Question

In a population of birds, the proportionate birth rate and death rate are 0.45 and 0.65 per year, respectively. Immigration occurs at a constant rate of 2000 birds per year and emigration at a constant rate of 1000 birds per year. Formulate the governing equations of the model and solve it. Describe the long-term behaviour of the population, when
initial population is 3000 or 8000

Answer 1

The model equation includes an increase in the number of births per year, a decrease in mortality, and an increase in immigration with a decrease in emigration.

i.e., the aviation has the form

$\Delta (N_p)=0.45N-0.65N+2000-1000$

Simplifying it

$=> \Delta(N_p)=-0.2N+1000$

If N=5000, ∆Np=0.

Balance.

If N<5000, ∆Np>0

The population will be increased to 5000

If N>5000, ∆Np<0

The population will be reduced to 5000

Initial N=3000

N<5000. The population will increase.

Initial N=8000. The population will reduce.