The phrase "prowled after" implies a predatory behavior of stalking or hunting. The antonyms for this phrase would be less aggressive actions such as avoiding, ignoring, or simply going about one's business. Other antonyms could include nonchalantly wandering, casually strolling, or peacefully meandering. These actions do not imply any pursuit or intent to harm or capture. Instead, they suggest a more relaxed and carefree attitude, free from any predatory or aggressive behavior. When it comes to animal behavior, the antonyms might include grazing, nest-building, or simply resting.