# How many geese in 2,4,10 years if

1. Jul 26, 2011

### Tregg Smith

Not sure where this goes. I like math but this is a little over my head. Can somebody do this for me and what branch of math is used? Our town has a goose manure problem so I'm gathering facts for my presentation. Here's the problem- If two geese produce 8 babies each year what would the population be in 2,4, ten, years? That's considering the babies in their second year will reproduce and it's in a closed system because they don't migrate. Could you show your work? Thanks!

Last edited: Jul 26, 2011
2. Jul 26, 2011

### pmsrw3

How many are you starting with? How long do they live? How long do they take to mature?

Taking the simplest possible case: geese live forever, and they mature and are fully fertile in a year, then the population increases by a factor of five every year. (It's five, not four, because the parents are assumed to survive.) So, if you started with two in year 0, you would have:

Year 0: 2
Year 1: 5 x 2 = 10
Year 2: 5 x 10 = 50
...
Year n: 2 x 5n
...
Year 10: 19,531,250

Let me add that if you presented me with these figures and tried to use them to persuade me that the goose problem was going to become unmanageable, I would be totally disgusted with you for showing me an unrealistically sensational extrapolation that has no relationship to reality. Obviously, you are not really going to get to 19 million geese in your town in 10 years.

If you want a realistic projection, that's much harder.

3. Jul 26, 2011

### gsal

Well, here is my estimate.

The first row is the heading and represents the year.
The first column is the age of the number of geese in that row.
The matrix contains how many geese you have at a given year, and how they are grouped by age.
The last row is the total number of geese at the end of such year.

Code (Text):

00   01   02   03   04   05   06   07   08   09   10
00   2         8    8   40   72  232  520 1448 3528 9320
01        2         8    8   40   72  232  520 1448 3528
02             2         8    8   40   72  232  520 1448
03                  2         8    8   40   72  232  520
04                       2         8    8   40   72  232
05                            2         8    8   40   72
06                                 2         8    8   40
07                                      2         8    8
08                                           2         8
09                                                2
10                                                     2
2    2   10   18   58  130  362  882 2330 5858 15178

So, basically, I started with 2 geese being born at time zero.
Year 1
2 geese became 1 year old (move the number from row-0 to row-1) and did not reproduce (do not fill in row-0)
Year 2
2 geese became 2-year old (move the number from row-1 to row-2) and
produced 8 more geese but they are age zero (fill in row-0).
Year 3
2 geese became 3-year old (move the number from row-2 to row-3);
8 geese became 1-year old (move the number from row-0 to row-1)
all geese 2-year old and older produce new geese, in this case, 2x4 = 8, fill row-0

etc, etc,

you basically need to keep making every group of geese 1-year older every year (move the numbers down one row)
then, take all geese 2-year old and older (add them up) and multiply by 4...this is the number of geese born that year...fill in row-0.
repeat process.

By the way, a search yielded that while the maximum number of eggs a goose may lay is 12, the average is between 3 and 6; so, you may want to reconsider your 8.

Also, depending on how many geese you start with and their ages, do not forget to start killing off geese once they turn 24 years old of whatever age...

Last edited: Jul 26, 2011
4. Jul 29, 2011

### Tregg Smith

Let me add that if you presented me with these figures and tried to use them to persuade me that the goose problem was going to become unmanageable, I would be totally disgusted with you for showing me an unrealistically sensational extrapolation that has no relationship to reality.

Who would believe it anyway! One source says it's likely only one of the brood lives past the second year. :rofl:

5. Jul 29, 2011

### pmsrw3

Yeah, the problem with these projections is that they're very sensitive to small changes in your assumptions.

6. Jul 29, 2011

### gsal

Certainly, nobody is going to believe the 19 million geese thing...if that was the case, we would have more geese than mosquitos, by now, certainly more geese than chickens...can you say "Kentucky Fried Geese"?

pmsrw3 assumed that geese are born one year and that they grow up, mature, get married, get pregnant and give birth by the very next year...I can't believe what a difference such assumption makes...I calculated only about 15 thousand geese by the 10th year by allowing geese to take 2 years to reproduce.

I quick internet search reveals a couple of stats, too, like geese population increases 10% a year, etc. You may be better off going about it that way.

7. Jul 29, 2011

### pmsrw3

Not surprising, really. That change alone doubles the generation time, which has the effect that the fold-increase is about the square root in your model compared to mine. Not exactly, of course, because your model was more realistic in some other ways, too. But that's the most important change.

Geese don't get pregnant and give birth, by the way

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