Question

Which of the following equations respresents a population growing in a habitat with limited resources?

• A. $\frac{dN}{dt}=rN$
• B. $\frac{dN}{dt}=rN\left(\frac{K-N}{K}\right)$
• C. $N_t=N_0{e}^{rt}$
• D. $\frac{dN}{N}=rt\left(\frac{K-N}{K}\right)$

Answer 1

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

Population growing in a habitat with limited resources shows initially a log phase, followed density reaches the carrying capacity. A plot population density (N) in relation to time (t) results in a sigmoid curve. This type of population growth is called Verhulst-Pearl logistic growth and is described by the following equation:

$\frac{dN}{dt}=rN\left(\frac{K-N}{K}\right)$ where
N = population density at time t
r = intrinsic rate of natural increase
K = carrying capacity.