The population grows exponentially in the case of the J-shaped growth curve, and after reaching its peak value, the population may suddenly decline. This population growth will continue until there is an abundance of food in the habitat.

After some time, as the population grows, the habitat’s food supply becomes scarce, which finally leads to a decline in the population. For instance, during the rainy season, many insect populations experience a dramatic growth in numbers, which is followed by their disappearance at the end of the season.

The following equation exhibits J-shaped growth:

dN/dt = rN

Here dN/dt represents rate of change in population size, r is biotic potential and N stands for population size.

When a few organisms are introduced to an area, the population growth occurs in three phases: a positive acceleration phase (also known as the lag phase), a logarithmic phase (also known as the exponential phase), and a negative acceleration phase (also known as the lag phase). These phases continue until an equilibrium is reached, at which point the population size fluctuates in response to environmental variability.

Carrying capacity (K) or saturation level refers to the point beyond which no significant increase is possible. Since the number of new creatures in the final phase is virtually equal to the number of individuals who die, the population size does not continue to expand.

The S-shaped sigmoid growth curve is represented by the following equation:

dN/dt = rN (K – N/K) = rN (1 – N/K)

Where, dN/dt is the rate of change in population size,

r is biotic potential

N is population size,

K – N/K or 1 – (N/K) is for environmental resistance.

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