Development of Multiple Linear Regression Models for Predicting Chronic Iron Toxicity to Aquatic Organisms.

We developed multiple linear regression (MLR) models for predicting iron (Fe) toxicity to aquatic organisms for use in deriving site-specific water quality guidelines (WQGs). The effects of dissolved organic carbon (DOC), hardness, and pH on Fe toxicity to three representative taxa (Ceriodaphnia dubia, Pimephales promelas, and Raphidocelis subcapitata) were evaluated. Both DOC and pH were identified as toxicity-modifying factors (TMFs) for P. promelas and R. subcapitata, whereas only DOC was a TMF for C. dubia. The MLR models based on effective concentration 10% and 20% values were developed and performed reasonably well, with adjusted R2 of 0.68-0.89 across all species and statistical endpoints. Differences among species in the MLR models precluded development of a pooled model. Instead, the species-specific models were assumed to be representative of invertebrates, fish, and algae and were applied accordingly to normalize toxicity data. The species sensitivity distribution (SSD) included standard laboratory toxicity data and effects data from mesocosm experiments on aquatic insects, with aquatic insects being the predominant taxa in the lowest quartile of the SSD. Using the European Union approach for deriving WQGs, application of MLR models to this SSD resulted in WQGs ranging from 114 to 765 µg l-1 Fe across the TMF conditions evaluated (DOC: 0.5-10 mg l-1 ; pH: 6.0-8.4), with slightly higher WQGs (199-910 µg l-1 ) derived using the US Environmental Protection Agency (USEPA) methodology. An important uncertainty in these derivations is the applicability of the C. dubia MLR model (no pH parameter) to aquatic insects, and understanding the pH sensitivity of aquatic insects to Fe toxicity is a research priority. An Excel-based tool for calculating Fe WQGs using both European Union and USEPA approaches across a range of TMF conditions is provided. Environ Toxicol Chem 2023;42:1386-1400. © 2023 The Authors. Environmental Toxicology and Chemistry published by Wiley Periodicals LLC on behalf of SETAC.

Comparison of Multiple Linear Regression and Biotic Ligand Models for Predicting Acute and Chronic Zinc Toxicity to Freshwater Organisms.

Multiple linear regression (MLR) models for predicting zinc (Zn) toxicity to freshwater organisms were developed based on three toxicity-modifying factors: dissolved organic carbon (DOC), hardness, and pH. Species-specific, stepwise MLR models were developed to predict acute Zn toxicity to four invertebrates and two fish, and chronic toxicity to three invertebrates, a fish, and a green alga. Stepwise regression analyses found that hardness had the most consistent influence on Zn toxicity among species, whereas DOC and pH had a variable influence. Pooled acute and chronic MLR models were also developed, and a k-fold cross-validation was used to evaluate the fit and predictive ability of the pooled MLR models. The pooled MLR models and an updated Zn biotic ligand model (BLM) performed similarly based on (1) R2 , (2) the percentage of effect concentration (ECx) predictions within a factor of 2.0 of observed ECx, and (3) residuals of observed/predicted ECx versus observed ECx, DOC, hardness, and pH. Although fit of the pooled models to species-specific toxicity data differed among species, species-specific differences were consistent between the BLM and MLR models. Consistency in the performance of the two models across species indicates that additional terms, beyond DOC, hardness, and pH, included in the BLM do not help explain the differences among species. The pooled acute and chronic MLR models and BLM both performed better than the US Environmental Protection Agency's existing hardness-based model. We therefore conclude that both MLR models and the BLM provide an improvement over the existing hardness-only models and that either could be used for deriving ambient water quality criteria. Environ Toxicol Chem 2023;42:393-413. © 2022 SETAC.

Comparative Performance of Multiple Linear Regression and Biotic Ligand Models for Estimating the Bioavailability of Copper in Freshwater.

