Which one of the following growth curves is related to Verhulst-Pearl…

The correct answer is Option (3) → Sigmoid Curve

When food and space are limited, a population cannot grow without end. It grows slowly at first, then quickly, and then levels off when it reaches the carrying capacity (K), the largest population the habitat can support. A plot of population size against time then looks like the letter S. This is the Verhulst-Pearl logistic growth.

(1) Bell-shaped curve — Incorrect. A bell-shaped curve rises and then falls. A logistic curve rises and then stays level.

(2) J-shaped curve — Incorrect. The J-shaped curve is exponential growth, \( \frac{dN}{dt} = rN \). It applies when resources are unlimited, so it has no levelling-off.

(3) Sigmoid Curve — Correct. It matches logistic growth.

(4) Straight line — Incorrect. Neither growth equation gives a straight line.

NCERT Extract:
Population Growth – “… A plot of N in relation to time (t) results in a sigmoid curve. This type of population growth is called Verhulst-Pearl Logistic Growth (Figure 11.3) and is described by the following equation:
\( \displaystyle\frac{dN}{dt} = rN\left(\frac{K-N}{K}\right) \)
Where N = Population density at time t
r = Intrinsic rate of natural increase
K = Carrying capacity
Since resources for growth for most animal populations are finite and become limiting sooner or later, the logistic growth model is considered a more realistic one.”

Figure 11.3 Population growth curve a when responses are not limiting the growth, plot is exponential, b when responses are limiting the growth, plot is logistic, K is carrying capacity