May 5, 2003


Guy LeBas


Human Demographic Dynamics: Within the Population Curve?



All exponential growth must have a limit.  There is simply no getting around this reality for the following reason: any population or other object which grows exponentially will eventually overtake the size of the universe, a physical impossibility, at least as we conceptualize physics.  Take the example of Standard Oil, run by John D. Rockefeller, the largest monopoly this country has seen.  Just past the beginning of the twentieth century, Standard Oil was growing at an exponential pace greater than that of the economy.  That single business came to make 14% of the US’s GDP (today. 12% is about the entire size of the healthcare industry, from HMO’s to your neighborhood physician) and eventually grew so large it had no market and collapsed.  The same must happen to the human population, though ideally in not such a catastrophic manner.  Eventually, human population size will bump up against the limits of what our finite resources can support, resulting in the fulfillment of the Malthusian prophecy.  The only questions that remain are: when will this occur? and how can we prepare the human race for this occurrence?


To go more in depth regarding exponential growth, traditional logistic organism population growth models, and resource limitations, I’ve included several mathematical functions (which produce related graphs; use a graphing calculator while plugging in the appropriate values to view these) in with this piece.  The basic exponential model which identifies population size (“P”) next year (period “t”) based on a growth rate over a period of time (“g”) is: P(t)=P(t-1) x (1+g).  Of note is that this is an exponential growth model that depends on a given growth rate.  Entering a past “g” and assuming it will continue into the future is not necessarily accurate as it only predicts future population size based on past statistics.  Such a method is less prediction and more regression and assumption.  More realistically, the population growth rate is determined by the following function in which “N” represents the population at time “t-1,” “r” represents the instantaneous present growth rate, and “K” the carrying capacity of the environment: g=(1+r)N[(K-N)/K].  This part of the population growth model effectively governs infinite exponential population growth with the introduction of the carrying capacity concept.  Carrying capacity is simply the ability of the environment to support a population, measured in terms of numbers of individuals.  Therefore, as the population size approaches the carrying capacity, [(K-N)/K] approaches zero.  The ultimate effect is a decreased “g” and likewise, a lower population at time “t.”  Take the integral of this function, which represents the total population and the end result is a “sigmoidal” shaped population curve, one that looks something like an “S” turned on its side.  As far as estimating inputs for this model, we know that the current human population growth rate is around 1.3% (UN Population Project, 1991), making for a population doubling time of roughly 53 years.  What we do not know is the carrying capacity of our environment. 


The crux of the population argument—both for the proponents of population control measures and the believers in the “tech fix”—lies in the determination of “K,” the aforementioned carrying capacity.  Many argue that we have already surpassed Earth’s capacity to provide for our population and, as such, the human population will begin to shrink through a number of devices in the coming decades.  Many others argue that the planet can easily hold billions more humans before “K” even becomes a factor.  Still others argue that we will develop technologies that allow humans to live outside the bounds of the Earth and therefore greatly increase “K” to the point where it is irrelevant.  Current estimates for “K” range from 3 to 50 billion (though most run around 15-20 billion) and derive numbers from the presumed limit of available food sources.  Factors such as the amount of land available for agriculture, crop yields, type of diet, and size of diet all go into estimating the size of available food stores.  Ecologists generally begin by calculating the productive capacity of land in six categories: arable land, pastures, forest, ocean, developed land, and fossil-energy land (land used to absorb CO2 from industrial production).  The average person needs around two hectares of land to thrive.  Currently, each person on this planet can “afford” to use as much as 6.4 hectares of land—called the maximum usable “ecological footprint”, indicating that the population will have to roughly triple before we bump up against “K.”  Note that in the US, however, the average person has an ecological footprint of 8.4 hectares of land for their own personal use.  Most industrial nations, owing to their higher standards of living, have ecological footprints far greater that their carrying capacities.  In that sense, industrialized nations effectively prey on their less-industrialized counterparts to provide carrying capacity through economic and political means.


For the purpose of this argument, we will assume a “K” value of 19 billion, which is based on the above ecological footprint estimates.  Entering that in to our population growth rate model gives us: g={(13)(N)[(19b-N)/19b]}.  In short, this tells us what we have been thinking for some while, that when the population hits 19 billion, the population growth rate will hit zero, a total fertility rate of approximately 2.06, or the “replacement rate.”  The logistical population curve indicates that the human population will reach a stable value of 19 billion in slightly over 600 years.  Over that time frame, the human population growth rate will slowly fall to zero—reaching .65% after only around 50 years and hitting .01% in three hundred. 


Since we know what will occur, the question now becomes how can we improve the quality of human life in light of this limitation?  A few short suggestions will have to suffice for now.  Especially in industrialized nations, we should decrease our use of resources.  The best way to do this is simple: do away with air conditioning and reduce heating in the winters by only 5°F.  Decrease the amount of meat in our diets.  Walk rather than drive—in short, all of the suggestions those protecting the environment have shared with us for years.  These slight changes will amount to a much greater average quality of life in the coming decades of the population crunch.  The only way to make the future better for humans as a population is for the higher-level members of the good consumption chain to cut back.  Convincing the public to start suffering now for our future is, however, unlikely in the extreme.