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

Abstract

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.

Graphical Abstract

Highlights

• •The integrated LSM and LMH-SFQ graph analyses were developed to select copper toxicity.
• •Six selected toxic effects were chosen from sixteen effects based on ten LSM criteria.
• •The LMH graph is useful to view CRRs over broad Cu concentration of 5 µg.L⁻¹ l.s.
• •SFQ graph displayed two highly selected effects with ∆ log C ≤ 1 µg.L⁻¹ l.s. and k ≥ 6.
• •The LSM-LMH-SFQ is relevant in supporting risk assessment of Cu in aquatic organisms.

List of symbols

Symbol description unit Symbol description and unit

a

constant in LSM, Unitless

ACR

acute to chronic ratio (Eq. 19), Unitless

ALT

alanine amino transferase, -

AST

aspartate amino transferase, -

APD

anti parasitic dose, µg.L⁻¹

B

behavioral toxicity, -

CRR

concentration response relationship, -

CV

coefficient of variation (Eq. 9), %

EC

effective concentration, µg.L⁻¹

G

growth toxicity, -

k

slope of concentration response relationship, L.µg⁻¹

∆ k

difference between the two k values, L.µg⁻¹

k_m

median slope of concentration response relationship, L.µg⁻¹

L

lethal toxicity, -

${\mathit{LC}}_{50}^c$

chronic LC₅₀ (Eq. 19), µg.L-1

LC^f

lethal concentration of Cu on fish ((16), (17), (18)), µg.L⁻¹

LC^par

lethal concentration of Cu on parasites ((16), (17), (18)), µg.L⁻¹

LMH

low medium high concentration, -

log C

log EC or log LC (Eq. 1), µg.L⁻¹

∆ log C

difference between log C₁₆ and log C₈₄ ((4), (5)), µg.L⁻¹

l.s.

log scale, -

LSM

logistic sigmoid model, -

O

olfactory toxicity, -

Ø

concentration ratio (Eq. 6), unitless

OBGL

olfactory behavioral growth and lethal toxicity, -

OC

occurrence concentration, µg.L⁻¹

PO

proportion of overlap (Eq. 10), unitless

Q

constant in LSM (Eq. 1), unitless

R

response (Eq. 1), %

R_adj

adjusted response (Eq. 8), %

SF

slope function (Eq. 7), unitless

SF_SL

slope function of sublethal O,B,G toxicity, unitless

SF_SL*

slope function of sublethal B and G toxicity, unitless

SF_L

slope function of lethal toxicity, unitless

SFQ

sigmoid flat quadrant, -

TBARS

Thiobarbituric Acid Reactive Substances, -

WQG

water quality guideline, µg.L⁻¹

1. Introduction

Cu is a naturally occurring element in surface water [1]. Its concentrations in surface water vary widely from 0.19 µg.L⁻¹ (Lake Hauroko, NZ) [2] to 96,849 µg.L⁻¹ (Lake Kalimanci, Macedonia) [3], and the range between the two mentioned studies was approximately six log scales (l.s.). Copper sulfate is used as an antiparasitic agent in aquaculture [4]. Cu caused olfactory (O) effects such as damage to hair cells in lateral lines [5], behavior (B) effects such as abnormal behavior [6] and avoidance behavior [7], growth (G) effects [8] including biochemical-hematological effects [9], [10], and lethal (L) toxicities [11] in fish. Toxic effect concentrations of copper sulfate vary widely, ranging from 0.301 µg.L⁻¹ (l.s.) as a neurobehavioral effect concentration in fish [12] to 3.477 µg.L⁻¹ (l.s.) as lethal effect concentration in fish ectoparasites [13], or the range between the mentioned effect concentrations is ± 4 µg.L⁻¹ l.s. Biomonitoring of metals, including Cu, in fish and parasites has been evaluated by [14].

Reviews of data of sublethal and lethal effects of copper sulfate [11], including toxicity mechanisms on aquatic organisms [15], can be used as input data of the logistic sigmoid model (LSM) to characterize concentration-response relationships (CRRs) of copper sulfate on aquatic organisms. Sigmoid CRRs are mainly used for log EC₅₀ for sublethal effect and log LC₅₀ for lethal effect determination [16]. Another LSM parameter, such as slope (k), is rarely used to describe CRR. It is difficult to visualize many sigmoid curves in a graph, so the use of diverse types of graph plots [17], such as sigmoid, flat, and quadrant (SFQ) graphs, will enhance CRR analysis.

The wide ranges of exposure and effect concentrations need support from a graph with low, medium, and high (LMH) interval classification. Graphs are used to display CRRs, to reduce the assessment work due to high numbers of toxicant effects [18], to display sequential mechanisms of toxicity [19], and to compare with occurrence concentrations (OC) [20], water quality guidelines (WQG), and antiparasitic doses (APD) of Cu in the aquatic environment [4].

While many studies have reported CRRs of copper sulfate in aquatic organisms, there has been limited studies addressing uses of LSM parameters and graphical representations and discussing the relevant applicability of the model and graph combination (LSM-LMH-SFQ). A study that can provide a broader view of sublethal and lethal CRRs of copper sulfate on aquatic organisms, display graphs viewing integrated OBGL responses, discuss sublethal-lethal comparability, and highlight fish-parasite lethal effects of copper sulfate in aquaculture is urgently important.

Three problems of the CRRs of copper sulphate in aquatic organisms are diverse types of toxicities, wide ranges of effect concentrations, and various patterns of graphical analysis. As a first step in fixing the problem, the current work uses toxic effect selection criteria based on LSM results to identify a few chosen toxic effects from the various toxicities of copper sulfate as described by [18]. By presenting a low-medium-high (LMH) concentration graph and doing sequential and overlap pattern analysis in each concentration interval, the second issue of copper sulfate toxicities associated with broad ranges of impact concentrations is resolved. Furthermore, in contrast to [21] recommendation that the control group not be taken into account when conducting toxicity testing, the current study adjusts the concentration of copper sulfate in the experimental groups to that in the control group. In order to address the issue of disparate graphical representations as noted by [17], the current study also harmonizes three graph types, sigmoid-flat-quadrant (SFQ).

The aims of the present study are (1) using selection criteria based on the LSM to select sublethal and lethal CRRs of copper sulfate toxicity in aquatic organisms, (2) developing low, medium, and high (LMH) and sigmoid, flat, and quadrant (SFQ) graphs based on LSM to facilitate analysis and interpretation of CRRs of copper sulfate in aquatic organisms, and (3) applying LSM-LMH-SFQ to assess CRRs of copper sulfate on aquatic organisms in sublethal-lethal effect comparability, fish-parasite effect comparability, and risk assessment in aquaculture.

