Question

In the logistic growth equation: \[ \frac{dN}{dT} = rN \left[ \frac{K - N}{K} \right] \] What does the variable ‘r’ represent?

• A. Population density
• B. Intrinsic rate of natural increase
• C. Carrying capacity
• D. Age distribution

Hint:

In population ecology, \( r \) = rate of natural increase, \( K \) = carrying capacity, \( N \) = population size.

Answer 1

The Correct Option is B

- In the logistic growth equation, each term has a specific ecological meaning:
- \( N \) = population density at time \( T \)
- \( K \) = carrying capacity of the environment
- \( r \) = intrinsic rate of natural increase (or per capita growth rate)
- The intrinsic rate of natural increase \( r \) defines the potential growth rate of a population under ideal environmental conditions with unlimited resources.
Thus, in the equation \(\frac{dN}{dT} = rN \left[ \frac{K - N}{K} \right]\), ‘r’ specifically refers to the intrinsic rate of increase.

Answer 2

The logistic growth equation models how a population grows in an environment with limited resources. The equation is:

\[ \frac{dN}{dT} = rN \left[ \frac{K - N}{K} \right] \]

Here, \(N\) is the population size, \(T\) is time, and \(K\) is the carrying capacity of the environment, which is the maximum population size that the environment can sustain.

The variable ‘r’ in this equation represents the intrinsic rate of natural increase or the maximum per capita growth rate of the population under ideal conditions, without any limitations from resources or environmental factors.

This rate ‘r’ reflects how quickly the population would grow if there were unlimited resources. However, as the population size \(N\) approaches the carrying capacity \(K\), the growth slows down because resources become scarce, which is captured by the term \(\left[ \frac{K - N}{K} \right]\).

Therefore, ‘r’ is a key parameter indicating the potential growth rate of the population under optimal conditions.