Farley et al.: Comparison of Four Modeling Approaches, File SI-3:1
Supplemental Information for
Metal Mixtures Modeling Evaluation: 2. Comparison of Four Modeling Approaches
File SI-2: USGS Model Description (2012 Version)
Application of the Biotic Ligand Model-Tox Approach: Predicting Biological Response &
Relative Importance of Toxicants in Metal Mixtures
Laurie S. Balistrieri† and Christopher A. Mebane‡,*
†
‡
U.S. Geological Survey, School of Oceanography, University of Washington, Box 355351,
Seattle, Washington 98195 USA;
U.S. Geological Survey, 230 Collins Road, Boise, Idaho 83702 USA
E-mail: cmebane@usgs.gov; Telephone: 1-208-387-1308
Number of pages: 103
Number of tables: 4
Number of figures: 49
1
Farley et al.: Comparison of Four Modeling Approaches, File SI-3:2
Application of the Biotic Ligand Model-Tox Approach: Predicting
Biological Response & Relative Importance of Toxicants in Metal Mixtures
By Laurie S. Balistrieri1 and Christopher A. Mebane2
July 7, 2012 (with editorial updates, January 2014)
Contents
January 2014 Note ..................................................................................................................................................... 6
July 2012 Summary ....................................................................................................................................................... 6
Overarching Conclusions ........................................................................................................................................... 7
Background ................................................................................................................................................................... 8
Part 1: Developing a common set of equilibrium constants for cation-biotic ligand interactions for use in a
multiple-toxicant BLM ...................................................................................................................................................10
Part 2: Assessing Toxicity and Identifying the Relative Importance of Toxicants in Metal Mixtures ..............................17
Modeling Approach ...................................................................................................................................................17
WHAM 7 ................................................................................................................................................................18
Multiple -Toxicant BLM ..........................................................................................................................................19
Tox ........................................................................................................................................................................19
Generalized Logit I ................................................................................................................................................20
Determination of α and β values ........................................................................................................................20
Key Concepts of Our Modeling Approach .............................................................................................................23
Model Fits and Relative Importance of Toxicants in Project Data Sets .................................................................26
Index 1: Hyalella azteca and fatmucket mussel tested in sediment porewaters ..............................................26
Modeling does not address sub-lethal responses ..........................................................................................26
Index 4: Daphnia magna with Cd, Cu, and Zn .................................................................................................28
Index 4: Focus ...............................................................................................................................................29
Index 5: Daphnia pulex with Cd and Zn ..........................................................................................................38
Index 6: Cutthroat and Rainbow Trout with Cd, Pb, and Zn ..............................................................................39
Index 6: Focus ...............................................................................................................................................40
Index 7: Green algae with Cd, Cu, Ni, Pb, and Zn, using field collected water .................................................46
Index 8: Green algae with Cd, Cu, Ni, Zn, laboratory waters .............................................................................47
Index 9: Lettuce with Cu and Zn in hydroponic exposures ...............................................................................50
Index 9: Focus ...............................................................................................................................................51
Competition of multiple toxicants at the biotic ligand .............................................................................................54
Tox50 ....................................................................................................................................................................56
Dissolved metal ratios ...........................................................................................................................................57
Pre-Workshop Conclusions.......................................................................................................................................58
Post-workshop thoughts regarding modeling metal mixtures .......................................................................................59
References ...................................................................................................................................................................65
Appendices ...................................................................................................................................................................76
1
U.S. Geological Survey, University of WA, Oceanography, Seattle, WA, USA; balistri@usgs.gov; +1-206-5438966 (phone)
2
U.S. Geological Survey, Boise, ID, USA; cmebane@usgs.gov; 1-208-387-1308 (phone)
2
Farley et al.: Comparison of Four Modeling Approaches, File SI-3:3
Appendix 1: Developing the Unified individual BLMs ................................................................................................76
Testing the robustness and generality of the single-metal BLMs with different organisms and diverse
waters....................................................................................................................................................................76
Zinc ....................................................................................................................................................................76
Cadmium ...........................................................................................................................................................79
Lead...................................................................................................................................................................79
Copper ...............................................................................................................................................................81
Trout tests with major ions .............................................................................................................................81
Copper and pH...............................................................................................................................................82
Fathead minnows ...........................................................................................................................................85
The soft water problem ..................................................................................................................................88
Invertebrates ..................................................................................................................................................88
Nickel ....................................................................................................................................................................91
Comparisons of benthic invertebrate tissue residues and predicted metal loading using our multipletoxicant BLM and evaluation of the diversity of benthic invertebrate communities using the BLM-Tox
approach ...............................................................................................................................................................96
Metal tissue residues in aquatic insects in streams ...........................................................................................96
Stream aquatic insect diversity predicted from BLM-Tox ...................................................................................98
Appendix 2 - Calculation of the speciation of the biotic ligand ................................................................................100
Appendix 3: Illustrations of the concentration-addition toxic unit and the BLM-Tox approaches to
evaluating mixture toxicity .......................................................................................................................................101
List of Tables
Table 1.
