Accounting for the temporal variation of spatial effect improves inference and projection of population dynamics models

Population dynamics models incorporating density dependence and habitat heterogeneity are useful tools to explain and project the spatiotemporal variation of wildlife abundance. Despite their wide application in ecology and conservation biology, the inference and projection of these models may be problematic when residual spatial autocorrelation (SAC) is found. We aimed to improve the inference and projection of population dynamics models by accounting for residual SAC. We considered three Gompertz models that incorporated density dependence and the effect of wetland habitat to explain and project the abundance of Mallard (Anas platyrhynchos). We compared a conventional model that did not account for residual SAC (ENV) with two novel models accounting for residual SAC, one incorporating a spatial effect (a spatially autocorrelated process error) that did not vary over time (STA) and the other incorporating a spatial effect that varied over time (DYN). We evaluated model inference using data from 1974 to 1998 and projection using data from 1999 to 2010. We then forecasted Mallard abundance from 2011 to 2100 under different levels of wetland habitat loss. The DYN model eliminated residual SAC and had better model fit than the ENV and STA models (ΔD¯=2498.3and1988.8, respectively). The projection coverage rate of the DYN model was the closest to the nominal value among the three models. The DYN model forecasted smaller areas with decrease in Mallard abundance under future wetland habitat loss than the ENV and STA models. The novel and conventional population dynamics models we considered in this study, combined with the practical model evaluation approach, can provide reliable inference and projection of wildlife abundance, and thus have wide application in ecological studies and conservation practices that aim to understand and project the spatiotemporal variation of wildlife abundance under environmental changes. In particular, when conservation decision-making is based on model projections, the DYN may be used to minimize the risk of reducing conservation effort in areas that still have high conservation value, due to its favorable projection performance.