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

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

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.

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