2. Materials and methods

2.1. Materials

Data on the effects of copper sulfate on aquatic organisms were searched in Google Scholar with the terms “copper”, “toxicity”, “aquatic”, ”fish”, “sublethal”, “olfactory”, “behavior”, “growth” and “lethal”. Nine selected articles report CRRs of sublethal effects, which consist of three olfactory, three behavioral, and three growth effects. Seven selected articles report CRRs of lethal effects (three fish lethality—taxonomic orders, three fish lethality—life stages, and an article on parasite lethality). Each sublethal and lethal article reports CRRs from a control group (no copper sulfate exposure) and treatment groups (with copper sulfate exposure).

The selected articles for olfactory effects are [5], [22], [23] for motor neuron, mean hair cells, and cell count in myoseptum, respectively. The three articles for behavior effects are [6] for velocity and abnormal behavior and [24] for acetylcholinesterase. CRRs of growth effects were obtained from [25] for Thiobarbituric Acid Reactive Substances (TBARS) and [26] for ALT (Alanine Aminotransferase—treatment) in gills and AST (Aspartate Aminotransferase—recovery) in gills. CRRs of lethal toxicities for three fish orders (Cypriniformes, Salmoniformes, Cichliformes), three fish life stages (fry, fingerling, adult), and parasite lethality were from [11]. Finally, a total of sixteen CRRs, consisting of nine sublethal and seven lethal ones, are analyzed by LSM and its 10 selection criteria.

The CRRs were compared with standard water quality guidelines (WQG) for Cu [27], influences of water hardness on copper sulfate toxic concentrations [28], and an antiparasitic dose (APD) of copper sulfate in water [29]. The minimum and maximum of WQGs were determined based on chronic and acute toxicity criteria of Cu on aquatic life, which were 3.1 µg.L⁻¹ (0.491 µg.L⁻¹ l.s.) and 4.8 µg.L-1 (0.681 µg.L⁻¹ l.s.), respectively [27]. The [27] was chosen as the regulatory reference standard, as it covers the national level with wide regions of water bodies, includes freshwater and marine organisms, and incorporates both acute and chronic values. Another guideline [30] has limitations such as being for specific use for local environmental conditions and being limited to freshwater only. The discussion of the influence of water hardness on Cu concentrations used the values determined by the [28].

The Cu concentrations adjusted to the minimum chronic value (water hardness of 30 mg.L⁻¹) and the maximum acute value (water hardness of 150 mg.L⁻¹) were 0.2 µg.L⁻¹ (-0.699 µg.L⁻¹ l.s) and 46.9 µg.L⁻¹ (1.671 µg.L⁻¹ l.s), respectively [28]. The minimum and maximum APDs were based on water hardness of 50 and 250 ppm, respectively, resulting in copper sulfate concentrations of 500 µg.L⁻¹ (2.699 µg.L⁻¹ l.s.) and 2500 µg.L⁻¹ (3.398 µg.L⁻¹ l.s.) [29].

2.2. Methods

The logistic sigmoid model (LSM) is described by a function

$$R=\frac{a}{1+e^{\left[-k\left\{\log C-\log (C.q)\right\}\right]}}$$ (1)

where log C (µg.L⁻¹) is the concentration, R (%) is response, k is slope, a is an optimum contant, log (C.q) is a constant, and e is the natural number. Log C consists of log EC (µg.L⁻¹) or log LC (µg.L⁻¹). Responses at specific concentrations (R) were calculated as

$$\frac{R_m-R_0}{R_i-R_0}=\frac{100}{R}$$ (2)

where R_m, R_i, and R_o are maximum response (which is equivalent to 100 %), the response at any concentration of a Cu-treated group, and the response in the control group (without Cu exposure), respectively. With further arrangement, Eq. 2 can be rewritten,

$$R=\frac{100(R_i-R_0)}{\left(R_m-R_0\right)}$$ (3)

where the unit of R is %, which makes comparisons among effects possible. By inputting a data set (log C and R) of a CRR to a mathematical application software, OriginPro® [31], a data set of LSM parameter (k) and constants (a and log C.q) can be obtained. Having known the values of each parameter and constants, the log EC₁₆ is calculated by using the R value in Eq. 1 equal to 16 %, and with the use of R of 50 % and 84 %, the values of log EC₅₀, log EC_84, log LC₁₆, log LC_50, and log LC₈₄ could also be determined.

In the next step, a set of 10 selection criteria was developed by using parameter and

constants of LSM and the concentrations (log EC₁₆, log EC₅₀, log EC_84, log LC₁₆, log LC_50, and log LC₈₄). The first criterion is log EC₅₀ or log LC₅₀, the most frequent parameter used. The lowest value indicates the most sensitive effect. Criteria two is the concentration range (∆ log C) between two log Cs and can be calculated as

$$∆\mathrm{log\; EC}={\mathrm{log\; EC}}_{84}-{\mathrm{log\; EC}}_{16}$$ (4)

$$∆\mathrm{log\; LC}={\mathrm{log\; LC}}_{84}-{\mathrm{log\; LC}}_{16}$$ (5)

Criteria three is the concentration ratio (Ø) which can be calculated as,

$$\mathrm{Ø}=\frac{\left({\log \mathit{EC}}_{84}-{\log \mathit{EC}}_{50}\right)}{\left({\log \mathit{EC}}_{50}-{\log \mathit{EC}}_{16}\right)}$$ (6)

Slope Function (SF) as criteria four of a sublethal effect is calculated as follows

$$\mathit{SF}=\left(\frac{{\mathit{EC}}_{84}/{\mathit{EC}}_{50}}{{\mathit{EC}}_{50}/{\mathit{EC}}_{16}}\right)/2$$ (7)

Similarly, SFs of lethal effects can be calculated by replacing the EC symbols in Eq. 7 with LC values. Criteria five is adjusted response $R_{\mathit{adj}}$, calculated by replacing k (Eq. 1) with $k_m$ (Eq. 8). The$k_m$ is a median value of k values of each group. For example, $\mathrm{olfactory}{k}_m$ is the median of three k values in the olfactory group.

$$R_{\mathit{adj}}=\frac{a}{1+e^{\left[-k_m\left\{\log C-\log (C.q)\right\}\right]}}$$ (8)

Criteria six, seven, and eight are coefficients of variation (CVs) of k, a, and log (C.q), respectively. The OriginPro® software [31] provides standard deviation (SD) and mean of each of k, a, and log (C.q) values, which CV is determined by Eq. 9.

$${\mathit{CV}}_i(\%)=({\mathit{SD}}_i/{\stackrel{\circledR }{X}}_i)\times 100\%$$ (9)

where SD and $\stackrel{\circledR }{\mathrm{X}}$are the standard deviation and the mean of the value, respectively. Criteria nine (ꭕ²) and 10 (R²) are data fitness to the model, also generated by OriginPro®. In the next step, each of the three CRRs in the five effect groups (olfactory, behavior, growth, lethality-taxonomic, and lethality-life stage) was evaluated by the 10 selection criteria. The CRR with the largest number of fulfilled criteria (*) was determined as the selected effect among the three CRRs in each group. The criteria symbol (*) is given to the lowest value of each criterion, except for criteria five and 10 (to the highest value). The parasite lethality group consists of one CRR only, which is determined as one of the selected CRRs.

