Hierarchical modeling strengthens evidence for density dependence in observational time series of population dynamics

The extent to which populations in nature are regulated by density‐dependent processes is unresolved. While experiments increasingly find evidence of strong density dependence, unmanipulated population time series yield much more ambiguous evidence of regulation, especially when accounting for effects of observation error. Here, we reexamine the evidence for density dependence in time series of population sizes in nature, by conducting an aggregate analysis of the populations in the Global Population Dynamics Database (GPDD). First, following the conventional approach, we fit a density‐dependent and a density‐independent variant of the Gompertz state‐space model to each time series. Then, we conduct an aggregate analysis of the entire database by considering two random‐effects density‐dependent models that leverage information across data sets. When individual time series are tested independently, we find very little evidence for density dependence. However, in the aggregate, we find very strong evidence for density dependence, even though, paradoxically, estimated strengths of density dependence for individual time series tend to be weaker than when each individual time series is analyzed independently. Furthermore, a hierarchical model that accounts for taxonomic variation in the strength of density dependence reveals that density dependence is consistently stronger in insects and fish than in birds and mammals. Our findings resolve apparent inconsistencies between observational and experimental studies of density dependence by revealing that the observational record does indeed contain strong support for the hypothesis that density dependence is widespread in nature. The extent to which natural populations are regulated, and the relative importance of internal processes such as density dependence vs. environmental forcing, has raged in the ecological literature for at least 60 yr (Andrewartha and Birch 1954, Hassell et al. 1976). Population regulation has important implications for population replenishment, for the resilience of populations buffeted by environmental perturbations, and thus for the stability of ecosystem functions performed by populations (Chesson and Warner 1981, Dennis et al. 2006, Thibaut et al. 2012). Population regulation also has evolutionary implications, influencing the nature of selection (Charlesworth 1971). Moreover, accurate estimates of the strength of density dependence have practical implications for the sustainable exploitation of populations, population viability analysis, pest control and ecotoxicology (Hilborn et