Partitioning macroscale and microscale ecological processes using covariate-driven non-stationary spatial models

Ecological inference requires integrating information across scales. This integration creates a complex spatial dependence structure that is most accurately represented by fully non-stationary models. However, ecologists rarely use these models because they are difficult to estimate and interpret. Here, we facilitate the use of fully non-stationary models in ecology by improving the interpretability of a recently developed non-stationary model and applying it to improve our understanding of the spatial processes driving lake eutrophication. We reformulated a model that incorporates non-stationary correlation by adding environmental predictors to the covariance function, thereby building on the intuition of mean regression. We created ellipses to visualize how data at a given site correlate with their surroundings (i.e., the range and directionality of underlying spatial processes). We applied this model to describe the spatial dependence structure of variables related to lake eutrophication across two different regions: a Midwestern United States region with highly agricultural landscapes, and a Northeastern United States region with heterogeneous land use. For the Midwest, increases in forest cover increased the homogeneity of the residual spatial structure of total phosphorus, indicating that macroscale processes dominated this nutrient's spatial structure. Conversely, high forest cover and baseflow reduced the spatial homogeneity of chlorophyll a residuals, indicating that microscale processes dominated for chlorophyll a in the Midwest. In the Northeast, increases in urban land use and baseflow decreased the homogeneity of phosphorus concentrations indicating the dominance of microscale processes, but none of our covariates were strongly associated with the residual spatial structure of chlorophyll a. Our model showed that the spatial dependence structure of environmental response variables shifts across space. It also helped to explain this structure using ecologically relevant covariates from different scales whose effects can be interpreted intuitively. This provided novel insight into the processes that lead to eutrophication, a complex and pervasive environmental issue.

Automated summary

Ecologists often avoid using fully non-stationary models due to difficulty in estimation and interpretation. However, by improving the interpretability of these models and applying them to study lake eutrophication, new insights can be gained into the spatial processes involved. This study demonstrates the importance of incorporating environmental predictors into covariance functions and visualizing spatial correlation patterns for a better understanding of ecological phenomena.