Forty years later in 1838, the Belgian mathematician Pierre-François Verhulst was the first to describe mathematically a sigmoid curve for population growth that was constrained to an asymptote. This curve he called the "logistique" as opposed to the "logarithmique" of Malthus.
However, Malthus was also aware of the logistic relationship in his "principle of population" and so this curve is perhaps best described as the "Malthus-Verhulst logistic equation" (Berryman, 1992).
Figure 6.29 (Begon et al. 1996) Exponential and sigmoidal increase in density (N) with time (t) for continuously breeding populations.
In addition to these single species uses, the logistic equation has also been used to describe interactions between two species. The Italian physicist Vito Volterra used the logistic in 1926 to model interspecific competition. He also modeled prey-predator interactions, but with a “mass-action” approach, and this work was mirrored at the same time in the USA by Alfred Lotka, a mathematician and demographer.
Thus this two-species model of predation is now known as the Lotka-Volterra predation model and provides a starting point for most considerations of predation, and despite the fact that this is not a logistic model it is simple to add a self-limiting, logistic term to the model.
Although Lotka did not work on competitive interactions to the same extent as Volterra (Kingsland, 1991), the logistic model of interspecific competition is also widely known as the Lotka-Volterra competition model.
This page was created, by J. Siry, for use in classes about population for college students..