Modeling Time‐Dependent Aquatic Toxicity of Hydrocarbons: Role of Organism Weight, Temperature, and Substance Hydrophobicity

Abstract

Oil spill exposures are highly dynamic and are not comparable to laboratory exposures used in standard toxicity tests. Toxicokinetic–toxicodynamic (TKTD) models allow translation of effects observed in the laboratory to the field. To improve TKTD model calibration, new and previously published data from 148 tests were analyzed to estimate rates characterizing the time course of toxicity for 10 fish and 42 invertebrate species across 37 hydrocarbons. A key parameter in the TKTD model is the first‐order rate that incorporates passive elimination, biotransformation, and damage repair processes. The results indicated that temperature (4–26 °C), organism size (0.0001–10 g), and substance log octanol–water partition coefficient (2–6) had limited influence on this parameter, which exhibited a 5th to 95th percentile range of 0.2–2.5 day⁻¹ (median 0.7 day⁻¹). A species sensitivity distribution approach is proposed to quantify the variability of this parameter across taxa, with further studies needed for aliphatic hydrocarbons and plant species. Study findings allow existing oil spill models to be refined to improve effect predictions. Environ Toxicol Chem 2022;41:3070–3083. © 2022 ExxonMobil Biomedical Science Inc. Environmental Toxicology and Chemistry published by Wiley Periodicals LLC on behalf of SETAC.

INTRODUCTION

Exposures to chemicals in the environment are often transient in space and time, including exposures through non‐point‐source runoff, permitted outfalls, and accidental releases (van Leeuwen & Vermeire, ²⁰⁰⁷). In contrast, hazard data used to characterize the thresholds of toxicity are often based on laboratory methods using constant exposures to promote replication and to minimize potential confounding variables (Rand, 1995). Although constant‐exposure hazard data and associated test methods have dramatically improved our understanding of the aquatic toxicity of these substances, such data are not representative of effects characteristic of dynamic exposures in the environment.

Dynamic water quality modeling is one strategy used to predict time‐variable exposure concentrations (Chapra, 2008; EFSA Panel on Plant Protection Products and Their Residues et al., ²⁰¹⁸). These models are applied to characterize the relevant transport and transformation processes dictating chemical fate over space and time as well as to model bioaccumulation in aquatic life and resulting toxicity. An important class of such tools includes oil spill models (French‐McCay, 2002; Keramea et al., ²⁰²¹). These modeling tools are widely used in environmental impact assessments, spill response planning and training, response decision‐making during spills, and natural resource damage assessments after spills.

Existing oil spill models that evaluate effects to aquatic life use a combination of pseudocomponents, or hydrocarbon blocks, to represent the oil composition in fate simulations so that dissolved oil exposures can be predicted and assumed toxicokinetic–toxicodynamic (TKTD) relationships can be used to estimate the resulting aquatic effects of complex oil substance releases (French‐McCay, 2004; Reed et al., ¹⁹⁹⁹). Simulating oil composition in terms of hydrocarbon blocks is needed to address and simplify the complexity of petroleum substances for modeling purposes. Each block represents a discrete group of oil constituents with similar properties that is used to simulate fate in the environment (Foster et al., 2005). Toxicokinetic models are coupled to the exposure estimates obtained by fate modeling to predict the time‐dependent toxicity of the hydrocarbon blocks. An additive toxicity model is then applied to sum up the contribution of each block to predicted aquatic toxicity (French‐McCay, 2004).

A common framework that is applied for effects assessment assumes that toxicity occurs once the accumulation of contaminants (i.e., hydrocarbons in the case of petroleum substances) exceed a molar concentration threshold within the organism (Di Toro et al., 2000; Veith et al., ¹⁹⁸³). For nonpolar organic chemicals, bioconcentration factors (BCFs), which describe the partition coefficient of a substance between the organism and water, are often modeled as a first‐order process as the ratio of the chemical uptake or clearance rate k ₁ (liters per kilogram wet wt per day), to the rate of elimination, k ₂ (per day; Thomann, ¹⁹⁸⁹). Generally, because uptake is fast, the elimination rate controls the extent to which a chemical is bioconcentrated (Arnot & Gobas, 2006; Goss et al., ²⁰¹³; Mackay & Fraser, ²⁰⁰⁰).

$$\text{BCF}=k_1/k_2$$ (1)

Toxicokinetic–toxicodynamic modeling uses a similar approach to model the accumulation of chemicals as well as accrual of damage relative to the recovery and elimination processes within an organism (Ashauer et al., 2016; Jager et al., ²⁰¹¹; Lee et al., ²⁰⁰²). In this context the overall elimination rate, k _e, is considered to be a lumped parameter that implicitly includes passive excretion, biotransformation, and damage repair (Jager et al., 2011). It has also been reported that this lumped parameter varies as a function of organism size, water temperature, and the log octanol–water partition coefficient (log K _OW) of the substance (Gergs et al., 2015; Hendriks et al., ²⁰⁰¹; McCarty et al., ¹⁹⁹²).

The objective of the present study was to improve the technical basis of the TKTD models used in oil spill impact assessments by specifically reexamining the role that these variables serve in influencing k _e across different hydrocarbons and test species. The assumed form of the elimination rate (k _e, per day) as a function of organism weight, environmental temperature, and log K _OW is

$$\log k_e=a_1\log K_{\text{OW}}+a_2\log \mathrm{W}+a_3(T_1-25)+\mathit{b}$$ (2)

where W is organism weight (grams), T ₁ is temperature (Celsius) normalized to 25 °C, and a ₁, a ₂, a ₃, and b are empirical constants.

The parameters in Equation 2 were originally based on calibration to bioconcentration data (Baussant et al., 2001; Feijtel et al., ¹⁹⁹⁷; French‐McCay, ²⁰⁰²; Spacie & Hamelink, ¹⁹⁸²), which are certainly related to toxicokinetics that describe toxicity; that is, k ₂ is assumed to approximate k _e. The role of organism weight on k _e is predicted using the allometric scaling term a ₂ of −0.2 (Arnot & Gobas, 2004). The log K _OW represents the influence of chemical structure, with a ₁ equal to −0.41 and the constant, b, given as 1.47 (French‐McCay, 2002). The influence of temperature is modeled using the Q₁₀ approach (Downs et al., 2008) such that a ₃ is 0.048 (note the conversion from natural log, to log‐base 10 from equation 17 in French‐McCay [2002]). This results in a three‐fold reduction for a 10 °C decrease in temperature, that is, the ratio of k _e at 15 °C to 25 °C, k _e,T=15 °C/k _e,T=25 °C = 10^{[0.049 × (15–25)]} = 10^−0.49 = 0.32.

