Exponential Growth and Population

Human population increases exponentially:

While humans may eventually define a logistic growth curve ; currently there is no evidence that this is the case. The only think that is demonstrable, as shown below, is that the rate of growth of the world's population is decreasing, but it's still exponential in nature. here is the data

In other words, the population doubling time is increasing, but there still is a characteristic doubling time. (70/n). Its currently an open question if the whole world will also conform to the logistic growth curve that has been obtained by the developed world.

Often times exponential growth is plotted as a straight line on a semi-log plot. The Y-axis is logarithmic and the X-axis is linear.

Note:

basic math:

ex =y

ln (ex) = ln y

ln y = x

Here is an example: The difference between linear growth (constant number of units growth per year) vs exponential growth (constant percentage increase) is difficult to see initially, if the exponential growth rate is small.

We can use the Statistical Graphical Tool to help understand this.

Here is some data:

• 1 100
• 2 110
• 3 121
• 4 133
• 5 146
• 6 160
• 7 176
• 8 193
• 9 213
• 10 235

First we try a linear fit which will clearly be seen as bogus.

Then we will try an exponential fit with 10% growth rate to see its much better. ## Population Growth and Finite Resources

Current Population Clocks

Some Issues:

• Is population growth really exponential in nature?

• Can the Clock be Stopped? the reality of Zero Population Growth

• Can new resources be found to replaced used resources?

• Can equilibrium be achieved through clever recycling?

• This is not my problem.

Zero Population Growth in the US:

This depends on three factors:

• The average births per female note, the rise in teenage pregnancy severely impacts this estimate
• The average life expectancy
• The annual net immigration rate

Birth Rate Expectancy Immigration Projections
1.9 75.3 350,000 293M (2030) 285M (2050)
2.2 82.6 880,000 263(1995) 392M(2050)
2.6 87.5 1.4 million 522M(2050)

In addition to this, the US population is undergoing a significant regional re-distribution ZPG is only achieved in a model which limits immigration (a very politically sensitive issue), restricts birthrates to no more than 2 per female (more politics), and makes no attempt to increase life expectancy.

The fertility rate has gone up. In 1988 the rate was 1.8 per female, now its 2.0 this increase is entirely due to teenage pregnancy.

Equilibrium is difficult to achieve because exponential growth produces demographics such that they are substantially more people entering their reproductive years than those which are dying of old age.

What about ZPG for the World? Worst case scenario assumes 2.5 children per couple 28 billion people by 2150

Best case assumes 1.7 7.8 billion in 2050 declining to 4.3 billion by 2150

Current fertility rate is 3.3. Fertility rate in 1970 was 4.5

The above calculations, however, do not adequately factor in increases in global life expectancy.     Other resources

Population Growth Map The above map shows the that the "industrialized" world has stabilized somewhat to population growth rates less than 1% a year. But 1% is still a doubling time of 70 years and the calculated growth rates are based, in this study, on only 5 years worth of data.

What does fertility rate depend on? Regression (to be discussed later) suggests that literacy is a key factor. Education may be the single biggest contributor towards ZPG.

When did we know there would be a problem?

Historical Estimates of World Population (accurate to 10--20%) • 1000 AD 0.25 Billion
• 1100 AD 0.30
• 1200 AD 0.36
• 1250 AD 0.40
• 1300 AD 0.36 (three cheers for war and disease!)
• 1350 AD 0.44
• 1400 AD 0.35
• 1500 AD 0.43
• 1600 AD 0.55
• 1650 AD 0.47 So during this period of 650 years the world population was stable and fluctuated around a mean value of about 400 million.

Is this the "natural" carrying capacity of the planet? 