Examples of equilibrium constants for biotic ligand-cation complexes (log KBL-cation) ............. 12
Table 2.
Summary of reactions and associated log K values for biotic ligand (BL-) interactions with
cations determined from single metal toxicity data and used in a multiple-toxicant Biotic Ligand
Model to predict toxicity of metal mixtures. The fractions of total biotic ligand sites occupied by
metal at 50% mortality (f_50% mortality) in single metals tests also are summarized. ................... 16
Table 3.
Fitting parameters (i.e., weighting coefficients (α) and logistic constants (β values) ) for Tox
versus biological response, the Pearson correlation coefficient (r) for predicted and observed
biological response, the number (n) of samples included in each fit, and calculated values for Tox
at 20 (Tox20) and 50 (Tox50) % biological response for the project data sets. .............................. 22
Table 4.
Summary of the values of dissolved metal ratios where the relative importance of toxicants to
Tox is equal in the project data sets. .............................................................................................. 58
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Farley et al.: Comparison of Four Modeling Approaches, File SI-3:4
List of Figures
Figure 1.
Cutthroat trout survival in relation to Zn with or without secondary additions of Cd or Pb. ....... 8
Figure 2.
Variations in the sum of the fractions of total biotic ligand sites (BL total) sites occupied by metal
(BLmetal) and in the speciation of biotic ligands of C. dubia at LC50 in solutions with metal mixtures
using our multiple-toxicant BLM........................................................................................................ 9
Figure 3.
Zinc toxicity as LA50 values versus Ca concentrations, contrasting calculations using initial
and optimized BL-Ca log K values of 3.6 (left) and 5.0 (right). LA50 values are metal accumulations
on the gill associated with 50% mortality. ....................................................................................... 13
Figure 4.
Cadmium, copper, lead, and zinc toxicity as LA50 values versus dissolved Ca concentrations
using initial and optimized BL-Ca log K values of 3.6 and 5.0, respectively. .................................. 14
Figure 5.
Acute toxicity of metals to rainbow trout relative to the biotic ligand-metal equilibrium
constants (log K (BL-Me)) derived for the multiple-metal BLM (our study) and literature values .... 17
Figure 6.
Overview of our multiple-toxicant BLM-Tox approach. ........................................................... 18
Figure 7.
Comparison of total metal load on the biotic ligand considering competition and no
competition between Cd and Zn for the biotic ligand in the synthetic binary metal (Cd, Zn) data set
resembling Index 6. ........................................................................................................................ 24
Figure 8.
A) Total metal load on the biotic ligand for single metal (Cd or Zn) and mixtures of Cd and Zn
in the synthetic binary metal (Cd, Zn) data set resembling Index 6. B) Total and relative loads of
Cd and Zn for 11 tests at ~50% mortality and associated dissolved Cd to Zn ratios in the synthetic
binary metal (Cd, Zn) data set resembling Index 6 ......................................................................... 25
Figure 9.
