Incorporating Ecological Data and Associated Uncertainty in

Mar 2, 2009 - Incorporating Ecological Data and Associated Uncertainty in Bioaccumulation Modeling: Methodology Development and Case Study. Frederik D...
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Environ. Sci. Technol. 2009, 43, 2620–2626

Incorporating Ecological Data and Associated Uncertainty in Bioaccumulation Modeling: Methodology Development and Case Study FREDERIK DE LAENDER,* DICK VAN OEVELEN, JACK J. MIDDELBURG, AND KARLINE SOETAERT NIOO-KNAW, Netherlands Institute of Ecology, Centre for Estuarine and Marine Ecology

Received October 5, 2008. Revised manuscript received February 4, 2009. Accepted February 5, 2009.

Bioaccumulation models predict internal concentrations of hydrophobic chemicals by incorporating key gain/loss processes reflecting the ecology of the exposed species and the characteristics of the chemical. Here, we propose a new methodology that uses ecological data and the principle of mass balance in food webs to estimate bioaccumulation in food webs. To this end, we combine linear inverse models (LIMs) that estimate food web flows based on mass balance with a mechanistic bioaccumulation model (OMEGA). In a case study we show that uncertainty ranges on bioaccumulation predictions were on average estimated a factor of 4 lower by LIMOMEGA than by an OMEGA application that does not consider mass balance within food webs, most notably for chemicals with log Kow > 5, reflecting an increasing importance of uptake through food ingestion for those chemicals. Ranges of internal concentrations predicted by LIM-OMEGA were smaller in enclosures with fish, as strong predation pressure from the latter on mesozooplankton constrains food web flows and thus bioaccumulation.

Introduction The presence of chemicals in the environment that accumulate in biological tissues has long been acknowledged as a potential problem, both for the organisms that inhabit contaminated water bodies, as well as for their predators, i.e., humans and fish-eating wildlife. To predict the accumulation potential of a chemical in an organism, one has to consider properties of the substance and of the organism. Bioaccumulation assessments often rely on predictions by mathematical models that amalgamate a number of key processes to simulate accumulation kinetics of chemical substances using properties of the chemical and the organism as parameters (1-3). In these models, absorption from water and assimilation from food are pathways of uptake, while substances get cleared via excretion to water, egestion with faeces, and biotransformation if the compound is labile. Additionally, the accumulated chemical may get diluted by (re)production. The processes of absorption and excretion * Corresponding author phone: +0113 57 73 22; fax: +0113 57 36 16; e-mail: [email protected]. 2620

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are mainly related to substance properties, biochemical composition of the organism and environmental conditions such as temperature and less by species ecology (4, 5). In contrast, ecological properties of species are the main determinants of processes such as assimilation, egestion, and dilution. In recent years, considerable effort has been spent on the incorporation of ecological information in bioaccumulation models, as reviewed by Borga et al. (6). Recent examples include the incorporation of life-style (7) and exotic species invasion (8). Additionally, the propagation of the uncertainty associated with such ecological information to resulting risk estimates of bioaccumulating substances has been increasingly dealt with (9-12). The way in which uncertainty of ecological properties of a species are quantified in such exercises is an important issue as this will likewise determine the resulting uncertainty on internal concentrations (13). Often, uncertainty factors based on the range of values found back in literature are used to characterize uncertainty on ecology (14). A number of ecological properties of species relate to flows of matter that enter and leave an organism such as assimilation efficiency and rates of prey ingestion and (re)production rate. Their incorporation in bioaccumulation models has been shown to result in acceptable predictions for species at different trophic levels (3). Despite the fact that these ecological properties and their associated uncertainty are difficult to quantify per se, consideration of these properties within a mass-balanced food web context offers possibilities for their quantification. Indeed, flows within a food web are linked, e.g., the production rate of a prey sets upper limits on the feeding rate of a predator. Such relations can be formalized by the principle of mass balance on which robust modeling frameworks have been based (15, 16) to simultaneously estimate all flows in a food web. These frameworks have been successfully applied in ecosystems worldwide to retrieve element budgets based on different ecological data types and biological constraints (17-20). Recently, the linear inverse modeling framework (15) has been extended to additionally estimate uncertainty associated with food web flows (21). Because of the simultaneous consideration of mass balance in the food web and system-specific data, uncertainty estimates from linear inverse models (LIM) may be smaller than original ranges found in the literature. As the principle of mass balance and system-specific data can, in theory, reduce uncertainty of food web flows, and therefore of ecological properties of species that codetermine bioaccumulation, it can be hypothesized that the same principle constrains uncertainty ranges of bioaccumulation predictions as well. In this paper, we propose a new methodology that incorporates the principle of mass balance and systemspecific ecological data in food webs to more precisely assess uncertainty ranges of bioaccumulation model predictions. The methodology relies on a combination of a LIM (15) with a state-of-the-art bioaccumulation model, OMEGA (3). The former uses literature constraints, mass balance and field data sets to estimate food web flows and uncertainty ranges (19, 21). These flow values are used to estimate uncertainty ranges for parameters of a bioaccumulation model that describe ecological properties of species, i.e., specific ingestion and production (f singestion and f sproduction, kg prey kg predator-1 d-1 and kg predator kg predator-1 d-1, respectively) assimilation efficiency (p, kg kg-1). Subsequently, uncertainty ranges of internal concentrations in different biota are predicted. We apply this new methodology (LIM-OMEGA) 10.1021/es802812y CCC: $40.75

