Rethinking the lake trophic state index.

Lake trophic state classifications provide information about the condition of lentic ecosystems and are indicative of both ecosystem services (e.g., clean water, recreational opportunities, and aesthetics) and disservices (e.g., cyanobacteria blooms). The current classification schemes have been criticized for developing indices that are single-variable based (vs. a complex aggregate of multi-variables), discrete (vs. a continuous), and/or deterministic (vs. an inherently random). We present an updated lake trophic classification model using a Bayesian multilevel ordered categorical regression. The model consists of a proportional odds logistic regression (POLR) that models ordered, categorical, lake trophic state using Secchi disk depth, elevation, nitrogen concentration (N), and phosphorus concentration (P). The overall accuracy, when compared to existing classifications of trophic state index (TSI), for the POLR model was 0.68 and the balanced accuracy ranged between 0.72 and 0.93. This work delivers an index that is multi-variable based, continuous, and classifies lakes in probabilistic terms. While our model addresses aforementioned limitations of the current approach to lake trophic classification, the addition of uncertainty quantification is important, because the trophic state response to predictors varies among lakes. Our model successfully addresses concerns with the current approach and performs well across trophic states in a large spatial extent.

The implications of Simpson's paradox for cross-scale inference among lakes.

Using cross-sectional data for making ecological inference started as a practical means of pooling data to enable meaningful empirical model development. For example, limnologists routinely use sample averages from numerous individual lakes to examine patterns across lakes. The basic assumption behind the use of cross-lake data is often that responses within and across lakes are identical. As data from multiple study units across a wide spatiotemporal scale are increasingly accessible for researchers, an assessment of this assumption is now feasible. In this study, we demonstrate that this assumption is usually unjustified, due largely to a statistical phenomenon known as the Simpson's paradox. Through comparisons of a commonly used empirical model of the effect of nutrients on algal growth developed using several data sets, we discuss the cognitive importance of distinguishing factors affecting lake eutrophication operating at different spatial and temporal scales. Our study proposes the use of the Bayesian hierarchical modeling approach to properly structure the data analysis when data from multiple lakes are employed.

A study of anthropogenic and climatic disturbance of the New River Estuary using a Bayesian belief network.

The present paper utilizes a Bayesian Belief Network (BBN) approach to intuitively present and quantify our current understanding of the complex physical, chemical, and biological processes that lead to eutrophication in an estuarine ecosystem (New River Estuary, North Carolina, USA). The model is further used to explore the effects of plausible future climatic and nutrient pollution management scenarios on water quality indicators. The BBN, through visualizing the structure of the network, facilitates knowledge communication with managers/stakeholders who might not be experts in the underlying scientific disciplines. Moreover, the developed structure of the BBN is transferable to other comparable estuaries. The BBN nodes are discretized exploring a new approach called moment matching method. The conditional probability tables of the variables are driven by a large dataset (four years). Our results show interaction among various predictors and their impact on water quality indicators. The synergistic effects caution future management actions.