Question

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

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

Answer 1

Answer: (D)

In logistic growth model population growth equation is described as
$\frac{dN}{dt} = rN ( \frac{K - N}{K}) $
where,
N = Population density at time t
r = Intrinsic rate of natural increase
K = Carrying capacity
When, N/K = 1 then
$\frac{K- N}{K} = 0 $
$\therefore \, \frac{dN}{dt} =0 $