Pierre François Verhulst

Pierre François Verhulst (28 October 1804, Brussels – 15 February 1849, Brussels) was a mathematician and a doctor in number theory from the University of Ghent in 1825.

Verhulst published in 1838 the equation:

where N(t) represents number of individuals at time t, r the intrinsic growth rate, and ${\displaystyle \alpha }$ is the density-dependent crowding effect (also known as intraspecific competition). In this equation, the population equilibrium (sometimes referred to as the carrying capacity, K), ${\displaystyle N^{*}}$, is

Later, Raymond Pearl and Lowell Reed popularized the equation, but with a presumed equilibrium, K, as

where K sometimes represents the maximum number of individuals that the environment can support. In relation to the density-dependent crowding effect, ${\displaystyle \alpha ={\frac {r}{K}}}$. The Pearl-Reed logistic equation can be integrated exactly, and has solution

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