The biotic ligand model (BLM) of acute metal toxicity to aquatic organisms is based on the idea that mortality occurs when the metal-biotic ligand complex reaches a critical concentration. For fish, the biotic ligand is either known or suspected to be the sodium or calcium channel proteins in the gill surface that regulate the ionic composition of the blood. For other organisms, it is hypothesized that a biotic ligand exists and that mortality can be modeled in a similar way. The biotic ligand interacts with the metal cations in solution. The amount of metal that binds is determined by a competition for metal ions between the biotic ligand and the other aqueous ligands, particularly dissolved organic matter (DOM), and the competition for the biotic ligand between the toxic metal ion and the other metal cations in solution, for example, calcium. The model is a generalization of the free ion activity model that relates toxicity to the concentration of the divalent metal cation. The difference is the presence of competitive binding at the biotic ligand, which models the protective effects of other metal cations, and the direct influence of pH. The model is implemented using the Windermere humic aqueous model (WHAM) model of metal-DOM complexation. It is applied to copper and silver using gill complexation constants reported by R. Playle and coworkers. Initial application is made to the fathead minnow data set reported by R. Erickson and a water effects ratio data set by J. Diamond. The use of the BLM for determining total maximum daily loadings (TMDLs) and for regional risk assessments is discussed within a probabilistic framework. At first glance, it appears that a large amount of data are required for a successful application. However, the use of lognormal probability distributions reduces the required data to a manageable amount.

Although per capita rates of increase (r) have been calculated by population biologists for decades, the inability to estimate uncertainty (variance) associated with r values has until recently precluded statistical comparisons of population growth rates. In this study, we used two computerintensive techniques, Jackknifing and Bootstrapping, to estimate bias, standard errors, and sampling distributions of r for real and hypothetical populations of cladocerans. Results generated using the two techniques, using data on laboratory cohorts of Daphnia pulex, were almost identical, as were results for a hypothetical D. pulex population whose sampling distribution was approximately normal. However, for another hypothetical population whose sampling distribution was negatively skewed due to high juvenile mortality, Bootstrap and full-sample estimates of r were negatively biased by 3.3 and 1.8%, respectively. A bias adjustment reduced the bias in the Bootstrap estimate and produced estimates of rand SE(r) almost identical to those of the Jackknife technique. In general, our simulations show that the Jackknife will provide more cost-effective point and interval estimates of r for cladoceran populations, except when juvenile mortality is high (at least > 25%). Coefficients of variation in the mean of r within laboratory cohorts of D. pulex were one-half to one-third the magnitude of the corresponding coel!!.cients of variation in the mean of total reproduction and in the mean day to death (range of values of cv[r] = 1.6 to 3.8%). This suggests that extremes in reproductive output and survival of individuals tend to be dampened at the population level, and that within-cohort variability in r is not explosive. Moreover, between-cohort variability in r can be much greater than within-cohort variability, as indicated by a statistically significant difference of30% (P < .01) between the high and low r values that were computed for four cohorts of D. pulex born during a 1-mo period from the same laboratory stock population. Based on variability in per capita rates of increase that have been estimated for several cladoceran species, we suggest that the precision for reporting r values should in most cases be limited to two significant figures.

The biotic ligand model (BLM) was developed to explain and predict the effects of water chemistry on the acute toxicity of metals to aquatic organisms. The biotic ligand is defined as a specific receptor within an organism where metal complexation leads to acute toxicity. The BLM is designed to predict metal interactions at the biotic ligand within the context of aqueous metal speciation and competitive binding of protective cations such as calcium. Toxicity is defined as accumulation of metal at the biotic ligand at or above a critical threshold concentration. This modeling framework provides mechanistic explanations for the observed effects of aqueous ligands, such as natural organic matter, and water hardness on metal toxicity. In this paper, the development of a copper version of the BLM is described. The calibrated model is then used to calculate LC50 (the lethal concentration for 50% of test organisms) and is evaluated by comparison with published toxicity data sets for freshwater fish (fathead minnow, Pimephales promelas) and Daphnia.

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Standard static-exposure acute lethality tests were conducted with Daphnia magna neonates exposed to binary or ternary mixtures of Cd, Cu, and Zn in moderately hard reconstituted water that contained 3 mg dissolved organic carbon/L added as Suwannee River fulvic acid. These experiments were conducted to test for additive toxicity (i.e., the response to the mixture can be predicted by combining the responses obtained in single-metal toxicity tests) or nonadditive toxicity (i.e., the response is less than or greater than additive). Based on total metal concentrations (>90% dissolved) the toxicity of the tested metal mixtures could be categorized into all 3 possible additivity categories: less-than-additive toxicity (e.g., Cd-Zn and Cd-Cu-Zn mixtures and Cd-Cu mixtures when Cu was titrated into Cd-containing waters), additive toxicity (e.g., some Cu-Zn mixtures), or more-than-additive toxicity (some Cu-Zn mixtures and Cd-Cu mixtures when Cd was titrated into Cu-containing waters). Exposing the organisms to a range of sublethal to supralethal concentrations of the titrated metal was especially helpful in identifying nonadditive interactions. Geochemical processes (e.g., metal-metal competition for binding to dissolved organic matter and/or the biotic ligand, and possibly supersaturation of exposure waters with the metals in some high-concentration exposures) can explain much of the observed metal-metal interactions. Therefore, bioavailability models that incorporate those geochemical (and possibly some physiological) processes might be able to predict metal mixture toxicity accurately.