On paper, predators and prey have a pretty straightforward relationship when it comes to population totals. A lion kills a zebra, so there’s one less zebra in a herd. However, new research suggests that predators might have a deeper, longer-lasting effect on their prospective meals: fear.

This fear of predators can impact the reproductive success of prey animals, a team from Canada’s Western University argues. The team, headed by wife and husband researchers Liana Zanette and Michael Clinchy at Western’s biology department, came to its conclusions after performing an experiment on free-living wild song sparrows. The study’s authors say there’s reason to believe that the phenomenon they found among the sparrows would be present in other species as well—at least in birds and mammals that care for their offspring.

“The presence of the predator is actually dramatically changing the behavior of the prey to a degree and over a period that it can actually affect the prey population,” Clinchy told Ars.