game, always win an animal when you create an pasture.
Look my suggestion:
They must have two different expeditions: one to discover an animal, and another to bring an animal.
And remove animal by building a pasture (0 animal).
It must be this way:
You build your pasture (0 cows). He begins an expedition (missing feature) and wins his first cow. Send the second expedition, get another cow ... and start reproducing.