Population limitation is a fundamental tenet of ecology, but the relative roles of exogenous and endogenous mechanisms remain unquantified for most species. Here we used multi-model inference (MMI), a form of model averaging, based on information theory (Akaike's Information Criterion) to evaluate the relative strength of evidence for density-dependent and density-independent population dynamical models in long-term abundance time series of 1198 species. We also compared the MMI results to more classic methods for detecting density dependence: Neyman-Pearson hypothesis-testing and best-model selection using the Bayesian Information Criterion or cross-validation. Using MMI on our large database, we show that density dependence is a pervasive feature of population dynamics (median MMI support for density dependence = 74.7-92.2%), and that this holds across widely different taxa. The weight of evidence for density dependence varied among species but increased consistently, with the number of generations monitored. Best-model selection methods yielded similar results to MMI (a density-dependent model was favored in 66.2-93.9% of species time series), while the hypothesis-testing methods detected density dependence less frequently (32.6-49.8%). There were no obvious differences in the prevalence of density dependence across major taxonomic groups under any of the statistical methods used. These results underscore the value of using multiple modes of analysis to quantify the relative empirical support for a set of working hypotheses that encompass a range of realistic population dynamical behaviors.