Predators directly affect their prey by eating them up. But they can also influence their prey’s population dynamics in another important way, a new study reveals.

While experimenting with song sparrows, a team of researchers found that merely the perceived risk of predation—even if no actual predator was nearby—could decrease the number of offspring produced by the sparrows. And this perceived risk of predation also reduced the survival rates of the fledgling sparrows that were hatched, they say.