 2009 American Chemical Society

Published on Web 03/02/2009

to a published enclosure experiment where simple food webs were exposed to four chemicals with octanol-water partition coefficients (Kow) ranging from 104.7 to 106.9 as described in Ridal et al. (22). The uncertainty ranges on predicted concentrations in fish and mesozooplankton derived by LIMOMEGA are compared with uncertainty estimates from a nonmass-balanced approach, termed C-OMEGA (conventional-OMEGA) to test the hypothesis that bioaccumulation models that account for mass balance will yield less uncertain predictions than current models that rely on the full range of literature values without considering mass balance.

Experimental Section Linear Inverse Modeling. A linear inverse model (LIM) has the mass balances of the food web constituents as a backbone and uses measured biological constraints and system-specific field data to estimate n flows of matter f between compartments of a food web (15). In this context, a “mass balance” relates to the balance of carbon between and within food web compartments. Mathematically spoken, a LIM is expressed as a set of linear equality equations: Aq,nfn ) bq

(1)

and a set of linear inequality equations: Gqc,nfn g hqc

(2)

Each element fi in vector fn represents a food web flow (gC m-2 d-1). The equality equations contain the mass balances over the different compartments and the system-specific data, which are all linear functions of the flows. Each row in Aq,n and bq is a mass balance or data point expressed as a linear combination of the food web flows. Numerical data enter bq, which are the rates of change of each compartment or the measured value in the case of field data. Here, we assume steady-state of the mass balances and hence the rates of change in bq equate to 0. This is an approximation, but numerical twin experiments have shown that even during nonsteady-state food web dynamics, food web flows can be robustly retrieved with a LIM (23). The inequality equation is used to place upper and/or lower bounds on single flows or combinations of flows. The absolute values of the bounds are in vector hq,c and the constraints coefficients, signifying whether and how much a flow contributes to the constraint, are in matrix Gqc. In the current application, eq 2 contains the range of values found back in literature for specific ingestion and production rates (f singestion and f sproduction with s for weight specific and units kg prey kg predator-1 d-1 and d-1) and assimilation efficiencies (p, kg kg-1), i.e., a linear combination of ingestion and egestion flows. These ranges may represent uncertainty and variability of f singestion, f sproduction, and p. Inverse food web models typically have less equality equations than unknown flows, i.e., q < n (20), making the problem mathematically underdetermined. Consequently, the n elements of the vector fn are quantifiable within certain ranges only. These ranges are derived using linear distance programming (ldp, ref 24,) and may result in ranges for f singestion, f sproduction, and p that are smaller than suggested by the original uncertainty ranges in eq 2 because of additional consideration of mass balance and system-specific data (eq 1) and other inequality constraints (eq 2) upon solving the LIM. From these ldp-solved uncertainty ranges, N equally likely food web realizations can be sampled using a Markov Chain Monte Carlo procedure (21). It is important to realize that each of the N solutions corresponds to a set of n values, i.e., one value per food web flow (gC m-2 d-1), and obeys mass balance within the food web, as well as data and constraint equations (eqs 1 and 2). Each of the N individual

food web solutions can be used to infer values for f singestion and f sproduction (kg prey kg predator-1 d-1) using the standing stocks (gC m-2) of the feeding and producing species, respectively. Ingestion and egestion flows allow calculation of p (1 - fraction of ingestion that is egested). Bioaccumulation Model: OMEGA. The rate of change of the concentration ci of a nonbiotransforming chemical in compartment i can be expressed by the OMEGA model as (3) dci ) dt