An increasing number of metal bioavailability models are available for use in setting regulations and conducting risk assessments in aquatic systems. Selection of the most appropriate model is dependent on the user's needs but will always benefit from an objective, comparative assessment of the performance of available models. In 2017, an expert workshop developed procedures for assessing metal bioavailability models. The present study applies these procedures to evaluate the performance of biotic ligand models (BLMs) and multiple linear regression (MLR) models for copper. We find that the procedures recommended by the expert workshop generally provide a robust series of metrics for evaluating model performance. However, we recommend some modifications to the analysis of model residuals because the current method is insensitive to relatively large differences in residual patterns when comparing models. We also provide clarification on details of the evaluation procedure which, if not applied correctly, could mischaracterize model performance. We found that acute Cu MLR and BLM performances are quite comparable, though there are differences in performance on a species-specific basis and in the resulting water quality criteria as a function of water chemistry. In contrast, the chronic Cu MLR performed distinctly better than the BLM. Observed differences in performance are due to the smaller effects of hardness and pH on chronic Cu toxicity compared to acute Cu toxicity. These differences are captured in the chronic MLR model but not the chronic BLM, which only adjusts for differences in organism sensitivity. In general, we continue to recommend concurrent development of both modeling approaches because they provide useful comparative insights into the strengths, limitations, and predictive capabilities of each model. Environ Toxicol Chem 2021;40:1649-1661. © 2021 The Authors. Environmental Toxicology and Chemistry published by Wiley Periodicals LLC on behalf of SETAC.

Effects of Maternally Transferred Egg Selenium on Embryo-Larval Survival, Growth, and Development in Arctic Grayling (Thymallus arcticus).

Selenium (Se) toxicity to fish is primarily manifested via maternal transfer to the eggs, which may result in adverse effects on larval survival and development. The present study assessed the effects of egg Se concentrations derived via maternal transfer on early life-stage development, survival, and growth of Arctic grayling (Thymallus arcticus), a salmonid species not previously assessed for Se sensitivity. Fish gametes were collected from 4 streams in Alaska known to exhibit a range of egg Se concentrations. Eggs were fertilized and reared in the laboratory from hatch through post-swim-up. Larvae were assessed for survival, length, and weight, as well as deformities (skeletal, craniofacial, fin-fold) and edema based on a graduated severity index. Eggs from a total of 47 females were collected, with egg Se concentrations ranging from 3.3 to 33.9 mg kg-1 dry weight. No relationships were observed between larval endpoints evaluated and parent females' egg, muscle, or whole-body Se concentrations. Therefore, Se 10% effective concentrations (EC10s) were defined as the maximum measured Se concentrations: >33.9, >17.6, and >19.7 mg kg-1 dry weight for eggs, muscle, and whole-body tissue, respectively. Collectively, these data indicate that Arctic grayling are relatively insensitive to maternally transferred Se compared to other fish species. Environ Toxicol Chem 2021;40:380-389. © 2020 SETAC.

Updated Multiple Linear Regression Models for Predicting Chronic Aluminum Toxicity to Freshwater Aquatic Organisms and Developing Water Quality Guidelines.

Multiple linear regression (MLR) models for predicting chronic aluminum toxicity to a cladoceran (Ceriodaphnia dubia) and a fish (Pimephales promelas) as a function of 3 toxicity-modifying factors (TMFs)-dissolved organic carbon (DOC), pH, and hardness-have been published previously. However, the range over which data for these TMFs were available was somewhat limited. To address this limitation, additional chronic toxicity tests with these species were subsequently conducted to expand the DOC range up to 12 mg/L, the pH range up to 8.7, and the hardness range up to 428 mg/L. The additional toxicity data were used to update the chronic MLR models. The adjusted R2 for the C. dubia 20% effect concentration (EC20) model increased from 0.71 to 0.92 with the additional toxicity data, and the predicted R2 increased from 0.57 to 0.89. For P. promelas, the adjusted R2 increased from 0.87 to 0.92 and the predicted R2 increased from 0.72 to 0.87. The high predicted R2 relative to the adjusted R2 indicates that the models for both species are not overly parameterized. When data for C. dubia and P. promelas were pooled, the adjusted R2 values were comparable to the species-specific models (0.90 and 0.88 for C. dubia and P. promelas, respectively). This indicates that chronic aluminum EC20s for C. dubia and P. promelas respond similarly to variation in DOC, pH, and hardness. Overall, the pooled model predicted EC20s that were within a factor of 2 of observed in 100% of the C. dubia tests and 94% of the P. promelas tests. Environ Toxicol Chem 2020;39:1724-1736. © 2020 SETAC.

