Math for Doomers

I was interested in an easy way to figure out how population could change over time at different replacement rates. I haven't come across any ready formulas, so decided to make my own (and sorry if it doesn't read so easily without subscripts and superscripts):

The main concern is population, so let X be any given population. To track changes over time in one year increments, we can make our starting point X0, the one year point X1, two years X2 and so on. X1 will then most simply equal the effect of births - deaths on X0, so we can use the customary birth and death rates as percentages and say X1=X0 +X0(birth rate – death rate)). If we take a potentially attainable number, using the 2008 numbers from Italy, for instance, with a birth rate of .00836 and a death rate of .01061, the formula becomes X1=X0+X0*-.00225. This only gives us the change over one year, though, and we need to apply the changes of each year to the next year's number to get anywhere past X1, which gets a little more complex or repetitive.

Fortunately its about the same thing as calculating compound interest, so rather than puzzling it out I just borrowed that formula. The problem can be stated simpler, then, as X1=X0(1+-.00225), or X1=X0(.99775). Then X2=X0(.99775) to the power of 2, X3=X0(.99775) to the power of 3 and so on.

Moving on, the question that would be the whole reason for the math is: how doomed are we? Or are our population problems intractable to the point that starvation and war are inevitable, given peak oil and climate change.

If the current population of the planet attained the longevity and birth rate of Italy, which is considered to be at the forefront of the European population decline attributed to affluence and education, at "X100", or 100 years from now, our population would only naturally drop to 5.4 billion or so. It would take more than 500 years for the population of the planet to drop naturally to the 2 billion mark which has sometimes been offered as the planet's carrying capacity...

Having gone over the numbers pretty well myself, I think, I was just posting this in case someone can find an error or something I've missed.

To know which way the wind is blowing...

In other words, you say that the current adjusted birth rate in Italy is -.00225, but what if it's dropping by another 2% each year? Then, it's not just simple interest any more. It becomes a lot more complicated than I could even hope to write out, and it could drastically reduce the time needed for Italy's population to drop to a given level.

I think this covers it:
http://www.arachnoid.com/lutusp/populati.html

and nothing really more encouraging.

The question I started with more specifically was whether an easy policy or natural means could lead to a soft landing for human population, somewhere within the carrying capacity of the planet over the next 100 years or so. Italy has one of the lowest birth rates of any country, without particularly trying (lower than China's, for instance, in spite of the One Child policy), so they're a decent example of a declining population that's not skewed toward early death by war, disease or poverty.

Anyway, it looks like the answer to the question is "no", or "not likely".

is arbitrary and thus meaningless. Hamden Rice has pretty well demolished that assumption many tmes.

its just what I remember from a study a few years ago (Columbia University, I think). I don't think a non-arbitrary carrying capacity can be determined at all, given the uncertainty in climate change models.

Not clear what your position is on this.

The 2 billion figure often mentioned is more a guess than an assessment -- do you have a figure based on a less arbitrary assessment, or are you saying that estimating sustainable carrying capacity is itself a meaningless undertaking?

I'm not familiar with Rice's argument, or exactly what "that assumption" refers to -- maybe you could recap for us.

It comes down to how much of the biosphere we are willing to sacrifice, and what quality of life we are prepared to accept. After all, carrying capacity just means the number of humans the planet can "support" in relative perpetuity. It traditionally doesn't factor in the harm done to other "non-resource" species or the quality of life of those humans.

So, at the extremes:

If we were willing to sacrifice all non-resource species, and accepted a quality of life that involved little more than eating and keeping the rain off, the carrying capacity of the planet might be very high (say in the tens of billions).

If we want to preserve the biosphere in a better-than-current condition, allow other species to regenerate and establish a Western quality of life for all humans, the number might be very low (on the order of a billion?)

So we're talking about carrying capacity estimates that vary by a couple of orders of magnitude. That's too broad for sensible debate, because choosing where in that range one plants their picket pin is more of an exercise in personal psychology than science.