Construction of a comprehensive bio-toxicity index for heavy metals across multiple trophic levels based on the integration of lethal concentration-response curves using entropy weighting method

Abstract

Heavy metals remain pervasive environmental stressors, yet comparative hazard ranking often relies on single-point metrics (e.g., EC₅₀) and limited test species, potentially obscuring concentration–response (C–R) shape information and cross-trophic variability. Here, acute C–R relationships for ten metals were quantified across four organisms representing distinct trophic levels (Danio rerio, Daphnia magna, Aliivibrio fischeri, and Scenedesmus obliquus). Probit regression was used to derive multi-point effect concentrations (EC₁₀–EC₁₀₀) and characterize curve-shape differences. An entropy weight method was then applied to objectively weight ECx information within species and integrate evidence across species to construct a Comprehensive Bio-toxicity Index (CBTI). Marked interspecific variability was observed, with metal rankings differing substantially among taxa and with EC₉₀/EC₁₀ ratios indicating notable differences in curve steepness. The CBTI yielded a multi-trophic hazard hierarchy in which HgCl₂ showed the highest aggregate toxicity (94.41), followed by ZnSO₄ (84.56) and Pb(NO₃)₂ (78.22), while Na₂MoO₄ was least hazardous (24.59). These findings support curve-aware, entropy-weighted multi-trophic integration as a transparent bridge between single-endpoint testing and holistic ecotoxicity evaluation.

1 Introduction

Chemical pollution by heavy metals remains a pervasive and persistent stressor to aquatic and terrestrial ecosystems worldwide. Unlike many organic contaminants, metals do not degrade and can accumulate in biota and sediments, with effects that span from acute mortality to subtle, sub-lethal impairments (Danovaro et al., 2023; Jomova et al., 2025; Singh et al., 2024). Regulatory hazard assessments and environmental guidelines therefore rely heavily on standardized toxicity tests and summary metrics such as the median lethal or effect concentration (LC₅₀/EC₅₀) to compare substances and set protective thresholds (ICCA Global Product Strategy, 2011; Masner et al., 2017). While these point estimates are convenient, they capture only a single location on the concentration–response (lethality) curve and may overlook information contained in the curve’s shape (e.g., slope, inflection, and tail behaviour), which can be toxicologically and ecologically meaningful (Demidenko et al., 2017; Hendriks et al., 2013; van der Most et al., 2024).

A growing body of research argues that the full concentration–response relationship carries critical information about mechanisms of action, inter-specific variability, and risk under fluctuating exposures (Solomon and Takacs, 2001; Aldenberg et al., 2001). For example, two metals with identical LC50 values can have markedly different low-dose slopes, implying different population-level risks at environmentally relevant concentrations (Pillai et al., 2021). Curve-based approaches such as the benchmark dose (BMD) method have been increasingly advocated in human health and ecotoxicology because they use more of the observed data, quantify uncertainty, and decouple effect magnitude from arbitrary test concentrations (Haber et al., 2018; Filipsson et al., 2003). Nevertheless, routine ecological risk assessments still often default to single-point metrics (e.g., LC50 or NOEC), partly because of tradition, perceived simplicity, and data limitations, and the statistical properties of alternative summary metrics remain debated (Green et al., 2013; Warne and Van Dam, 2008; Murado García and Prieto, 2013; Tanaka et al., 2018; Isnard et al., 2001). The relative merits of single-point versus curve-based metrics therefore remain an active area of methodological discussion, especially regarding their comparability across taxa and chemicals and their implications for ranking hazards.

Another important limitation is that chemical hazard is frequently inferred from one or a few test species, even though real ecosystems comprise interacting taxa across multiple trophic levels. Multi-species frameworks such as species sensitivity distributions (SSDs) have been developed to summarize interspecific variability and derive protective concentrations, and they remain highly valuable for regulatory threshold setting when sufficiently broad species datasets are available (Awkerman et al., 2014; Baillard et al., 2020; Xu et al., 2015; Forbes et al., 2002; Dowse et al., 2013). However, SSDs typically rely on one effect metric per species (often EC₁₀ or EC₅₀) and therefore do not explicitly retain the within-species concentration–response profile. The CBTI proposed here is not intended to replace SSDs; rather, it is designed as a complementary comparative-ranking tool for situations in which full or near-full concentration–response information is available for a defined set of representative taxa and the goal is to integrate both cross-species variability and within-species curve characteristics.

