作者：Baird, B., Borah, S., Elser, J. & Obenour, D.

Lake eutrophication remains a significant challenge for water-quality management across the world. Many management strategies focus on reducing nutrient inputs, but other environmental factors can substantially influence the yield of algal biomass for a given level of nutrients. While various large-scale studies have explored how different lake characteristics impact eutrophication, there remains a need to integrate these factors into a comprehensive model capable of assessing nitrogen vs. phosphorus limitation. In this study, we refine chlorophyll-nutrient relationships across the conterminous United States by considering auxiliary variables (i.e., temperature, lake depth, and nutrient enrichment) within a Bayesian hierarchical framework. We leverage over 4000 sampling events of 2755 different lakes from the National Lakes Assessments (2007-2022) to inform model development. We first consider auxiliary variables independently, exploring how they influence the intercept, slope, and critical nutrient ratio (nitrogen : phosphorus) in a regression to predict chlorophyll based on the limiting nutrient. Next, we integrate significant auxiliary variables into a comprehensive model for chlorophyll prediction. Results indicate that the critical nutrient ratio increases in relation to increased lake depth, and the slope of the nutrient-chlorophyll relationship increases with increasing temperature. We apply the model to map mean summer conditions across US lakes and find that 23% and 16% of lakes are strongly limited by phosphorus and nitrogen, respectively (i.e., at > 90% probability). These proportions, however, vary substantially across different subregions. Overall, the probabilistic modeling approach and results can serve as an effective tool to inform water resources management, especially at large spatial scales.

湖泊富营养化仍是全球水质管理的重大挑战。许多管理策略聚焦于削减营养盐输入，但在给定营养盐水平下，其他环境因素也会显著影响藻类生物量的产量。尽管已有诸多大尺度研究探讨了不同湖泊特征对富营养化的影响，但仍需将这些因素整合到一个能够评估氮限制 vs. 磷限制的综合模型中。本研究在美国（本土48州，conterminous United States）范围内精化了叶绿素—营养盐关系，在贝叶斯层级模型框架下纳入了辅助变量（即温度、湖泊深度与营养盐富集程度）。利用国家湖泊评估计划（National Lakes Assessments，2007—2022年）中2755个湖泊的4000余次采样数据支撑模型构建。首先逐一考察各辅助变量，探究它们如何影响以限制性营养盐预测叶绿素的回归中的截距、斜率及临界营养盐比值（氮:磷）；随后，我们将显著的辅助变量整合为一个用于叶绿素预测的综合模型。结果表明：临界营养盐比值随湖泊深度增加而升高，而营养盐—叶绿素关系的斜率随温度升高而增大。将模型应用于绘制美国湖泊夏季平均状况的空间分布图，发现分别有23%和16%的湖泊受磷和氮的强限制（即概率 > 90%）。然而，这些比例在不同子区域间差异显著。总体而言，该概率建模方法及结果可作为一种有效工具，为水资源管理提供决策依据，尤其适用于大空间尺度。

（来源：Limnology and Oceanography 2026 Issue 4  DOI: 10.1002/lno.70375）