The LMH graph provides a general view of CRRs of copper sulfate at wide concentration ranges and comparisons to OC-WQG-APD. The concentrations lower than the WQG maximum value are considered low, the concentrations higher than the minimum of APD are considered high, and the concentrations between the two mentioned values are determined to be in the medium interval. The LMH graph is plotted with ∆ log EC or ∆ log LC as the abscissa and no specific value as the ordinate.

The SFQ graph consists of three parts, which are sigmoid and flat CRRs and a quadrant graph of selected effects. The sigmoid CRR graphs are drawn as log EC or log LC in abscissa and k value in ordinate. The flat graph is drawn similar to the LMH graph but is limited only to selected six effects instead of sixteen. The quadrant graph is drawn with ∆ log C as abscissa and k as ordinate.

The combined LSM-LMH-SFQ is used to analyze sublethal-lethal comparability, fish parasite effect comparability, and risk assessment of copper sulfate. The initial comparability includes ∆ log C, the ∆ log C – k correlation, the k - SF correlation, and the intersection of sublethal and lethal effects. The second comparability encompasses the log LC₅₀ (fish)–log LC₅₀ (parasite) correlation, the k (fish)–k (parasite) correlation, and the structure of paired fish–parasite studies. The LSM-LMH-SFQ is utilized to assess acute to chronic, intra- to inter-fish order, and laboratory-to-field extrapolations.

3. Results and discussions

3.1. Logistic sigmoid model (LSM)

3.1.1. Selection criteria one to five of LSM (concentration and response parameters)

The OriginPro® software [31]. provides values for the LSM parameters (log C, k) and constants, “a” and log (C.q) (Table 1). From the lowest to the highest values, the slope (k) values (Table 1) ranged from 0.93 (LC₅₀ Cichliformes) to 10.36 L.µg⁻¹ (LC₅₀ adult). In the same experiment, two curves displayed closed k values: the gills ALT curve (2.84) and the gills AST curve (2.85) [26] (App.1). For Cypriniformes, Salmoniformes, and Cichliformes, the discrepancy between fish ‘k’ and parasite ‘k’ values was 0.25, 0.47, and 0.84 L.µg⁻¹, respectively (Table 1). The "a" constants had values between 94 and 168 (Table 1). The average ‘a’ constants for lethal effects (116 ± 12) and sublethal effects (118 ± 30) were comparatively similar. The sublethal and lethal values of log (C.q) were 1.64 ± 0.78 and 2.72 ± 0.48, respectively, while the log (C.q) values ranged from 0.57 to 2.89 (Table 1).

Table 1.

Parameter values of logistic sigmoid distribution of sublethal effects of copper in aquatic biota.

Type	Toxicity	Symbol	Response	Parameters of sigmoid logistic distribution*)			Log C (µg.L−1)**			Data sources in present study
				k (L.µg−1)	a	Log (C.q)	Log C16	Log C50	Log C84
Lethal	Lethal Toxicity	P	Fish Parasite	1.77 ± 0.22	112.06 ± 7.84	2.89 ± 0.05	1.876	2.765	3.510	Tavarez-Dias et al., 2021
	Fish Lifestage (S) Differences	S−3	Adult	10.36 ± 1.42	99.55 ± 3.45	2.67 ± 0.01	2.510	2.671	2.833	Tavarez-Dias et al., 2021
		S−2	Fingerling	1.49 ± 0.12	113.22 ± 4.79	2.72 ± 0.04	1.509	2.563	3.429	Tavarez-Dias et al., 2021
		S−1	Fry	2.74 ± 1.28	120.36 ± 33.25	2.34 ± 0.12	1.659	2.215	2.646	Tavarez-Dias et al., 2021
	Fish Taxonomy (T) Differences	T−3	Cichliformes	0.93 ± 0.10	139.28 ± 12.48	3.65 ± 0.11	1.605	3.022	4.063	Tavarez-Dias et al., 2021
		T−2	Cypriniformes	1.52 ± 0.06	113.32 ± 2.48	2.62 ± 0.02	1.316	2.481	3.354	Tavarez-Dias et al., 2021
		T−1	Salmoniformes	2.24 ± 0.40	113.63 ± 11.20	2.12 ± 0.05	1.313	2.013	2.585	Tavarez-Dias et al., 2021
Sub-lethal	Growth Toxicity (G)	G−3	AST (recovery) Gills	2.85 ± 2.17	95 ± 14	2.85 ± 0.08	2.288	2.887	3.561	Karan et al., 1998
		G−2	ALT (treatment) Gills	2.84 ± 2.18	104 ± 24	2.69 ± 0.10	2.089	2.663	3.251	Karan et al., 1998
		G−1	TBARS-Liver	7.60 ± 3.75	99.1 ± 16	1.39 ± 0.05	1.174	1.393	1.617	Sevcikova et al., 2016
	Behavioral Toxicity (B)	B−3	Acetylcholinesterase	1.54 ± 1.08	158 ± 95	2.04 ± 0.45	0.621	1.539	2.121	Vieira et al., 2009
		B−2	Abnormal Behavior	5.05 ± 0.28	101 ± 1	0.70 ± 0.01	0.369	0.696	1.016	Calfee et al., 2016
		B−1	Velocity	8.34 ± 3.35	94 ± 7	0.57 ± 0.04	0.380	0.585	0.825	Calfee et al., 2016
	Olfactory Toxicity (O)	O−3	Cell Count in Myoseptum	1.61 ± 0.48	96 ± 8	1.54 ± 0.12	−0.540	1.591	2.747	d'Allencon et al., 2010
		O−2	Mean Hair Cells	3.18 ± 1.39	148 ± 49	1.50 ± 0.12	−0.836	1.289	1.586	Linbo et al., 2006
		O−1	Motor Neuron Mild Deficits	0.95 ± 0.55	168 ± 81	1.46 ± 0.55	−0.909	0.557	1.460	Sonnack, 2015

^*generated by OriginPro®

^**EC or LC

The present study analyzed two additional parameters of concentrations, ∆ log C (Eq. 4, Eq. 5) and Ø (Eq. 6), whereas general CRR commonly uses log C and R only (Eq. 1). The ranges of log EC₅₀ and log LC₅₀ (criteria one) were 0.557–2.887 and 2.013–3.022 µg L⁻¹ (l.s.), respectively (Table 1). The intervals of ∆ log EC₅₀ and ∆ log LC₅₀ (criteria two) were 0.443–3.287 and 0.333–2.458 µg L⁻¹ (l.s.), respectively (Table 1). The values of Ø (criteria three) ranged from 0.14 to 1.17 (Table 1). Of the nine sublethal effects, only motor neurons and TBARS fulfilled the three first criteria completely (Table 2).

