Let x(t) be a harmful insect population (aphids?) that under natural conditions is held somewhat in check by a benign predator insect population y(t) (ladybugs?). Assume that x(t) and y(t) satisfy the predator–prey equations in (1), so that the stable equilibrium populations are x_E = b/q and y_E = a/p. Now suppose that an insecticide is employed that kills (per unit time) the same fraction f < a of each species of insect. Show that the harmful population x_E is increased, while the benign population y_E is decreased, so the use of the insecticide is counterproductive. This is an instance in which mathematical analysis reveals undesirable consequences of a well-intentioned interference with nature.