A female rat reaches fertile maturity in 5 to 12 weeks.
Her gestation period is beween 3 to 4 weeks.
She will produce between 8 to 18 young.
Lets say that the rat you saw in March wasn't just fat, she was PREGNANT, and gave birth the following day
Lets also say (for ease of maths) that this female came from a strain that were fertile after 8 weeks, the gestation period was 4 weeks after which they produced an average of 12 young of which 50% were females.
Lets also say (again for ease of maths) that Potteric Carr only had the one fertile male rat and he came by every 12 weeks just after the females gave birth (I think you can see where I am heading).
Come May we would have 7 pregnant females.
Come June we would have 84 newborn
Come August we would have 49 pregnant females (84/2 + 7)
Come September we would have 588 newborn
This month there would be 343 pregnant females. (588/2 + 42 + 7)
If you were to visit Potteric Carr next month you just might find 4,801 little rats running about the place all as a result of that one single female feeding below the bird table (4116 newborn + 343 earlier females + 342 earlier males):evil: