LAUSR

The effect of nutrients on phytoplankton biomass in lakes continues to be a subject of debate by aquatic scientists. However, determining whether or not chlorophyll a (CHL) is limited by phosphorus (P) and/or nitrogen (N) is rarely considered using a probabilistic method in studies of hundreds of lakes across broad spatial extents. Several studies have applied a unified CHL-nutrient relationship to determine nutrient limitation, but pose a risk of ecological fallacy because they neglect spatial heterogeneity in ecological contexts. To examine whether or not CHL is limited by P, N, or both nutrients in hundreds of lakes and across diverse ecological settings, a probabilistic machine learning method, Bayesian Network, was applied. Spatial heterogeneity in ecological context was accommodated by the probabilistic nature of the results. We analyzed data from 1382 lakes in 17 US states to evaluate the cause-effect relationships between CHL and nutrients. Observations of CHL, total phosphorus (TP), and total nitrogen (TN) were discretized into three trophic states (oligo-mesotrophic, eutrophic, and hypereutrophic) to train the model. We found that although both nutrients were related to CHL trophic state, TP was more related to CHL than TN, especially under oligo-mesotrophic and eutrophic CHL conditions. However, when the CHL trophic state was hypereutrophic, both TP and TN were important. These results provide additional evidence that P-limitation is more likely under oligo-mesotrophic or eutrophic CHL conditions and that co-limitation of P and N occurs under hypereutrophic CHL conditions. We also found a decreasing pattern of the TN/TP ratio with increasing CHL concentrations, which might be a key driver for the role change of nutrients. Previous work performed at smaller scales support our findings, indicating potential for extension of our findings to other regions. Our findings enhance the understanding of nutrient limitation at macroscales and revealed that the current debate on the limiting nutrient might be caused by failure to consider CHL trophic state. Our findings also provide prior information for the site-specific eutrophication management of unsampled or data-limited lakes.