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Science Forum Index » Mathematics Forum » Simple Formula Required
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| Matthew Baker |
 Posted: Thu May 01, 2008 6:02 pm |
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Greeting all
I am sorry if this seems elementary to you folks, but I cannot find a
formula.
I am playing a game that revolves around raising livestock. I am trying to
determine the size of my flock after one and two years. Here is what I
know.
A doe gives birth to three females and three males every two months.
An infant reachs maturity after three months and can be inseminated
......first litter is five months after birth
I could likely do this manually, but it would take a BIG sheet of paper.
Can any of you supply a simple formula for this???
Thanks |
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| Ross |
| Posted: Thu May 01, 2008 6:02 pm |
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On May 1, 4:02 pm, Matthew Baker <n...@math.guy> wrote:
Quote: Greeting all
I am sorry if this seems elementary to you folks, but I cannot find a
formula.
I am playing a game that revolves around raising livestock. I am trying to
determine the size of my flock after one and two years. Here is what I
know.
A doe gives birth to three females and three males every two months.
An infant reachs maturity after three months and can be inseminated
.....first litter is five months after birth
I could likely do this manually, but it would take a BIG sheet of paper.
Can any of you supply a simple formula for this???
Thanks
There probably is no simple formula, but a small spreadsheet (one row
for each month by six columns) is sufficient. The columns are the
types of livestock: males, does that gave birth last month, does that
did not give birth last month, infant females, one month females, and
two month females. For each type of livestock, enter the rule for how
many you have this month. For example males this month = males last
month + 3*does that did not give birth last month. Month 0 has your
starting population. Once you enter the equations for month 1, just
copy down. |
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| Ray Vickson |
| Posted: Thu May 01, 2008 6:02 pm |
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On May 1, 4:02 pm, Matthew Baker <n...@math.guy> wrote:
Quote: Greeting all
I am sorry if this seems elementary to you folks, but I cannot find a
formula.
I am playing a game that revolves around raising livestock. I am trying to
determine the size of my flock after one and two years. Here is what I
know.
A doe gives birth to three females and three males every two months.
An infant reachs maturity after three months and can be inseminated
.....first litter is five months after birth
Here are some questions that need answering before you can start. How
many males and females are present at the start? Are they all fertile?
Can a male start inseminating females at age three months, and
inseminate a female every month after that? Does one male inseminate
just one female in one month? In particular, if there are, say 5
fertile females and 3 fertile males, do the 3 males pick 3 of the 5
females to inseminate, and leave the remaining 2 females alone for
that month? Similarly, if there are 3 fertile females and 5 fertile
males, do 3 of the males inseminate the females and the other two
males sit idle for that month? Are there no deaths?
R.G. Vickson
Quote:
I could likely do this manually, but it would take a BIG sheet of paper.
Can any of you supply a simple formula for this???
Thanks |
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| Dave |
| Posted: Thu May 01, 2008 6:02 pm |
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On May 1, 7:14 pm, Matthew Baker <n...@math.guy> wrote:
Quote: Holy cow (no pun intended) I see that this could be even more complex...
Start with a single Doe which has been impregnated and zero Bucks.
All animals are always fertile every other month.
Insemination can be done artificially so Buck fertility is immaterial.
Deaths should not be a factor (possible, but not included for this
calculation.
I tried to count out the herd size after one year and came up with 377
animals (Doe Alpha plus 376 offspring). My limited math knowledge tells
me that I cannot just double the 376.
Here's what I got:
D-BTM = does born this month
D-ITM = does impregnated this month
B = bucks
Month D-BTM D-ITM B Total
0 0 1 0 1
1 0 0 0 1
2 3 1 3 7
3 0 0 3 7
4 3 1 6 13
5 0 3 6 13
6 3 1 9 19
7 9 6 18 37
8 3 1 21 43
9 18 9 39 79
10 3 10 42 85
11 27 12 69 139
12 30 28 99 199
13 36 15 135 271
14 84 55 219 439
15 45 45 264 529
16 165 91 429 859
17 135 129 564 1129
18 273 136 837 1675
19 387 294 1224 2449
20 408 271 1632 3265
21 882 567 2514 5029
22 813 658 3327 6655
23 1701 975 5028 10057
24 1974 1540 7002 14005
Dave |
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| Matthew Baker |
| Posted: Thu May 01, 2008 7:14 pm |
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Ray Vickson <C6L1V@shaw.ca> wrote in
news:1ce7f313-db4d-4508-acf4-c25d77849f29@w8g2000prd.googlegroups.com:
Quote: On May 1, 4:02 pm, Matthew Baker <n...@math.guy> wrote:
Greeting all
Holy cow (no pun intended) I see that this could be even more complex...
Start with a single Doe which has been impregnated and zero Bucks.
All animals are always fertile every other month.
Insemination can be done artificially so Buck fertility is immaterial.
Deaths should not be a factor (possible, but not included for this
calculation.
I tried to count out the herd size after one year and came up with 377
animals (Doe Alpha plus 376 offspring). My limited math knowledge tells
me that I cannot just double the 376.
Thanks to all who have replied so far.
Quote: I am sorry if this seems elementary to you folks, but I cannot find a
formula.
I am playing a game that revolves around raising livestock. I am
trying to determine the size of my flock after one and two years.
Here is what I know.
A doe gives birth to three females and three males every two months.
An infant reachs maturity after three months and can be inseminated
.....first litter is five months after birth
Here are some questions that need answering before you can start. How
many males and females are present at the start? Are they all fertile?
Can a male start inseminating females at age three months, and
inseminate a female every month after that? Does one male inseminate
just one female in one month? In particular, if there are, say 5
fertile females and 3 fertile males, do the 3 males pick 3 of the 5
females to inseminate, and leave the remaining 2 females alone for
that month? Similarly, if there are 3 fertile females and 5 fertile
males, do 3 of the males inseminate the females and the other two
males sit idle for that month? Are there no deaths?
R.G. Vickson
I could likely do this manually, but it would take a BIG sheet of
paper. Can any of you supply a simple formula for this???
Thanks
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| Tim Little |
| Posted: Thu May 01, 2008 11:38 pm |
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On 2008-05-01, Matthew Baker <non@math.guy> wrote:
Quote: A doe gives birth to three females and three males every two months.
The males can be essentially ignored. Just note that the number of
males born is equal to the number of females.
Quote: An infant reachs maturity after three months and can be inseminated
.....first litter is five months after birth
The odd-numbered offset between birth and maturity makes it quite a
messier problem than if all litters were synchronous. If you want an
exact number, a spreadsheet would probably be easiest.
- Tim |
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