1. A major challenge in biodiversity conservation is to facilitate viable populations of large apex predators in ecosystems where they were recently driven to ecological extinction due to resource conflict with humans. 2. Monetary compensation for losses of livestock due to predation is currently a key instrument to encourage human–carnivore coexistence. However, a lack of quantitative estimates of livestock losses due to predation leads to disagreement over the practise of compensation payments. This disagreement sustains the human–carnivore conflict. 3. The level of depredation on year-round, free-ranging, semi-domestic reindeer by large carnivores in Fennoscandia has been widely debated over several decades. In Norway, the reindeer herders claim that lynx and wolverine cause losses of tens of thousands of animals annually and cause negative population growth in herds. Conversely, previous research has suggested that monetary predator compensation can result in positive population growth in the husbandry, with cascading negative effects of high grazer densities on the biodiversity in tundra ecosystems. 4. We utilized a long-term, large-scale dataset to estimate the relative importance of lynx and wolverine predation and density-dependent and climatic food limitation on claims for losses, recruitment and population growth rates in Norwegian reindeer husbandry. 5. Claims of losses increased with increasing predator densities, but with no detectable effect on population growth rates. Density-dependent and climatic effects on claims of losses, recruitment and population growth rates, were much stronger than the effects of variation in lynx and wolverine densities. 6. Synthesis and applications. Our analysis provides a quantitative basis for predator compensation and estimation of the costs of reintroducing lynx and wolverine in areas with free-ranging semi-domestic reindeer. We outline a potential path for conflict management which involves adaptive monitoring programs, open access to data, herder involvement, and development of management strategy evaluation (MSE) models to disentangle complex responses including multiple stakeholders and individual harvester decisions.