A) Total fractional metal load on the biotic ligand for single metal (Cd or Zn) and mixtures of
Cd and Zn in the synthetic binary metal (Cd, Zn) data set resembling Index 6. B) Tox versus
fractional mortality in the synthetic data set. C) Relative importance of Cd and Zn to Tox as a
function of the dissolved Cd to Zn ratio in the mixtures in the synthetic data set. ........................... 25
Figure 10. Model results for Index 1. ....................................................................................................... 27
Figure 11. Model results for Index 4. ....................................................................................................... 29
Figure 12. D. magna mortalities following exposures to Cd + constant Cu (Index 4, series Cu-Cd #12). 32
Figure 13. D. magna mortalities following exposures to Cd and Cu, where Cu was titrated into constant 5
µg/L Cd (Index 4, series Cu-Cd #16).............................................................................................. 33
Figure 14. D. magna mortalities following exposures to Cd and Cu, where Cu was titrated into constant 9
µg/L Cd. ......................................................................................................................................... 34
Figure 15. D. magna mortalities following exposures to Cd and Cu, individually and in mixtures, similar
to the previous example (i.e., Cu-Cd #17). ..................................................................................... 35
Figure 16. D. magna mortalities following exposures to Zn and Cu, with copper titrated onto two fixed Zn
exposures. ...................................................................................................................................... 36
Figure 17. D. magna mortalities following exposures to Zn titrated into constant Cu concentrations. ..... 37
Figure 18. Model results for Index 5. ....................................................................................................... 38
Figure 19. Model results for Index 6. ....................................................................................................... 39
Figure 20. Rainbow trout mortalities with varying Zn, with Cd and or Pb nearly constant at about half
their expected EC50s (Index 6, “Series 1). ..................................................................................... 42
Figure 21. Cutthroat trout mortalities with Pb and Zn in mixtures where both increased proportionally
(Index 6, Series 2.) ......................................................................................................................... 43
Figure 22. Rainbow trout mortalities with Cd and Zn in mixtures where both increased proportionally
(Index 6, "Series 3“) ........................................................................................................................ 44
Figure 23. Rainbow trout mortalities with Cd, Pb, or Zn in mixtures targeting USEPA Aquatic Life Criteria
(EPA) or prospective site-specific criteria (SSC) ............................................................................ 45
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Farley et al.: Comparison of Four Modeling Approaches, File SI-3:5
Figure 24. Model results for Index 7. ....................................................................................................... 47
Figure 25. Model results for Index 8........................................................................................................ 49
Figure 26. Model results for Index 8 with comparison to Index 7. ........................................................... 50
Figure 27. Model results for Index 9. ....................................................................................................... 52
Figure 28. Growth inhibition in lettuce following hydroponic exposures to Zn and Cu. ........................... 53
Figure 29. Comparison of total metal load on the biotic ligand considering competition and no
competition, using actual data from Indexes 4, 6, and 9. ................................................................ 55
Figure 30. The fraction of total biotic ligand sites occupied by metal for the competitive and noncompetitive cases for Index 4, 6, and 9. ......................................................................................... 56
Figure 31. Tox at 50% mortality or growth retardation (Tox50) for organisms in the project data sets.... 57
Figure 32. Zinc predicted and empirical acute EC50s with rainbow and cutthroat trout: ......................... 78
Figure 33. Cadmium predicted and empirical acute EC50s with rainbow and cutthroat trout: ................ 80
Figure 34. Lead predicted and empirical acute and chronic effects with fish: ......................................... 81
Figure 35. Copper predicted and empirical trout LC50s with varying major ions: ................................... 83
Figure 36. Copper empirical and predicted LC50s from rainbow trout tests with varying pH .................. 84
Figure 37. Copper empirical and predicted LC50s from fathead minnow tests with varying pH .............. 85
Figure 38. Copper predicted and empirical LC50s from large fathead minnow datasets developed over a
wide range of water chemistry conditions ....................................................................................... 87
Figure 39. Copper predicted and empirical EC50s from cladocerans in diverse waters. ........................ 89
Figure 40. Copper predicted and empirical 21-day NOECs with Daphnia magna ................................ 90
Figure 41. Nickel predicted and empirical effects for rainbow trout and Daphnia magna. .................... 94
Figure 42.
