Applying a constant-effort model of harvesting to the Lotka–Volterra equations (1), we obtain the system
x = x(a − αy − E1), y = y(−c + γx − E2).
When there is no harvesting, the equilibrium solution is (c/γ, a/α).
(a) Before doing any mathematical analysis, think about the situation intuitively. How do you think the populations will change if the prey alone is harvested? if the predator alone is harvested? if both are harvested?
(b) How does the equilibrium solution change if the prey is harvested, but not the predator (E1 > 0,E2 = 0)?
(c) How does the equilibrium solution change if the predator is harvested, but not the prey (E1 = 0,E2 > 0)?
(d) How does the equilibrium solution change if both are harvested (E1 > 0,E2 > 0)?