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Population Mathematics and Humanity

I will begin with a conclusion which is... uncomfortable to say the least.  Then I will walk through how this conclusion was reached.  It is something which will have you call bullshit on me off the bat, but please hear me out (or read me out?).  I have written a theoretical ecology paper last summer which shows that the human population will stop growing no later than 2031, and will drop (not plateau) shortly thereafter.  The cause?  Resource depletion.  Please, read me out.

Now, how did I come to this conclusion?  By the power of maths!

In ecology, there is a situation where, when a major cause of death for a species is removed, the population of that species goes through what is called exponential growth.  This is where the rate of change (percent change) is constant, and since the population today is more than it was yesterday, the greater the net change.  Let's say the percent change is 1% and we started with $100.  Tomorrow, we would have $100+($100x0.01)=$101.  The next day, since we start with $101, we calculate from that to have $101+($101x0.01)=$102.01.  An additional penny is added on.  If that money goes untouched for a week, we have $107.21.  It would rise faster as the base amount increases.   This is exponential growth, which is what the above population would go through.

This applies to species as well, and there comes a point where that species' environment can no longer support the population, much less the population growth.  As a result, there is mass starvation and die-offs, which causes the population to crash.  This is rarely ever a complete crash, but is often time a crash big enough for the population to be further below their carrying capacity (the maximum population which a niche can support comfortably) than they were before the exponential growth began.

We have witnessed this enough with mammals that we have created a mathematical model from them (see three weeks ago for my schpeel on mathematical models), one which we have since refined.  This mathematical model for population dynamics is now a full theory in ecology.  So now I have a mathematical model do break to my will in order to figure out when the human population will peak.

The problem with this model is that it depends on carrying capacity, which is a value that we cannot seem to pin down for humans on Earth; that value ranges anywhere from 4 billion to 16 billion, depending on who you ask.  With those two facts combined, I needed to find a way to get an answer which had some degree of certainty, and this couldn't be done with carrying capacity.

So what I did was to go through a mathematical manipulation of the population model to remove carrying capacity from it.  This was not a simple task by any stretch of the imagination, but it appears that I was successful.  The maths professors who I have shown this proof to did not see anything wrong with the proof, including the professor whose class the paper was for.  The paper ended up being 9 pages long, most of which was assumptions and proof.  The assumptions were as basic as "Population change due to immigration and emigration is zero", because, you know, I don't think there are very many people moving to or from Earth.

After all was said and done, I had a mathematical model for population growth and decay which was independent of carrying capacity.  With this, I calculated the human population peak to be the year 2029, give or take 2 years.  In other words, anywhere between 2027 and 2031.  Not a pleasant thought, especially when it is due to resource depletion rather than climate change.

This is not to say that I don't believe in climate change or that it won't affect us; climate change is real, it is observed, it is human caused, and it will hit us hard.  This post just goes to show that climate change will hit us hard AFTER resource depletion does.  You don't need to be an economist to see how that will affect our economy and therefor our society.
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