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.

中文翻译：

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使用协变量驱动的非平稳空间模型划分宏观和微观生态过程

生态推理需要跨尺度整合信息。这种集成创建了一个复杂的空间依赖结构，该结构由完全非平稳模型最准确地表示。然而，生态学家很少使用这些模型，因为它们难以估计和解释。在这里，我们通过提高最近开发的非平稳模型的可解释性并将其应用于提高我们对驱动湖泊富营养化的空间过程的理解，促进在生态学中使用完全非平稳模型。我们通过将环境预测变量添加到协方差函数中重新构建了一个包含非平稳相关性的模型，从而建立在均值回归的直觉之上。我们创建了椭圆来可视化给定站点的数据如何与其周围环境相关联（即，潜在空间过程的范围和方向性）。我们应用这个模型来描述两个不同地区与湖泊富营养化相关的变量的空间依赖性结构：美国中西部地区具有高度农业景观，以及美国东北部地区具有异质的土地利用。对于中西部，森林覆盖率的增加增加了总磷剩余空间结构的同质性，表明宏观过程主导了这种养分的空间结构。相反，高森林覆盖率和基流降低了叶绿素的空间同质性 美国中西部地区具有高度农业景观，以及美国东北部地区具有不同的土地利用。对于中西部，森林覆盖率的增加增加了总磷剩余空间结构的同质性，表明宏观过程主导了这种养分的空间结构。相反，高森林覆盖率和基流降低了叶绿素的空间同质性 美国中西部地区具有高度农业景观，以及美国东北部地区具有不同的土地利用。对于中西部，森林覆盖率的增加增加了总磷剩余空间结构的同质性，表明宏观过程主导了这种养分的空间结构。相反，高森林覆盖率和基流降低了叶绿素的空间同质性a残差，表明微尺度过程在中西部的叶绿素a中占主导地位。在东北部，城市土地利用和基流的增加降低了磷浓度的均匀性，表明微尺度过程占主导地位，但我们的协变量都没有与叶绿素a的剩余空间结构密切相关。我们的模型表明，环境响应变量的空间依赖结构在空间上发生变化。它还有助于使用来自不同尺度的生态相关协变量来解释这种结构，其影响可以直观地解释。这为导致富营养化的过程提供了新的见解，这是一个复杂而普遍的环境问题。