When evidence from multiple endpoints and multiple taxa is integrated, a further methodological question arises: how should different indicators be weighted? Equal weighting is simple but assumes that all ECx levels and all taxa contribute the same amount of discriminatory information to hazard ranking, whereas expert-based weighting can incorporate ecological judgment but also introduces subjectivity and may be difficult to reproduce across studies (Suter et al., 2017; Hammitt and Zhang, 2013). In this context, the entropy-weighting method (EWM) offers a transparent, data-driven alternative (Wahyudi et al., 2013; Yang and Zhang, 2012; Yi, 2006). Indicators that vary more strongly across the tested metals contribute more information to ranking and therefore receive greater weight, whereas endpoints with little discriminatory power contribute less. In the present study, entropy-derived weights are used as a statistical tool for evidence integration rather than as a direct measure of ecological importance.

Accordingly, this study proposes and tests an entropy-weighted, multi-trophic framework for comparative toxicity evaluation of heavy metals. Using four organisms representing distinct trophic levels and ten metals as a case study, the study: (1) derives a suite of ECx/LCx values across multiple effect levels for each species; (2) applies entropy weighting to integrate information within species and across species; and (3) computes a composite toxicity index for each metal. The resulting index is compared with rankings based on conventional single-point descriptors, and the extent to which curve shape and cross-species variability influence conclusions is examined. In doing so, the study aims to provide a reproducible proof-of-concept framework for curve-aware, multi-taxa toxicity integration while also clarifying its current scope and limitations.

2 Materials and methods

2.1 Chemicals and reagents

Ten heavy metal compounds were selected for comparative toxicity evaluation: potassium antimony tartrate (C₄H₄KO₇Sb), copper sulfate (CuSO₄.5H₂O), zinc sulfate (ZnSO₄.7H₂O), cadmium chloride (CdCl₂.2.5H₂O), mercury chloride (HgCl₂), manganese chloride (MnCl₂.4H₂O), nickel chloride (NiCl₂.6H₂O), ferric chloride (FeCl₃.6H₂O), sodium molybdate (Na₂MoO₄.2H₂O), and lead nitrate (Pb(NO₃)₂). The ten species were chosen to cover metals and metalloids with high environmental and regulatory relevance rather than to imply that all of them occur at equal abundance in the environment. Specifically, Cu, Zn, Mn, Fe and Mo represent elements that are naturally present and/or essential at trace levels but can become toxic at elevated concentrations; Cd, Hg, Pb and Ni represent priority toxic metals widely considered in aquatic pollution assessment; and Sb was included because antimony compounds are associated with mining, industrial and material-related contamination and remain comparatively less represented in multi-trophic toxicity ranking studies. Thus, the selected compounds span a broad range of environmental occurrence, chemical behavior, and expected toxicity potency, allowing the CBTI framework to be tested under contrasting response patterns. All reagents were of analytical grade (purity ≥99%) and were dissolved in deionized water (Milli-Q, 18.2 MΩ cm at 25 °C) to prepare stock solutions. Working solutions were freshly prepared in the corresponding test media immediately before exposure to minimize hydrolysis/precipitation (particularly for FeCl₂). For cross-species comparability, all exposure concentrations were expressed both as nominal salt concentrations and as dissolved metal-equivalent concentrations (mg/L), the latter being used for concentration–response modelling and subsequent index construction.

2.2 Test organisms and trophic representation

Four model organisms spanning different trophic levels were employed: Decomposer (employed to represent major biological components of aquatic ecosystems and to avoid relying on a single surrogate species. A fischeri fischeri (): Freeze-dried luminescent bacteria (strain NRRL B-11177) was used as a microbial decomposer model because its bioluminescence response is rapid and standardized for acute toxicity screening. S. obliquus was selected as a primary producer representing algal photosynthetic organisms at the base of aquatic food webs. Daphnia magna neonates (<24 h old) were used as a primary consumer and a standard invertebrate model for freshwater toxicity testing. Zebrafish (D. rerio) were used as a vertebrate secondary-consumer model. These four organisms were therefore selected because they are widely used in ecotoxicology, have clear and rapid response endpoints, and collectively provide trophic-level coverage from bacteria and algae to invertebrates and fish. Freeze-dried V fischeri were commercially obtained and reconstituted according to standard protocols [34]. Axenic algal S. obliquus algal cultures were maintained in sterile BG-11 medium at 25 °C ± 1 °C under continuous illumination (4,000 lux) and cells in the exponential growth phase were harvested for testing. D. Primary Consumer (D. magna): Clones magna clones were cultured in aerated standard freshwater at 25 °C ± 1 °C with a 12:12 h light:dark photoperiod. Healthy, and healthy neonates were selected for experiments. Secondary Consumer: Zebrafish (syn. Danio Healthy zebrafish (D rerio) were acclimatized for at least 2 weeks in dechlorinated tap water at 25 °C ± 1 °C and were fasted for 24 h prior to exposure to minimize metabolic variability.

2.3 Short-term acute toxicity assays

To facilitate a high-throughput comparative assessment, short-term exposure protocols were standardized across the trophic levelslevels as far as possible. The experimental workflow is summarized in Figure 1. Range-finding tests were conducted for each metal to establish the appropriate geometric concentration series. All definitive tests were performed in triplicate with appropriate negative controls.

FIGURE 1

2.3.1 Aliivibrio fischeri bioluminescence inhibition assay

The acute toxicity to bacteria was assessed following the ISO 11348–3 standard protocol (ISO, 2007). Bacterial suspensions were exposed to the test solutions for a contact time of 15 min at 25 °C. The relative inhibition of bioluminescence compared to the control was measured using a toxicity analyzer (HACH Eclox).

2.3.2 Scenedesmus obliquus short-term inhibition assay

Rapid algal toxicity tests were conducted using a modified short-term exposure protocol. Algal suspensions (initial density ≈10⁶ cells/mL) were exposed to metal concentrations for 1 h under standard culture conditions. The endpoint was the inhibition of physiological activity (inferred from optical density or fluorescence response) relative to controls. While standard OECD guidelines typically require 72 h, this 1-h assay focuses on immediate acute stress responses and rapid interactions at the cell surface.

2.3.3 Daphnia magna rapid immobilization assay

Short-term acute toxicity to daphnids was evaluated via a 1-h static test. Ten neonates were introduced into 50 mL glass vessels containing the test solution. After a 1 h exposure period, immobilization was recorded. Organisms were considered immobile if they were unable to swim within 15 s after gentle agitation of the test vessel. This duration targets the immediate neurotoxic or physiological shock response.

2.3.4 Danio rerio acute lethality assay

Fish toxicity was determined using a rapid acute lethality assay. Seven fish were randomly assigned to glass tanks containing the test solutions. The exposure duration was strictly limited to 1 h. Mortality was monitored continuously during the exposure period, defined by the cessation of opercular movement and lack of response to mechanical stimuli. This timeframe characterizes the hyper-acute toxicity range of the metals.

2.4 Dose-response modeling

Dose-response curves were constructed by plotting the experimentally determined response rates (bioluminescence/growth inhibition or mortality) against the corresponding heavy metal concentrations. The curves were fitted using regression analysis following the method described by Litchfield and Wilcoxon. To ensure computational accuracy and consistency, all data processing and curve fitting procedures were performed using IBM SPSS Statistics (Version 26.0). Specifically, the Probit regression analysis module within SPSS was utilized to calculate the effective concentrations (EC_x) or lethal concentrations (LC_x) across the full spectrum of effect levels. This included endpoints ranging from 10% to nearly 100% effect (i.e., EC₁₀–EC₁₀₀ or LC₁₀–LC₁₀₀), providing a comprehensive dataset to characterize the shape of the toxicity curve for each metal-species pair.

