164
THE VIRTUAL INCREASE
OF THE POPULATION IS
LIMITED BY THE FERTILITY
OF THE COUNTRY
THE VERHULST EQUATION
P
ierre-François Verhulst was
a Belgian mathematician
who, after reading Thomas
Ma lthus’s An Essay on the Principle
of Population, became fascinated by
human population growth. In 1845,
he published his own model for
population dynamics, which was
later named the Verhulst equation.
Although influenced by the
ideas of Malthus, Verhulst realized
that there was a major flaw in his
predictions. Malthus had claimed
that human population tends to
increase geometrically, doubling
at regular time intervals. Verhulst
thought this to be too simplistic,
reasoning that the Malthus modeldid not take into account a larger
population’s difficulty in finding
food. He argued instead that “the
population gets closer and closer
to a steady state,” in which the rate
of reproduction is proportionate to
both the existing population and
the amount of available food. In
Verhulst’s model, after the point of
maximum population growth—the
“point of inflection”—the growth
rate becomes progressively slower,
gradually leveling off to reach the
“carrying capacity” of an area—the
number of individuals it can sustain.
When visualized, Verhulst’s model
produces an S-shaped curve, which
was later called a logistic curve.Practical demonstrations
Verhulst’s model was ignored for
several decades, partly because he
himself was not entirely convinced.
However, in 1911, Scottish army
physician and epidemiologist
Anderson McKendrick used the
logistic equation to forecast
growth in populations of bacteria.
Then, in 1920, Verhulst’s equation
was adopted and promoted in
America by Raymond Pearl.
Pearl conducted experiments
with fruit flies and hens. He gave
a constant quantity of food to fruitIN CONTEXT
KEY FIGURES
Thomas Malthus
(1766–1834), Pierre-François
Verhulst (1804 – 49)BEFORE
1798 Thomas Malthus argues
that populations increase
exponentially, based on a
common ratio, whereas food
supplies grow more slowly at
a constant rate, leading to
potential food shortages.1835 Belgian statistician
Adolphe Quetelet suggests
that population growth tends
to slow down as population
density increases.AFTER
1911 Anderson McKendrick,
working as an army physician,
applies the Verhulst equation
to bacteria populations.1920 American biologist
Raymond Pearl proposes the
Verhulst equation as a “law”
of population growth.The hypothesis of
geometric progression
can hold only in very
special circumstances.
Pierre-François VerhulstUS_164-165_Verhulst_equation.indd 164 12/11/18 6:25 PM