Predators can indirectly affect prey survival and reproduction by evoking costly antipredator responses. Such nonconsumptive effects may be as strong or stronger than consumptive predator effects. However, evidence for this in large terrestrial vertebrate systems is equivocal and few studies quantify the actual fitness costs of nonconsumptive effects. Here, we investigated whether nonconsumptive effects elicited by Eurasian lynx (Lynx lynx), a large terrestrial predator, reduced survival in an ungulate prey, the European roe deer (Capreolus capreolus). To reveal the behavioral processes underlying nonconsumptive effects, we distinguished between proactive risk avoidance of areas with high lynx encounter probability, and reactive risk avoidance in response to actual lynx encounters and analyzed these responses using step selection functions. We also quantified the consequences of these behaviors for deer survival. Deer reacted differently at day and at night, but avoided high-risk areas proactively during the day and at night in the summer. During a predator encounter, deer increased avoidance of high-risk areas at night but not during the day. Thus, roe deer exhibited a behavioral response race that involved temporally and spatially varying tradeoffs with environmental constraints. We found evidence that nonconsumptive effects of lynx predation risk reduced deer survival and that survival was more sensitive to variation in nonconsumptive effects of lynx than to variation in human proximity. Our findings highlight that nonconsumptive effects may depend on the spatiotemporal distribution of risks and the environmental context, and we discuss how human factors contribute to predator–prey dynamics in human dominated landscapes.