Density‐dependence produces spurious relationships among demographic parameters in a harvested species

1. Harvest of wild organisms is an important component of human culture, economy, and recreation, but can also put species at risk of extinction. Decisions that guide successful management actions therefore rely on the ability of researchers to link changes in demographic processes to the anthropogenic actions or environmental changes that underlie variation in demographic parameters. 2. Ecologists often use population models or maximum sustained yield curves to estimate the impacts of harvest on wildlife and fish populations. Applications of these models usually focus exclusively on the impact of harvest and often fail to consider adequately other potential, often collinear, mechanistic drivers of the observed relationships between harvest and demographic rates. In this study, we used an integrated population model and long‐term data (1973–2016) to examine the relationships among hunting and natural mortality, the number of hunters, habitat conditions, and population size of blue‐winged teal Spatula discors, an abundant North American dabbling duck with a relatively fast‐paced life history strategy. 3. Over the last two and a half decades of the study, teal abundance tripled, hunting mortality probability increased slightly ([Formula: see text]), and natural mortality probability increased substantially ([Formula: see text]) at greater population densities. We demonstrate strong density‐dependent effects on natural mortality and fecundity as population density increased, indicative of compensatory harvest mortality and compensatory natality. Critically, an analysis that only assessed the relationship between survival and hunting mortality would spuriously indicate depensatory mortality due to multicollinearity between abundance, natural mortality and hunting mortality. 4. Our findings demonstrate that models that only consider the direct effect of hunting on survival or natural mortality can fail to accurately assess the mechanistic impact of hunting on population dynamics due to multicollinearity among demographic drivers. This multicollinearity limits inference and may have strong impacts on applied management actions globally.