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Aim Location Methods Results Main Conclusions Land‐use change and overexploitation are major threats to biodiversity, and climate change will exert additional pressure in the 21st century. Although there are strong interactions between these threats, our understanding of the synergistic and compensatory effects on threatened species' range geography remains limited. Our aim was to disentangle the impact of habitat loss, hunting and climate change on species, using the example of the endangered Chacoan peccary (Catagonus wagneri).Gran Chaco ecoregion in South America.Using a large occurrence database, we integrated a time‐calibrated species distribution model with a hunting pressure model to reconstruct changes in the distribution of suitable peccary habitat between 1985 and 2015. We then used partitioning analysis to attribute the relative contribution of habitat change to land‐use conversion, climate change and varying hunting pressure.Our results reveal widespread habitat deterioration, with only 11% of the habitat found in 2015 considered suitable and safe. Hunting pressure was the strongest single threat, yet most habitat deterioration (58%) was due to the combined, rather than individual, effects of the three drivers we assessed. Climate change would have led to a compensatory effect, increasing suitable habitat area, yet this effect was negated by the strongly negative and interacting threats of land‐use change and hunting.Our study reveals the central role of overexploitation, which is often neglected in biogeographic assessments, and suggests that addressing overexploitation has huge potential for increasing species' adaptive capacity in the face of climate and land‐use change. More generally, we highlight the importance of jointly assessing extinction drivers to understand how species might fare in the 21st century. Here, we provide a simple and transferable framework to determine the separate and joint effects of three main drivers of biodiversity loss. [ABSTRACT FROM AUTHOR]