Use of Multiple Linear Regression Models for Setting Water Quality Criteria for Copper: A Complementary Approach to the Biotic Ligand Model

Biotic Ligand Models (BLMs) for metals are widely applied in ecological risk assessments and in the development of regulatory water quality guidelines in Europe, and in 2007 the United States Environmental Protection Agency (USEPA) recommended BLM-based water quality criteria (WQC) for Cu in freshwater. However, to-date, few states have adopted BLM-based Cu criteria into their water quality standards on a state-wide basis, which appears to be due to the perception that the BLM is too complicated or requires too many input variables. Using the mechanistic BLM framework to first identify key water chemistry parameters that influence Cu bioavailability, namely dissolved organic carbon (DOC), pH, and hardness, we developed Cu criteria using the same basic methodology used by the USEPA to derive hardness-based criteria but with the addition of DOC and pH. As an initial proof of concept, we developed stepwise multiple linear regression (MLR) models for species that have been tested over wide ranges of DOC, pH, and hardness conditions. These models predicted acute Cu toxicity values that were within a factor of +/- 2 in 77% to 97% of tests (5 species had adequate data) and chronic Cu toxicity values that were within a factor of +/- 2 in 92% of tests (1 species had adequate data). This level of accuracy is comparable to the BLM. Following USEPA guidelines for WQC development, the species data were then combined to develop a linear model with pooled slopes for each independent parameter (i.e., DOC, pH, and hardness) and species-specific intercepts using Analysis of Covariance. The pooled MLR and BLM models predicted species-specific toxicity with similar precision; adjusted R2 and R2 values ranged from 0.56 to 0.86 and 0.66-0.85, respectively. Graphical exploration of relationships between predicted and observed toxicity, residuals and observed toxicity, and residuals and concentrations of key input parameters revealed many similarities and a few key distinctions between the performances of the two models. The pooled MLR model was then applied to the species sensitivity distribution to derive acute and chronic criteria equations similar in form to the USEPAs current hardness-based criteria equations but with DOC, pH, and hardness as the independent variables. Overall, the MLR is less responsive to DOC than the BLM across a range of hardness and pH conditions but more responsive to hardness than the BLM. Additionally, at low and intermediate hardness, the MLR model is less responsive than the BLM to pH, but the two models respond comparably at high hardness. The net effect of these different response profiles is that under many typical water quality conditions, MLR- and BLM-based criteria are quite comparable. Indeed, conditions where the two models differ most (high pH/low hardness and low pH/high hardness) are relatively rare in natural aquatic systems. We suggest that this MLR-based approach, which includes the mechanistic foundation of the BLM but is also consistent with widely accepted hardness-dependent WQC in terms of development and form, may facilitate adoption of updated state-wide Cu criteria that more accurately account for the parameters influencing Cu bioavailability than current hardness-based criteria.