Spatial heterogeneity, especially in mortality risk, is a major factor shaping population dynamics. Here we study the impacts of spatial heterogeneity in hunting pressure on the demography of Eurasian woodcock Scolopax rusticola, a relatively long-lived migratory game bird. We develop capture-recapture-recovery models in which both seasonality and spatial variation in hunting pressure are accounted for, and fit them to individual-based data collected across the French wintering range ([44000 banded individuals) as well as recoveries from spring stopovers and breeding grounds in Europe. Our results quantify spatial variation in survival probability in the wintering areas. They highlight the role of source-sink dynamics involving juvenile settlement decisions, as well as the importance of mortality outside the winter quarters. We also discuss the impact of spatial heterogeneity for demographic parameter estimation and data collection at the range scale.