The model has three parameters: the starting population, the maximum population, and the time it takes to reach half-maximal. It defines a sigmoidal shaped curve that defines the population at any time. Integrate that differential equation, and the result is called a logistic equation. So the rate of change of population is proportional to Nt(Nmax - Nt). ![]() But population growth slows down as it reaches the maximum, so is also proportional to (Nmax - Nt). The rate of change of population at any time t is proportional to the number of individuals alive at that time (Nt). Population growth is limited, so can't ever exceed some value we'll call Nmax. The term "logistic" was first invented in the nineteenth century to describe population growth curves. ![]() The terms logistic has three meanings which have little relationship to each other (1).
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