Development of Empirical Bioavailability Models for Metals.

Recently, there has been renewed interest in the development and use of empirical models to predict metal bioavailability and derive protective values for aquatic life. However, there is considerable variability in the conceptual and statistical approaches with which these models have been developed. In the present study, we review case studies of empirical bioavailability model development, evaluating and making recommendations on key issues, including species selection, identifying toxicity-modifying factors (TMFs) and the appropriate environmental range of these factors, use of existing toxicity data sets and experimental design for developing new data sets, statistical considerations in deriving species-specific and pooled bioavailability models, and normalization of species sensitivity distributions using these models. We recommend that TMFs be identified from a combination of available chemical speciation and toxicity data and statistical evaluations of their relationships to toxicity. Experimental designs for new toxicity data must be sufficiently robust to detect nonlinear responses to TMFs and should encompass a large fraction (e.g., 90%) of the TMF range. Model development should involve a rigorous use of both visual plotting and statistical techniques to evaluate data fit. When data allow, we recommend using a simple linear model structure and developing pooled models rather than retaining multiple taxa-specific models. We conclude that empirical bioavailability models often have similar predictive capabilities compared to mechanistic models and can provide a relatively simple, transparent tool for predicting the effects of TMFs on metal bioavailability to achieve desired environmental management goals. Environ Toxicol Chem 2019;39:85-100. © 2019 SETAC.

Multiple linear regression models for predicting chronic aluminum toxicity to freshwater aquatic organisms and developing water quality guidelines.

The bioavailability of aluminum (Al) to freshwater aquatic organisms varies as a function of several water chemistry parameters, including pH, dissolved organic carbon (DOC), and water hardness. We evaluated the ability of multiple linear regression (MLR) models to predict chronic Al toxicity to a green alga (Pseudokirchneriella subcapitata), a cladoceran (Ceriodaphnia dubia), and a fish (Pimephales promelas) as a function of varying DOC, pH, and hardness conditions. The MLR models predicted toxicity values that were within a factor of 2 of observed values in 100% of the cases for P. subcapitata (10 and 20% effective concentrations [EC10s and EC20s]), 91% of the cases for C. dubia (EC10s and EC20s), and 95% (EC10s) and 91% (EC20s) of the cases for P. promelas. The MLR models were then applied to all species with Al toxicity data to derive species and genus sensitivity distributions that could be adjusted as a function of varying DOC, pH, and hardness conditions (the P. subcapitata model was applied to algae and macrophytes, the C. dubia model was applied to invertebrates, and the P. promelas model was applied to fish). Hazardous concentrations to 5% of the species or genera were then derived in 2 ways: 1) fitting a log-normal distribution to species-mean EC10s for all species (following the European Union methodology), and 2) fitting a triangular distribution to genus-mean EC20s for animals only (following the US Environmental Protection Agency methodology). Overall, MLR-based models provide a viable approach for deriving Al water quality guidelines that vary as a function of DOC, pH, and hardness conditions and are a significant improvement over bioavailability corrections based on single parameters. Environ Toxicol Chem 2018;37:80-90. © 2017 SETAC.

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.

Lentic, lotic, and sulfate-dependent waterborne selenium screening guidelines for freshwater systems.

There is consensus that fish are the most sensitive aquatic organisms to selenium (Se) and that Se concentrations in fish tissue are the most reliable indicators of potential toxicity. Differences in Se speciation, biological productivity, Se concentration, and parameters that affect Se bioavailability (e.g., sulfate) may influence the relationship between Se concentrations in water and fish tissue. It is desirable to identify environmentally protective waterborne Se guidelines that, if not exceeded, reduce the need to directly measure Se concentrations in fish tissue. Three factors that should currently be considered in developing waterborne Se screening guidelines are 1) differences between lotic and lentic sites, 2) the influence of exposure concentration on Se partitioning among compartments, and 3) the influence of sulfate on selenate bioavailability. Colocated data sets of Se concentrations in 1) water and particulates, 2) particulates and invertebrates, and 3) invertebrates and fish tissue were compiled; and a quantile regression approach was used to derive waterborne Se screening guidelines. Use of a regression-based approach for describing relationships in Se concentrations between compartments reduces uncertainty associated with selection of partitioning factors that are generally not constant over ranges of exposure concentrations. Waterborne Se screening guidelines of 6.5 and 3.0 µg/L for lotic and lentic water bodies were derived, and a sulfate-based waterborne Se guideline equation for selenate-dominated lotic waters was also developed. Environ Toxicol Chem 2017;36:2503-2513. © 2017 SETAC.

