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Ankle Deep in Mice

Posted in Pest Advice on June 21, 2018

How Many Mice? 

In order to emphasise the breeding capacity of the house mouse I have often used the 'story' told to me by a scientist working for one of the largest pest control companies; that if you put 2 mice, one male and one female, into the United Kingdom and there was no restriction on food and shelter, and no predators, disease or rodent control, within two years the UK could be knee-deep in mice.

I thought I should do the calculation:

Assuming

  • At time 0 one baby male and one baby female mouse
  • Females mature at 6 weeks and breed immediately
  • Gestation takes 3 weeks
  • Litters are an average of 8 babies

Then the progression is the following, approximately a doubling every three weeks:

Week Females  Males  Babies Total Mice
3 1 1 0 2
6 1 1 0 2
9 1 1 8 10
12 1 1 8 18
15 1 1 8 26
18 5 5 40 66
21 9 9 72 138
24 13 13 104 242
27 33 33 264 506
30 69 69 552 1,058
33 121 121 968 2,026
36 253 253 2,024 4,050
39 529 529 4,232 8,282
42 1,013 1,013 8,104 16,386
45 2,025 2,025 16,200 32,586
48 4,141 4,141 33,128 65,714
51 8,193 8,193 65,544 131,258
54 16,386 16,386 131,088 262,346
57 32,772 32,772 262,176 524,522
60 65,544 65,544 524,352 1,048,874
63 131,088 131,088 1,048,704 2,097,578
66 262,176 262,176 2,097,408 4,194,986
69 524,352 524,352 4,194,816 8,389,802
72 1,048,704 1,048,704 8,389,632 16,779,434
75 2,097,408 2,097,408 16,779,264 33,558,698
78 4,194,816 4,194,816 33,558,528 67,117,226
81 8,389,632 8,389,632 67,117,056 134,234,282
84 16,779,264 16,779,264 134,234,112 268,468,394
87 33,558,528 33,558,528 268,468,224 536,936,618
90 67,117,056 67,117,056 536,936,448 1,073,873,066
93 134,234,112 134,234,112 1,073,872,896 2,147,745,962
96 268,468,224 268,468,224 2,147,745,792 4,295,491,754
99 536,936,448 536,936,448 4,295,491,584 8,590,983,338
102 1,073,872,896 1,073,872,896 8,590,983,168 17,181,966,506

So after 2 years there could be more than 17 trillion mice. Assuming a mouse weighs 20 g, 17 trillion would weigh about 340,000 tonnes (metric tons).

To make the 'story' more relevant I have chosen New Zealand rather than the UK as the home for these mice (the areas are similar, 268,000 km2 vs 242,000 km2).

How deep would 17 trillion mice be in New Zealand? This would equate to about 0.063 mice per square metre of New Zealand. Scary but not knee-deep, not even ankle-deep.

However, this assumed the original mice were babies. What if we start with a pair of adult mice (6 weeks old)? So let's add another 6 weeks to our progression.

Week Females Males Babies Total Mice
105 2,147,745,792 2,147,745,792 17,181,966,336 34,363,932,842
108 4,295,491,584 4,295,491,584 34,363,932,672 68,727,865,514

Now we have nearly 70 trillion mice........it is getting crowded in New Zealand. This equates to 0.254 mice per square metre, one mouse every 4 square metres. Considering they would be jumping about I think we can say 'tuck your trousers in your socks!' But not ankle-deep.

We wouldn't have to wait much longer to be ankle-deep. Assuming a mouse to be about 20 cm2 then 500 per square metre would be one layer of mice. At week 144 we would reach 1050 mice per square metre (ankle deep) and at week 156 (3 years) we reach 16,805 mice per square metre, which would, most certainly, be knee-deep. So maybe the story should be New Zealand could be knee-deep in mice after 3 years.

Week Females Males Babies Total Mice
156 281,509,336,449,024 281,509,336,449,024 2,252,074,691,592,190 4,504,149,383,184,550

Thankfully, mice are controlled, they do have a few predators, they do get diseases, food and shelter are not always available and they do not always breed to their full potential. But what this progression does show is that they will breed quickly to a point where there is a limiting factor and that can still be a lot of mice.

David Brittain
Kiwicare

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