1129 words - 5 pages

Population Growth and the Malthusian Prophecy

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...

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