## Quick Reference

(logistic model)

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: d*N*/d*T* = *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.

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