Pierre François Verhulst

Verhulst developed the logistic function in a series of three papers between 1838 and 1847, based on research on modeling population growth that he conducted in the mid 1830s, under the guidance of Adolphe Quetelet; see Logistic function § History for details.

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.

The Pearl-Reed logistic equation can be integrated exactly, and has solution where C = 1/N(0) − 1/K is determined by the initial condition N(0).

The solution can also be written as a weighted harmonic mean of the initial condition and the carrying capacity, Although the continuous-time logistic equation is often compared to the logistic map because of similarity of form, it is actually more closely related to the Beverton–Holt model of fisheries recruitment.

The concept of R/K selection theory derives its name from the competing dynamics of exponential growth and carrying capacity introduced by the equations above.