Comparing methods for analyzing overdispersed binary data in aquatic toxicology

Testing an application of a biotic ligand model to predict acute toxicity of metal mixtures to rainbow trout

The authors tested the applicability of a previously developed biotic ligand model (BLM) to predict acute toxicity of single metals and metal mixtures (cadmium, lead, and zinc) to rainbow trout fry (Oncorhynchus mykiss) from a single available dataset. The BLM used in the present study hypothesizes that metals inhibit an essential cation (calcium) and organisms die as a result of its deficiency, leading to an assumption that the proportion of metal-binding ligand (f) is responsible for the toxic effects of metals on the survival of rainbow trout. The f value is a function of free-ion concentrations of metals computed by a chemical speciation model, and the function has affinity constants as model parameters. First, the survival effects of single metals were statistically modeled separately (i.e., f-survival relationship) by using the generalized linear mixed model with binomial distribution. The modeled responses of survival rates to f overlapped reasonably irrespective of metals tested, supporting the theoretical prediction from the BLM that f-survival relationships are comparable regardless of metal species. The authors thus developed the generalized linear mixed model based on all data pooled across the single-metal tests. The best-fitted model well predicted the survival responses observed in mixture tests (r = 0.97), providing support for the applicability of the BLM to predict effects of metal mixtures.

Application of a generalized linear mixed model to analyze mixture toxicity: survival of brown trout affected by copper and zinc

Increased concerns about the toxicity of chemical mixtures have led to greater emphasis on analyzing the interactions among the mixture components based on observed effects. The authors applied a generalized linear mixed model (GLMM) to analyze survival of brown trout (Salmo trutta) acutely exposed to metal mixtures that contained copper and zinc. Compared with dominant conventional approaches based on an assumption of concentration addition and the concentration of a chemical that causes x% effect (ECx), the GLMM approach has 2 major advantages. First, binary response variables such as survival can be modeled without any transformations, and thus sample size can be taken into consideration. Second, the importance of the chemical interaction can be tested in a simple statistical manner. Through this application, the authors investigated whether the estimated concentration of the 2 metals binding to humic acid, which is assumed to be a proxy of nonspecific biotic ligand sites, provided a better prediction of survival effects than dissolved and free-ion concentrations of metals. The results suggest that the estimated concentration of metals binding to humic acid is a better predictor of survival effects, and thus the metal competition at the ligands could be an important mechanism responsible for effects of metal mixtures. Application of the GLMM (and the generalized linear model) presents an alternative or complementary approach to analyzing mixture toxicity.

Estimating population-level HC5 for copper using a species sensitivity distribution approach

Estimation of population-level benchmark concentrations for protecting aquatic organisms from chemicals is important for value-relevant ecological risk assessments. By employing a species sensitivity distribution (SSD) approach, the authors aimed to derive the population-level hazardous concentration for 5% of species (PHC5) for copper. Based on available information on copper toxicity and population models, the authors estimated population threshold concentrations at which the population size is stable (that is, 0 net population growth) for 13 freshwater species (3 algal, 6 invertebrate, and 4 fish species). The PHC5 for copper was then estimated (6.8 µg/L; 95% confidence interval [CI], 1.8-13.6 µg/L), by fitting a log-normal distribution to the population threshold concentrations obtained. The close overlap between the present study's estimate of the PHC5 and a field-derived threshold concentration suggests that the population-level SSD approach provides a reasonable level of protection for species richness in the natural environment. By contrast, and counterintuitively, the authors' estimate was comparable with the individual-level HC5 reported in the European Union risk assessment. Although the present study cannot determine the underlying reasons for the similar figures, the result provides an indication that the margin between individual-level and population-level benchmarks derived from SSD approaches can be very small. The results therefore suggest that attention is needed to achieve population-level protection using an individual-level SSD approach.

Comparison of population-level effects of heavy metals on fathead minnow (Pimephales promelas)

To evaluate the population-level effects of heavy metals (copper, zinc, cadmium, hexavalent chromium, nickel) on fathead minnow, Pimephales promelas, we first estimated the concentration-effect relationships between the metal concentrations and individual traits (juvenile survivability, hatchability, fertility) by using toxicity data collected from the literature. A Leslie matrix model of fathead minnow was used to calculate population growth rates from these relationships. The population threshold concentrations (PTCs) leading to zero net growth of the fish population were as follows: Cu, 27.4; Cd, 33.2; Zn (soft water), 81.5; Zn (hard water), 85.8; Ni, 504.8; Cr, 3251.6 (microg L(-1)). By comparing the PTCs with no observed effect concentrations (NOECs), we found that some PTCs were equivalent to or even lower than the corresponding NOECs. This result suggests that current ecological risk assessments based on the NOECs can be inadequate for protecting aquatic populations and more efforts on the population-level studies are needed.