Table 2.

Evaluation of parameters of logistic sigmoid model of copper toxicity in aquatic biota.

Toxicity		Symbol	Endpoint/stage/taxa	Log C			SF (4)	Radj(%) (5)	CV (%)			Model & Data Fitness		∑ *	Selected response
				Log C50(1)	∆ Log C (2)	Ø (3)			k (6)	a (7)	log C.q (8)	ꭕ2(9)	R2(10)
Lethal	Lethal Toxicity	P	Parasite	2.765	1.634	0.84	0.4	50	12	7	2	37	0.956	-	-
	Lethal Toxicity – Life Stage (S)	S−3	Adult	2.671	0.323 *	0.73	18.6	37	14	3 *	0 *	12	0.986	3	Fry (4*) > Fingerling (3*) > Adult (3*)
		S−2	Fingerling	2.563	1.920	0.75	11.0	59	8 *	4	1	7 *	0.992 *	3
		S−1	Fry	2.215 *	0.987	0.82 *	4.4 *	74 *	47	28	5	32	0.963	4
	Lethal Toxicity – Taxonomic (T)	T−3	Cichliformes	3.022	2.458	1.01 *	1.5 *	51	11	9	3	12	0.987	3	Cypriniformes (5*) > Salmoniformes (3*) Cichliformes (2*) >
		T−2	Cypriniformes	2.481	2.038	0.82	9.3	56	4 *	2 *	1 *	10 *	0.988 *	5
		T−1	Salmoniformes	2.013*	0.987*	0.78	3.2	80 *	18	10	2	55	0.942	2
Sub-lethal	Growth Toxicity (G)	G−3	AST (recovery) Gills	2.887	1.273	1.13	4.3	0.1	76	15 *	3 *	176	0.888 *	3	TBARS liver (6*) > Gills AST (3*) > Gills ALT (1*)
		G−2	ALT (treatment) Gills	2.663	1.162	1.01	3.8	0.2	77	23	4	110 *	0.841	1
		G−1	TBARS-Liver	1.393 *	0.443 *	1.02 *	1.7 *	7 *	49 *	16	4	159	0.885	6
	Behavioral Toxicity (B)	B−3	Acetylcholinesterase	1.539	1.500	0.63	6.1	1	40	7	7	117	0.919	0	Abnormal behavior (6*) > Velocity (4*) > Acetylcholinesterase (0*)
		B−2	Abnormal Behavior	0.696	0.647	0.98 *	2.1	33	6 *	1 *	1 *	2 *	0.999 *	6
		B−1	Velocity	0.585 *	0.445 *	1.17	1.7 *	41 *	70	60	22	89	0.939	4
	Olfactory Toxicity (O)	O−3	Cell Count in Myoseptum	1.591	3.287	0.54	74.9	23	30 *	8 *	8	60	0.941	2	Motor neuron (7*) > Cell count in myoseptum (2*) > Mean hair cells (1*)
		O−2	Mean Hair Cells	1.289	2.422	0.14	67.6	36	44	33	7 *	46	0.967	1
		O−1	Motor Neuron	0.557 *	2.369 *	0.62 *	18.7 *	43 *	58	48	38	16 *	0.978 *	7

All symbols are explained in the equations in the text.

The CRR with the largest number of fulfilled criteria (*) was determined as the selected effect among the three CRRs in each group.

The criteria symbol (*) is given to the lowest value of each criterion, except for criteria five and 10 (to the highest value).

Three sublethal effects exhibited in both selection criteria four (SF) and five (R_adj) were motor neuron, velocity, and TBARS. For the lethal effects, only the LC₅₀ of fry showed similar characteristics (Table 2). The selected k_m values as the median of the three k values of O, B, and G effects were determined as 1.61, 5.05, and 2.85 L.µg⁻¹, respectively (Table 1), resulting in the R_adj for the highest response of the O, B, and G groups being 43 % (motor neuron), 41 % (abnormal behavior), and 7 % (TBARS), respectively (Table 2).

3.1.2. Selection criteria six to 10 of LSM (coefficients of variations and data fitness to the model)

For criteria six, seven, and eight, the means and standard deviations of CVs for k, a, and log (C.q) (Table 2) were 37 ± 26 %, 17 ± 17 %, and 7 ± 10 %, respectively, with k and log (C.q) having the highest and lowest CVs, respectively. The data fit the model best for ALT (recovery gills) (176) and abnormal behavior (0.999) with the highest values of ꭕ² (criteria nine) and R² (criterion 10), respectively (Table 2). Two sublethal effects—motor neurons and aberrant behavior—exhibited both of the χ² and R² selection criteria. Table 2 shows that the LC₅₀ of Cypriniformes and the LC₅₀ of fingerlings were two lethal effects that satisfied the last two requirements. For CRR assessment, the 10 selection criteria—which included three concentration parameters (log C, ∆ log C, and Ø), two response parameters (SF and R_adj), and three CVs of LSM parameters and constants, and two data fitness (ꭕ² and R²) to LSM, were appropriate in the current study.

Out of 10 criteria, the sublethal and lethal effects met 6–7 and 4–5 criteria, respectively (Table 2). Three sublethal effects (motor neuron, aberrant behavior, and TBARS) and three lethal effects (LC₅₀ of fry, LC₅₀ of Cypriniformes, and LC₅₀ of parasite) were selected from a total of sixteen effects using 10 selection criteria. It is anticipated that the chosen effects will exhibit 8–10 criteria with additional CRR data in the future. To meet the requirements for reporting and assessing toxicity data [32], LSM and its effect selection criteria might be further developed. A graphical representation of the six chosen CRRs (LMH and SFQ) was used for additional analysis. The slope value (k) and other LSM parameters (∆ log C, Ø, SF) were shown in the LMH (Fig. 1) and SFQ (Fig. 2) graphs to help better understand the CRRs.

