Can logistic growth predict the carrying capacity of the U.S. population?
In a groundbreaking paper published in 1920, Pearl and Reed examined the fit of several different mathematical models to U.S. census data for the period 17901910. Several of the approaches they tested did a good job of matching the historical data, but none included limits to the eventual size of the U.S.
population. To address this shortcoming, they derived the logistic equation, which, unknown to them, had been first described in 1838 by the Belgian mathematician P. F. Verhulst. Pearl and Reed argued that the logistic equation provided a sensible way to represent population growth because it included limits to growth. When they fit the census data to the logistic curve, they obtained an excellent match, from which they estimated that the U.S. population had a carrying capacity of K = 197,274,000 people.The logistic curve estimated by Pearl and Reed provides a good fit to U.S. population data through 1950. After that time, however, the actual population size differed considerably from Pearl and Reed's projections (FIGURE 11.15). By 1967, the carrying capacity (197 million) they had predicted had been surpassed. Pearl and Reed intended their estimate of the carrying capacity to represent the number of people that could be supported in the United States in a self-sufficient manner. They recognized that if conditions changed—for example, if agricultural productivity increased or if more resources were imported from other countries—the population could increase beyond 197 million. These and other changes have occurred, leading some ecologists and demographers to shift their focus from the number of humans that make up the
carrying capacity to the total area of land required to support humans (the “ecological footprint,” discussed in Connections in Nature).
FIGURE 11.15 Fitting a Logistic Curve to the U.S. Population Size In 1920, Pearl and Reed fitted a logistic curve to U.S. census data for 1790-1910. They estimated the nation's carrying capacity (K) as 197 million people. (Data through 1910 from R. Pearl and L. J. Reed. 1920.
Proc Natl Sci Acad USA 6: 275-288; other data from Statistical Abstracts, U.S. Census Bureau.) View larger image
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