The first step in our analysis was to apply the framework presented in Equation 2 to a large data set compiled from literature in a meta‐analysis of available aquatic toxicity data. The second step involved separate analysis of Equation 2 with new time‐dependent toxicity data generated as part of the present study in our laboratory for a fish and selected invertebrates with different sizes and test temperatures to limit intralaboratory variability inherent in the meta‐analysis. The outcome of the present study is intended to refine the TKTD models used in current oil spill models to provide more accurate predictions of effects to aquatic life in the field.

METHODS

Approach

Three aquatic toxicity data sets were used to address the objective of the present study. The first data set is a compilation of published hydrocarbon toxicity studies across a range of fish and invertebrate species, organism sizes, and test temperatures. Two new focused data sets (A and B) included a series of toxicity tests conducted at ExxonMobil Biomedical Sciences to specifically evaluate the role of organism weight and temperature on the time‐dependent toxicity of selected aromatic hydrocarbons. These studies are described and reported as part of our study.

The additional toxicity data generated in the present study were included in the meta‐analysis with the literature data set and analyzed separately to further evaluate the potential influence of test variables on the time dependence of observed toxicity using data from within the same laboratory and test organism populations. In the present study, hydrocarbons are assumed to have a similar mode of acute toxic action (e.g., narcosis) consistent with current practice used in oil spill effect models (French‐McCay, 2004).

Literature data set

Toxicity data generated using standard 48–96‐h test protocols were identified in the published literature. Mortality data (or other commonly reported acute effect endpoints for invertebrates, e.g., immobilization) over time and at different exposure concentrations were collected from tables or through digitization of figures (DigitizeIt software) in the original publications. Only data sets that provided measured exposure concentrations and included treatments that reported near or complete mortality (fraction surviving ranging from 1 to ≤0.2) were selected to allow for reliable model calibration. Toxicity tests including ultraviolet light exposures were excluded in this compilation to avoid the potential confounding influence of phototoxicity.

In addition to the hydrocarbon test substance, measured exposure concentrations, and mortality data, test temperature and organism weights were compiled from each study. In cases where organism weight was not reported, weights were estimated from available literature given the reported life stage, age, or length of the test organism used. Data sets included in this compilation reported survival data for multiple treatment concentrations over time. Additional toxicity studies with typical duration ≤5 days that reported acute median effect and median lethal concentrations (LC50s) as a function of exposure duration or time to death (TTD) as test endpoints were also compiled to support derivation of the required TKTD parameters. Longer‐term toxicity studies were excluded in the present study to minimize duration‐dependent bias in model parameterization.

Data Set A

The present study was performed to evaluate the effect of organism size (i.e., wet wt) and temperature on the toxicokinetics of 2‐methylnaphthalene. Three organisms were used following standardized acute toxicity test protocols: Oncorhynchus mykiss (Organisation for Economic Co‐operation and Development [OECD] 203 [2019], rainbow trout at 0.11 and 1.3 g), Daphnia magna (OECD 202 [2004], daphnids, <24 h old, ~0.5 mg), and Lumbriculus variegatus (aquatic only version of OECD 225 [2007], blackworm, ~8 mg). Tests were performed under flow‐through conditions at both 10 °C and 18 °C using four nominal concentrations of 0.4, 1.4, 4.5, and 15 mg/L plus a control treatment.

Test solutions for each treatment were prepared by passive dosing with silicone cord. The cord was prepared by equilibration with a methylnaphthalene‐spiked methanol solution for 24 h at various concentrations to provide a range of silicone concentrations for test media dosing. Clean test media (20 L) was then allowed to equilibrate in large glass aspirator bottles with a loaded silicone cord for 24 h to provide different treatment concentrations and the control (silicone cord loaded with methanol alone). After this equilibration period, a peristaltic pump was used to deliver clean test media at a flow rate of 12.9 ml/min to each dosing bottle prepared for each treatment and control. All dosing bottles were vigorously mixed with a 7.5 × 1.3–cm Teflon^TM‐coated stir bar on a magnetic stir plate to facilitate rapid partition‐controlled delivery and homogenous substance concentrations.

Simultaneously, separate peristaltic pumps delivered test media from the dosing bottles to each replicate exposure chamber containing test organisms at approximately 5.55 ml/min to the two replicates for trout and approximately 0.44 ml/min for the two replicates for daphnids and worms (e.g., (2 × 5.55) + (4 × 0.44) = 12.9 ml/min). Thus, the inflow of fresh dilution water to bottles used in passive dosing for each treatment was approximately equal to the outflow of test solutions delivered to the exposure test chambers. Each exposure chamber included additional silicone loaded at the same concentration as the dosing bottle to buffer potential losses in the presence of test organisms. This dosing system has been shown to maintain stable aqueous test concentrations during toxicity tests (Butler et al., 2016) Fish were held in closed 4‐L test chambers, whereas invertebrates were exposed in closed 0.25‐L vessels. The number of fish, daphnids, and worms per replicate was 14, 20, and 20, respectively. Daphnia magna were exposed for 48 h, whereas O. mykiss and L. variegatus were exposed for 96 h.

Test media samples were collected with no headspace in 20‐ml volatile organic analysis (VOA) vials for analytical confirmation using headspace gas chromatography (GC) with flame ionization detection. Sufficient replicates were taken to permit triplicate or quadruplicate analysis at each sampling interval. Sampling and analysis were done several days prior to initiation of the in‐life test to confirm that stable exposure concentrations were established at the targeted levels. Sampling continued daily during the in‐life portion of the tests, with more frequent samples being taken during the first 24 h of exposure. Samples were taken from the effluent side of the test chambers so that measured concentrations represent actual exposure. Samples were refrigerated at 4 °C if not analyzed on the day collected. Details of analytic methods are provided in the Supporting Information. Effect observations were collected at 2, 4, 6, 8, 24, 48, 72, and 96 h. Temperature, dissolved oxygen, and pH were monitored daily to ensure acceptable water quality.