Long-term monitoring of arsenic, copper, selenium, and other elements in Great Salt Lake (Utah, USA) surface water, brine shrimp, and brine flies.

This paper presents long-term monitoring data for 19 elements with a focus on arsenic (As), copper (Cu), and selenium (Se), in surface water (2002-2011), brine shrimp (2001-2011), and brine flies (1995-1996) collected from Great Salt Lake (GSL, Utah, USA). In open surface waters, mean (±standard deviation [SD]; range; n) As concentrations were 112 (±22.1; 54.0-169; 47) and 112 µg/L (±35.6; 5.1-175; 68) in filtered and unfiltered surface water samples, respectively, and 16.3 µg/g (±5.6; 5.1-35.2; 62) dry weight (dw) in brine shrimp. Mean (±SD; range; n) Cu concentrations were 4.2 (±2.1; 1.3-12.5; 47) and 6.9 µg/L (±6.6; 1.9-38.1; 68) in filtered and unfiltered surface water samples, respectively, and 20.6 µg/g (±18.4; 5.4-126; 62) dw in brine shrimp. Finally, mean (±SD; range; n) dissolved and total recoverable Se concentrations were 0.6 (±0.1; 0.4-1.2; 61) and 0.9 µg/L (±0.7; 0.5-3.6; 89), respectively, and 3.6 µg/g (±2.2; 1.1-14.9; 98) dw in brine shrimp. Thus, Se in open lake surface waters was most often in the range of 0.5-1 µg/L, and concentrations in both surface water and brine shrimp were comparable to concentrations measured in other monitoring programs for the GSL. Temporally, the statistical significance of differences in mean dissolved or total recoverable As, Cu, and Se concentrations between years was highly variable depending which test statistic was used, and there was no clear evidence of increasing or decreasing trends. In brine shrimp, significant differences in annual mean concentrations of As, Cu, and Se were observed using both parametric and nonparametric statistical approaches, but, as for water, there did not appear to be a consistent increase or decrease in concentrations of these elements over time.

From sediment to tissue and tissue to sediment: an evaluation of statistical bioaccumulation models.

Biota-sediment accumulation factors (BSAFs) and biota-sediment accumulation regressions (BSARs) are statistical models that may be used to estimate tissue chemical concentrations from sediment chemical concentrations or vice versa. Biota-sediment accumulation factors and BSARs are used to fill tissue concentration data gaps, set sediment preliminary remediation goals (PRGs), and make projections about the effectiveness of potential sediment cleanup projects in reducing tissue chemical concentrations. We explored field-based, benthic invertebrate biota-sediment chemical concentration relationships using data from the US Environmental Protection Agency (USEPA) Mid-Continent Ecology Division (MED) BSAF database. Approximately two thirds of the 262 relationships investigated were very poor (r(2) < 0.3 or p-value ≥ 0.05); for some of the biota-sediment relationships that did have a significant nonzero slope (p-value < 0.05), lipid-normalized tissue concentrations tended to decrease as the colocated organic carbon (OC)-normalized sediment concentration increased. Biota-sediment relationships were further evaluated for 3 of the 262 datasets. Biota-sediment accumulation factors, linear regressions, model II regressions, illustrative sediment PRGs, and confidence intervals (CIs) were calculated for each of the three examples. These examples illustrate some basic but important statistical practices that should be followed before selecting a BSAR or BSAF or relying on these simple models of biota-sediment relationships to support consequential management decisions. These practices include the following: one should not assume that the relationship between chemical concentrations in tissue and sediment is necessarily linear, one should not assume the model intercept to be zero, and one should not place too much stock on models that are heavily influenced by one or a few high chemical concentration data points. People will continue to use statistical models of field-based biota-sediment chemical concentration relationships to support sediment investigations and remedial action decisions. However, it should not be assumed that the models will be reliable. In developing and applying BSAFs and BSARs, it is essential that best practices are followed and model limitations and uncertainties are understood, acknowledged, and quantified as much as possible.

