According to The Theory of natural selection, the organisms are in competition for limited resources (struggle for existence).
Only organisms with favourable variations survive. And this leads to the evolution of new species with favourable variations. They become accustomed to the new environment.
This new species produce more number of offsprings (overproduction).
Here the pests have variations to overcome the DDT. Organisms with favourable variations survive and lead to the evolution of new species which can survive DDT.