Consider a population of insects, such as moths, that damage an agricultural crop. But suppose the crop is sprayed repeatedly with an insecticide like DDT, to reduce the moth population even more. The problem is that both spiders and moths die from the poison, so the DDT may do more harm than good. Here is another example, connected with Volterra's original studies of fish catches in the Adriatic Sea. One species preys upon the other, and both are caught in nets.
Continual fishing reduces the breeding population of each species.
Proceed in the following way. Thus we must decrease x ' by hx and y ' by hy . That is, examine the model before any harvesting occurs. Determine the new equilibrium values of x and y . Explain your position clearly.