Data Set B

The second experimental study was performed to evaluate the acute toxicity of o‐xylene, 2‐methylnaphthalene, and phenanthrene (>98.5% purity; Sigma‐Aldrich) at 5 °C and 18 °C to rainbow trout, O. mykiss (1.0 g wet wt), in a 96‐h static test (OECD 203; [2019]) with 24‐h renewals with eight fish per treatment level. Exposure solutions of o‐xylene and methylnaphthalene were prepared at the test temperature by adding the appropriate amount of test substance dissolved in acetone, via stainless steel and glass syringes, to 20 L of vehicle/dilution water in glass aspirator bottles (capacity 22 L) and stirring on magnetic stir plates for 24 h (±1 h) in a temperature‐controlled environmental chamber. Toxicity tests were performed using a control and either four or five treatment concentrations. For phenanthrene, only two test exposures were investigated. Test solutions were prepared via passive dosing by first saturating silicone with phenanthrene and then diluting this oil to 50% and 25% using clean silicone oil (Dow Corning 200® Fluid, 100 cst).

The diluted silicone oils were added to silicone tubing and equilibrated with 20 L of the test media for 24 h at room temperature while mixing with a 7.5‐cm stir bar at 60 rpm using a magnetic stir plate. The dosed test media were allowed to cool to test temperature in a water bath for approximately 1 h without stirring before use in toxicity testing. Aqueous exposures were prepared daily using these procedures on the day preceding each renewal. Three replicate test chambers were used per treatment. Temperature, dissolved oxygen, and pH were measured in each “new” treatment and the control on Day 0 and daily, prior to renewals, and on the “old” solutions (composite of the replicates) daily. Effect observations were collected to characterize the time course of toxicity as described for Data Set A. Triplicate samples were collected for analytical confirmation with GC–mass spectrometry on renewal, as well as observations for mortality at 0.25, 0.75, 1.25, 1.75, 2.25, 3.25, 4.25, 24, 48, 72, and 96 h. Additional details describing sample extraction and analytical confirmation of test substance concentrations for all toxicity tests are provided in the Supporting Information.

TKTD modeling

The approach taken in the present study combines model constructs used in different fields to describe toxicokinetics, bioconcentration, and critical body burden concepts. Each discipline uses somewhat different terms to describe similar first‐order processes. For the present study, a consistent terminology is adopted to avoid confusion. However, the reader is encouraged to review the cited references to understand the different nomenclature that has been used for the same or related terms described in the present study.

The lumped elimination/damage repair rate constant, k _e, is used to describe the rate that toxicity (e.g., mortality) accrues following exposure to a toxicant. This parameter was estimated by fitting the observed acute data at each treatment concentration with the general unified threshold model of survival (GUTS; Jager et al., ²⁰¹¹). This implementation of the GUTS modeling framework is a one‐compartment model with first‐order kinetics. The exposure framework models the accumulation of chemicals predicted in target tissues as the difference between the external exposure and internal concentrations:

$$\frac{d{C}_{\mathrm{w}}\left(t\right)}{\mathit{dt}}=k_{\mathrm{e}}\left[C_{\mathrm{W}}\left(t\right)-C_W\left(t\right)\text{BCF}\right]$$ (3)

In Equation 3, k _e (per day) is the elimination/damage repair parameter, C _W(t) is the external aqueous concentration, and the term “C _W(t) × BCF” expresses the internal lipid‐normalized concentration (C _L[t]). The BCF was defined in Equation 1 as the ratio of uptake (k ₁) to elimination (k ₂). In the modeling analysis for the present study, the corresponding k ₂ term is referred to as the lumped elimination rate (k _e) because model calibration is based on observed acute toxicity, not tissue residues, and incorporates additional damage/repair processes (Ashauer et al., 2016; Jager et al., ²⁰¹¹). For varying $C_{\mathrm{W}}(t)$, Equation 3 can be solved numerically at each time step, t. For a constant $C_{\mathrm{W}}\left(t\right)=$ $C_{\mathrm{W}}(0)$ the analytical solution is

$$C_{\mathrm{L}}\left(t\right)={\text{BCF}\times C}_{\mathrm{W}}\left(0\right)(1-e^{{-k}_{\mathrm{e}}t})$$ (4)

The GUTS framework provides either a stochastic death (SD) or individual tolerance (IT) approach for modeling toxicity. The SD approach implies that mortality will occur at some point once the threshold has been exceeded, whereas the IT approach predicts that effects occur in proportion to the accumulated body burden as indexed by $C_{\mathrm{L}}(t)$ relative to a threshold (Ashauer et al., 2016; Jager et al., ²⁰¹¹). In practice it is difficult to distinguish between these two modeling approaches (Ashauer et al., 2016; Baudrot & Charles, ²⁰¹⁹; Baudrot et al., ²⁰¹⁸; Newman & McCloskey, ²⁰⁰⁰) because both approaches can be used to satisfactorily model the same data sets using various combinations of model parameter values.

In the present study, the IT model was chosen because it is compatible with the critical body residue models (Di Toro et al., 2000; Veith et al., ¹⁹⁸³) previously adopted in oil spill impact assessments (French‐McCay, 2002; Reed et al., ¹⁹⁹⁹). The adoption of the IT model allows the target lipid model (TLM), which has been widely used for aquatic hazard and risk assessments of hydrocarbons (McGrath et al., 2018) to be extended to oil spill modeling applications.

The IT model is evaluated using the cumulative logistic distribution of tolerances.

$$F(t)=\frac{1}{1+{\left[\frac{\max \mathrm{}\left(C_{\mathrm{L}}(t)\right)}{\text{CTLBB}}\right]}^{\beta }}$$ (5)

In Equation 5, $F(t)$ is the fractional mortality at time t, CTLBB is the critical target lipid body burden (millimoles per gram of lipid) used as the toxicity threshold concentration, and $\beta$ is the slope term of the dose–response function. The internal exposure concentration, $C_{\mathrm{L}}(t)$ (millimoles per gram of lipid), is compared with the threshold CTLBB, which describes the sensitivity of an organism/endpoint in the TLM species database (Di Toro et al., 2000). The general form of the TLM is given by,

$$\log \text{LC}50=-0.94\times \log K_{\text{OW}}+∆c+\log \text{CTLBB}$$ (6)

In Equation 6, the log LC50 ($C_{\mathrm{W}}^{*}$, millimoles per liter) is linearly related to the log K _OW, the chemical class correction factor ($∆c$; −0.025 for monoaromatics, −0.362 polyaromatics, 0 for aliphatic hydrocarbon classes), and the CTLBB. The bioconcentration term in the TLM,

$$\log \text{BCF}=0.94\times \log K_{\text{OW}}+∆c$$ (7)

is used in the present study to convert between external aqueous concentrations and internal target lipid concentrations within the GUTS framework (Equations 3 and 4).

