Question

Study the image given below related to the pattern of population growth. Identify A and B and choose the correct option.

• A. A - dN/dt = rN, B - dN/dt = rN (K - N)/K
• B. A - dN/dt = rN (K - N/K), A - dN/dt = rN
• C. A - dN/dt = KN, B - dN/dt = rN (K - N/K)
• D. A - dN/dt = rN (K - N/K), B - dN/dt = KN

Answer 1

The correct option is A A - dN/dt = rN, B - dN/dt = rN (K - N)/K

The growth of population in a habitat shows a logistic growth model or exponential growth model depends on the availability of resources (food, mating, shelter, etc).

In an ideal condition, where there is an unlimited supply of food and resources, the population growth will follow an exponential model in which the population shows a steady increase in the number of individuals over time. This can be graphically represented by a J-shaped curve, as shown by curve A in the given diagram. The graph follows the equation,
$\frac{\mathrm{dN}}{\mathrm{dt}}=\mathrm{rN}$
where dN/dt is change in population density
r is the intrinsic rate of natural increase. It is the difference between the birth rate (b) and death rate (d) in a population i.e (b-d)
N is the initial population density

In a logistic growth model, a population in a habitat has limited resources. It initially shows slow growth (lag phase), followed by phases of acceleration (log phase) and then deceleration. It finally reaches the last phase (stationary phase) in which it attains carrying capacity i.e the maximum number of individuals of a population that can be sustained in a given habitat. After reaching carrying capacity, population growth slows down or stops altogether. This can be graphically represented by a sigmoid curve, as shown by curve B in the given image. The graph follows the equation,
$\frac{\mathrm{dN}}{\mathrm{dt}}=\mathrm{rN}\left(\frac{K-N}{K}\right)$
where dN/dt is change in population density
r is the intrinsic rate of natural increase
N is the initial population density
K is carrying capacity