∑

m j)1

kup,food,jfi·cj + kup,water,i·cwater - (kout,eg,i + kdil,pr,i + kout,water,i)·ci (3)

where cj and cwater represent the chemical concentration in prey item j and the freely dissolved water concentration (µg kg-1 wet weight and µg L-1, respectively), kup,food,ji and kup,water,i the chemical uptake rates through feeding on compartment j and directly from water (d-1 and L kg-1 d-1, respectively), kdil,pr,i the chemical dilution rate through production (d-1), and kout,eg,i and kout,water,i the rates of egestion with faeces and excretion to water (both d-1). Expressions for rate constants k in OMEGA, and how they relate to f singestion, f sproduction, and p can be found in Supporting Information (SI) Table S1. The set of differential equations for all m compartments in a food web is cast in matrix notation as c˙ ) Kup,food·c + Kup,water·cwater - Kout+dil·c

(4)

where c˙ is the rate of change of the internal concentration vector c, Kup,food is a m × m matrix with elements kup,food,ji on row i, column j, Kup,water is a column vector with m elements kup,water,i and Kout+dil a m × m diagonal matrix with elements kout,eg,i + kdil,pr,i + kout,water,i. Internal concentrations in small particles such as microzooplankton, phytoplankton, detritus, protozoa, and bacteria, are assumed to be in rapid equilibrium with the water phase (25) and may be calculated as (26) ∗ ) cwater·OCINST·Koc cINST

(5)

where c*INST denotes the concentration vector for model compartments that are in instant equilibrium with the surrounding water (µg kg-1 wet weight), OCINST their organic carbon fraction (-), and KOC, the organic carbon-water partition coefficient (L kg-1), calculated as 0.41KOW (27), with KOW the octanol-water partition coefficient. Mass Balanced Uncertainty Assessment: LIM-OMEGA. Uncertainty ranges of f singestion, f sproduction, and p estimated with a LIM, and thus obeying mass balance, are propagated through OMEGA thus obtaining uncertainty ranges for Kup,food and Kout+dil, and finally for c using the expressions listed in SI Table S1. To this end, the N solutions for f singestion, f sproduction, and p generated with the Monte Carlo approach are used to calculate N different predictions for c. From these N predictions, upper (95th) and lower (5th) percentiles can be used to represent uncertainty on c. Conventional Uncertainty Assessment: C-OMEGA. A bioaccumulation modeling exercise not accounting for mass balance nor including system-specific data, hereafter termed “C-OMEGA’”, is essentially done by considering the complete range of literature values for the parameters f singestion, f sproduction, and p for the species involved (in essence, eq 2) without solving the LIM. For each of these three parameters, M random samples are taken from the corresponding range. Each of these M parameter sets was put into the OMEGA equations listed in SI Table S1, as such generating M different predictions on c, again characterizing uncertainty on internal concentrations, yet now without accounting for mass balVOL. 43, NO. 7, 2009 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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FIGURE 1. Ranges and median values (black dots) for specific rates of ingestion fsingestion (kg prey kg predator-1 d-1 or d-1) production fsproduction and for assimilation efficiencies p of mesozooplankton and fish found in literature and used in the conventional bioaccumulation modeling technique (C-OMEGA) and constrained by mass balance and ecological data and used in the proposed methodology (LIM-OMEGA). ance within the food web. Again, 95th and 5th percentiles of c are used for uncertainty representation. Both modeling approachessLIM-OMEGA and C-OMEGAswere implemented and solved in the free software R (28) and will be made freely available as an R package at http://cran-mirror.cs.uu.nl/. R packages limSolve (24) and deSolve (29) were used for solving inverse models and differential equations, respectively. Case Study: Lake Enclosures Exposed to Hydrophobics. The two techniques for bioaccumulation modeling (LIMOMEGA and C-OMEGA) were applied to experimental freshwater lake enclosures (Lac Croche, Canada) that were spiked with eight hydrophobic organic compounds (HOCs) (22) during a 107 day period. Parameters for sample size N and M were both set at 1000. For brevity, we only discuss results for pp-methoxychlor (log Kow ) 4.7), trans-chlordane (log Kow ) 6.1), trans-nonachlor (log Kow ) 6.4), and mirex (log Kow ) 6.9), as this selection spans the range of log Kow of the cited substances. Hexachlorocyclohexane (log Kow )3.85) was not considered because of problematic recovery from the dissolved phase and thus unreliable data series (22, 30). Predicted concentrations of pp-methoxychlor in fish are not presented, as this chemical is prone to biotransformation in fish (31), a loss process not included here. Prior to exposure, food web compositions in the enclosures were manipulated by additions of planktivorous fish and/or nutrients giving four types of food webs: planktonic (coded “C”), planktonic with nutrient addition (coded “N”) (47.97 mg N m-2, 3.69 mg P m-2), planktonic with planktivorous fish (coded “F”), and planktonic with planktivorous fish and nutrient additions (coded “FN”). The trophic links in the mass-balances of each LIM are identical, except that the fish compartment is only present in F and FN (SI Figure S1). Field data for the lake enclosures (SI Table S2), mass balance equations, and biological constraints (SI Table S3) were used to setup a LIM for every enclosure. Note that constraints contained literature ranges for f singestion, f sproduction, and p of mesozooplankton and fish, which were represented by uniform distributions. As explained above, C-OMEGA uses these ranges completely, whereas LIM-OMEGA only uses those parts of the ranges allowed by the LIM solution. Additional model parameters required by the OMEGA model and related to species weight, physiology, and/or chemistry were set to default values for both approaches and are provided in SI Table S5). Equation 4 was solved dynamically for the two approaches as the freely dissolved 2622

