A tiny Paramecium starts with just one individual and, through binary fission, doubles in numbers every day. Food and space are taken to remain unlimited.
Which of the following describes the growth of this population?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → dN/dt = rN, giving a J-shaped curve when N is plotted against time
The case says that food and space remain unlimited. When resources are unlimited, a species can fully use its innate potential to grow in number, and the population grows in an exponential or geometric fashion. This growth is written as dN/dt = rN, where r is the intrinsic rate of natural increase. Plotting N against time gives a J-shaped curve. The equation with the term (K − N)/K is used only when resources are limited and a carrying capacity (K) exists.
Option (1) dN/dt = rN [(K − N)/K], giving a sigmoid curve when N is plotted against time — Incorrect. This pair is correct for logistic (Verhulst-Pearl) growth, which happens when resources are limited. Here food and space are unlimited, so there is no carrying capacity to slow the growth.
Option (2) dN/dt = rN, giving a J-shaped curve when N is plotted against time — Correct. Unlimited resources give exponential growth. Its equation is dN/dt = rN, and the plot of N against time is J-shaped.
Option (3) dN/dt = rN [(K − N)/K], giving a J-shaped curve when N is plotted against time — Incorrect. This mixes the two models. The logistic equation gives a sigmoid curve, not a J-shaped one, and it does not fit unlimited food and space.
Option (4) dN/dt = rN, giving a sigmoid curve when N is plotted against time — Incorrect. The equation is right but the curve is wrong. dN/dt = rN gives a J-shaped curve; the sigmoid curve belongs to logistic growth.
NCERT Extract:
Growth Models – “… Ideally, when resources in the habitat are unlimited, each species has the ability to realise fully its innate potential to grow in number, as Darwin observed while developing his theory of natural selection. Then the population grows in an exponential or geometric fashion.”
Growth Models – “… Let (b–d) = r, then dN/dt = rN … The above equation describes the exponential or geometric growth pattern of a population (Figure 11.3) and results in a J-shaped curve when we plot N in relation to time.”
Growth Models – “… Now think of a tiny Paramecium starting with just one individual and through binary fission, doubling in numbers every day, and imagine what a mind-boggling population size it would reach in 64 days. (provided food and space remain unlimited)”
Figure 11.3 Population growth curve: a, exponential (dN/dt = rN); b, logistic