Question

When does the growth rate of a population following the logistic model equals zero? The logistic model is given as
dN/dt = rN (1-N/K)

• A. When N/K is exactly one
• B. When N nears the carrying capacity of the habitat
• C. When N/K equals zero
• D. When death rate is greater than birth rate

Answer 1

The correct option is A

When N/K is exactly one

The logistic growth model is the one where resources are limited. The resources for growth for most animal populations are finite and limiting therefore the logistic growth model is considered to be a more realistic growth model. It is called Verhulst-Pearl logistic growth/ sigmoid growth curve.
Logistic growth is described by the following equation:
dN/dt = rN(1-N/K) or
dN/dt = rN (K-N/ K)

Where N = Population density at time t
r = Intrinsic rate of natural increase
K = Carrying capacity
When the value of N/K is exactly 1, then,
dN/dt = rN(1-N/K)
dN/dt = rN(1-1)
dN/dt = rN(0)
dN/dt = zero
As the density- dependent factor (1- N/K) reaches zero, the intraspecific competition becomes more intense.
So, the growth rate of a population will be equal to zero, when the value of N/K is equal to exactly 1.
N/K =1 means the population density has reached the maximum carrying capacity as they have become equal (N=K), this means that the habitat cannot allow any more population growth.