Last week’s blog established various time targets for the existence of our civilization and thus tried to establish an absolute level of sustainability. Granted, some of the targets I provided were rather trivial, like the desire to see another *“Thanksgivukkah,” *(an event where Thanksgiving coincides with Hanukkah). Such event could take place in as little as 60 years if we don’t care about the specific candle (which night of Hanukkah) or as long as 70,000 years if we are fussy about the candle. On the other hand, on a more serious note, we can give ourselves about 1,000 years to develop propulsion technology capable of moving people outside the solar system, while we identify a suitable, unspoiled, environment that can sustain us. As we will see shortly, the exact numbers are not very important here; the element we need to focus on right now is independent of our talks about the differences between a few hundred or a few thousand years. The most direct parameter that we can analyze for compatibility is the population.

Most population projections are based on the United Nation Population Division’s estimates. I went to Wikipedia to get a summary, and I hit on the following relevant paragraph:

Current UN projections show a continued increase in population in the near future (but a steady decline in the population growth rate), with the global population expected to reach between 8.3 and 10.9 billion by 2050.

^{[11]}^{[12]}UN Population Division estimates for the year 2150 range between 3.2 and 24.8 billion;^{[13]}mathematical modeling supports the lower estimate.^{[14]}Some analysts have questioned the sustainability of further world population growth, highlighting the growing pressures on the environment, global food supplies, and energy resources.^{[15]}^{[16]}^{[17]}

Projections for 2150, the very shortest end of our need for the definition of absolute sustainability, range between 3.2 and 24.8 billion people. I thought that this must have been a typo, because this kind of range is not much different from the “small” range of 0 – infinity, and you really don’t need any professional input for that kind of an estimate.

Well, I went to the source (“Long-Range Population Projections” *Proceedings of the United Nations Technical Working Group on Long-Range Population Projections* (New York: United Nations: Department of Economic and Social Affairs). 2003. Retrieved July 3, 2010. ) for the following paragraph:

Future population size is sensitive to small but sustained deviations of fertility from replacement level. Thus, the low scenario results in a declining population that reaches 3.2 billion in 2150 and the high scenario leads to a growing population that rises to 24.8 billion by 2150.

Well, it’s not a typo, but it involves a bit of trivial math. Here is the methodology:

The long-range projections prepared by the United Nations Population Division include several scenarios for population growth for the world and its major areas over the period 1995-2150.The medium scenario assumes that fertility in all major areas stabilizes at replacement level around 2050; the low scenario assumes that fertility is half a child lower than in the medium scenario; and the high scenario assumes that fertility is half a child higher than in the medium scenario. The constant scenario maintains fertility constant during 1995-2150 at the level estimated for 1990 – 1995, and the instant-replacement scenario makes fertility drop instantly to replacement level in 1995 and remain at that level thereafter.

One cannot plan for a fertility rate to be equal to replacement rate. Fertility rate is a global statistical value of a collective behavior that is based on decision making by individuals. A government or the world cannot declare a policy of replacement value. The replacement value of the current global fertility rate is now 2.1 children per woman in the developed world and about 2.5 children per woman in the developing world. About two years ago, we passed a landmark when the global population crossed the 7 billion mark. When I was born the world population was around 2 billion. In my lifetime I have welcomed around 5 billion new neighbors, and I am still kicking. It is true that the fertility rate almost everywhere is in sharp decline since the end of World War II; as a direct result, the population growth rate has been decreasing since that period. This does not mean stabilization at replacement with constant population.

To stabilize the population we need to work on it. In the next blog I will start to explore what needs to be done with particular emphasis on factors such as poverty, education and availability of birth control options.

The present world population is 7.1 billion people with a 2.1% (this is a typo – see Aisha’s comment and my response – the current population growth rate is 1,12%-values are going to be corrected accordingly) growth rate and shrinking. Within a business as usual scenario (continuing present rates of growth) the doubling time for the present population would be Td = 69/1.12 = 62 years (this is a simple formula that derives from the mathematics of exponential growth).

How long will it take, given a business as usual scenario, for population growth everywhere to reach the density of the most densely populated city in the world?

The city that holds that title today is Mumbai (India), which boasts a shocking 29,650 people/km^{2}. In the US, the equivalent is Los Angeles (ranked 90th globally), with 2,750 people/km^{2}. Our total global land area comes out to 130 million km^{2} (without Antarctica), or 148.94 million km^{2} if we count Antarctica.

“Simple” exponential growth math shows that with the present rate of growth, it will take 571 years for the global population to grow to be as dense as Mumbai is today. That calculation provides for fully populated areas, at the same density as Mumbai today, everywhere – including Antarctica, the Sahara and Gobi deserts and other virgin areas throughout the world. If this prospect doesn’t sink in, a “short” trip to Mumbai might serve to convince. If we allow for some land dedicated to food production and recreation, the time period to reach such densities shrinks.

Let’s go to the other extreme. Poland, Ukraine, South Korea and Belarus are all countries with populations greater than 20 million, but they have among the smallest fertility rates: around 1.2 births/woman (as of 2009). Their recent population growth rates (in %) are as follows: Ukraine is -0.76, Belarus -0.5 and Russia -0.51. These numbers include immigration and emigration. Let us now explore the extreme case of the world adapting to the reproductive statistics of these countries and in turn, reducing population growth to -0.5%/year. In such a scenario, it would only take about 460 years for the global population to shrink to 10% of its current number.

In the next blogs, I will explore the possible consequences of such a dramatic reduction. There is no mechanism that I am aware of that would allow the population to stabilize itself with a constant replacement rate.

Aisha is absolutely right. The 2.1% is a typo that I am apologizing for. It probably got there from a mix-up in my brain with the replacement rate.

Thanks and I will edit the blog accordingly

This blog brings to light some very interesting information about population growth. My interest lies in the Business as Usual scenario which you calculated using very simple math. Reviewing your calculations for scenario, it correlates with my calculations but the data used was slightly different. With the present population at 7.1 billion the global annual growth rate is not at 2.1% (it hasn’t been since 1964) but in fact 1.12% (2011). This information can be easily calculated using this formula: (P2-P1)/P1. This would change the doubling time Td = 69/2.1 = 33 years to Td = 69/1.12 = 63 years. From the exponential growth plot, it will take approximately 564 years for the global population to be as dense as Mumbai.