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 USEPA’s 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.