Assuming there's more than one ant inhabiting the nest, it's "ants' nest". You write down who or what owns the nest (= ants) and then put the apostrophe after it.
I Shall Be a Weather Forecaster In My Next Life Or...
What to do when you are not needed for childcare as they get older



???
but DS1 used to say 'Amnt I?' when he was small.