2.5 Construction of the comprehensive bio-toxicity index (CBTI)

The Entropy Weight Method (EWM) was applied to integrate the multi-point (LC₁₀-LC₁₀₀/EC₁₀-EC₁₀₀) and multi-species data into a unified toxicity index. EWM was selected because the ECx indicators and species did not contribute equally to discrimination among the ten tested metals. Endpoints showing greater dispersion across metals were treated as more informative for ranking, whereas relatively invariant indicators contributed less. This approach reduces dependence on arbitrary equal weighting or purely expert-assigned weights and improves analytical transparency and reproducibility. Importantly, entropy-derived weights in this study are interpreted as statistical weights reflecting information content within the present dataset, not as direct estimates of trophic or ecological importance in natural ecosystems.

2.5.1 Data standardization

Since toxicity metrics (EC_x orLC_x) are “smaller-is-better” indicators (lower values concentrations imply higher toxicity), the original data matrix X = [x_ij] (where x_ij represents the LC_x value of the jth indicator for the ith metal) was normalized to a [0, 1] scale using Equation 1:

2.5.2 Entropy and weight calculation

The normalized value Y_ij was converted to the proportional value p_ij using Equation 2, and the information entropy (E_j) for each indicator was calculated asusing Equation 3:

The objective weight Wj was then determined by the dispersion of the datadata using Equation 4:

2.5.3 Index integration

The final CBTI for each metal was computed by summing the weighted normalized values across all indicators and species using Equation 5:

A higher CBTI value indicates a greater comprehensive toxicity hazard across the tested trophic levels. In Equations 1–5, i indexes the tested metal compounds (i = 1, 2, …, n; n = 10), j indexes the toxicity indicators (j = 1, 2, …, m), and m is the total number of valid ECx/LCx indicators retained for CBTI construction across species and effect levels. xᵢɼ is the original ECx or LCx value for the ith metal under the jth indicator; Yij is the normalized toxicity score; pij is the proportional value used for entropy calculation; Ej is the entropy value of the jth indicator; Wj is the corresponding entropy-derived weight; and CBTIi is the comprehensive bio-toxicity index of the ith metal. In Equation 1, max (xj) and min (xj) are calculated across all metals for indicator j. When pij = 0, the term pij ln (pij) was defined as 0.

2.6 Statistical analysis

All bioassays were performed in triplicate. Data were expressed as mean ± standard deviation. The goodness-of-fit for dose-response curves was evaluated using the coefficient of determination (R²).

3 Results

3.1 Concentration-response relationships and species sensitivity

Concentration–response curves were successfully established for all ten heavy metals across the four representative trophic levels, with Probit regression providing statistically significant fits (p < 0.05) and enabling the estimation of multi-point effective concentrations from EC₁₀ to EC₁₀₀. The curves (Figure 2) visually illustrate the pronounced variability in both the position and the shape of the response profiles among metals and species. Mercury (Hg) and cadmium (Cd) consistently exhibited the steepest and left-shifted curves across most species, indicating high acute toxicity. In contrast, manganese (Mn) and sodium molybdate (Na₂MoO₄) showed shallower, right-shifted curves, reflecting lower potency. Notably, for certain metal–species pairs (e.g., NiCl₂ and Na₂MoO₄ in algae), the upper tail of the curve (EC₉₀–EC₁₀₀) could not be reliably captured within the tested concentration range, highlighting either a wide response window or limitations in the experimental design for near-complete effects. These multi-point ECx profiles not only confirm the expected interspecific differences in absolute sensitivity but also provide a quantitative basis for evaluating curve-shape attributes—such as slope and concentration span between low and high effects—which are critical for the subsequent entropy-based integration.

FIGURE 2

3.2 Species-specific toxicity profiles based on EC50

To facilitate inter-metal comparison within each organism, EC₅₀ values (nominal aqueous concentrations; same units as dosing solutions) were used as the primary single-point descriptor. Marked differences in both absolute sensitivity and metal ranking were evident across trophic levels.

