A Bayesian network model for estimating stoichiometric ratios of lake seston components

Abstract

The elemental composition of seston provide insights into the functioning of lake food webs and how nutrients cycle through the environment. Here, we describe a Bayesian network model that simultaneously estimates relationships between dissolved and particulate nutrients, suspended volatile and non-volatile sediments, and algal chlorophyll. The model provides direct estimates of the phosphorus and nitrogen content of phytoplankton, suspended non-living organic matter, and suspended inorganic sediment. We apply this model to data collected from reservoirs in Missouri, USA to test the validity of our assumed relationships. The results indicate that, on average among all samples, the ratio of nitrogen to phosphorus (N:P) in phytoplankton and non-living organic matter in these reservoirs were similar, although under nutrient replete conditions, N:P in phytoplankton decreased. Phosphorus content of inorganic sediment was lower than in phytoplankton and non-living organic matter. The analysis also provided a means of tracking changes in the composition of whole seston over time. In addition to informing questions regarding seston stoichiometry, this modeling approach may inform efforts to manage lake eutrophication because it can improve traditional models of relationships between nutrients and chlorophyll in lakes.

Figure 1.

Schematic representation of model for Chl-TP relationship. Observed TP originates from phytoplankton, which is associated with chlorophyll (Chl), dissolved P (P_diss), sediment bound P (NVSS), and P associated with non-living organic matter (VSS_NP). The shaded box for VSS_NP indicates that direct measurements of this parameter were not available, and its value is inferred statistically.

Figure 2.

Predicted TP and TN versus observed TP and TN (upper panels). Root mean square error (RMSE) as a function of predicted values (lower two panels). Dashed lines (upper panels) show 1:1 relationships. Solid line in lower two panels shows the increase in residual standard deviation expected from Gamma distribution. Open circles in lower panels show estimated RMSE computed from approximately 20 samples in a bin around the indicated predicted TP or TN.

Figure 3.

Predicted relationships between Chl and particulate TN for different levels of VSS_NP. Solid line: relationships between Chl and TN_p when VSS_NP is negligibly small. Dashed lines: relationship between Chl and TN_p for different quantiles of VSS_NP (as indicated).

Figure 4.

Relationships between Chl and VSS and TP_p.. Solid lines show estimated limiting relationship between Chl and VSS (left panel), between Chl and particulate TP (right panel) in the absence of contributions from any other factors.

Figure 5.

Allocation of P and N to different compartments for a mesotrophic lake (left column) and eutrophic lake (right column). Dark gray: proportion of nutrient attributed to phytoplankton biomass, medium gray: proportion of nutrient attributed to NVSS (TP plots only), and light grey: proportion of nutrient attributed to non-phytoplankton VSS. Dissolved proportions of N and P account for remaining proportions for each stack of bars.

Figure 6.

Relationship between TP_p and TN_p. Solid line: N:P = 19 ratio expected in phytoplankton dominated sample. Filled circles: samples with DIN > 50 μg/L.

Figure 7.

National lakes assessment observations of TP, TN, and Chl. Solid lines are relationships for TP_p and TN_p estimated from MO lakes.

Figure 8.

Hypothesized effect of zooplankton grazing on relationship between TNp and Chl. Solid line: predicted relationship between TN_p and Chl assuming a constant value of VSS_np at the median value of VSS_np. Dashed line: predicted relationship between TN_p and Chl, assuming VSS_np equal to the 75^th percentile of observed values.