Empirically-based modeling and mapping to consider the co-occurrence of ecological receptors and stressors

Abstract

Part of the ecological risk assessment process involves examining the potential for environmental stressors and ecological receptors to co-occur across a landscape. In this study, we introduce a Bayesian joint modeling framework for use in evaluating and mapping the co-occurrence of stressors and receptors using empirical data, open-source statistical software, and Geographic Information Systems tools and data. To illustrate the approach, we apply the framework to bioassessment data on stream fishes and nutrients collected from a watershed in southwestern Ohio. The results highlighted the joint model's ability to parse and exploit statistical dependencies in order to provide empirical insight into the potential environmental and ecotoxicological interactions influencing co-occurrence. We also demonstrate how probabilistic predictions can be generated and mapped to visualize spatial patterns in co-occurrences. For practitioners, we believe that this data-driven approach to modeling and mapping co-occurrence can lead to more quantitatively transparent and robust assessments of ecological risk.

Keywords: Bayesian joint distribution model; Ecological risk assessment; Ecological risk mapping.

Fig. 1.

Maps of values for landscape-based covariates used as predictors in the case study application; locations of OEPA bioassessment sites (N=83) across the EFLMR watershed, where empirical data on nutrient chemistry and stream fish community composition were collected; and boundaries of NHDPlus catchments (for crop cover and septic density maps only) which served as the fundamental spatial data framework for the case study modeling effort. Individual catchments are colored according to standard deviations from the population mean values (i.e., mean across all catchments) for consistency and comparison with the standardization used on predictors in the joint model inputs.

Fig. 2.

MVP model parameter summaries from the case study example (N=83 sites) illustrating modeled posteriors (horizontal bars) for all 27 species included in the model and the total phosphorus (TP) criterion. Panels include the intercept (β₀) of the linear predictor and parameters for the effects of the standardized predictors, including drainage area (β_log(AREA)), crop cover (β_CROP), and density of septic systems (β_SEP). Posterior distributions for the fishes are color-coded according to family, whereas posteriors for TP are color-coded in red. Short, vertical bars indicate posterior medians, whereas horizontal bars indicate 50% (thick bars) and 90% (thin bars) credible intervals. Effects were vertically ordered in each panel according to the posterior median. All predictors were first standardized by subtracting the mean and dividing by 2 standard deviations.

Fig. 3.

Network diagram depicting posterior medians of residual correlations (Ω) among the 28 model responses after accounting for the effects of environmental predictors. Only correlations where the 90% credible interval did not include zero are shown. Blue lines indicate positive correlation while red indicate negative correlation. The magnitude of correlation, summarized as the posterior mode, is indicated along line midpoints. TP response indicated by “P_exc”.

Fig. 4.

Maps illustrating the spatial distribution of predicted occurrence and co-occurrence of silverjaw minnow and TP exceedances, based on the median of the posterior predictive distributions generated from the case study model derived from empirical distribution data from N=83 sites. Map panels indicate (A) the marginal probability of presence for silverjaw minnow; (B) the marginal probability of TP exceedance; (C) the probability of co-occurrence of silverjaw minnow and TP exceedance based on the joint distribution; and (D) the probability of co-occurrence of silverjaw minnow and TP exceedance, when assuming the two responses are statistically independent (i.e., Ω=0).

Fig. 5.

Graphical summaries of the posterior predictive distributions from the case study model, based on empirical distribution data from N=83 sites, for silverjaw minnow, TP exceedance, and their co-occurrence for each of the 815 catchments in the EFLMR HUC9. The panels show (top) the unconditional probability of presence of silver jaw minnow, (middle) the unconditional probability of TP exceedance, and (bottom) the joint probability of their co-occurrence. The graphed summaries depict the 50% (dark gray, vertical bars) and 90% (light gray, vertical bars) credible intervals for each catchment. The summaries were ordered, left to right, based on the value of the posterior median for each catchment.

Fig. 6.

Maps illustrating spatial variability in predictive certainty following from the case study model based on empirical distribution data from N=83 sites. Map panels indicate spatial variability in (A) the posterior probability that co-occurrence probability, p, is very low, or less than 0.1; (B) that p is greater than 0.5, or more likely than not; and (C) that p is very high, or greater than 0.9.