I think it has already happened. I've spent time in lots of tropical countries where European visitors would blanche at the size of the rodents. But since coming home to Scotland, I've been amazed at the number and size of rats in Edinburgh.
Only last week I saw an enormous one walking along Easter Road, bold as brass.
I have no idea what Edinburgh City Council does to control this menace, having never seen anyone taking any action – but can't imagine what it will be like after this poison ban comes into effect. Surely there is some kind of way of sterilising these rodents.