Adam and Eve population Equation.

[Mr_E]

Is there an equation out there that calculates how many children each person would have needed to produce, in order to go from 2 people to 7 billion in 6000 years. And after that taking into account the set backs like the flood, plagues, wars, infertility rates, murder and so on. If not, could you help me device one.

[brimstoneSalad]

This sounds like a school assignment. Is it?

[Cirion Spellbinder]

I would also like such a formula, but alas, I'm low on that mathematical ladder.

This sounds like a school assignment. Is it?

Is help on school projects not allowed the forum?

[brimstoneSalad]

Is help on school projects not allowed the forum?

Not necessarily, but people should know if that's what it's for so they can decide for themselves.

[PsYcHo]

I'd be willing to help you consider some of the variables needed for the equation, but the actual legwork is up to you. Of course the variables vary depending if you are coming from the theist perspective or strictly scientific. (For example, biblical text claim that people lived up to a thousand years in the past, which would dictate a whole different mathematical reasoning)

To keep it simple, we'll stick to scientific. (not my area of expertise, but perhaps it can give you something to work on) I would first start with researching the average birthrate per person in third-world countries, as for most of history scientific advances that save lives on a mass scale were not invented. That would give you a base-line approximation of how many children a couple could be expected to have if they lived an average human lifespan, keeping in mind that females are only fertile for about 40 yrs on average.

Now a major problem straight off is inbreeding. However, this could be countered with the fact that some species are not harmed by incestual copulation. Lab rats are not considered inbred until the 20th generation, so it could be reasoned that early humans were the same. So to start I would calculate how many offspring these two could have had starting at puberty. Factor for 50% being male and 50% being female, deducting average losses before sexual maturity age.

Now for the tricky part. Once you figure out how many females are 2nd generation, factor for them being pregnant and birthing from puberty until menopause. This will get progressively more difficult, because for the purposes of this thought experiment, inbreeding is not a problem until the 20th generation. I would advise using a spread-sheet program for the math. By the 20th generation, there should be enough genetic diversity to assume interbreeding will no longer be an issue.

For the factoring of losses due to flood, famine, etc. Follow the above formula to get the total amount possible from start to finish. Look up the current world population for the past 60 or so years, as records are better for this time period. Research recorded deaths from the same time period due to natural disasters, and get your percentage of deaths by nature. Use this percentage against your total possible human population. Bam! (hey if you do the math, let me know! It would be neat.)

[inator]

It's difficult to get much information on global population numbers before the 1600's, you might have to do some digging. It took humanity 200,000 years to go from 0 to 0,5 billion in the 1600's. Then it took 200 years to get to 1 billion. And then another 200 years to get from 1 billion to today's 7 billion people. A population growth of about 1,3% per year since the industrial revolution is what got us here.

You could theoretically calculate an average annual population growth rate that would be necessary in order to get from 2 people to 0,5 billion in 5600 years. Do you also want to include the flood? Then you'd have to start out with three couples (Noah's sons and their wives) around 4400 years ago.
So, if you can't find other information, all you can do is calculate the average growth rate between 4400 years ago (allegedly 6 people) and 400 years ago (0,5 billion people).

Here are two formulas for that. You'll get roughly the same number with both.
http://www.nscb.gov.ph/ru11/glossary/population/PGR.htm
http://www.coolmath.com/algebra/17-expo ... -growth-01

And then make estimations about how many surviving children each couple needed to have on average to maintain this growth rate (depending on average life expectancy and assuming that everyone was strictly monogamous).

[Mr_E]

This sounds like a school assignment. Is it?

Nah. Im not in school anymore. Would have loved to do this kind of assignment though.

[Mr_E]

I think you guys missunderstood or, i simply explained my self poorly. What i meant was, lets go straight for the end goal. The current population and then the original 2 people. We should actually start 4000 years ago with 9 people after the flood. What i am trying to figure out, is whether or not it is possible for 9 to turn into 7 billion in 4000 years. What i had in mind was to start out simple by finding out how many children would be needed per person to multiply the population up 7 billion from 9 people in 4000 years. Then if that was possible, add in the other variables, such as the war setbacks, plagues, infertility murder, so on. And end at a result that is either somewhere between "each couple would have to produce at least 3 children" = do-able. or "each couple would have to have produced 20+ children". Something like that. I just have no idea how to handle the multiplying, into more multiplying as the population grows. Always hated math whilst in school. Now i am slowly trying to remedy it.

[Cirion Spellbinder]

^
Is a god helping them move along? Otherwise, I'd imagine that the constant incest will lead to plenty of offspring with bad genes and they should all die off in a few generations.

[brimstoneSalad]

I think you guys missunderstood or, i simply explained my self poorly. What i meant was, lets go straight for the end goal. The current population and then the original 2 people. We should actually start 4000 years ago with 9 people after the flood. What i am trying to figure out, is whether or not it is possible for 9 to turn into 7 billion in 4000 years.

Very easily. It's exponential growth.

4000 years / generation = generations.

If a generation is 16 years, and each couple has two kids every 16 years on average:

9 * (2^(4,000 / 16)) = 16 Trillion Vigintillion (this is a number so large you can't comprehend it, and I had difficulty naming it)

This does not account for mortality, but those numbers are trivial compared to the growth.

If the population doubles only every hundred years:

9 * (2^(4,000 / 100)) = 9.89 trillion

It's not hard to double your population every hundred years. Your reproduction only has to very slightly exceed mortality.

In order to reach seven billion, the population must double almost every 135 years:

9 * (2^(4,000 / 135)) = 7.45 billion

So, you just need to figure out how often the population has to double, and see if that's reasonably possible.