Setting site-specific water-quality standards by using tissue residue criteria and bioaccumulation data. Part 1. Methodology.

We have developed a method for determining site-specific water-quality standards (SSWQSs) for substances regulated based on tissue residues. The method uses a multisite regression model to solve for the conditional prior probability density function (PDF) on water concentration, given that tissue concentration equals a tissue residue threshold. The method then uses site-specific water and tissue concentration data to update the probabilities on a Monte Carlo sample of the prior PDF by using Bayesian Monte Carlo analysis. The resultant posterior PDF identifies the water concentration that, if met at the site, would provide a desired level of confidence of meeting the tissue residue threshold contingent on model assumptions. This allows for derivation of a SSWQS. The method is fully reproducible, statistically rigorous, and easily implemented. A useful property of the method is that the model is sensitive to the amount of site-specific data available, that is, a more conservative or protective number (water concentration) is derived when the data set is small or the variance is large. Likewise, as the site water concentration increases above the water-quality standard, more site-specific information is needed to demonstrate a safe concentration at the site. A companion paper demonstrates the method by using selenium as an example.

Setting site-specific water-quality standards by using tissue residue thresholds and bioaccumulation data. Part 2. Calculating site-specific selenium water-quality standards for protecting fish and birds.

In a companion paper, a method for deriving tissue residue-based site-specific water-quality standards (SSWQSs) was described. In this paper, the methodology is applied to selenium (Se) as an example. Models were developed to describe Se bioaccumulation in aquatic-dependent bird eggs and whole fish. A simple log-linear model best described Se accumulation in bird eggs (r2 = 0.50). For fish, separate hockey stick regressions were developed for lentic (r2 = 0.65) and lotic environments (r2 = 0.37). The low r2 value for the lotic fish model precludes its reliable use at this time. Corresponding tissue residue criteria (i.e., tissue thresholds) for bird eggs and whole fish also were identified and example model predictions were made. The models were able to predict SSWQSs over a wide range of water-tissue combinations that might be encountered in the environment. The models also were shown to be sensitive to variability in measured tissue residues with relatively small changes in variability (as characterized by the standard error) resulting in relatively large differences in SSWQSs.

Analysis of field and laboratory data to derive selenium toxicity thresholds for birds.

In this paper, we critically evaluate the statistical approaches and datasets previously used to derive chronic egg selenium thresholds for mallard ducks (laboratory data) and black-necked stilts (field data). These effect concentration thresholds of 3%, 10% (EC10), or 20% have been used by regulatory agencies to set avian protection criteria and site remediation goals, thus the need for careful assessment of the data. The present review indicates that the stilt field dataset used to establish a frequently cited chronic avian egg selenium threshold of 6 mg/kg dry weight lacks statistical robustness (r2 = 0.19-0.28 based on generalized linear models), suggesting that stilt embryo sensitivity to selenium is highly variable or that factors other than selenium are principally responsible for the increase in effects observed at the lower range of this dataset. Hockey stick regressions used with the stilt field dataset improve the statistical relationship (r2 = 0.90-0.97) but result in considerably higher egg selenium thresholds (EC10 = 21-31 mg/kg dry wt). Laboratory-derived (for mallards) and field-derived (for stilts) teratogenicity EC10 values are quite similar (16-24 mg/kg dry wt). Laboratory data regarding mallard egg inviability and duckling mortality data provide the most sensitive and statistically robust chronic threshold (EC10) with logit, probit, and hockey stick regressions fitted to laboratory data, resulting in mean egg selenium EC10 values of 12 to 15 mg/kg dry weight (r2 = 0.75-0.90).