|Fig. 1: Average number of children per women versus life expectancy for a variety of nations in 2010. Each dot represents a country, with its size corresponding to its population and its color to its geographic region (see inset map). (Courtesy of Gapminder.)|
To maximize the probability of continual prosperity, a population of organisms in a resource-limited environment should simultaneously modulate the total number of organisms in the environment and the amount of resources consumed per organism. An unchecked increase in either of these parameters may result in degraded living conditions or even collapse.
Using this principle, let's attempt to determine the conditions that give rise to stability for the human population on Earth. Instead of considering the full complexity of the issues at hand, let's make simplified arguments in order to derive simple - but hopefully still useful - results.
The average number of children per woman, or CPW, is a proxy for the degree of population stability exhibited by a group of people. If the CPW is just over 2.0 then the population is static. However, if the CPW departs from this 'replacement rate' the population will increase or decrease, threatening the stability of the group. 
The annual energy use per person, or EPP, is a measure of resource use per person. In addition to taxing obvious resources like a limited supply of fossil fuels, energy consumption exhausts hidden resources. For example, the moderate temperature of the Earth is a resource that is depleted when non-solar energy is used. Further, energy use scales with consumption of other key resources like water, land, and useful minerals. If the EPP rises too high, even for a relatively small number of people, resource scarcity will jeopardize the security of the population.
Figs. 1 and 2, respectively, show the CPW and the EPP as a function of life expectancy for various nations worldwide.  Each dot represents a country, with the size corresponding to the country's population and the color to its geographic region.
|Fig. 2: Annual energy use per person versus life expectancy for a variety of nations in 2010. The energy unit used here is tonnes of oil equivalent (toe), which is the amount of energy released by burning one tonne (1,000 kilograms) of crude oil, and is roughly equal to 42 billion Joules. (Courtesy of Gapminder.)|
Recall that to maximize stability the human population should fix the CPW just over 2.0 and minimize the EPP. However, the trends in the data demonstrate the ostensible conundrum represented by these two stability requirements: as life expectancy increases, the CPW decreases while the EPP increases! Apparently you can't have your cake and eat it too.
Or maybe you can. The shape of the EPP versus life expectancy plot suggests a solution. The steepness of the curve in the high life expectancy regime implies that there is a set of countries with a wide range of EPP values that all have high life expectancy. For example, the U.S. has a high life expectancy of 79 years and a high EPP of about 7.2 tonnes of oil equivalent. Meanwhile, Japan, France, and Germany have higher life expectancies than the U.S. but use only about 55 percent the energy. Spaniards, Italians, and Israelis also live longer than Americans, with only about 40 percent the EPP. Costa Ricans and Cubans live as long as Americans, but use less than 14 percent the energy!
The data demonstrate that it is possible for a nation to have a CPW near 2.0 and a low EPP, all while maintaining a long-lived populace. To ensure the stability of the human population, perhaps we should study healthy, low-consumption nations and make a global push for the lower-right corners of these plots.
The arguments presented here are extremely rough, and the real-world challenges exceedingly complex. To further explore these issues, interested readers should peruse Dr. Hans Rosling's Gapminder website. The interactive graphical presentations of world statistics found there constitute both the basis for the figures presented above and a rich, accessible database for learning about global trends.
© Justin Briggs. The author grants permission to copy, distribute and display this work in unaltered form, with attribution to the author, for noncommercial purposes only. All other rights, including commercial rights, are reserved to the author.
 T. Espenshade, J. Guzman, and C. Westoff, "The Surprising Global Variation in Replacement Fertility," Population Res. Policy Review 22, 575 (2003).
 N. Singer, "When the Data Struts Its Stuff," New York Times, 2 Apr 11.