Logistic population growth curve or S-shaped or sigmoid growth curve is shown by the populations of most organisms.

It has the following phases: lag phase, log phase, exponential phase and stationary phase. In lag phase there is little or no increase in population. In log phase increase in population starts and occurs at a slow rate in the beginning. During exponential phase, increase in population becomes rapid and soon attains its full potential rate. This is due to the constant environment, availability of food and other requirements of life in plenty, absence of predation and interspecific competition and no serious intraspecific competition so that the curve rises steeply upward. The growth rate finally slows down as environmental resistance increases.

Finally, the population becomes stable during the stationary phase because now the number of new cells produced almost equals to the number of cells that die. Every population tends to reach a number at which it becomes stabilized with the resources of its environment. A stable population is said to be in equilibrium, or at saturation level. This limit in population is a constant K and is imposed by the carrying capacity of the environment.

The sigmoid growth form is represented by the following equation:

\(\frac{dN}{dt}\) = rN\(\Big(\frac{K-N}{K}\Big)\)

= rN\(\Big( 1 - \frac{N}{K}\Big)\)

where \(\frac{dN}{dt}\) = rate of change in population size

r = intrinsic rate of natural increase

N = population density at time t; K = carrying capacity.