Exploring non-stationary and scale-dependent relationships between walleye (Sander vitreus) distribution and habitat variables in Lake Erie

Global regression techniques that assume spatial stationarity are usually used to study the interaction between aquatic species distribution and habitat variables. In the present study, a local regression model, named geographically weighted regression (GWR), was used to question the spatial stationarity assumption in exploring the relationships between walleye (Stizostedion vitreum) distribution and habitat variables in Lake Erie. The GWR model resulted in a significant improvement of model performance over the two global linear and non-linear regression methods (a generalised least-squares (GLS) model and a generalised additive mixed model (GAMM)), accounting for residual spatial autocorrelation using the same response and explanatory variables as in the GWR model. The values of local regression coefficients from the GWR model changed among spatial locations significantly, implying spatially varying and scale-dependent relationships between walleye distribution and habitat variables. The k-means cluster analyses based on the t-values of local regression coefficients of GWR model characterised special zones of species-environment relationships of walleye in Lake Erie. In conclusion, spatial stationarity needs to be questioned in studying the relationships between aquatic species distribution and habitat variables and a non-stationary approach, such as GWR, is recommended as a complementary tool.