Logistic growth
Growth that starts out fast and nearly exponential, then slows and levels off at a ceiling: the S-shaped curve first described by Verhulst in 1838.
Logistic growth describes a population that grows quickly at first, then slows as it approaches a limit, often called the carrying capacity. Plotted over time it makes an S-shaped curve.
An everyday example: yeast in a jar of sugar water, or fruit flies in a bottle. They multiply fast while food and room are plentiful, then their numbers level off as resources run short.
The Belgian mathematician Pierre-François Verhulst proposed the equation in Brussels in 1838 and named it 'logistique' in 1845. He predicted that Belgium would level off at about 9.4 million people; it had about 10.1 million in 1994, helped by immigration. The curve was rediscovered by Raymond Pearl and Lowell Reed in 1920.
A common misconception is that the ceiling is fixed forever. For humans it is not: new technology and choices about family size can move it, which is why population forecasts are revised regularly.
