Combining nutrient, productivity, and landscape‐based regressions improves predictions of lake nutrients and provides insight into nutrient coupling at macroscales

Abstract

Empirical nutrient models that describe lake nutrient, productivity, and water clarity relationships among lakes play a prominent role in limnology. Landscape‐based regressions are also used to understand macroscale variability of lake nutrients, clarity, and productivity (hereafter referred to as nutrient‐productivity). Predictions from both models are used to inform eutrophication management globally. To date, these two classes of models are generally conducted separately, which ignores the known dependencies among nutrient‐productivity variables. We present a statistical model that integrates nutrient‐productivity and landscape‐based regressions—where lake nutrients, productivity, and clarity variables are modeled jointly. We fitted a joint nutrient‐productivity model to over 7000 lakes with three nutrients (total phosphorus, total nitrogen, nitrate concentrations), chlorophyll a concentrations, and Secchi disk depth as response variables and landscape features as predictor variables. Because lakes in different regions respond to landscape features differently, we focused our analysis on two subregions with different dominant land uses, the agricultural Midwest and the forested Northeast U.S. Predictive performance was enhanced by modeling nutrient‐productivity variables jointly. We also found strong evidence that nutrient‐productivity variables were coupled, and that only nitrate may be decoupled from other nutrient‐productivity variables in the forested region. We speculate that these regional differences may be related to differences in the strength of biogeochemical cycles and stoichiometric controls between these regions. Jointly modeling nutrient‐productivity variables in lakes effectively integrates the two dominant approaches for studying lakes nutrient‐productivity relationships and provides novel insight into macroscale patterns of the coupling of nutrients, chlorophyll, and water clarity in lakes.

Winter Precipitation and Summer Temperature Predict Lake Water Quality at Macroscales

“…In addition, others have argued that the connections between biogeochemical cycles of different elements make it important to consider multiple nutrients when evaluating the effects of climate on ecosystems (Whitehead & Crossman, ). We found that leveraging information about correlated water quality variables improved precision and accuracy compared to traditional approaches that fail to account for covariance, which is consistent with related studies (Wagner & Schliep, ). Correlations among predictors, responses, and space are often viewed as problems in the data that limit interpretation and must be dealt with prior to analysis, yet we describe a model that uses those characteristics to inform the relationship between climate and lake ecosystems outside the spatial and temporal scope of individual lake data sets.…”

“…Previous work suggests that both precipitation and temperature are mechanistically linked to lake ecosystems (Figure 1), precipitation through the delivery of nutrients from watersheds to lakes (e.g., Arvola et al, 2015;Rose et al, 2017), and temperature by influencing processing rates (e.g., decomposition or primary production) and physical aspects of lakes like stratification (e.g., Kraemer et al, 2015;Kraemer, Chandra, et al, 2017) that can have a strong influence on biology and nutrient cycles. Because different measures of nutrients and productivity are often correlated, modeling them jointly can improve predictions (Wagner & Schliep, 2018).…”

Identifying and characterizing extrapolation in multivariate response data

“…In our inland lakes example we addressed the issue of large-scale predictions to fill in missing data using a joint linear model presented by Wagner and Schliep [13]. With our novel approach for identifying and characterizing extrapolation in a multivariate setting This work results in identification of extrapolated lake locations as well as further understanding of the unique covariate space they occupy.…”

“…water quality measurements and variables that describe a lake's ecological context at multiple scales and across multiple dimensions (such as hydrology, geology, land use, and climate). Wagner and Schliep [13] jointly modelled lake nutrient, productivity, and clarity variables and found strong evidence that these nutrient-productivity variables are dependent and that predictive performance was greatly enhanced by explicitly accounting for the multivariate nature of these data. Filstrup et al [1] more closely examined the relationship between Chl a and TP and found that nonlinear models fit the data better than a log-linear model.…”

“…Following Wagner and Schliep (2018), we take a Bayesian approach and specify priors for all model parameters. Further, using our novel numeric measure of extrapolation, we aim to take advantage of the multivariate response variable information to explore when we may identify an additional observation's (i.e.…”