The rate of population growth slows as the population size approaches carrying capacity, leveling to a constant level.
Logistic growth curve or S-shaped growth curve (sigmoid growth curve) is characteristic of all higher animals including man and microbes like yeast cells growing in a natural environment.
Logistic growth is a pattern of growth in which the population density of few individuals introduced into the new habitat increases slowly initially, in a positive acceleration phase (lag phase) then increases rapidly, approaching an exponential growth rate (log phase) due to abundance of food, favourable environmental conditions such a climate, few predators and low levels of disease. Then declines in a negative acceleration phase.
This decline reflects increasing environmental resistance 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 rates, is termed the saturation value or carrying capacity (K) of the environment for that organism.
When population growth rate is plotted graphically against time S shaped or sigmoid curve is obtained. This type of population growth is also called Verhulst- pearl logistic growth. The mathematical equation for sigmoid growth is
dN / dt = rN(N – K)/k
Where
N = Population size at a given time
t = Time,
r = intrinsic rate of natural increase
k = Saturation value or carrying capacity for that organism in that environment.
