A mathematical description of growth rates for a simple population in a confined space with limited resources. The equation summarizes the interaction of biotic potential with environmental resources, as seen in populations showing the S-shaped growth curve, as: dN/dT = rN(K − N)/K where N is the number of individuals in the population, T is time, r is the biotic potential of the organism concerned, and K is the saturation value or carrying capacity for that organism in that environment. The expression (K − N)/K is the term that ensures the slowing down of the growth rate as N approaches K. When N = K the term is zero and population growth ceases. The resulting growth rate or logistic curve is a parabola, while the graph for organism numbers over time is sigmoidal. Compare J-shaped growth curve.
Subjects: Plant Sciences and Forestry — Ecology and Conservation.