The survival probability, S(t), for IT is a function of the hazard rate, F(t) (Equation 5) and background mortality, h _b,

$$S(t)={[1-F(t)]e}^{-h_{\mathrm{b}}t}$$ (8)

The GUTS_IT approach for the present study utilizes the implementation developed for the computing language R (Albert et al., 2016). This package provides features to optimize the three model parameters k _e, $\beta$, and CTLBB and to estimate corresponding confidence intervals.

The main parameter of interest that controls the time dependence of toxicity is the elimination/damage repair rate constant, k _e. For the global fit to the literature data set, the slope term $\beta$ and the threshold concentration CTLBB were constrained to focus analysis on improved characterization of k _e. Typically, CTLBBs are determined as the median for all toxicity data for a given species. However, it is recognized that there is some variability; therefore, the CTLBB was fit to each individual data set so that determination of k _e could be achieved without confounding variability from the slope and CTLBB terms. The threshold concentration, CTLBB, was determined empirically based on 2‐ or 4‐day LC50 for each data set using Equation 6, depending on the species and endpoint (see Results). The rationale for defining CTLBB prior to analysis is that in practice the thresholds for effects would be selected from existing compilations of CTLBBs (McGrath & Di Toro, 2009), for which the range and variability are well known for short‐term tests (McGrath et al., 2018).

The slope parameter is generally steep for acute hydrocarbon toxicity data, consistent with prior applications to nonpolar organics (range 1–8 [Ashauer et al., ²⁰¹⁵]). Therefore, the slope parameter $\beta$ was determined as the average slope of the entire literature data set of 4‐day or 2‐day mortality and across all exposure concentrations. The background hazard rate h _b is typically low (h _b < 0.001 day⁻¹) in short‐term standard tests (<4 days) and was fit empirically to control response data. This framework was applied to each individual data set (e.g., study, species, hydrocarbon) to derive a best‐fit k _e. Estimates for k _e were determined by visual fitting of the individual data sets, which were then used as an input to the optimization routines that were used also to calculate confidence intervals. Once the k _e parameters were estimated, the general linear model regression package in the R platform (Albert et al., 2016) was used to perform multiple linear regressions on the entire set and subsets of this larger data set to evaluate the role of temperature, organism weight, and substance hydrophobicity (log K _OW) in explaining the observed variability. However, for subsequent evaluation of the individual experimental Data Sets A and B, all three model parameters (k _e, $\beta$, CTLBB) were fitted individually.

In the case of compiled toxicity data sets that involved reported median effect concentrations and LC50s over time, the data were fit to the first‐order model:

$$\text{LC}50\left(t\right)={{\text{LC}50}_{\mathrm{\infty }}(1-e}^{-k_{\mathrm{e}}t})$$ (9)

In Equation 9, $\text{LC}50\left(t\right)$ indicates the concentration causing 50% effect at exposure time t in days and ${\text{LC}50}_{\infty }$ represents the incipient value below which a 50% response is not achieved. A different data type, TTD describes the time required to reach 50% mortality at a constant exposure. For TTD data, survival times were modeled as described by Mackay et al. (2017):

$$C_{\mathrm{w}}={\mathrm{L}{\mathrm{C}50}_{\mathrm{\infty }}/(1-e}^{-k_{\mathrm{e}}\text{TTD}})$$ (10)

In Equation 10, ${\mathit{C}}_{\mathrm{w}}$ is the exposure concentration and TTD is the time to death in days for each organism exposed to the concentrations investigated; $\mathrm{L}{\mathrm{C}50}_{\mathrm{\infty }}$ and k _e were estimated using the solver tool in Excel for each data set. The CTLBB was derived from the estimated $\mathrm{L}{\mathrm{C}50}_{\mathrm{\infty }}$ and log K _OW of the test substance by rearrangement of Equation 6.

RESULTS AND DISCUSSION

Summary of toxicity data sets

New experimental data had control survival of 100% across all tests. The dissolved oxygen value remained above 60% of the air‐saturation value throughout all tests except for one “old” sample in Data Set B at 72 h for the 18 °C group, which were at 50% but remained above 60% for all other measurements. Mean measured concentrations and observed mortality for 2‐methylnaphthene toxicity tests are presented in Supporting Information, Tables S1–S4, for the three test species and two fish weights at 18 °C and two fish weights at 10 °C in Supporting Information, Tables S5–S6 (Data Set A). Exposure concentrations were maintained with relative standard deviations (RSDs) ranging from 3.8% to 30% across treatments with an average of 9.3%. Complete survival was observed at the two lowest treatment concentrations at or below 1.2 mg/L, whereas time‐dependent mortality occurred in the two higher treatment concentrations across the three test organisms investigated. Mean measured concentrations and observed mortality for toxicity tests performed for trout exposed individually to three aromatic hydrocarbons at two test temperatures (Data Set B) are reported in Supporting Information, Tables S7–S9. The RSDs of measured concentrations ranged from 0.1% to 49% across treatments, with an average of 4.4%, 25.4%, and 15.7% for xylene, methyl naphthalene, and phenanthrene, respectively. Limited differences in the time course of toxicity were observed for both test temperatures investigated. All toxicity tests performed as part of the present study were deemed reliable for inclusion for use in further analysis.

The literature database (including experimental Sets A and B) was subjected to toxicokinetic analysis using the GUTS modeling framework for the full dose–response data sets (Supporting Information, Table S10) and is comprised of 121 toxicity tests across 49 test species (eight fish, 41 invertebrates) and 33 individual hydrocarbons that span a log K _OW range from approximately 2 to 6. Additional literature studies reporting time‐dependent LC50s or TTD data (Supporting Information, Table S11) provided another 27 toxicity tests and added three additional hydrocarbons (butyl benzene, ethyl and dimethyl naphthalene) and test species (two fish, one invertebrate). These data were analyzed with Equations 9 and 10. Toxicity tests were conducted at test temperatures that ranged from 4 to 26 ºC (median 20.8 °C) and for organism weights from approximately 0.0001 to 10 g (median 0.24 g; Supporting Information, Table S12). Some of the tests specifically varied temperature for a particular organism, whereas other tests were conducted at a specified temperature, which could affect the interpretation of the apparent trends between k _e and temperature (see below, Regression analysis of k _e ).

Validation of modeling constraints

The present study focused solely on the derivation of k _e by constraining the threshold (CTLBB) and slope ($\beta$) terms in the GUTS framework (Equation 5) or by estimating the incipient LC50 using Equations 9 and 10. The CTLBB was determined with the 2‐ or 4‐day full dose–response data, either as reported through the studies or estimated with logistic regression. The species‐specific CTLBBs derived from the present study (Supporting Information, Table S12) ranged from 12 to 501 (median 71) mmol/kg lipid and were very similar in magnitude and shape of the distribution (Supporting Information, Figure S1) to TLM‐derived CTLBBs reported in prior work (McGrath et al., 2018). This confirms that the toxicity data used in the present study are representative of toxicity previously reported for aquatic species.

