Spatial and temporal variation of density dependence, environmental effects, and spatial autocorrelation in waterfowl population dynamics

Background/Question/Methods

Although traditional population models succeed in accounting for endogenous (e.g., density-dependent) and exogenous (e.g., environment) factors governing population dynamics, they tend to ignore the spatial structure of demographic parameters and the interaction among local populations. We developed a model that (1) incorporates density dependence, environmental effects, and spatial autocorrelation simultaneously, (2) allows for spatial variation of the parameters, and (3) properly accounts for small and zero counts. The model assumes an underlying Poisson process that follows the Gompertz form, and includes an intrinsic conditional auto-regression component to account for spatial autocorrelation. We applied the model to count data for four North American duck species, Mallard (Anas platyrhynchos), Northern Pintail (A. acuta), American Wigeon (A. americana), and Scaup spp. (Aythya marila and Aythya affinis), and climate information including precipitation and temperature. The data, from 1979-2010, cover a large spatial extent from American prairies through boreal forest to taiga and tundra habitats, and are summarized to 0.3^o of latitude/longitude. Our objectives were to (1) examine spatial variation in the parameters and the relationships between these parameters and mean population density, and (2) examine the temporal changes in the parameters by comparing two periods (1979-1994 and 1995-2010) with different environment and population conditions.

Results/Conclusions

Our model provides estimates of density dependence and environmental effects, while accounting for spatial autocorrelation. Results show that density dependence and environmental effects are correlated to mean population density, although the correlations are generally weak and vary over time and across species. In contrast, the spatial random effect is always strongly correlated to mean population density, indicating that accounting for the interaction among local populations is important in spatial models of population dynamics. Density dependence differed between 1979-1994 and 1995-2010 for Northern Pintail, but not for Mallard, American Wigeon, and Scaup; the effect of precipitation differed between the two periods for all the four species; and the effect of temperature differed between the two periods for Mallard and American Wigeon, but not for Northern Pintail and Scaup. Such temporal changes in parameters may indicate potential adaption of waterfowls to their changing environment, as wetland availability and waterfowl population have increased during the last three decades, along with concurrent increase in precipitation. Although the biological and behavioral bases of the spatial and temporal variation of parameters remain to be investigated, our study provides an example for fine spatial scale modeling of population dynamics that are useful for scientific and management purposes.