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exponential growth

exponential growth A form of population growth in which the rate of growth is related to the number of individuals present. Increase is slow when numbers are low but rises sharply as numbers increase. If population number is plotted against time on a graph a characteristic J-shaped curve results (see graph). In animal and plant populations, such factors as overcrowding, lack of nutrients, and disease limit population increase beyond a certain point and the J-shaped exponential curve tails off giving an S-shaped (sigmoid) curve.

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exponential growth

exponential growth A form of growth in which the logarithms of a value increase linearly in any given period of time. This means that the value grows more rapidly than it would by linear growth. An example of exponential growth would be a population that grows by 10 per cent of its value in each unit of time. Thus, a population that starts with a value of 100 would grow as: 100, 110 (100 + 10% of 100), 121 (110 + 10% of 110), 132.1 (121 + 10% of 121), …

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exponential growth

exponential growth The exponential family of curves (Y = ex) describes growth at an increasing (geometrical) ratio (as in the example of compound interest rates). Thomas Malthus (Essay on the Principle of Population, 1789) pointed out that if food resources increase in linear (arithmetical) ratio, and population increases exponentially, extinction is inevitable. A more descriptive model for growth is logistic. See also LOGISTIC GROWTH.

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Exponential Growth

Exponential growth


The distinction between arithmetic and exponential growth is crucial to an understanding of the nature of growth. Arithmetic growth takes place when a constant amount is being added, as when a child puts a dollar a week in a piggy-bank. Although the total amount increases, the amount being added remains the same. Exponential growth, on the other hand, is characterized by a constant or even accelerating rate of growth.

At a constant rate of increase, measured in percentages, the amounts added grow themselves. Growth is then usually measured in doubling times because these remain constant while the amounts added increase. When the annual rate of increase is 1%, the doubling time will be 70 years. From this fact, a simple formula to calculate doubling times given a rate of increase can be derived: dividing 70 by the percentage rate will yield the number of years it takes to double the original amount.

A savings account with, say, a fixed annual interest rate of 5% furnishes a convenient example. If the original deposit is $1,000, then the growth over the first year is $50. Over the second year, growth will be $52.50. In 14 years, there will be $2,000 in the account (70 divided by 5 equals 14). In the first period of 14 years, then, total growth will be $1,000, but in the second period of 14 years total growth will be $2,000, and so on. During the tenth 14-year period, $512,000 is added, and at the end of that period the total amount in the account will be $1,024,000. As this example illustrates, growth will be relatively slow initially, but it will start speeding up dramatically over time. When growth takes place at an accelerating rate of increase, doubling times of course will become shorter and shorter.

The notion of exponential growth is of particular interest in population biology because all populations of organisms have the capacity to undergo exponential growth. The biotic potential or maximum rate of reproduction for all living organisms is very high, that is to say that all species theoretically have the capacity to reproduce themselves many, many times over during their lifetimes. In actuality, only a few of the offspring of most species survive, due to reproductive failure, limited availability of space and food, diseases, predation, and other mishaps. A few species, such as the lemming, go through cycles of exponential population growth resulting in severe overpopulation. A catastrophic dieback follows, during which the population is reduced enormously, readying it for the next cycle of growth and dieback. Interacting species will experience related fluctuations in population levels. By and large, however, populations are held stable by environmental resistance , unless an environmental disturbance takes place.

Climatological changes and other natural phenomena may cause such habitat disturbances, but more usually they result from human activity. Pollution , predator control , and the introduction of foreign species into habitats that lack competitor or predator species are a few examples among many of human activities that may cause declines in some populations and exponential growth in others.

An altogether different case of exponential population growth is that of humans themselves. The human population has grown at an accelerating rate, starting at a low average rate of 0.002% per year early in its history and reaching a record level of 2.06% in 1970. Since then the rate of increase has dropped below 2%, but human population growth is still alarming and many scientists predict that humans are headed for a catastrophic dieback.

[Marijke Rijsberman ]


RESOURCES

BOOKS


Cunningham, W., and B. W. Saigo. "Dynamics of Population Growth." In Environmental Science: A Global Concern. Dubuque, IA: Wm. C. Brown Publishers, 1990.

Miller, G. T. "Human Population Growth." In Living in the Environment. Belmont, CA: Wadsworth Publishing, 1990.

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