(serious) Math brainiacs to figure how many goats...

[Phinnaeus Gage]

Starting with 1,000 goats, half of which are does, how many goats would there be at the end of twenty years given:

• After one year of birth, a doe produces two offspring: One doe and one billy.
• 80% of the billies are eaten (or succumb) when they reached maturity (usually within a year, but calculate it as a full year), with the other 20% gone when they reach two years of age.
• Does are eaten after producing and weaning eight offspring (four live births). Figure five years total.
• Figure a 20% mortality rate per year for does, thus not producing any offspring.

Thus, after one year, there would be 500 (original) - 400 (80%) + 500 (offspring)= 600 billies, and 500 (original)- 100 (20%) + 500 (offspring)= 900 does.
After two years, we calculate again ridding the 20% of the original billies plus the other 80% for the yearlings, and maintaining the 20% mortality rate for the does.

I'm guessing the Earth would be overrun with goats, but love to see if the math proves my suspicions.

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[Phinnaeus Gage]

I guess it could be done longhand for the first 5/6 years to obtain a rate of growth, then extrapolate that for the remainder 14/15 years. Would that accomplish the task?

[Phinnaeus Gage]

Somebody check my math or weigh in as I calculate the number of goats after year two.

• Beginning: 1,000 goats (500 Billies and 500 Does)
• Start of year two: 1,500 Goats (600 Billies and 900 Does)
• Start of year three (calculated below): 2,540 Goats (920 Billies and 1,620 Does)

After one year, we now see a 50% increase, with 500 total goats eaten or succumbed by other means, and 400 does producing milk.

Now, to calculate the number of goats after year two, there would be 600 (original/Y2) - 480 (80%) - 100 (20%) + 900 (offspring)= 920 billies, and 900 (original/Y2) - 180 (20%) + 900 (offspring)= 1,620 does.

If I did the calculations correctly, at the start of the third year there would be 2,540 Goats, an increase of 154% since the start of the program.

[SgtSpike]

Starting with 1,000 goats, half of which are does, how many goats would there be at the end of twenty years given:

• After one year of birth, a doe produces two offspring: One doe and one billy.
• 80% of the billies are eaten (or succumb) when they reached maturity (usually within a year, but calculate it as a full year), with the other 20% gone when they reach two years of age.
• Does are eaten after producing and weaning eight offspring (four live births). Figure five years total.
• Figure a 20% mortality rate per year for does, thus not producing any offspring.

Thus, after one year, there would be 500 (original) - 400 (80%) + 500 (offspring)= 600 billies, and 500 (original)- 100 (20%) + 500 (offspring)= 900 does.
After two years, we calculate again ridding the 20% of the original billies plus the other 80% for the yearlings, and maintaining the 20% mortality rate for the does.

I'm guessing the Earth would be overrun with goats, but love to see if the math proves my suspicions.

Here's my calculation for year 1:

500B - 400B(eaten) - 50B(half of 20%) + 500D - 100D(# eaten each year) - 100D(20% mortality rate) + 400B + 400D (offspring, only after 1 year old) = 450B + 700D

[SgtSpike]

Also, throwing it into Excel real quick-like, I calculated 244,032 billies and 418,341 does at the end of 20 years.

[dree12]

Rounding is significant here, I guess. Here's my result with 5 minutes of Python:

Year 0 ending, 500 billies and 500 does (1000 goats)
Year 1 starting...
Year 1 ending, 600 billies and 900 does (1500 goats)
Year 2 starting...
Year 2 ending, 1000 billies and 1620 does (2620 goats)
Year 3 starting...
Year 3 ending, 1800 billies and 2916 does (4716 goats)
Year 4 starting...
Year 4 ending, 3240 billies and 5249 does (8489 goats)
Year 5 starting...
Year 5 ending, 5832 billies and 9285 does (15117 goats)
Year 6 starting...
Year 6 ending, 10335 billies and 16549 does (26884 goats)
Year 7 starting...
Year 7 ending, 18406 billies and 29493 does (47899 goats)
Year 8 starting...
Year 8 ending, 32803 billies and 52555 does (85358 goats)
Year 9 starting...
Year 9 ending, 58454 billies and 93644 does (152098 goats)
Year 10 starting...
Year 10 ending, 104155 billies and 166839 does (270994 goats)
Year 11 starting...
Year 11 ending, 185568 billies and 297267 does (482835 goats)
Year 12 starting...
Year 12 ending, 330635 billies and 529658 does (860293 goats)
Year 13 starting...
Year 13 ending, 589111 billies and 943721 does (1532832 goats)
Year 14 starting...
Year 14 ending, 1049653 billies and 1681477 does (2731130 goats)
Year 15 starting...
Year 15 ending, 1870221 billies and 2995974 does (4866195 goats)

[dree12]

Also, throwing it into Excel real quick-like, I calculated 244,032 billies and 418,341 does at the end of 20 years.

Hmm, I just realized that my numbers don't check out after the first year. I think Phinnaeus made the mistake here, though.

Now, to calculate the number of goats after year two, there would be 600 (original/Y2) - 480 (80%) - 100 (20%) + 900 (offspring)= 920 billies, and 900 (original/Y2) - 180 (20%) + 900 (offspring)= 1,620 does.

It seems that 80 billies die twice: of the 100 that die because they survived the last year, 80 died again through routine cleanup. This is probably an error. There should be 1000 billies at end of year 2.

