The Limits to Growth Is there a limit to that size?

The Limits to Growth Is there a limit to that size? How can we predict the size of the human population in the future? What are the consequences if the population grows to exceed that limit? Finally, can we really answer all these questions?

Is there a limit to the size of the human population? To answer that, you need some background information. There are two basic growth models that have been applied to population growth. The first, called an exponential growth model, describes growth with no limit. Resources needed to support growth are considered to be infinitely available.

The second model is growth towards some limiting value, called the carrying capacity (or K). The model is called logistic or ‘sigmoid’. Here there is a limit to resource availability.

What does human population growth look like? Pretty much exponential – but is it really exponential? If it is, then the intrinsic (or exponential) rate of increase should be constant. I can’t show you world data, but can show you what has happened in the U.S.

Human population growth in the United States… as population size has increased, the intrinsic rate of increase has slowed... Extrapolated using censuses from 1790 to 1910, the U.S. population should have come to equilibrium at ~200 million.

That didn’t happen. Better medicine, immigration, and many other factors kept the population growing. Globally, something similar has happened: Growth has slowed a bit, but the human population continues to grow.

Here’s a table extracted from Limits to Growth – the 30 year update showing world population, growth rate at each time, and the resultant number added to the population…

Is there a limit to that growth… There’s a history associated with the answer. William Petty, in "Another Essay in Political Arithmetic" (1683) estimated the K as a density of 2 people for every 5 acres of habitable land. That would yield an estimate of K (based on current habitable area) of 10 billion. In 1960, the Club of Rome, a gathering of experts in various fields related to predicting the future of the human population, developed a modern estimate of K, and came up with the same number – 10 billion. Many other estimates have been made, but there is absolute agreement that there is a limit – the earth can sustain a population somewhat larger than the ~7 billion on earth today, but not too many more.

How do we determine the future size of the human population? The tools used can be collected under the umbrella called demography. [Definition: the study of the age structure and growth of populations] There are neat graphical representations that can tell us in general terms whether a population is growing, holding steady, or declining, and even give us a general idea about how fast it’s growing. They’re called demographers’ curves. On the x-axis of each ‘curve’ is the proportion of the population in each group. On the y-axis are the age classes into which the population is grouped

Consider the third question: What are the consequences if the population grows to exceed that limit (the carrying capacity)? There’s a history to this question, too. Thomas Malthus (1766-1834), in his An Essay on the Principle of Population (1798), used the growth of the English immigrant population of North America to propose that the growth of the human population was (at that time) exponential. However, he noted that the growth of food production was only linear. Eventually, the population would exceed the support capacity of its resources. He said that the result would be “misery and vice”.

Once more there is a 20th century take on what may happen… We hope that improved technology (biotechnology, genetic engineering, new pollution control methods,… will solve the problems. Limits to Growth used a complex model to project what may happen based on differing scenarios. What follows are a series of graphs that show you model output under those differing ‘inputs’.

Scenario 1: ample supplies of non-renewable resources and improved pollution control technology

Scenario 2: Larger supplies of non-renewable resources, improved pollution control technology (as before), and enhancement of agricultural yields/unit area

There’s not much difference in either of those scenarios – the population ‘crashes’, resources decrease dramatically in availability, pollution increases until the lack of resources drives down industrial production. In terms of the human condition, life expectancy, as well as availability of food and consumer goods, declines. The only scenario in which the human population and its condition don’t markedly decline during the 21st century is one in which all of the previous steps are taken, and 1) protection against soil erosion (particularly on agricultural lands) is enforced, and 2) new technologies to improve resource use efficiency are developed. Here’s what the model then looks like:

Finally, are there answers to all those questions? No! The models are predictions that make enormous assumptions about our will to limit population growth, our ability to develop and demand greatly improved pollution control technology, our ability to use tools like genetic engineering to increase crop yields (and to accept the products of that genetic engineering), and our willingness to subjugate individual ‘rights’ to the common good in areas like prevention of soil erosion and the adaptation of resource-efficient technology. Today the hybrid car, tomorrow ??

The Limits to Growth Is there a limit to that size?