The second modeling constraint was the slope term ($\beta$, Equation 6) that defines the shape of the concentration–response relationship. This term was estimated by fitting a two‐parameter logistic model to the 2‐ or 4‐day mortality data from the compiled literature data set subjected to GUTS analysis (Supporting Information, Table S12). To allow mortality data across test species and hydrocarbons to be plotted on the same figure, the individual exposure concentrations were converted to toxic units (Equation 11) by dividing the exposure concentration (C _w, millimoles per liter) by the TLM‐predicted LC50s (Equation 6).

$$\text{Toxic unit }=\frac{C_{\mathrm{W}}}{\text{LC}50}$$ (11)

The logistic model (Equation 5) was fit to these data by fixing the center inflection of the logistic curve at toxic unit = 1.0, consistent with the definition of the toxic unit and LC50 (Equations 6 and 11) so that the slope ($\beta$) is the only optimizable term.

Based on this analysis, the fitted slope is 4.0 (standard error [SE] 0.31), which indicates that the acute toxic response of hydrocarbons is steep, resulting in either no effects or complete effects once toxic units fall below or above 1, respectively (Figure 1). In the full compiled data set, there are 823 individual entries for this subset of 2‐ and 4‐day toxicity values. Most data show either no to limited effects (>90% survival, n = 428) or complete mortality (<10% survival, n = 187), representing 74.7% of the available data. Thus, consistent with the fitted estimate for $\beta$, there are relatively few partial mortality data; and this observation appears generally consistent across all the species evaluated in the present study. Notable exceptions include coral species, which exhibit generally higher background mortality, which contributes to a shallow slope for these test species (1.9, SE 0.31). Consequently, data for these species were not included in the determination of the generalized slope (Turner & Renegar, 2017). However, this generalized slope was applied to the coral data sets in the TKTD analysis because the background mortality is explicitly accounted for in the model framework (Equation 8). The consistency in the observed slope term, and narrow standard errors, across most species, test conditions, and test chemicals reduces uncertainty in characterizing the concentration–response relationship and simplifies application of the TKTD frameworks for hydrocarbons. The global fitted slope (and SE) was used for estimation of the k _e parameter (Equation 6) described below.

Figure 1.

Comparing observed fraction surviving from 2‐ or 4‐day observation periods for all toxicity data sets except corals (Supporting Information, Tables S10, S12) to the toxic unit for individual exposures (e.g., different organisms, hydrocarbons, exposure concentrations). Horizontal and vertical lines represent the target (e.g., 50% survival at toxic unit = 1) and the logistic curve fit to the observed dose–response data, respectively.

This analysis can also be used to calculate the ratio between the LC50 (50% effects) and the LC1 (1% effects), which is a required input to oil spill effect models (French‐McCay, 2004). Using the fitted slope term (Figure 1, $\beta$ = 4.0) and rearranging Equation 5, the calculated ratio of LC50/LC1 is 3.2, reflecting the sharp observed dose–response for hydrocarbons.

These modeling constraints are considered acceptable because the CTLBBs derived in the present study are well aligned with estimates reported using independent data sets from the TLM validation (McGrath et al., 2018; Supporting Information, Figure S1), and the slope parameter is consistent across most of the data sets in the present study. Therefore, additional analysis of k _e was performed by limiting uncertainty from CTLBB and $\beta$.

Regression analysis of k _e

The GUTS model was applied to the literature data set compiled in the present study using the constrained CTLBB and $\beta$ (as described in the section Validation of modeling constraints). This approach resulted in an overall normalized root mean square error (Baudrot & Charles, 2019; EFSA Panel on Plant Protection Products and Their Residues et al., ²⁰¹⁸) of 0.17, which is judged to be satisfactory model performance, and validates the stepwise approach to constrain the TKTD parameters employed in the present study (Supporting Information, Figure S2). The k _e estimates derived from analysis of the full dose–response data set spanned from 0.04 to 3.8 day⁻¹ with a median of 0.7 day⁻¹ and the 5th–95th centile from 0.25 to 2.9 day⁻¹ (Supporting Information, Table S12). The variations in k _e data were then evaluated to examine relationships with relevant toxicity test variables: test temperature, organism weight, and log K _OW of the hydrocarbon investigated (Figure 2).

Figure 2.

The general unified threshold model of survival–derived k _e for the entire data set (Supporting Information, Table S12) for fish (upper row) and invertebrates (lower row) evaluated against log K _OW for the test chemical (A,D), test organism wet weight (B,E), and test temperature (C,F). k _e = overall elimination rate; K _OW = octanol–water partition coefficient.

In the case of fish, the log k _e appears to trend log‐linearly with log K _OW (a = 0.003) but with considerable variability (Figure 2A). In contrast, there is a lack of obvious trend with log K _OW for invertebrates with similar variability (Figure 2D). Further, there are no trends with log organism weight (a = 0.05) for either fish or invertebrates despite a wide range of test organism wet weights (∼0.0001 to ~10 g; Figure 2B,E). Similarly, no significant trend (a = 0.05) was observed with test temperature (Figure 2C,F). It is somewhat surprising to find no correlation with weight or temperature because of the common heuristics.

The TKTD parameters derived for the full dose–response data sets are similar in range and magnitude to values derived by fitting the time‐dependent LC50 (k _e range 0.1–10 day⁻¹, n = 17) and TTD (k _e range 0.14–2.7 day⁻¹, n = 10) data sets (Supporting Information, Table S12). Time‐dependent LC50 data are expected to yield similar estimates of k _e as full‐dose response data sets because both rely on the same experimental design using multiple treatment concentrations and observations over time. The TTD tests characterize the evolution of toxicity to individuals over time following exposure to given test substance concentration. The observed similarity of k _e obtained using the different experimental designs suggests that potentially simpler TTD tests should be more routinely integrated into future hazard assessments and toxicity model validation (Mackay et al., 2017).

A closer examination of the distribution of k _e by species is shown in Supporting Information, Figure S3. Within‐species variability in k _e estimates is similar to the overall variability observed in Figure 2. Organizing k _e for different species into broader taxonomic classes also provides little explanation of the observed variability (Figure 3). Fish (Actinoptherygii) are the single largest species class in terms of numbers of observations and exhibit a magnitude and range of k _e that is similar to other organism classes.

Figure 3.

