Quantile regression improves models of lake eutrophication with implications for ecosystem-specific management

Summary Although commonly used by those tasked with lake management, the statistical approach of data averaging (DA) followed by ordinary least-squares regression (OLSR) to generate nutrient limitation models is outdated and may impede the understanding and successful management of lake eutrophication. Using a 21-year data set from Lake Champlain as a case study, the traditional DA-OLSR-coupled approach was re-evaluated and improved to quantify the cause–effect relationships between chlorophyll (Chl) and total nitrogen (TN) or total phosphorus (TP). We confirmed that the commonly used DA-OLSR approach results in misleading cause–effect nutrient limitation inferences by illustrating how the process of DA reduces the range of data distribution considered and masks meaningful temporal variation observed within a given period. Our model comparisons demonstrate that using quantile regression (QR) to fit the upper boundary of the response distribution (99th quantile model) is more robust than the OLSR analysis for generating eutrophication models and developing nutrient management targets, as this method reduces the effects of unmeasured factors that plague the OLSR-derived model. Because our approach is statistically in line with the ecological ‘law of the minimum’, it is particularly powerful for inferring resource limitation with broad potential utility to the ecological research community. By integrating percentile selection (PS) with QR-derived model output, we developed a PS-QR-coupled approach to quantify the relative importance of TN and TP reductions in a eutrophic system. Utilising this approach, we determined that the reduction in TP to meet a specific Chl target should be the first priority to mitigate eutrophication in Lake Champlain. The structure of this statistically robust and straightforward approach for developing nutrient reduction targets can be easily adopted as an individual lake-specific tool for the research and management of other lakes and reservoirs with similar water quality data sets. Moreover, the PS-QR-coupled approach developed here is also of theoretical importance to understanding and modelling the interacting effects of multiple limiting factors on ecological processes (e.g. eutrophication) with broad application to aquatic research.