S-shaped growth curve

S-shaped growth curve(sigmoid growth curve) A pattern of growth in which, in a new environment, the population density of an organism increases slowly initially, in a positive acceleration phase; then increases rapidly, approaching an exponential growth rate as in the J-shaped curve; but then declines in a negative acceleration phase until at zero growth rate the population stabilizes. This decline reflects increasing environmental resistance which becomes proportionately more important at higher population densities. This type of population growth is termed density-dependent, since growth rate depends on the numbers present in the population. The point of stabilization, or zero growth rate, is termed the saturation value (symbolized by K) or carrying capacity of the environment for that organism. K represents the upper asymptote of the sigmoidal or S-shaped curve produced when changing population numbers are plotted over time. It is usually summarized mathematically by the logistic equation. See density-dependence; compare J-shaped growth curve.