The default is off, if you click it they will not get pregnant.
I discovered that because I suddenly had a plethora of adorable little warthhogs running around my ostriches and was wondering where they came from.
Red = Birth control is ON
Brown = OFF
The default is off. Easiest way to check which animals have it on/off would be through the zoo tab, under animal management.
You can see the control on the right in the zoo/animal panel or in the individual animals panel when you click on them. Looks like a little slider with a pill on the button.