Zebrafish exhibited the greatest sensitivity to ferric chloride, with an EC₅₀ of 0.261. Cadmium chloride was the next most potent (EC₅₀ = 1.918), followed by potassium antimony tartrate (EC₅₀ = 3.034) and lead nitrate (EC₅₀ = 3.659). The least toxic metals to zebrafish over the 1-h exposure were copper sulfate (EC₅₀ = 29.107) and sodium molybdate (EC₅₀ = 26.895). Overall, zebrafish EC₅₀ values spanned approximately two orders of magnitude (0.261–29.107), indicating strong metal-dependent hazard differentiation. For D. magna, mercury chloride and copper sulfate were the most toxic (EC50 = 1.388 and 1.460, respectively), followed by manganese chloride (EC₅₀ = 2.122) and potassium antimony tartrate (EC50 = 3.648). Ferric chloride was the least toxic to D. magna (EC₅₀ = 39.347). Compared with zebrafish, D. magna displayed a compressed EC₅₀ range (1.388–39.347), but still showed clear separation among metals. For Vibrio fischeri (15-min exposure), the lowest EC₅₀ values were observed for mercury chloride and lead nitrate (both 0.3756), followed by zinc sulfate (EC₅₀ = 0.9896) and potassium antimony tartrate (EC₅₀ = 1.897). In contrast, manganese chloride (EC₅₀ = 257.111) and nickel chloride (EC₅₀ = 97.746) were substantially less toxic within the tested range, producing a wide sensitivity span (0.376–257.111; ∼680-fold). In the algal 1-h assay, copper sulfate showed the highest potency (EC₅₀ = 9.771), followed by mercury chloride (EC₅₀ = 13.487) and zinc sulfate (EC₅₀ = 31.877). Cadmium chloride and lead nitrate exhibited comparatively weak acute effects to algae within 1 h (EC₅₀ = 297.114 and 224.031, respectively). EC₅₀ values for nickel chloride and sodium molybdate were not available from the provided dataset.

Substantial interspecies variability was observed for several metals when comparing EC₅₀ across taxa (Table 1). Metals such as lead nitrate and ferric chloride showed particularly large spreads in EC₅₀ values across trophic levels. For example, lead nitrate ranged from 0.3756 in V. fischeri to 224.031 in S. obliquus (≈596-fold). Ferric chloride ranged from 0.2613 in zebrafish to 97.853 in algae (≈375-fold). In contrast, potassium antimony tartrate exhibited comparatively consistent EC₅₀ values among the three species for which EC₅₀ was available (≈1.9-fold range). These findings indicate that hazard ranking based on any single organism would be metal-dependent and could differ markedly from a multi-trophic perspective. For instance, copper sulfate was highly potent to D. magna (EC₅₀ = 1.46) but substantially less potent to zebrafish and bacteria (EC₅₀ ≈ 29–33), whereas ferric chloride showed the opposite pattern, being most potent to zebrafish (EC₅₀ = 0.261) but comparatively weak to D. magna and algae.

3.3 Curve-shape information from multi-point EC (or LC) profiles

Beyond EC₅₀, the multi-point EC series revealed pronounced differences in concentration–response curve width among metals, which is toxicologically relevant for low-effect (environmentally realistic) exposures. As a simple descriptor, the EC₉₀/EC₁₀ ratio was used to reflect the concentration range required to progress from 10% to 90% effect (smaller ratios indicate steeper curves). In zebrafish, sodium molybdate displayed a relatively narrow EC₁₀–EC₉₀ interval (EC₉₀/EC₁₀ ≈ 1.39; 22.04–30.68), whereas potassium antimony tartrate and cadmium chloride showed much wider intervals (EC₉₀/EC₁₀ ˜ 11.15 and 9.94, respectively), indicating substantially shallower response transitions. In D. magna, cadmium chloride produced the widest transition (EC₉₀/EC₁₀ ≈ 29.1), while nickel chloride and sodium molybdate exhibited comparatively steep transitions (≈1.46 and 1.75, respectively). In algae, copper sulfate and mercury chloride displayed especially wide EC₁₀–EC₈₀/₉₀ ranges within the 1-h window, consistent with distinct curve shapes compared with zinc sulfate and ferric chloride. Collectively, these EC profiles demonstrate that metals with broadly similar EC₅₀ values could still differ substantially at low-effect levels (e.g., EC₁₀), underscoring the added discriminatory power gained by incorporating multiple quantiles of the concentration–response relationship rather than relying solely on a single-point metric.