Distribution of k _e by species class given in Supporting Information, Table S12. Actinoptherygii are fish, Anthozoa are corals, and others are general invertebrate classes. k _e = overall elimination rate.

A multiple linear regression was performed using k _e, temperature, and weight as explanatory variables for fish and invertebrates separately (Table 1) to further evaluate and refine calibration of the TKTD model (Equation 2) given that these classes represent two broad categories of aquatic resources considered in oil spill effect assessments.

Table 1.

Summary of significant (α = 0.05) model coefficients (and 95% confidence intervals) based on regression analysis of Supporting Information, Tables S13 and S14

Log k e model	Log K OW	Log W (g wet wt)	T = 25 (°C)	Intercept
Equation 2	−0.41	−0.2	0.048	1.47
Fish	−0.26 (0.09)	0	0	0.93 (0.31)
Invertebrate	0	0	0	−0.39 (0.28)

k _e = overall elimination rate; K _OW = octanol–water partition coefficient; W = weight.

Regression analysis results for fish show a significant relationship between log K _OW and k _e, which is similar to the original coefficients using the full data set (slope term −0.41 vs. −0.26, intercept 1.47 vs. 0.94; Table 1; Supporting Information, Tables S13 and S14). For invertebrates, there were no significant (α = 0.05) coefficients for temperature and weight consistent with the lack of visual trends in Figure 2.

The complete data set (Supporting Information, Table S12) was analyzed in more detail by further evaluating species‐specific results. Table 2 summarizes the literature database and indicates coverage of log K _OW, test temperature, and organism weight by species. Overall, the database includes representative data from aliphatic and one‐, two‐, three‐, and four‐ring aromatic hydrocarbon classes. The test species represent a wide range of habitats and ecological behaviors (e.g., saltwater, freshwater, juvenile fish, embryos, filter feeders, pelagic species, corals). Overall there are multiple data across trophic levels, which underscore the relevance of observations in the present study. Although there are clear data gaps (e.g., few aliphatic hydrocarbons, no algae or aquatic macrophytes), these data and the associated analyses appear sufficient to establish the range of TKTD behavior across a wide range of aquatic organisms exposed to representative hydrocarbon components in crude oil and other refined petroleum substances.

Table 2.

Number of individual hydrocarbons in major hydrocarbon class domains and significance of regressions between k _e and K _OW and test temperature by test species

	MAH	DAH	PAHs	Aliphatics	Log K OW	Temperature (°C)	Weight (g wet wt)	Log K OW regressiona	Temperature regressionb	Weight regressionc
Fish species
Aanoplopoma fimbria	1		2		2.5–4.3	10	3.0E−01	Not significant	NA	NA
Boreogadus saida		1			3.7	24.7	6.0E−03	NA	NA	NA
Danio rerio		3	2		3.2–5.0	22	2.4E−01	Not significant	NA	NA
Dicentrarchus labrax		1			3.7	12	1.3E+01	NA	NA	NA
Lepomis macrochirus	2				3.1	22	9.0E−01	NA	NA	NA
Menidia beryllina		1			4.1	22	1.5E−02	NA	NA	NA
Menidia menidia	1				3.1	22	8.0E−03	NA	NA	NA
Oncorhynchus mykiss	4	7	4		2.5–4.9	5–18	0.1–21	Significant (−0.29)	Not significant	Not significant
Pimephales promelas	12	4		4	2.0–5.8	22	6.0E−01	Not significant	NA	NA
Poecilia reticulata	2				4.5	20	2.5E−02	NA	NA	NA
All fish	22	17	8	4	2–5.8	5–22	0.1–21	Significant (−0.26)	Not significant	Not significant
Invertebrate species
Acropora cervicornis	1	1			2.5–3.7	26	Coral	NA	NA	NA
Americamysis bahia	1	4			3.1–4.1	22	1.0E−02	NA	NA	NA
Anomalocardia flexuosa		1			3.7	24.7	1.1E+00	NA	NA	NA
Anonyx nugax		1			3.7	24.7	2.0E+00	NA	NA	NA
Balanus balanus		1			3.7	23	4.0E−02	NA	NA	NA
Calanus finmarchicus		1			3.7	9	1.2E−03	NA	NA	NA
Ceriodaphnia dubia			2	6	2.9–6.1	25	8.0E−05	Not significant	NA	NA
Chironomus tentans			1		4.9	23	4.0E−03	NA	NA	NA
Chlamys islandica		1			3.7	24.7	5.0E−01	NA	NA	NA
Clibanarius vittatus		1			3.7	23	6.0E−01	NA	NA	NA
Crangon septemspinosus		1			4.1	22	3.1E−02	NA	NA	NA
Daphnia magna	3	1	1		2.9–3.5	20–18	5.0E−04	Not significant	NA	NA
Gammarus arctic		1			3.7	14.5	2.7E−01	NA	NA	NA
Gammarus minus		1			4.1	22	4.1E−02	NA	NA	NA
Gammarus pseudolimnaeus	1	1			2.5–4.3	20–16	2.3E−2	NA	NA	NA
Gammarus temperate		1			3.7	13	4.1E−02	NA	NA	NA
Gibbula umbilicalis		1			3.7	13	1.6E−01	NA	NA	NA
Goniobranchus annulatus		1			4.1	22	4.1E−02	NA	NA	NA
Homarus americanus	1	5	9		2.5–4.9	15	7.1E−02	Not significant	NA	NA
Hyalella azteca	2	1	4		3.1–4.5	20–23	4.0E−03	Not significant	NA	NA
Laeonereis culveri		1			3.7	10	3.0E+00	NA	NA	NA
Litorina littorea		1			3.7	14.5	2.7E−01	NA	NA	NA
Lophelia pertusa	1	1	1		2.5–4.3	5.7	Coral	Not significant	NA	NA
Lumbriculus variegatus	2	1			3.7–4.5	18–20	8.0E−03	NA	NA	NA
Margarites helicinus		1			3.7	11	1.1E+01	NA	NA	NA
Monokalliapseudes schubarti		1			3.7	14.5	1.0E−02	NA	NA	NA
Mytilus edulis		1			3.7	6	1.3E+00	NA	NA	NA
Neanthes arenaceodentata		1			4.1	22	4.0E−03	NA	NA	NA
Neritina virginea		1			3.7	6	1.3E+00	NA	NA	NA
Nymphon gracile		1			3.7	6	1.2E+01	NA	NA	NA
Palaemonetes pugio		4	3		3.1–4.3	20–22	2.5E−01	NA	NA	NA
Pandalus borealis	1	2	1		3.5–4.3	6–7.7	1–10	NA	NA	NA
Patella depressa		1			3.7	4.4	2.2E+00	NA	NA	NA
Peltoperla maria		1			4.1	22	2.0E−02	NA	NA	NA
Phrontis vibex		1			3.7	5	5.6E−01	NA	NA	NA
Porites astreoides	1	1			2.5–3.7	26	Coral	NA	NA	NA
Sclerocrangon boreas		1			3.7	6	6.5E−02	NA	NA	NA
Siderastrea siderea	1	1	1		2.5–4.3	26	Coral	Not significant	NA	NA
Solenastrea bournoni	1	1			2.5–3.7	26	Coral	NA	NA	NA
Stephanocoenia intersepta	1	1			2.5–3.7	26	Coral	NA	NA	NA
Strongylocentrotus droebachiensis		1			3.7	6	1.1E+01	NA	NA	NA
Testudinalia testudinalis		1			3.7	4.4	2.7E−01	NA	NA	NA
All invertebrates	17	51	23	6	2.5–6.1	4.4–22	8E−5 to 12	Not significant	Not significant	Not significant

