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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.

The effects of nutrients on stream invertebrates: a regional estimation by generalized propensity score