Question

In a habitat having limited food resource for geometric growth of a population, deceleration of density occurs once population reaches its maximum carrying capacity. This is best depicted by which of the following equations?

• A. dN/dt = rtN
• B. dN/dt = rN (N-K)/N
• C. $\mathrm{dN}/\mathrm{dt}=\mathrm{rN}\left(\frac{K-N}{K}\right)$
• D. dt/dN = rN (K-N)/K

Answer 1

The correct option is C $\mathrm{dN}/\mathrm{dt}=\mathrm{rN}\left(\frac{K-N}{K}\right)$

If any habitat is provided with unlimited resources, species living in it flourish at an exponential or geometric rate, this is referred to as a case of exponential growth.
Unlike the exponential growth curve, the habitat having limited food resources and space shows logistic growth. Since animals usually deal with limited food resources, the growth curve it undergoes is a logistic one.
Logistic growth shows a sigmoid shape (S-shaped) growth curve and this S-shaped growth curve is also known as Verhulst-Pearl logistic curve which is represented by the following formula.
Where
dN/dt = rate of change in population size
r = intrinsic rate of natural increase
N = Population density
K = Carrying capacity