INTRODUCTION The effects of nutrients on stream conditions within individual streams or small areas have been studied extensively, but the same effects over a large region have rarely been examined due to the difficulty of applying large-scale manipulative experiments. In this study, we estimated the causal effects of nutrients within the Western United States on invertebrate richness, an important biological indicator of stream conditions, by using observational data. METHODS We used the generalized propensity score method to avoid the common problem of statistical inference using observational data, i.e., correlation established based on observational data does not imply a causal relationship because the effects of confounding factors are not properly separated. RESULTS Our analysis showed a subsidy-stress relationship between nutrients and invertebrate taxon richness in the whole Western United States and in its sub-ecoregions. The magnitude of the relationship varies among these sub-ecoregions, suggesting a varying nitrogen effect on macroinvertebrates due, in large part, to the varying natural and anthropogenic conditions from ecoregion to ecoregion. Furthermore, our analysis confirmed that causal estimation results using regression can be sensitive to the imbalance of confounding factors. CONCLUSIONS Stratifying data into ecoregions with relatively homogeneous environmental conditions or adjusting data by generalized propensity score can improve the balance of confounding factors, thereby allowing more reliable causal inference of nutrient effects. Invertebrates respond to the same nutrient levels differently across different site conditions.

中文翻译：

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营养物质对河流无脊椎动物的影响：广义倾向得分的区域估计。

引言 养分对个别溪流或小区域内的溪流条件的影响已被广泛研究，但由于难以应用大规模的操作性实验，因此在大范围内的相同影响很少被研究。在这项研究中，我们通过使用观测数据估计了美国西部养分对无脊椎动物丰富度（河流条件的重要生物学指标）的因果影响。方法我们使用广义倾向评分法来避免使用观察数据进行统计推断的常见问题，即基于观察数据建立的相关性并不意味着因果关系，因为混杂因素的影响没有得到适当的分离。结果 我们的分析表明，在整个美国西部及其亚生态区，营养物质与无脊椎动物分类群丰富度之间存在补贴-压力关系。这些子生态区之间关系的大小各不相同，这表明氮对大型无脊椎动物的影响在很大程度上是由于生态区与生态区之间的自然和人为条件不同。此外，我们的分析证实，使用回归的因果估计结果可能对混杂因素的不平衡敏感。结论 将数据分层到环境条件相对均一的生态区或通过广义倾向评分调整数据可以改善混杂因素的平衡，从而可以更可靠地推断养分效应的因果关系。