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water concentration cwater, an input to eq 4, changed in time. Additionally, cwater on every time step was uncertain as well, prompting us to perform our simulations for upper and lower limits of the uncertainty range of cwater dynamics. Here, we give the overall uncertainty on predicted internal concentrations c, originating from uncertainty on f singestion, f sproduction, and p and from uncertainty on cwater. The latter is equal in LIM-OMEGA and C-OMEGA, so that differences between predicted ranges of c obtained by both approaches can be strictly attributed to the different way of uncertainty setting of f singestion, f sproduction, and p in LIM-OMEGA and C-OMEGA.

Results and Discussion In all four enclosures, uncertainty ranges for specific rates of ingestion f singestion, production f sproduction, and of assimilation efficiencies p of mesozooplankton calculated with the linear inverse models (LIMs) are 50-90% smaller than what is expected from original ranges found in the literature (Figure 1). This finding is most apparent in the enclosures with fish (F), especially for f sproduction and p of mesozooplankton and for f singestion, and f sproduction of fish. Low mesozooplankton abundance combined with a relatively high fish biomass in F, and to some extent in FN (SI Table S2), requires a mesozooplankton production rate close to its maximum in order to meet minimum daily carbon intake requirements of fish, i.e., about 1% of their body weight (SI Table S3). This reflects the well-known suppression of large bodied zooplankton abundance by fish consumption (32). Uncertainty ranges for all other flows are given in SI Table S4. As a result of the higher uncertainty in parameters f singestion, f sproduction, and p, the uncertainty on internal concentrations given by C-OMEGA was also higher than for LIM-OMEGA (Figures 2 and 3), most notably in the F enclosures. On average, predicted uncertainty ranges (95th percentile minus 5th percentile) of internal concentrations are a factor 4 smaller for LIM-OMEGA than for C-OMEGA. This factor varies between 1.3 (for mirex in mesozooplankton in the N enclosures) and 11.7 (for mirex in mesozooplankton in the F enclosures) and an overview can be found in SI Table S6). The decrease of ecology-related uncertainty by incorporation of LIM in OMEGA, relative to C-OMEGA, can also be seen when inspecting the proportion of uncertainty on c that is caused by the amalgam of ecological parameters (i.e., f singestion, f sproduction, and p) and by cwater in both approaches (SI Figures S2-S5). When using LIM-OMEGA (SI Figures S2-S3), ecol-

