Integrated logistic sigmoid model and graphical analyses of concentration-response relationships of copper sulfate toxicity in aquatic organisms

The logistic sigmoid model (LSM) of concentration-response relationships (CRRs) of copper sulfate in aquatic organisms encounters three problems, which are diverse types of toxicities, wide ranges of effect concentrations, and various patterns of graphical CRRs. These problems have caused difficulties in evaluating patterns of toxicities from abundant studies, comparing toxicities among various concentration levels, and drawing interpretations from numerous graphical analyses. A study addressing the problems and difficulties is urgently needed to increase the understanding of copper sulfate toxicity and its application in risk assessment and aquaculture. The aquatic organisms used in the present study consisted of fish (Cypriniformes, Cichliformes, and Salmoniformes) and invertebrate parasites (Amyloodinium spp., Icthyobodo spp., and Anacanthorus spp.). In this study, 10 LSM-based effect selection criteria were developed and used, a set of low-medium-high (LMH) and sigmoid-flat-quadrant (SFQ) graphs were created to evaluate a set of sublethal and lethal CRRs, and the usefulness of LSM-LMH-SFQ in aquatic toxicology was discussed. The 10 selection criteria included three concentration types, two slopes, three coefficients of variation, and two data fitness to the model requirements. Out of nine sublethal effects, three selected ones were chosen based on the 10 criteria. Likewise, three selected lethal effects out of seven were chosen. The SFQ graph identified a highly selected sublethal effect (Thiobarbituric Acid Reactive Substances, TBARS) and a highly lethal effect (LC₅₀ of fry), based on ∆ log C (differences between concentrations) ≤ 1 µg. L⁻¹ log scale and k (slope of CRR) ≥ 6. Lastly, the LSM-LMH-SFQ discussion emphasized its significance to applicability in sublethal-lethal and fish-parasite comparability and risk assessment of copper sulfate in aquatic animals.