Housecat Reproduction

[Hornbein]

Start with one hundred housecats. Given unlimited resources, in seven years you will have a billion housecats.

 

[pinball1970]

Start with one hundred housecats. Given unlimited resources, in seven years you will have a billion housecats.

Are they all female?

 

[pinball1970]

Start Jan 1st. For one female cat they can have 20 kittens in a year, average 4 litters and 5 kittens per litter.
Kitten can reach puberty at 4 months so they start contributing by August, 25 kittens between them.
There must be a geometric series that can do this easier than brute forcing it.

 

[Hornbein]

Are they all female?

If they were then after seven years you would have at most 100 housecats.

 

[pinball1970]

If they were then after seven years you would have at most 100 housecats.

"given unlimited resources" I took to mean access to males as well as Whiskers.

 

[pinball1970]

If they were then after seven years you would have at most 100 housecats.

So its a 50/50 split? 80/20? 95/5? It makes a difference.

 

[DaveC426913]

By the time there is 0.001% of that number, they won't be housecats any longer. They'll be yardcats and streetcats.

 

[256bits]

2 ³⁰ = 1,073,741,824

Each litter of 4 kittens in average 2 of each sex.
Only the female can reproduce, on average again every 4 months.

I would guessimate that starting with 100 cats, approx 2 ⁸ = 128
then we have 9 years of cat production
( 2 years initial for the 100 cats + 7 more years

2 to the 8 for the 100 cats + 2 to the 28 for 7 years
2³⁶ = 68,719,476,736 female cats + kittens
plus the same amount of male cats + kittems

Total == 137,438,953,472 domestic felines

Number of litter boxes unknown

 

[DaveC426913]

At an average of 18" in length (not including tail) and 4" width, that's exactly 2 cats per square foot, assuming a face-centred cube packing lattice.
137,438,953,472 cats would entirely fill a square 50 miles on a side.

And this is where the scenario loses all plausibility. Because it is well known that the difficulty of herding cats increases as a geometric function - starting with one.

 

[256bits]

There must be a geometric series that can do this easier than brute forcing it.

Someone will surely show the error in my guestimate.
2ⁿ would be for something like bacteria or cell division.
It neglects that real world where mommas and poppas cats can keep on producing offspring for the while timespan under investigation.
Perhaps the value should be closer to a trillion, rather than the billion as in the opening post.

 

[pinball1970]

Someone will surely show the error in my guestimate.
2ⁿ would be for something like bacteria or cell division.
It neglects that real world where mommas and poppas cats can keep on producing offspring for the while timespan under investigation.
Perhaps the value should be closer to a trillion, rather than the billion as in the opening post.

Would it be more like a growth factor? R?

 

[Averagesupernova]

This is just a numbers game. Unlimited resources includes prevention of unknown diseases that will surface with this type of reproduction rates? Implication is no neutering so lots of fights to the death between toms.

 

[256bits]

Would it be more like a growth factor? R?

I guestimated the population growth as if the cats procreated by mitosis, leaving the parents unable to contribute to the population after having one episode of fertilization, gestation and birth of young. The growth period of the young and time to maturity was assumed to be zero ( an unrealistic assumption ).
One can look at it as the growth of procreating couples from 1 pair, after 1 gestation period 2 pair, after 3 periods 4 pair.

If we include the parents as being able to procreate as well, then after 1 period there is 3 pair ( 1 pair of parents + 2 pair of young ), after 2 period 9 pair ( 3 parent pair + 6 young pair ), and so on.
In this case the rime frame in question is reduced to 32 gestation + birth ( 4 to reach close to 100 cats + the 7 years ) giving 3² = 1,853,020,188,851,841 pairs of cats at the end.

Surely these are incomplete models of unchecked population growth.
As mentioned,

This is just a numbers game. Unlimited resources includes prevention of unknown diseases that will surface with this type of reproduction rates? Implication is no neutering so lots of fights to the death between toms.

As well, unlimited resources can mean what exactly? Is there no predation?
Unlimited access to each individual is difficult to achieve as the 'colony' expands outwards. One model is that those on the periphery will have access to adequate clean food and space while those interior will suffer competition, starvation, disease, fouling of the area from excrement, etc. as the population density exceeds livable conditions.

How can one determine an R without knowing additional features of the 'colony'?

 

[Bandersnatch]

These are excellent analyses. I'm wondering about applications to astronomy.

 

[pinball1970]

How can one determine an R without knowing additional features of the 'colony'?

I have asked for the sex split and gone for average months to reach puberty, average litter size and average gestation period. unlimited resources in the OP.

 

[pinball1970]

These are excellent analyses. I'm wondering about applications to astronomy.

Star formation? Galaxy formation?