Fig. 1.

Ranges of values of log concentrations (EC₁₆ – EC₅₀ – EC₈₄) and (LC₁₆ – LC₅₀ – LC₈₄) of copper sulfate in the aquatic organisms and comparisons with field occurrence concentrations, water quality guidelines (WQG), and anti-parasitic dose (APD) of copper sulfate in water. Sources of concentration data are listed in Table 1. Six bold brackets indicate selected effects from each of the effect groups.

Fig. 2.

Summary of sublethal (olfactory, behavior, growth) and lethal toxicity of copper sulfate in aquatic organisms, analyzed by LSM, consisted of a concentration-response graph with slope (k) (sigmoid graph—Sub Fig. 2.A); ranges of log EC₁₆ – log EC₈₄ and log LC₁₆ – log LC₈₄, with ranges of low (L), medium (M), and high (H) concentrations are shown (flat graph—Sub Fig. 2.B). A plot of quadrant analysis between log ∆C vs k is provided (quadrant graph—Sub Fig. 2.C). Original data is provided in Table 2. Ranges of log concentrations (µg.L⁻¹ l.s.) are −2.000 to −0.690 (L1); −0.690–0.491 (L2); 0.491–0.681 (L3); 0.681–1.671 (M1); 1.671–2.699 (M2); 2.699–3.398 (H1); and 3.398–5.000 (H2).

3.2. Low-medium-high (LMH) concentration graph

3.2.1. General and wide view of LMH graph

The LMH graph's comparisons of the CRRs with OC, WQG, and APD provide a comprehensive analysis of copper sulfate exposures and impacts on aquatic organisms. Within the LMH graph, there were three concentration intervals: low (-0.909–0.681), medium (0.681–2.699), and high (2.699–4.064 µg.L⁻¹ l.s.). The LMH intervals were primarily associated with olfactory, behavioral, and growth-lethal effects, respectively (Fig. 1). The intervals of the OCs, the CRRs of sixteen effects, and the CRRs of six selected effects decreased from ≈ 6 to ≈ 5, and finally to ≈ 4 µg.L⁻¹ l.s., respectively (Fig. 1, Fig. 2). The last interval was comparable to a similar one reported by [19]. Labels consisting of ∆ log C, Ø, k, and SF were added in Fig. 1 and Fig. 2 to facilitate interpretation of CRRs graphical data harmonization among ecotoxicology data sets [33].

The current study's general LMH graph, which compares the CRRs of sublethal and lethal effects, covers low to high OCs, and links the CRRs to WQG and APD in one graph, facilitates the visual communication of toxicological data [17]. Additionally, the LMH graph indicated certain copper sulfate concentration ranges that might be taken into account for further studies [34]. Laboratory-to-field comparisons in the present study are appropriate since the CRR is response-specific (laboratory) whereas OC, WQG, and APD are environment-specific (field).

3.2.2. Eco-neurotoxicity at low Cu concentrations

Potential eco-neurotoxic consequences could result from low Cu concentrations. Cu values in natural freshwater range from 0.2 to 30 µg.L⁻¹ or −0.7–1.48 µg.L⁻¹ l.s. [19]. The protective Cu concentration for 99 percent of freshwater organisms is 0.340 µg L⁻¹ or −0.469 µg L⁻¹ l.s. [35] or similar to the L2 zone (Fig. 2.C). The limit of detection for copper sulfate was reported to be 0.02 µg.L⁻¹ or −1.699 µg.L⁻¹ (l.s.) [36]. Eco-neurotoxicity of Cu may manifest at concentrations as low as 0.3 µg.L⁻¹ or −0.523 µg.L⁻¹ (l.s.) [12].

The sequential olfactory-behavior effect is an example of aquatic eco-neurotoxicity [37], which has overlap ranges of ± 2 µg.L⁻¹ l.s. (Fig. 2.B). The ∆ log ECs of sublethal effects decreased from 2.4 to 3.3 for olfactory, to 0.4–1.5 for behavioral, and to 0.4–1.3 µg.L⁻¹ (l.s.) for growth effects (Table 2). Neurobehavioral and neuroendocrine changes led to zebrafish growth and reproduction outcomes that might happen at commonly detected Cu concentrations (1.001–1.602 µg.L⁻¹ l.s.), suggesting possible dangers to fish populations [38].

3.2.3. Incremental and sequential patterns of CRRs

The LMH graph displayed concentration intervals supported with patterns of incremental, overlapping, and sequential CRRs. Incremental pattern explains that a more adverse effect occurs at a higher concentration, such as growth effects generally occurring at higher concentrations than behavioral effects (Fig. 1). The CRRs in the present study followed the incremental pattern, from the lowest to the highest concentration, as olfactory, behavioral, growth, and lethal effects (Fig. 1), which was comparable to the adverse outcomes reported by [19]. Sequential pattern is the order of an occurrence of toxic effect, such as from olfactory to behavior and growth effects, supported by mechanisms of toxicity [15]. The incremental and sequential patterns were referred to as dose-response and dose-effect relationships, respectively [16].

3.2.4. Proportion of overlap (PO)

Overlap is the sharing of sections of concentrations between two effects, such as those between behavior and olfactory effects, as seen by the LMH graph (Fig. 1). The lower the proportion of overlap (PO), the more different the two effects are from one another. The graph by [19] did not demonstrate overlap between the sublethal and lethal effects of copper sulfate on fish survival. The current investigation, however, revealed that many responses overlapped each other (Fig. 1). The substantial overlap in olfactory effects could be explained by olfactory neuron degeneration and regeneration by zebrafish toxicity studies [39], [40]. Fish olfactory neurons lost their cilia when exposed to copper at low concentrations of 16–635 µg.L⁻¹ (1.204–2.803 µg.L⁻¹ l.s.), but they later recovered [40]. The concentration of copper sulfate that had a sublethal effect on the zebrafish's body length, yolk sac, and swim bladder was 3.204 µg.L⁻¹ l.s. [41], and it partially overlapped with the H1 zone in this investigation (Fig. 2.B).

The two highly selected effects (TBARS and LC₅₀ of fry) were assessed for the proportion of overlap (PO) as follows:

$$\mathit{PO}={\mathit{LC}}_1/{\mathit{EC}}_{99}$$ (10)

Following the calculation of the fry's LC₁ and the EC₉₉ (Eq. 10) of the three selected sublethal effects, the POs of motor neuron, aberrant behavior, and TBARS were 0.057, 0.132, and 0.161, respectively. PO levels increased in response to olfactory, behavioral, and growth effects. Analysis and interpretation of the LMH graph (Fig. 1) were impacted by sequential and incremental patterns that were observed and confirmed by narrow-moderate overlapping intervals of CRRs. While the sequential pattern was more qualitative and connected to the toxicity mechanism, the incremental and overlapping patterns were more quantitative.