FIGURE 2. Predictions of concentration ranges (5-95th percentile) in mesozooplankton of four chemicals (columns: pp-methoxychlor, trans-chlordane, trans-nonachlor, and mirex) in the different enclosure types (rows: C, N, F, FN) using C-OMEGA (gray) and LIM-OMEGA (orange). The orange area is superimposed on the gray area, but always overlaps completely with the underlying gray. Dashed and solid lines are the median of the concentration range of C-OMEGA and LIM-OMEGA, respectively. Abbreviations of enclosure types are discussed in the text. Data are represented by “+” signs and two signs on 1 date represent the two replicates per enclosure type. In case only one “+” sign is available, this means only the mean of two replicates was available and had to be used for comparison with simulations. ogy-related uncertainty on average contributed 20-40% and 40-60% to overall uncertainty in predictions of internal fish and mesozooplankton concentrations, respectively. The remaining uncertainty is due to uncertainty in cwater. With C-OMEGA, the ecology-related uncertainty contributed 20-30% more to the overall uncertainty on concentrations in mesozooplankton and fish (SI Figure S4-S5). For mesozooplankton, the median predictions by LIMOMEGA are higher than the median predictions by C-OMEGA (Figure 2). Likewise, uncertainty ranges predicted by LIMOMEGA are located in the higher regions of the ranges predicted by C-OMEGA (Figure 2). Hence, bioaccumulation scenarios included by C-OMEGA but discarded by LIMOMEGA are scenarios that suggest lower bioaccumulation.

This agrees with what is expected from the uncertainty on f singestion, f sproduction, and p. Ranges for these three parameters estimated by LIM (and thus used by LIM-OMEGA) are located in the upper, lower and upper regions of the ranges suggested by literature constraints alone (and thus used by C-OMEGA), respectively. For fish, LIM estimates ingestion and production in the enclosures to be in the lower range of what literature suggests (Figure 1), i.e., focusing on scenarios in which fish feed and produce less than reported in literature. These two ecological processes have opposite repercussions on bioaccumulation, i.e., more ingestion and higher dilution of chemical, respectively. Apparently, those two mechanisms compensate each other as the uncertainty ranges of LIMVOL. 43, NO. 7, 2009 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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FIGURE 3. Predictions of concentration ranges (5-95th percentile) in fish of three chemicals (columns: trans-chlordane, trans-nonachlor, and mirex) in the different enclosure types (rows: C, N, F, FN) using LIM-OMEGA (orange) and C-OMEGA (gray). The orange area is superimposed on the gray area, but always overlaps completely with the underlying gray. Line types are as in Figure 2. Abbreviations of enclosure types are discussed in the text. Results for pp-methoxychlor seriously overestimated bioaccumulation in fish as biotransformation was not incorporated in the considered OMEGA model and are thus not given. Data are represented by “+” signs, as in Figure 2. OMEGA predictions for fish are located near the median of the C-OMEGA predictions (Figure 3). Apart from mirex, the observations on days 0-30 are in the upper regions of the uncertainty ranges produced by LIM-OMEGA and C-OMEGA, both for mesozooplankton and fish (Figure 2). For mesozooplankton, it appears that the ranges and medians produced by LIM-OMEGA are higher than the ranges produced by C-OMEGA on most days (Figure 2) and thus closer to the data. However, for fish this is less pronounced, as LIM-OMEGA ranges are located near the median of the C-OMEGA ranges (Figure 3). The model-data comparison suggests that parameters other than ecological ones may require species-specific calibration. Bioaccumulation models indeed contain (bio)chemical parameters such as layer permeation resistances and the ratio of the organic carbon-water partition coefficient KOC to Kow, which are also uncertain and variable. Inferring the exact value of these parameters for a large number of chemicals is a daunting task. For both our approaches we adopted values that were calibrated for higher trophic levels for mesozooplankton and fish (SI Table S5), as no specific information was available for the biological species and substances involved. Predictions of internal concentrations can be equally sensitive to these biochemical parameters as shown by a modeling study for the Lake Ontario food web exposed to polychlorinated biphenyls (12). Hence, our model-data comparison may improve when values for these biochemical parameters become available that were derived for the species present in the considered enclosures. Irrespective of the approach used, the uncertainty on predicted internal concentrations increases with increasing log Kow in all enclosures for both zooplankton and fish (Figure 2624

