Which one of the following equations represents the Verhulst-Pearl Logistic Growth of population?

Question

Which one of the following equations represents the Verhulst-Pearl Logistic Growth of population?

1. A. dN/dt=r(K-N/K)
2. B. dN/dt=rN(K-N/K) (Correct answer)
3. C. dN/dt=rN(N-K/N)
4. D. dN/dt=N(r-K/K)

Correct Answer

Option B — dN/dt=rN(K-N/K)

Detailed Solution & Explanation

The correct answer is $\dfrac{dN}{dt}=rN\left(\dfrac{K-N}{K}\right)$.

Key Points

• Logistic (Verhulst-Pearl) growth of a population in a habitat with limited resources is described by $\dfrac{dN}{dt}=rN\left(\dfrac{K-N}{K}\right)$.
• Here $N$ = population size, $r$ = intrinsic rate of natural increase, and $K$ = carrying capacity. This gives the sigmoid (S-shaped) growth curve.