3.4 Comprehensive toxicity ranking and trophic contribution analysis

The final Comprehensive Bio-toxicity Index (CBTI) provided a quantitative hierarchy of hazard for the ten heavy metals (Figure 3). Mercury (HgCl₂) exhibited the highest aggregate toxicity with a score of 94.41, followed by Zinc (ZnSO₄, 84.56) and Lead (Pb (NO₃)₂, 78.22). Conversely, Sodium Molybdate (Na₂MoO₄) was identified as the least hazardous substance (24.59), significantly lower than all other tested compounds.

FIGURE 3

To visualize how each trophic-level organism contributed to the final comprehensive toxicity assessment, the relative contribution (%) of D. rerio, D. magna, Aliivibrio fischeri, and S. obliquus to each metal-specific composite score was calculated and displayed as radar (spider) plots (Figure 4). Overall, the contribution profiles were strongly metal-dependent, indicating that the multi-trophic integration did not rely on a single surrogate species but instead reflected distinct sensitivity patterns among taxa.

FIGURE 4

For CuSO₄, the composite toxicity was driven primarily by D. magna, A. fischeri, and S. obliquus (32.01%, 30.00%, and 32.14%, respectively), whereas D. rerio contributed only 5.84%, yielding a highly asymmetric radar shape. In contrast, HgCl₂ exhibited a near-uniform contribution distribution across all four taxa (23.24%–26.56%), producing an approximately symmetrical radar plot and indicating broadly consistent cross-trophic toxicity. ZnSO₄ also showed a relatively balanced pattern (22.06%–29.15%), whereas several metals were dominated by one or two trophic levels: Na₂MoO₄ was overwhelmingly driven by D. magna (65.97%) with a secondary contribution from fish (34.03%), while FeCl₃ showed negligible contribution from D. magna (0.29%) but substantial influence from fish (35.08%), bacteria (34.07%), and algae (30.55%). Metals such as CdCl₂ and NiCl₂ were more fish-influenced (35.35% and 35.46%), while MnCl₂ was mainly shaped by D. magna (34.12%) and algae (29.48%) with comparatively minor bacterial contribution (11.67%). For potassium antimony tartrate (K (SbO)C₄H₄O₆.1⁄2H₂O), contributions were distributed among fish (35.30%), daphnids (34.50%), and bacteria (30.20%), whereas the algal contribution was unavailable/zero in the present dataset, resulting in a three-axis dominance pattern.

4 Discussion

This study addressed two persistent challenges in metal hazard ranking: reliance on single-point descriptors that ignore concentration–response (C–R) shape, and extrapolation from one or a few surrogate species despite strong interspecific variability. Across four trophic-level organisms, Probit-fitted C–R curves confirmed pronounced species dependence in metal sensitivity, and the large EC₅₀ spreads observed for several metals reinforce that rankings derived from any single organism can differ markedly from a broader multi-trophic perspective. This pattern is consistent with prior ecotoxicological evidence showing that taxonomy, physiology, and mode-of-action related processes can strongly influence observed potency patterns across species (McCarty and Borgert, 2006; Escher and Hermens, 2002; Ashauer and Jager, 2018). In this sense, the results support the value of integrating information across taxa rather than treating one surrogate species as universally representative.

The multi-point EC_x profiles also showed that curve steepness carries information not captured by EC₅₀ alone. A steeper curve indicates that relatively small concentration changes are associated with a rapid transition from low effect to high effect, whereas a shallower curve implies a broader concentration interval over which effects accumulate. Ecologically, this distinction may matter in systems exposed to pulses, episodic releases, or spatially heterogeneous metal concentrations, because a metal with a steep response profile could produce disproportionately large biological changes once exposure approaches a narrow critical range. Conversely, shallower curves may reflect more gradual effect escalation and potentially greater heterogeneity in tolerance within the tested population. These interpretations remain inferential in the present study, but they help explain why metals with similar EC₅₀ values can differ in their lower-effect behavior and therefore in comparative hazard ranking.

The present framework should also be positioned clearly relative to existing approaches such as species sensitivity distributions (SSDs). SSDs remain the more established approach when the objective is to derive protective concentrations from a sufficiently broad species pool (Awkerman et al., 2014; Baillard et al., 2020; Xu et al., 2015; Forbes et al., 2002; Dowse et al., 2013). By contrast, CBTI serves a different purpose: it is a comparative integration framework that preserves within-species concentration–response information while combining evidence across a limited but trophically structured test set. CBTI therefore should be viewed as complementary to, rather than a substitute for, SSD-based risk characterization. A useful future direction would be to examine how CBTI rankings and SSD-derived hazard estimates converge or diverge when both full curve information and larger species datasets are available.