^a Regression applied to data sets with >1.5 log unit variation in test substance K _OW.

^b Regression applied to data sets with >5 °C variation in test temperature.

^c Regression applied to data sets with 10‐fold greater variation in weight.

k _e = overall elimination rate; K _OW = octanol–water partition coefficient; MAH = monocyclic aromatic hydrocarbon; DAH = dicyclic aromatic hydrocarbon; PAH = polycyclic aromatic hydrocarbon; NA = not applicable.

The overall relationship observed in the global fish data set appears to be driven mainly by O. mykiss because it is the only data set with a significant (α = 0.05) regression coefficient for log K _OW. There are 10 fish species but only four with more than four observations to support a regression analysis. Only the focused Data Sets A and B systematically varied temperature and test organism weight (discussed below), but no significant trends were observed for these new targeted studies. The invertebrate data set includes species from multiple organism classes including insects, corals, bivalves, and crustaceans. Six data sets have sufficient data (n > 4) to support a regression analysis (Table 2), and none of these data sets demonstrate a significant (α = 0.05) relationship with log K _OW.

Across both data sets (invertebrates and fish), coverage across hydrocarbon classes and test species is limited. Methylnaphthalene, a diaromatic molecule, is the most commonly tested hydrocarbon, followed by monoaromatic chemicals, and then three or more aromatics, for example, phenanthrene. There are only two toxicity studies for aliphatic hydrocarbons. The log K _OW coverage spanning approximately 2–6 reflects the most relevant range of components because hydrocarbons with log K _OW > 6 are often not acutely toxic because of low solubility, and hydrocarbons with log K _OW < 2 are often not present at relevant concentrations because of high volatility.

Summary of focused experimental Sets A and B

The results of the analysis of the global fit indicate that log K _OW, organism weight, and test temperature appear to have a limited influence on the observed hydrocarbon TKTD. This observation is partially affected by the composite nature of the data set, which could be masking various processes or more complex kinetics. Therefore, additional focused experimental data were performed in the same laboratory, with similar time frames, and with the same test methods to specifically focus on the role of organism size and test temperature.

A separate modeling analysis was performed with these subsets using the same framework used in the global analysis (Figure 2), but the slope and threshold concentration terms were allowed to vary independently. Conclusions of this separate analysis are the same as those of the global analysis (Figure 2 and Table 2) and are reported in the Supporting Information with experimental data provided in Supporting Information, Tables S1–S9, and modeling results and discussion given in Supporting Information, Figures S5–S8 and Tables S15–S17.

Summary of toxicokinetic modeling analysis

The regression analysis in Table 2 indicates that test organism weight, test temperature, and test chemical log K _OW are generally not significant variables that affect the observed k _e. Only the O. mykiss data set exhibit a significant dependence on log K _OW but with a low magnitude of effect (e.g., low coefficient for log K _OW, −0.26; Table 1). This suggests that Equation 2 may require refinement for improving use in oil spill effect assessments. A species‐sensitivity approach may be a pragmatic strategy for quantifying the role of observed TKTD variability in predicting effects of time‐variable exposures across a range of aquatic species. For example, Figure 4 provides the ranked distribution of species‐median k _e rates for fish and invertebrates based on data in Supporting Information, Table S12. The distributions for fish and invertebrates are similar in shape and magnitude. For example, the 10th, 50th, and 90th percentile rates are 0.33, 0.74, and 3.9 day⁻¹ for fish, respectively, and 0.28, 0.57, and 2.8 day⁻¹ for invertebrates, respectively. The original basis of the log K _OW‐dependent function in Equation 2 relied on elimination rate (k ₂) estimates derived from bioconcentration tests as for a limited data set including a wider range of organic chemicals than hydrocarbons. Further, as previously explained, the elimination rate is not equivalent to the lumped elimination rate used for modeling toxicity (Equation 1 vs. 4). This likely explains the discrepancy between the original model formulation and the findings in the present study.

Figure 4.

Ranked distribution of species median k _e; data from Supporting Information, Table S12, for fish (red triangles) and invertebrates (blue circles). k _e = overall elimination rate.

Further exploration of the results in Supporting Information, Table S12, confirms that the TKTD model parameters are not cross‐correlated. For example, there are no apparent relationships between the derived CTLBB, the slope term that defines the dose response for the individual data sets, or log K _OW (Supporting Information, Figure S9). This observation combined with earlier observations that variation is not correlated with species type (Supporting Information, Figures S3 and S4) may direct further work to focus on other physiological processes that control the TKTD of hydrocarbons. Further, it is notable that weight and temperature appear to have little impact. The role of temperature could be masked by the co‐occurrence of other compensating physiological processes (e.g., uptake, metabolism, internal distribution). For example, in a bioconcentration study with the amphipod Gammarus setosus, elimination of pyrene was dominated by biotransformation, which exhibited only a slight temperature dependence at the two test temperatures of 2 °C and 8 °C when compared with the passive elimination rate (Carrasco‐Navarro et al., 2015). Moreover, a cursory review of available literature suggests that the role of temperature on bioaccumulation and toxicity does not appear to be systematically observed across chemicals and testing scenarios (Carrasco‐Navarro et al., 2015; Dai et al., ²⁰²¹; Kleinow et al., ²⁰⁰⁶; Korn et al., ¹⁹⁷⁹; Landrum, ¹⁹⁸⁸). Further, the magnitude of the impact, where observed, appears low. These findings are generally consistent with the new experimental data (Sets A and B) and modeling analysis reported in the present study.