[SgtSpike]

Rounding is significant here, I guess. Here's my result with 5 minutes of Python:

Year 0 ending, 500 billies and 500 does (1000 goats)
Year 1 starting...
Year 1 ending, 600 billies and 900 does (1500 goats)
Year 2 starting...
Year 2 ending, 1000 billies and 1620 does (2620 goats)
Year 3 starting...
Year 3 ending, 1800 billies and 2916 does (4716 goats)
Year 4 starting...
Year 4 ending, 3240 billies and 5249 does (8489 goats)
Year 5 starting...
Year 5 ending, 5832 billies and 9285 does (15117 goats)
Year 6 starting...
Year 6 ending, 10335 billies and 16549 does (26884 goats)
Year 7 starting...
Year 7 ending, 18406 billies and 29493 does (47899 goats)
Year 8 starting...
Year 8 ending, 32803 billies and 52555 does (85358 goats)
Year 9 starting...
Year 9 ending, 58454 billies and 93644 does (152098 goats)
Year 10 starting...
Year 10 ending, 104155 billies and 166839 does (270994 goats)
Year 11 starting...
Year 11 ending, 185568 billies and 297267 does (482835 goats)
Year 12 starting...
Year 12 ending, 330635 billies and 529658 does (860293 goats)
Year 13 starting...
Year 13 ending, 589111 billies and 943721 does (1532832 goats)
Year 14 starting...
Year 14 ending, 1049653 billies and 1681477 does (2731130 goats)
Year 15 starting...
Year 15 ending, 1870221 billies and 2995974 does (4866195 goats)

Well, the problem is, PG and I came up with different equations based on the set of criteria.  I think PG made the assumption that all billies and does were 1 year of age at the start of the experiment, whereas I made the assumption that the age was already evenly distributed according to how the equation would eventually play out (i.e., 1/5 of the does were 5 years old, and thus were under the "mortality" rate, even in the first year).

[dree12]

Rounding is significant here, I guess. Here's my result with 5 minutes of Python:

Year 0 ending, 500 billies and 500 does (1000 goats)
Year 1 starting...
Year 1 ending, 600 billies and 900 does (1500 goats)
Year 2 starting...
Year 2 ending, 1000 billies and 1620 does (2620 goats)
Year 3 starting...
Year 3 ending, 1800 billies and 2916 does (4716 goats)
Year 4 starting...
Year 4 ending, 3240 billies and 5249 does (8489 goats)
Year 5 starting...
Year 5 ending, 5832 billies and 9285 does (15117 goats)
Year 6 starting...
Year 6 ending, 10335 billies and 16549 does (26884 goats)
Year 7 starting...
Year 7 ending, 18406 billies and 29493 does (47899 goats)
Year 8 starting...
Year 8 ending, 32803 billies and 52555 does (85358 goats)
Year 9 starting...
Year 9 ending, 58454 billies and 93644 does (152098 goats)
Year 10 starting...
Year 10 ending, 104155 billies and 166839 does (270994 goats)
Year 11 starting...
Year 11 ending, 185568 billies and 297267 does (482835 goats)
Year 12 starting...
Year 12 ending, 330635 billies and 529658 does (860293 goats)
Year 13 starting...
Year 13 ending, 589111 billies and 943721 does (1532832 goats)
Year 14 starting...
Year 14 ending, 1049653 billies and 1681477 does (2731130 goats)
Year 15 starting...
Year 15 ending, 1870221 billies and 2995974 does (4866195 goats)

Well, the problem is, PG and I came up with different equations based on the set of criteria.  I think PG made the assumption that all billies and does were 1 year of age at the start of the experiment, whereas I made the assumption that the age was already evenly distributed according to how the equation would eventually play out (i.e., 1/5 of the does were 5 years old, and thus were under the "mortality" rate, even in the first year).

Ah, I see. I used PG's method to obtain my numbers, which do seem to indicate more goat meat than 5 Earths in 20 years.

[Phinnaeus Gage]

Thanks, spike and dree. Assuming dree's spreadsheet is relatively close given my rough guidelines, it looks like the goat population doubles every year. In real life, this fact can easily be borne out by adjusting the percentages.

Another fact is that there is only 36,794,240,000 acres of land space on Earth. At the very least, each goat will require 1/10 of acre of land for grazing. Africa has 11,668,598 acres of land.

Now, some more questions, given the above. What's the most amount of goats a continent like Africa can sustain? How long would it take to reach that specific number? What's the maximum number of people that will benefit if they owned a breeding pair of goats? Once you place 10 goats on an acre of land, what land is used to grow other crops to feed 276,000,000 hungry Africans every day?

A little quick math proves that even if one goat could sustain one human for one year, ten million goats taking up one million acres of Africa (~1/10 total area available) would only sustain the same amount of people, still leaving 266,000,000 (and growing) hungry Africans. And they became even hungrier because crop growing acreage was turned over to the grazing of goats.

To be clear, I'm not dissing the goat giving programs, for they're truly needed. But now it can be clearly seen that there's only a certain number of goats that any one continent can handle. And that number is even greatly reduced when you implement other livestock programs to the same region (chickens, ducks, cows, pigs, etc.), some of which need more land to flourish, most of which don't go hand-in-hand with the raising of edible crops.

I say that any organization that starts with a 100 breeding pairs of goats, they would reach the maximum sustainable goat population in any region of the world in ten years max unless, of course, the project is designed in some nefarious way, then an infinite amount of years would still not reach said population.

[notme]

Wouldn't you eventually run into the problem of all billies spending every day fucking and some does still not getting pregnant?

[Phinnaeus Gage]

Wouldn't you eventually run into the problem of all billies spending every day fucking and some does still not getting pregnant?

Not if you eat the over-fuckers.  

Given that only 7% of the world's land is dedicated to agriculture, it amazes me that 2,575,596,800 acres feed 6,973,738,433. That equates to .36932799025 acres for every person currently on Earth. We all know that that number gets smaller daily to less land being used for agriculture and the population growing.