3.3. The sigmoid flat quadrant (SFQ) graph

3.3.1. From wide concentration intervals to narrow concentration zones

The SFQ graph's seven concentration zones were created by converting the three LMH graph concentration intervals into a more functional and constrained range of concentrations. The zones varied from −2–5 µg.L⁻¹ l.s. (Fig. 2.B) and were composed of three low (L1, L2, L3), two medium (M1, M2), and two high (H1, H2) zones. The seven zones may also be categorized as olfactory (L2–M1), behavioral (L3–M2), growth (M1–H1), lethal toxicity (H1–H2), and general biological responses (L2–H1). The L2 – M1 ranged from −0.699 µg.L⁻¹ to 1.671 µg.L⁻¹ l.s, which was determined by the adjustment to water hardness [28] (Fig. 2.B).

Out of the seven created SFQ zones, two were identified by the overlapping OBGL effects. In the SFQ, the overlap of sublethal effects was restricted to M1 zone (Fig. 2.B), whereas in the LMH graph, it initially comprised M1 and M2 zones (Fig. 1). Similarly, the lethal effect overlap that was first concentrated on the H1 and H2 zones (Fig. 1), was now restricted to the H1 zone alone (Fig. 2.B). The overlap included growth-lethality (M1), behavior-growth (L3-M1), and olfactory-behavior (L2-M1) zones (Fig. 2.B). Compared to sigmoid graphs alone (App. 1), a graph depicting a collection of effects with various curve types (Fig. 2) was more comprehensible. Observing flat graphs was simpler than sigmoid graphs, especially at the sublethal –lethal overlapping zone (M1) (Fig. 2.B).

The SFQ graph employed LSM-generated parameters to make CRR analyses and interpretations easier. The parameters were ∆ log C (Table 2) and k (Table 1). The SFQ graph abscissa (Fig. 2) showed concentrations that were represented by log C (sigmoid, Fig. 2.A), ∆ log C (flat, Fig. 2.B), and ∆ log C (quadrant, Fig. 2.C). Both the percentages of responses (Fig. 2.A) and k values (Fig. 2.C) were used to express the graph ordinates. There were also Ø and SF values provided for the flat graph (Fig. 2.B), showing that the Ø values were less varied than the SF values for both sublethal and lethal effects. Three of the six selected effects were found to be in the targeted quadrants (Q_II and Q_III) when the SFQ graph's plot of ∆ log C against k was examined. Additionally, a highly selected sublethal effect (TBARS) was found in Q_II (Fig. 2.C).

3.3.2. From selected to highly selected effects

In quadrant analysis, selectivity was done based on smaller ∆ log C and higher k values. The ratio of maximum to minimum value of k in SFQ was 11.1 (10.36/0.93) (Table 1), and a tentative k value of a half of 11.1, or 5.55, or rounded as 6, was used in quadrant analysis (Fig. 2.C). Ideal values for ∆ log C and k were ≤ 1 µg.L⁻¹ l.s. and k ≥ 6, respectively, which are located in Q_II (Fig. 2.C). The order of quadrants from the most to the least ideal, in consecutive order, was Q_II > Q_III > Q_IV > Q_I. Three sublethal effects were in each of separate Q_II (TBARS), Q_III (abnormal behavior), and Q_IV (motor neuron) (Fig. 2.C). In contrast, three lethal effects were in a single Q_III.

After analyzing 16 CRRs (Fig. 1), the current study identified six selected effects (Fig. 2.A and 2.B) and ultimately chose two highly selected effects (Fig. 2.C). The present study expressed CRRs as three distinct sigmoid, flat, and quadrant graphs (Fig. 2) and enriched diverse graphs of CRRs [17]. The SFQ can be created as an ecotoxicology database [42] or as a graphical database, as recommended by [33].

3.4. Application of LM-LMH-SFQ

3.4.1. Sublethal – lethal effect comparability

The LSM-LMH-SFQ was pertinent to four applications: sublethal-lethal comparability assessments, fish-parasite lethal comparison, use of zebrafish and fry life stage in toxicity studies, and risk evaluation of copper sulfate on aquatic species. In the initial application of LSM-LMH-SFQ, sublethal and lethal CRRs were shown together as a power function in a quadrant graph (Fig. 2.C), but separately as sigmoid (Fig. 2.A) and flat (Fig. 2.B) graphs. As shown in Fig. 1, the ranges of ∆ log ECs and ∆ log LCs were ± 4.5 and ± 2.5 μg.L⁻¹ l.s., respectively, and the intervals of the three sublethal effects (± 0.5–2 μg.L⁻¹ l.s.) were less than the three lethal effects (± 2–4 μg.L⁻¹ l.s.) (App. 1). According to Fig. 2.B, the total overlapping zone between lethal and sublethal effects was L2-M1 (± 2 µg.L⁻¹ l.s.). Relationships between slope functions (SF) (Eq. 7, Table 2) and slopes (k) (Eq. 1, Table 1) were used ((11), (12), (13)) to provide another comparison between sublethal and lethal effects.

$${\mathit{SF}}_{\mathit{SL}}={30.76k_{\mathit{SL}}}^{-1.314}(R^2=0.052\mathrm{;}n=9)$$ (11)

$${\mathit{SF}}_{\mathit{SL}*}={10.06k_{\mathit{SL}*}}^{-0.967}(R^2=0.780\mathrm{;}n=6)$$ (12)

$${\mathit{SF}}_L={8.94k_L}^{-0.812}(R^2=0.978\mathrm{;\; n}=7)$$ (13)

The relationship for lethal effects (Eq. 13) had a smaller slope, higher exponent, and higher R² than those of sublethal effects (Eq. 12), showing that variabilities in lethal effects were less than those of sublethal effects. The R² value (0.780) of Eq. 12 was higher than that of Eq. 13 (0.052) when olfactory effects were not included in the regression lines (SL*), indicating olfactory had wider variations than behavior and growth effects. The power function relationships between ∆ log C and k (Fig. 2.C) were described with higher R² found for six selected toxic effects (Eq. 14) than for 16 original effects (Eq. 15).

$$k=3.09{\left(∆\log C\right)}^{-1.176}({\mathrm{R}}^2=0.993\mathrm{;\; n}=6)$$ (14)

$$k=3.52{\left(∆\log C\right)}^{-0.862}({\mathrm{R}}^2=0.913\mathrm{;\; n}=16)$$ (15)

The three selected sublethal effects were scattered in three quadrants, which were TBARS (Q_II), abnormal behavior (Q_III), and motor neuron (Q_IV). In contrast, the three selected lethal effects were positioned in a single Q_III (Fig. 2.C).