Weight, or organism size, is commonly understood to affect physiological processes through various allometric scaling relationships. However, these effects are often noted as a change in first to second order of magnitude in a physiological property across many orders of magnitude change in organism size (Hendriks et al., 2001). Therefore, it could be possible that the database in the present study did not cover a sufficiently wide weight range (five orders of magnitude) to observe a statistically significant allometric relationship for the lumped TKTD parameter investigated in this analysis. Although interspecies dependencies appear small, it is possible that intraspecies differences (e.g., juvenile to adult) could result in different weight‐based dependencies and could be the subject of future work.

The result for invertebrates is surprising because these organisms are generally expected to have lower metabolic capabilities and thus lower overall elimination rates than fish. The observed distribution of k _e across invertebrate species does not appear to be dependent on ecological function or metabolic capacity. Future work is needed to understand the mechanistic linkage between the TKTD processes (damage repair, elimination of parent and metabolites) and bioaccumulation processes (e.g., elimination of parent substance and formation and elimination of metabolites).

Practical application to oil spill effects modeling

The present study demonstrated that a constant dose–response slope is a reasonable simplification for most organisms and that the critical body burden framework (e.g., GUTS‐IT approach) results in acceptable model performance. These findings support practical application of study results in a broader oil spill fate and effects context. The regression coefficients for the different k _e models in Table 1 are compared in Figure 5. The models have similar behavior showing rapid predicted responses within hours to days.

Figure 5.

Predicted time‐variable toxicity comparing the default model (gray solid line, Table 1, Equation 2), and the median revised coefficients derived in the present study for fish (red dotted line) and invertebrates (blue dashed line; Table 1) for an organism with high sensitivity (bold lines) and with moderate sensitivity (thin lines). The water solubility limit is denoted by solid horizontal lines. LC50 = median lethal concentration.

Benzene, naphthalene, phenanthrene, and pyrenes, as representatives of one‐, two‐, three‐, and four‐ring aromatics, are used in this example to illustrate the time‐dependent acute toxicity of representative mono‐, di‐ and polyaromatic hydrocarbons which span the range of log K _OW evaluated in the present study. The revised models (Equation 2 and Table 1) derived in the present study (fish and invertebrates denoted by red and blue lines, respectively, Figure 4) indicate a slower progression to reach the incipient acute toxicity threshold than the original model (gray lines, Figure 4) for smaller molecules (e.g., benzene and naphthalene). The predicted time course is almost identical for phenanthrene, while the order of the model predictions is reversed for pyrene because of the slight dependence of k _e on log K _OW (Table 1).

The role of organism sensitivity was also evaluated by choosing a CTLBB at the lower end of the known species sensitivity distribution (McGrath et al., 2018; CTLBB 15 mmol/kg lipid, bold lines, Figure 4) for comparison to an organism of median sensitivity (e.g., CTLBB 90 mmol/kg lipid, thin lines, Figure 4). Functionally, this choice of CTLBB shifts the predicted time series up or down in a linear fashion based on Equation 6. The solubility limit of these chemicals is presented as horizontal lines in Figure 4 to show the influence of solubility in potentially limiting effects over short exposure durations for species with differing sensitivities.

Comparing the time‐variable toxicity against the solubility limit provides a basis for estimating the constituents that would be drivers of potential effects under different exposure durations. For example, the VOA chemicals (e.g., benzene, toluene, ethylbenzene, xylene) show predicted toxicity at very short time frames (e.g., <12 h) that are well below solubility. In contrast, short‐term (<6 h) predicted toxicities for naphthalene and phenanthrene are often above the solubility limit of the individual chemical, which suggests that these types of constituents would only be fractional contributors to short‐term effects in an oil mixture. The results for pyrene indicate that no acute toxicity is predicted for a median sensitivity species because the incipient acute threshold is above the limit of solubility. In contrast, toxicity is expected for a sensitive species if exposed for 1 day at the solubility limit (Figure 4D). This is consistent with the, frequently, observed lack of toxicity for low–water solubility chemicals (Mackay et al., 2015; Redman et al., ²⁰¹²).

Summary of findings

The present study is a comprehensive evaluation of the relevant TKTD parameters for hydrocarbons that supports oil spill toxicity modeling or evaluations of other time‐variable release scenarios. The present study, further, demonstrates that previously proposed modulating variables (e.g., temperature, weight, log K _OW) had a minor influence on the observed variation in k _e. This general observation appears true even if the subset of new focused toxicity data reported in the present study is evaluated independently (i.e., Data Sets A and B).

Further modeling work would benefit from future targeted hydrocarbon toxicity studies on plant species to evaluate if the general observations provided in the present study can be extended to primary producers. Additional systematic evaluation of toxicity data for chemical classes, particularly more soluble aliphatic hydrocarbons, with relevant aquatic species can help further characterize and refine relationships between TKTD model parameters and hydrocarbon structure. Further application of this modeling framework to pulsed exposures could also provide a bridge between constant exposure tests and actual spill exposures in the field, which are typically highly dynamic. Validation of the TKTD framework using toxicity tests with crude oil or other petroleum substances will provide additional confidence in extrapolating results derived from single hydrocarbons for predicting the toxicity of time‐variable oil spill exposures in the field. This is consistent with recent recommendations to use high‐quality laboratory studies to train mechanistic models to support laboratory to field extrapolations so that effects can be evaluated under the diverse exposure scenarios encountered in the field (National Academies of Sciences, Engineering, and Medicine, 2019).

Supporting Information

The Supporting Information is available on the Wiley Online Library at https://doi.org/10.1002/etc.5476.

Author Contributions Statement

Aaron D. Redman: Conceptualization; Data curation; Formal analysis; Funding acquisition; Investigation; Methodology; Project administration; Software; Visualization; Writing—original draft; Writing—review & editing. Thomas F. Parkerton: Conceptualization; Data curation; Formal analysis; Supervision; Validation; Visualization; Writing—original draft; Writing—review & editing. Dominic M. Di Toro: Conceptualization; Supervision; Methodology; Validation; Visualization; Writing—review & editing. Daniel J. Letinski: Data curation; Resources; Writing–review & editing. Cary A. Sutherland: Data curation; Resources; Writing—review & editing. Josh D. Butler: Data curation; Resources; Writing—review & editing.

Supporting information

This article includes online‐only Supporting Information.

Supporting information.

Supporting information.

Data Availability Statement

All data are provided in Supporting Information tables. Modeling equations are presented in the main text, and R packages are cited and publicly available.