aka The Trouble with Ants
Story, first published: Fantastic Adventures, Jan. 1951 as The Trouble with Ants
"The Simple Way" is set ten thousand years later after "Hobbies" (about 13,500 A.D.). The peace of the Brotherhood of Beasts is threatened by Joe's experiment with the ants. The dogs have discovered how to travel to alternate worlds and have set up a lottery to relieve the population pressure. Homer, the leader of the dogs, visits the wild robots and hears from Andrew, a 10,000-year-old robot, the story of man and the dogs and the tale of the mutant Joe and the ants. One day Joe broke the glassite dome that covered the ants and scattered the ants with his foot. The liberated ants have erected a mighty building covering the area of a township and are obviously planning on taking over the Earth. To get help, the ants plant tiny devices resembling fleas on the animals that irresistibly summon the animals' robots to work on the building.
Jenkins returns from the alternate world to help Homer (the humans disappeared four thousand years ago). Should the dogs desert to the Cobbly worlds and leave the Earth to the ants? Jenkins goes to Geneva to seek advice from the last remaining websters. He awakens Jon Webster, but Webster's solution is typically human - poison the ants. But the dogs have no chemistry - and no art of killing for five thousand years, not even a flea.
Once more Jenkins has foolishly asked humankind for advice and the answer is - "Exterminate the brutes!" The human race knows only one solution - kill the other fellow if he stands in your way. The superior species of the Dogs, who believe in brotherhood and despise hatred and killing, have learned to solve their problems of overpopulation and competition from the ants by the simple non-violent expedient of moving away, also surrendering one of humanity's most cherished and fought-for values, property rights.
Ewald, Robert J.: When the Fires Burn High and the Wind is from the North, p.47-48