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2). This increase can be fully attributed to ecology-related uncertainty, i.e., to f singestion, f sproduction, and p, and not to uncertainty on cwater, as the contribution of the latter to overall uncertainty decreases with increasing log Kow (SI Figures S2-S5). Uncertainty on concentrations of pp-methoxychlor (log Kow ) 4.7) in mesozooplankton are notably lower than for substances with higher log Kows (Figure 2) and predominantly reflect uncertainty in cwater (SI Figures S2-S5). The high uncertainty in the C enclosure thus merely reflects uncertainty in cwater of pp-methoxychlor. Accumulation of more hydrophobic chemicals, such as trans-chlordane (log Kow ) 6.1) and mirex (log Kow ) 6.9), is highly uncertain and internal concentrations span an order of magnitude, on average. For fish, the same differences between predictions for pp-methoxychlor and for chemicals with higher log Kows were found, although not shown here because of biotransformation issues discussed in the experimental section. The negligible propagation of uncertainty on f singestion, s f production, and p to bioaccumulation estimates for substances with log Kow < 5 suggests a minor role of species ecology in the accumulation of moderately hydrophobic substances. Indeed, the incorporation of ecological processes has been shown to improve the predictive capacity of bioaccumulation models for substances with log Kow > 5 (33). This can be illustrated by the relative importance of ecology-driven vs chemical processes in uptake and loss of pp-methoxychlor (log Kow ) 4.7) and mirex (log Kow ) 6.9) in the FN enclosures (SI Figure S6). For mesozooplankton, the more hydrophobic substance (mirex) is primarily taken up by food and is thus mostly determined by food web ecology. In contrast, chemical partitioning between water and tissue dominates uptake of pp-methoxychlor. Differences between both substances

regarding the relative importance of uptake and loss processes in fish can be understood as for mesozooplankton. The number of truly site-specific data points needed to set up the LIMs used in this exercise (9) is limited and mainly comprises rather simple measures such as standing stocks (7) next to data on two food web flows (primary production and phytoplankton sedimentation). The remaining information for LIM development consists of 21 constraints on food web flows which can be found in literature and should not necessarily be measured in the considered ecosystem (SI Table S3). Rather, they reflect the biology of a given species, regardless of the food web in which it thrives. From these 21 constraints, 7 were also necessary for C-OMEGA application as they concern ingestion, production, and assimilation efficiency of fish and mesozooplankton. One could thus say that the extra effort needed to apply LIM-OMEGA instead of C-OMEGA was limited. The aqueous chemical concentrations in the case study are well below reported effect concentrations for the biota present (22), and thus exposure can be studied independently from effects. Higher concentrations may induce a change in the food web structure due to changes in the organisms physiology. In that case, the biological constraints from the literature no longer apply and a more data-demanding approach that integrates physiological effects within exposure modeling would be warranted. Such models have been developed (34), although not intensively validated, and require substantial calibration efforts before they can be successfully applied. We have shown that ecological data can be used to reduce the uncertainty associated with food web structure and function and thus with bioaccumulation model predictions. As modern risk assessments increasingly adopt probabilistic approaches (35, 36) this information is useful, if not necessary, for proper characterization of the exposure uncertainty. The mass-balanced LIM-OMEGA method we present here by definition excludes unrealistic exposure scenarios by excluding food web flow values that are impossible, based on available data and mass balance considerations. As much as the method we propose was developed using the OMEGA bioaccumulation model, other bioaccumulation models can also be equipped with a food web flow estimation technique such as LIMs, as outlined here, as these other models also use specific feeding and production rates to estimate chemical ingestion and dilution (1, 2).

Acknowledgments This study was performed for the CORAMM project which is funded by StatoilHydro. We thank Jeffrey Ridal, Asit Mazumder, and David R.S. Lean for providing the raw data of the enclosure experiments, Jan Hendriks for useful feedback on the OMEGA model, Mathijs G. D. Smit for comments on the draft version, and three anonymous reviewers for their useful remarks on the final version.

Supporting Information Available OMEGA rate constant equations, conversion factors, nature and origin of used data and constraints for inverse food web model construction, ranges of food web flows, parameter values used in the bioaccumulation model, factor difference between LIM-OMEGA and C-OMEGA uncertainty ranges, food web structure, dynamics of chemical uptake and loss rates in the enclosure with fish and elevated nutrients (FN), and contribution to overall variance of uncertainty on water concentrations and of ecological uncertainty. This material is available free of charge via the Internet at http://pubs.acs.org.

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