By integrating multiple ECx values and multiple taxa using EWM, the CBTI operationalizes a transparent weighting scheme that reduces dependence on subjective expert assignment (Suter et al., 2017; Hammitt and Zhang, 2013; Wahyudi et al., 2013; Yang and Zhang, 2012; Yi, 2006). In the present dataset, HgCl₂ ranked as the highest aggregate hazard, followed by ZnSO₄ and Pb(NO₃)₂, whereas Na₂MoO₄ was the least hazardous. The trophic contribution analysis further illustrates why multi-trophic integration matters: some metals were influenced strongly by one or two taxa, whereas others, such as HgCl₂, showed relatively balanced contributions across the four tested organisms. This pattern suggests that the proposed framework is sensitive not only to absolute toxicity magnitude but also to how toxicity evidence is distributed across trophic levels, which may be relevant when considering broader questions of species sensitivity and trophic transfer in risk interpretation (Spurgeon et al., 2020; Huang et al., 2024).

Several limitations should be emphasized more explicitly. First, the dataset is restricted to acute responses from only four species, so the resulting rankings should be interpreted as a structured proof-of-concept rather than a complete representation of ecosystem-level sensitivity. Second, exposure durations differed among assays and concentrations were nominal, which limits strict cross-taxa comparability (Gioria et al., 2011). Third, ECx coverage at the high-effect tail was incomplete for some metal–species combinations, and this may influence curve characterization and weighting. Fourth, the current framework addresses acute lethality or acute effect endpoints only; it does not incorporate chronic toxicity, sublethal impairment, recovery dynamics, bioaccumulation, or indirect ecological interactions, all of which are important for heavy metals in natural systems. Finally, the entropy-derived weights quantify discriminatory information within the present dataset, but they should not be overinterpreted as definitive ecological weights for the corresponding taxa.

Another limitation is that the CBTI scores in this study were derived from point estimates of EC_x/LC_x values and entropy-derived weights. Although all bioassays were performed in triplicate and the concentration–response fits were evaluated statistically, uncertainty from toxicity inputs and indicator weighting was not propagated into the final CBTI scores. We did not perform a formal Monte Carlo sensitivity analysis because complete uncertainty information for all EC_x/LC_x estimates was not available across all tested metal–species combinations. Introducing arbitrary uncertainty distributions or weight perturbation ranges without sufficient empirical support could lead to misleading confidence intervals. Future applications of the CBTI framework should incorporate sensitivity analysis by varying both toxicity inputs and indicator weights and by reporting uncertainty ranges for CBTI scores and ranking stability when sufficient raw data are available.

Taken together, these considerations suggest that the main contribution of the present study lies in methodological integration rather than in redefining metal toxicity knowledge in itself. The framework demonstrates how full concentration-response information can be retained during multi-species synthesis and how a transparent, data-driven weighting strategy can be implemented. Future work should expand the taxonomic coverage, include chronic and sublethal endpoints, improve environmentally relevant exposure design, and compare CBTI directly with SSD-based or equal-weight approaches to determine in which contexts each framework is most informative for ecological risk assessment.

5 Conclusion

An entropy-weighted integration of multi-point concentration-response information across four trophic levels provides a practical alternative to EC₅₀-only comparisons for the ten heavy metals examined here. Within the present acute dataset, the approach captured curve-shape differences, reflected strong interspecific variability, and yielded an interpretable composite ranking in which HgCl₂ showed the highest overall hazard and Na₂MoO₄ the lowest. At the same time, the current results should be interpreted cautiously because they are based on a limited four-species, acute-toxicity dataset. Accordingly, CBTI is best regarded at this stage as a complementary, curve-aware ranking framework that merits further testing alongside broader species coverage, chronic endpoints, and established approaches such as SSDs before broader ecological generalization is made. Further validation using broader species coverage, chronic endpoints, and formal sensitivity analyses will be necessary to evaluate the robustness and general applicability of the CBTI framework.

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