# Can a pair of rats multiply to 200 within a year?

A story on the BBC News website makes the following claim:

Brown rats are one of the planet's most serious mammalian pests, ruining crops and harbouring disease. Expert jumpers, climbers and swimmers, a single pair can multiply to 200 within a year.

Can rats multiply this quickly?

-

According to this site rats:

• reach sexual maturity at 4 months (for females, who are the limiting factor here)
• can give birth seven times a year
• have litters of about 8

Starting with two sexually mature rats (and assuming averages of all the above throughout), the original pair will produce 7 litters of 8 rats in a year - 56 rats. The second generation become fertile at 4 months after birth (5 months from the start of the year), and so the four females in that generation will have around 7/12*7 = 4 litters each in the year - 128 rats. That's so close to the 200 that we don't need to worry about the remaining generations. Rats are clearly capable of becoming at least 200 within a year.

-
I was just doing a similar calculation based on the Wikipedia values, which were sexual maturity at 5 weeks, typically 7 per litter, can give birth 5 times a year. – Oddthinking Jul 12 '12 at 14:09
Do you mean "so close to the 100" ? – Walkerneo Jul 12 '12 at 20:44
@Walkerneo The figure given was "200 in a year". 128+56=184, so close to 200 with many generations still to go that the total will clearly exceed 200. – DJClayworth Jul 12 '12 at 21:08
@DJClayworth, Sorry, I thought the question had asked if 100 was possible. My mistake. – Walkerneo Jul 12 '12 at 21:54
Quite scary. Didn't realise rats had such large litters or that female rats can breed again so soon after giving birth. – Tom77 Jul 13 '12 at 9:02