Allee effects, positive effects of population density on fitness, are of broad interest in ecology due to their role in increasing extinction risk in low density populations. Despite the prevalence of mechanisms that cause Allee effects in a broad range of taxa, measuring Allee effects at the population level is challenging due to the inherent difficulties associated with studying low density populations, specifically low sample sizes and high demographic stochasticity. I identify two additional factors that could mask Allee effects in time series data: sampling error and dispersal. Previous authors have demonstrated that census error results in spurious detection of negative density dependence (Type I error). The same effect will mask positive density dependence, i.e., Allee effects, in time series data (Type II error). Moreover, net dispersal into low density patches on a landscape of heterogeneous population densities may further mask Allee effects. I use a hierarchical modelling approach in a Bayesian framework to explicitly handle census error due to sampling error and unbalanced dispersal in a simulated time series with Allee effects. I compare the ability of the structured modeling approach with that of other statistical models at quantifying the underlying Allee effect in simulated time series.
Results/Conclusions
In simulated time series without census error and dispersal, the Hierarchical model (HM) and a nonlinear model (NLM) performed similarly and outperformed a general linear model (GLM) at characterizing the shape of the Allee effect. In contrast, when census error and dispersal were included in the time series, HM outperformed GLM and a nonlinear model (NLM). Both the GLM and NLM greatly underestimated the y-intercept and slope of the Allee effect. For example, when the latent growth rate at the y-intercept was a = -2.8, the GLM and NLM estimated a = 0.1 and a = 0.6, respectively. In contrast, the HM estimated a = -1.8 for the same time series. The GLM overestimated r by 20-50%, while the NLM and HM were unbiased estimates when r =2. The hierarchical modeling approach was largely effective at overcoming the Allee effect masking due to census error and dispersal. Application of this method to empirical time series may reveal Allee effects in a broad range of taxa, and elucidate extinction risk of rare species and invasion dynamics of pest species.