Q.The logistic population growth is expressed by which equation?

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.

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'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 …