Q.Write a note on: Carrying capacity.

The logistic growth model accounts for limited resources by including the carrying capacity K, so growth rate declines as the population nears K.

In a habitat with limited resources, population growth follows the logistic (sigmoid/S-shaped) growth model, described by the equation:

$\frac{dN}{dt} = rN\left(\frac{K-N}{K}\right)$

where N is population size, r is the intrinsic rate of natural increase, and K is the carrying capacity of the environment.

• When N is small compared to K, the term (K − N)/K is close to 1, so growth approximates exponential growth.
• As N approaches K, (K − N)/K approaches 0, so the growth rate slows and eventually plateaus at K. …

An S-shaped population growth curve is the logistic growth pattern: population increases slowly initially, then rapidly, and finally levels off/plateaus as the population reaches the environment's carrying capacity.

In a habitat with limited (finite) resources, a population cannot keep growing exponentially forever; as resources like food and space become scarcer, the rate of growth slows down. This is modelled by the logistic growth equation: dN/dt = rN(K-N)/K, where N is population size, r is the intrinsic rate of increase, and K is the carrying capacity of the environment.

…

'A' marks the plateau of the sigmoid growth curve, i.e. the carrying capacity (K) of the environment.

The sigmoid (S-shaped) or logistic growth curve has three broad phases: a slow lag phase when the population is small and growth is limited by the time needed for individuals to acclimatise and begin reproducing; an exponential phase where growth accelerates rapidly because resources are abundant; and finally a levelling-off as resource limitation (food, space, competition) increasingly checks the birth and death rates. The final plateau, marked 'A' in the graph, represents the …

A curve that rises steeply without levelling off represents exponential (J-shaped) population growth, seen when resources are unlimited.

When a population grows in an environment with unlimited resources (no restriction on food, space or other necessities) and no significant predation/competition, individuals reproduce at their maximum intrinsic rate and the population size increases without any slowing, plotted as a curve that rises ever more steeply over time, resembling the letter 'J'. This contrasts with the S-shaped (sigmoid) logistic growth curve, in which growth slows and levels off (reaches …