Abstract
In the past 10,000 years of human history, the exponential rise of world population takes place only since the end of the seventeenth century. Joel E. Cohen drew a graph to show the historical change of human population from One Million B.C. up to the present. It looks like a reverse L-shaped curve with a long tail. It suggests a possible extinction of the human population. It indicates the powerful nature of exponential growth, but it can also be observed as every moment from the past to the present, and to the future. Differently, the population wave model shows that the development of human population is a continual wave with many demographic transitions. It has multifractal structure and composed of innumerable logistic waves in a short term, which are integrated into a single logistic wave at the end. Back to Malthus’ theory, what he said was reexamined. Simple simulations show the exponential growth is unsustainable beyond the narrow ranges of the population growth rate. When the growth rate deviates too far from the replacement level, either exploding or shrinking will occur and the balance between population and society will collapse. The principle of sustainable population indicates that only the society can be existed and be sustainable, if it can successfully maintain or recover its population to a stationary level.
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Notes
- 1.
Ernst Georg Ravenstein (1834–1913) was a German-English geographer.
- 2.
C.T. De Wit (1924–1993) was a Plant, Soil, and Microbial Scientist.
- 3.
- 4.
If one calculates the world population with a growth rate of 0.04% from 10,000 BC to Year zero until present, we can see an exact same pattern showing in other extinction curves (Figs. 2.1, 2.3, 2.4), even though the world population would not reach 6 billion in 2100. Thus, an explosive growth rate of over 2% is not necessary for an extinction curve, if exponential growth will not continue for a certainly long time.
- 5.
“Out-of-Africa” means the early migration of modern humans (Homo sapiens) from northern Africa to other part of the world, possibly beginning as early as 270,000 years ago, and certainly during 130,000–115,000 ago. There were various waves and the most “recent” wave took place about 70,000 years ago, via the so-called “Southern Route”, spreading along the coast of Asia and reaching Australia by around 65,000–50,000 years ago. At the same time, Europe was populated by an early offshoot which was settled at the Near East and Europe less than 55,000 years ago (WIKI 2019a).
- 6.
Edward S. Deevy, “The Human Population,” Scientific American, vol. 203, no. 9, September 1960, pp. 195–204 (Cohen 1998: 512–513).
- 7.
Without log conversion of both axes, a series of waves are compressed and visually seems to be an extinction curve (Fig. 2.1).
- 8.
If Pop shoots K over, KPRatio takes a minus value, which is slightly smaller than 0 and decreases to −1. This simple model doesn’t include any variable to generate an overshoot of Pop. Therefore, Pop is staying at K.
- 9.
The concept of fractal was born from mathematics. Fractals tend to appear nearly the same at different levels. Regrettably, it is beyond my reach to define this multifractal structure mathematically, but I believe it is possible.
- 10.
He has missed to recognize the simple fact that subsistence (food production) must increase also in a geometrical ratio, as far as population increases in a geometrical ratio, if food is necessary for the existence of man. And that was happened in human history at least until today.
- 11.
This r is a decimal number not in %.
- 12.
Maybe, he would have thought of “the low of diminishing returns” in Economics. However, as mathematically regarding, even in this case, the food production doesn’t increase linearly (i.e. in an arithmetical ratio).
- 13.
“The limits of growth” is the title of the first report of the Club of Rome (Meadows et al. 1972). The computer simulations of this report demonstrated that economic growth at that time could not continue indefinitely because of resource and environmental limitation. After the oil crisis in 1973, this concept was widespread in the world.
- 14.
Sustainable development (or sustainability) was initially described in three terms, the environment, the economy and the society, proposed by the economist René Passet in 1979. In 2015, the United Nations adopted ‘The 2030 Agenda for Sustainable Development’, a set of 17 Sustainable Development Goals (SDGs) (WIKI 2019b; DSDG 2017).
- 15.
The annual population growth rate of Japan recorded −0.18% in 2016–2017. It is expected to be −1.06% in 2060–2065 (IPSS 2017).
- 16.
The rapidly shrinking population can devastate natural environment including human activity in its balance.
- 17.
This r is a decimal number, not in %.
- 18.
Maximum intrinsic rate of increase means the theorical value of intrinsic increase rate under ideal conditions (for example enough food, space, etc.).
- 19.
If N is nearly to Zero, (K − N) is nearly to K. Then, the value of (K − N)/K is K/K = 1. If N is nearly to K, (K − N) is nearly to Zero. Then, the value of (K − N)/K will be 0/K = 0.
- 20.
This case was not included originally in a classic model.
- 21.
For example, another historical process at least is thinkable, from relatively low fertility and mortality in hunter gatherer, to relatively high fertility and mortality in agricultural society.
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Hara, T. (2020). The Principle of Sustainable Population. In: An Essay on the Principle of Sustainable Population. SpringerBriefs in Population Studies(). Springer, Singapore. https://doi.org/10.1007/978-981-13-3654-6_2
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