3.4.2. Fish-parasite LC₅₀ comparability

The LSM-LMH-SFQ used linear regression lines that passed the points of origin to compare the log LC₅₀ of fish and that of the parasite ($\log {\mathit{LC}}_{50}^{\mathit{Par}})$ (in its second pertinency, as follows):

$$\log {\mathit{LC}}_{50}^{\mathit{Cyp}}=0.899\log {\mathit{LC}}_{50}^{\mathit{Par}}\left(n=3,R^2=0.991\right)$$ (16)

$$\log {\mathit{LC}}_{50}^{\mathit{Cic}}=1.091{\mathrm{log\; LC}}_{50}^{\mathit{Par}}(n=3,R^2=0.991)$$ (17)

$$\log {\mathit{LC}}_{50}^{\mathit{Sal}}=0.728\log {\mathit{LC}}_{50}^{\mathit{Par}}(n=3,R^2=0.999)$$ (18)

where superscripts Cyp, Cic, and Sal refer to fish orders Cypriniformes, Cichliformes, and Salmoniformes, respectively. The three fish orders and Siluriformes are the four major fish orders in aquaculture [43]. All regression lines ((16), (17), (18)) showed high regression coefficients (R² > 0.900), with the highest R² for Salmoniformes (Eq. 18) and the closest slope differences to an ideal slope of 1.0 for Cichliformes (Eq. 17). The differences between k of fish and that of parasite (∆ k) were 0.84 (Cichliformes), 0.47 (Salmoniformes), and 0.25 (Cypriniformes), with the latest being the selected fish order due to its smallest ∆ k (0.25) and the highest number of selection criteria (5*) (Table 2).

Paired toxicity studies can be developed to address the interaction between copper sulfate toxicity and parasite infections [44], such as sublethal effects of antioxidant-acetylcholinesterase [45]; sublethal (operculum movement, air gulping) and lethal effects of fish [46]; paired sublethal (swimming speed) and lethal effects of parasites [47]; and paired fish-parasite lethality [48]. Morphological, histological, biochemical, and behavioral effects of heavy metals, including Cu, are important parameters in fish – parasite biomonitoring [14].

3.4.3. Use of fry life stage and zebrafish in Cu toxicity studies

Fish life stages that are susceptible to copper sulfate toxicity can be evaluated in three different methods in its third applicability, all while following the LC₅₀ values, R_adj and k_m values, and 10 selection criteria. For fry, fingerlings, and adults, the corresponding LC₅₀ values were 2.013, 2.481, and 3.022 µg.L⁻¹ (l.s.) (Table 2). The life stage that is most vulnerable is fry because it has the lowest LC₅₀. Secondly, the reaction with the highest R_adj (fry) was the most sensitive; according to median slope k_m, the results were 74 % (fry) > 59 % (fingerling) > 37 % (adult). In comparison to fingerlings (3*) and adults (3*), fry (4*) exhibited the highest sensitivity, possessing the greatest number of four criteria. These consistent findings led to the conclusion that the fry life stage was the most vulnerable. Channel catfish fry was reported as more sensitive to copper sulfate in water with low alkalinity and hardness than in water with high alkalinity and hardness [49]. The reaction of the early life stage of fish to copper sulfate toxicity is better understood by comparing the findings of [49] with the juvenile guppies' olfactory system [50].

The use of zebrafish as a pertinent biomodel in aquaculture studies [51], [52], [53] and in olfactory investigations in this work (Table 1) supported the laboratory-to-field extrapolation of LSM-LMH-SFQ. According to McCluskey and [54], zebrafish belong to the Cypriniformes, hence the distinctions between them and other Cypriniformes in aquaculture can be regarded as intraorder variations. The LC₅₀ of copper sulfate in zebrafish was 8400 µg.L⁻¹ (3.924 µg.L⁻¹ l.s.) and was used to set up a maximum permissible concentration in Brazil [41], which was comparable to the H2 zone (Fig. 2.B). The LC₅₀ for zebrafish is 300 µg.L⁻¹ (2.477 µg.L⁻¹ l.s.) [55], and it is within the range of LC₅₀ of Cypriniformes in the present study (2.481 µg.L⁻¹ l.s.) (Table 1). The LC₅₀ reported by [41] differed by a factor of 28 compared to that noted by [55], which can be considered as an intra-order variation. Assessment of interorder variation among major aquaculture fish orders can be done based on differences of lateral line structures [56], [57].

3.4.4. Application of LSM-LMH-SFQ related to APD of copper sulfate in aquaculture

The LSM-LMH-SFQ proved appropriate for use in risk assessment of copper sulfate on aquatic animals, including farmed fish, in its fourth relevance. LSM-LMH-SFQ used both concentration and concentration ranges, covered variations in sublethal effects, particularly growth and reproduction impacts, which are significant fish health indicators influencing aquaculture productivity, and discovered a set of selected effects rather than a single sensitive effect. Cu-induced growth effects are linked to neuroendocrine [58] and bioenergetic [15] parameters, which in turn influence the results of reproduction [19]. WQG of Cu in Brazilian waters of 0.204–0.644 µg.L⁻¹ l.s. [59] is comparable to WQG in the USA of 0.491–0.681 µg.L⁻¹ l.s. [27]. Uncertainty can be decreased by regionally tailored Predicted No Effect Concentration (PNEC) guidelines for aquatic environments in Brazil [60].

In order to assess its relevance to field situations, the current LSM-LMH-SFQ study investigated copper sulfate concentrations in aquaculture that have been reported in the literature, both in the field and in regulations. As an adjustment to water chemistry parameters, the current investigation used values ranging from −0.699–1.671 µg.L⁻¹ l.s. [28], which was displayed as minimum L2 to maximum M1 (Fig. 1). The maximum M1 in the current investigation is comparable to the maximum copper sulfate concentration (1.710 µg.L⁻¹ l.s.) that is advised for largemouth bass aquaculture in Brazil [41]. The H1 zone (2.699–3.398 µg.L⁻¹ l.s.) (Fig. 2.B) is similar to Taiwan's maximum permissible copper sulfate concentration for shrimp aquaculture (3.001 µg.L⁻¹ l.s.) [61]. Copper sulfate concentrations in aquaculture were recorded as M1–H1 zones, with reference to [28], [38], [61].

