A cross-scale view of N and P limitation using a Bayesian hierarchical model

We propose a bivariate Bayesian hierarchical model (BBHM), which adds a perspective on a century-long subject of research, nitrogen (N) and phosphorus (P) dynamics in freshwater and coastal marine ecosystems. The BBHM is differentiated from existing approaches by modeling multiple aspects of N-P relationships―N and P concentration variability, ratio, and correlation―simultaneously, allowing these aspects to vary by seasonal and/or spatial components. The BBHM is applied to three aquatic systems, Finnish Lakes, Saginaw Bay, and the Neuse Estuary, which exhibit differing landscapes and complexity of nutrient dynamics. Our model reveals N and P dynamics that are critical to inferring unknown N and P distributions for the overall system as well as for within system variability. For Finnish lakes, strong positive within- and among-lake N and P correlations indicate that the rates of N and P biogeochemical cycles are closely coupled during summer across the different lake categories. In contrast, seasonal decoupling between N and P cycles in Saginaw Bay is evidenced by the large variability in monthly correlations and the seasonal changes in the N distribution. The results underscore the pivotal role that dreissenids have had on the cycling of nutrients and resurgence of eutrophication. The presence of clear seasonality and a spatial gradient in the distributions and N and P in the Neuse Estuary suggest that riverine N input is an important source in the season-space N dynamics, while summer sediment release is a major process regulating seasonal P distribution.