3.4.5. Application of LSM-LMH-SFQ in aquatic risk assessment of copper sulfate

A pertinent illustration of chronic copper sulfate exposure at both low and high concentrations is the acute-to-chronic extrapolation of Cu on Salmoniformes. The acute-to-chronic ratio (ACR) for low concentrations and sublethal effects can be calculated by dividing the acute WQG for aquatic biota protection (4.8 µg.L⁻¹) by the chronic one (3.1 µg.L⁻¹) [27]. This yields an ACR of 1.55. For high concentrations and lethal effects, the ACR was determined by the following equation:

$${\mathit{LC}}_{50}^c=\frac{{\mathit{LC}}_{50}}{\mathit{ACR}}$$ (19)

where LC₅₀ was the acute LC₅₀ for Salmoniformes (2.013 µg.L⁻¹ l.s. or 103 µg.L⁻¹) and ${\mathit{LC}}_{50}^c$

was the chronic LC₅₀ for Salmoniformes (Table 2). The average of 4.5–7.8 [62] or 6.15 was used to determine the ACR of Salmoniformes. Consequently, 103/6.15 = 16.7 µg.L⁻¹ or 1.223 µg.L⁻¹ l.s. was determined to be the ${\mathit{LC}}_{50}^c$ of Salmoniformes (chronic). This chronic LC₅₀ was less than the acute LC₅₀, at 0.79 µg.L⁻¹ l.s. The two ACR values were 1.55 [27] and 6.15 [62]. Sublethal and lethal chronic values were estimated using these two values (1.55 and 6.15, respectively) (Fig. 2.B).

Concentration-response modeling [63] and laboratory studies of copper sulfate toxicity [1] shown that the chosen toxic effects were well-supported by toxicity mechanisms and an integrated mathematical model and graph analysis. Uncertainty related to the use of the lowest value (log EC₁₆ or log LC₁₆) and the highest value (log EC₈₄ or log LC₈₄) in the present study was that the analysis covered only 68 % of the population at risk and not a higher proportion (e.g., 95 %). The range between the 16th and 84th percentiles in the present study minimized the variations, as the range is in the linear section of the CRR [16]. Uncertainty in the risk assessment of copper sulfate in aquaculture is caused by naturally occurring copper in surface water [1]. This uncertainty was reduced by adjusting the background concentration [21], as was done in the current study (Eq. 2).

Some of the uncertainties that have been identified as being primarily related to field situations and aquaculture practices are fish-parasite interactions [44], predator-prey relationships [64], water hardness [65], dietary copper for aquaculture organisms [66], [67], [68], recovery of copper sulfate exposed aquaculture fish [69], and regional variations in APD levels [41], [61]. Some of the uncertainties presented by modeling and laboratory studies of copper sulfate toxicities on aquatic organisms are acute to chronic ratio [62], concentration setting [34], single Cu and metal mixture toxicity effects [70], precedence for female swimming activity [71], omission of behavioral toxicity results [72], and differences in lateral line and olfactory system structures among fish orders [57].

Numerous uncertainties exist in the laboratory-to-field extrapolation of CRRs of copper sulfate; however, these uncertainties can be minimized by choosing the highly selected effects in the current study (TBARS and fry lethality). The relevance to aquaculture is increased by measuring TBARS [9] as a key growth parameter and sperm quality [73] as a major reproductive metric. There may be less uncertainty if these impacts are measured from the fry [74] to the adult life stage of aquaculture fish. This method gives individual-to-population and acute-to-chronic extrapolations a stronger scientific foundation for justification.

The inputs, processes, and outputs of the LSM-LMH-SFQ are summarized in Fig. 3. Based on previous discussion of LSM (3.1), LMH (3.2), and SFQ (3.3), the LSM-LMH-SFQ increased the selectivity of concentration-response data starting from 16 reported, to six selected, and finally to two highly selected effects. The highly selected effects contribute practical considerations in risk assessment and aquaculture. The LSM-LMH-SFQ also applies to shrimps, other aquatic invertebrate parasites, and other aquaculture fish that are not members of the Cypriniformes, Cichliformes, or Salmoniformes orders. Other heavy metals in aquaculture, including As, Cd, Cr, and Pb [75] can also be analyzed using the LSM-LMH-SFQ.

Fig. 3.

The inputs, processes, and outputs of the LSM-LMH-SFQ. The inputs are concentration-response data of the reported effects. The processes are screening of the reported effects by ten selection criteria of the LSM. The outputs are selected and highly selected effects. Descriptions of symbols are provided in the list of symbols and texts.

4. Conclusions and recommendations

The use of LSM with 10 selection criteria to pick six out of sixteen sublethal and lethal impacts of copper sulfate on aquatic organisms was appropriate. LSM-LMH tentatively was applicable to classify eco-neurotoxicity (< 0.681), overlapping of sublethal-lethal (0.681–2.699), and fish-parasite lethality (> 2.699 µg.L⁻¹ l.s.), provisionally. LSM-SFQ was suitable to choose two highly selected effects (TBARS and LC₅₀ of fry) out of the six selected effects based on ∆ log C ≤ 1 µg.L⁻¹ l.s. and k ≥ 6. LSM-LMH-SFQ was pertinent to the analysis of sublethal-lethal comparability, fish-parasite comparability, and risk assessment in aquaculture.

With the addition of new CRRs, it is expected that future LSM will meet eight to 10 of the current four to seven selection criteria, and future LSM-SFQ will provide more highly selected effects. With adjustment to regional OC, WQG, and APD, the LSM-LMH applicability will increase. The risk evaluation of copper sulfate on aquaculture species would have been more appropriate if uncertainty factors from modeling, laboratory, field, and regulatory investigations of LSM-LMH-SFQ had been supplied.

Author statement

The author states that the submitted article has not been published previously and the article is not under consideration for publication elsewhere. The single author conducted the study design, data analysis and interpretation, and drafting and revising the article.

CRediT authorship contribution statement

Djohan Djohan: Writing – review & editing, Writing – original draft, Visualization, Methodology, Investigation, Formal analysis.

Declaration of generative AI and AI-assisted technologies in the writing process

During the preparation of this work, the author used QuillBot in order to check the grammar and vary the writing styles. After using this tool/service, the author reviewed and edited the content as needed and takes full responsibility for the content of the publication.

Funding

This research received a grant from the Directorate of Research and Community Service of Satya Wacana Christian University, with grant number 108.a/DRPM/PEN-MANDIRI/4/2024.

Declaration of Competing Interest

The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: Djohan Djohan reports a relationship with Satya Wacana Christian University that includes: employment. The author has no conflict of interests to disclose. If there are other authors, they declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Handling Editor: Prof. L.H. Lash

Appendix A. Supplementary material

Supplementary material

Data availability

The data is available in the original cited articles.