Nickel predicted and empirical EC50s for (A) cultured green algae Pseudokirchneriella
subcapitata, (B) field collected green microalgae and field collected Ceriodaphnia quadrangula
and (C) chronic Ceriodaphnia dubia exposures .......................................................................... 95
Figure 43. Correlations between tissue residues of Cd, Cu, and Zn measured in three stream
invertebrate species collected from Colorado, USA streams and predicted metal loading on the
biotic ligand..................................................................................................................................... 97
Figure 44. Relationships between species richness of EPT aquatic insects collected from Colorado, USA
streams and water chemistry and relative importance of metals to toxicity using the BLM-Tox
approach. Aquatic insect occurrences and stream chemistry data are from Schmidt et al. (2010). 99
Post-Workshop figures
Figure 45. Tissue residues of Cd, Cu, and Zn in Rhithrogena mayflies modeled by the WHAM-7 humic acid
approach or by a revised BLM approach
Figure 46. Cd and Pb single metal exposures and rainbow trout gill accumulations modeled with a two-site
biotic ligand model
Figure 47. Cd and Pb mixture exposures metal rainbow trout gill accumulations modeled with a two-site
biotic ligand model
Figure 48. Zn single metal exposures and rainbow trout gill accumulations modeled with a two-site biotic
ligand model
Figure 49. Zn, Cd, and Pb mixture exposures resulting in with “less than additive” toxicity (Index 6, “series
1”) modeled with the two-site biotic ligand model
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Farley et al.: Comparison of Four Modeling Approaches, File SI-3:6
January 2014 Note
This supplement describes the 2012 version of the “U.S. Geological Survey (USGS)
BLM-TOX” metals mixtures toxicity model which was compared to other models in Farley and
others’ article “Metal Mixtures Modeling Evaluation Project: 2. “Comparative Evaluation” to
which this supplement is appended. The published version of our BLM-TOX model (Balistrieri
and Mebane 2014) has substantive differences from the earlier version described in the main
article by Farley and others. Because the early version of our model, as described in the main
article, is not available elsewhere, we append here the full description of our modeling approach
that corresponds with the critical review in the main article.
Following a May 2012 workshop on comparative modeling approaches, we made
substantive revisions to the “pre-workshop” modeling approach described here. Major
differences between the version described here and our revised “2014 fish model” which focused
on rainbow and cutthroat trout (Balistrieri and Mebane 2014) include:


In the 2012 version, binding affinities for metals accumulation on the biotic
ligand were defined using measured toxicity responses and metals accumulations
were a modeling construct. In the 2014 fish model, binding affinities were defined
directly from published gill accumulation studies.
The 2012 model version described here assumed a single site of toxic action on
the biotic ligand whereas our 2014 fish model assuming two sites of toxic action
on the biotic ligand provided better fits to the measured data.
The following describes our 2012 version, as described in the main article, Farley and
others’ comparative evaluation of four modeling approaches.
July 2012 Summary
This work is part of a larger modeling effort that is assessing the toxicity of metal (Cd,
Cu, Ni, Pb, and Zn) mixtures to aquatic organisms and evaluating the relative importance of
these metals as toxicants in the mixtures. The sponsor of the larger modeling effort, i.e., the
International Lead Zinc Research Organization (ILZRO), supplied four modeling groups with
seven data sets. These data sets included the composition of freshwaters and associated
biological responses (i.e., survival or growth metrics) from laboratory and field studies that had
either paired single and multiple metal solutions or just multiple metal solutions. Our tasks were
to model the data sets, provide insight into the hierarchy of metal toxicity in the mixtures,
summarize our results in a report, and participate in a collaborative workshop to integrate results
from the four modeling groups. This document summarizes the modeling results of our group.
We evaluated the data sets using an integrated modeling approach (Figure 6), which
includes:
1. determining the loading of toxicants on biotic ligands in the solutions using WHAM 7
and a common set of equilibrium constants for biotic-ligand interactions that is
incorporated into a multiple-toxicant biotic ligand model (BLM);
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Farley et al.: Comparison of Four Modeling Approaches, File SI-3:7
2. defining a function called Tox that incorporates the fractional loading of biotic ligands by
hydrogen and metal toxicants and weights their relative toxicity to biota through toxicity
coefficients;
3. evaluating the relative importance of metal toxicants in the metal mixtures by examining
each term in the Tox function; and
4. using the Generalized Logit I equation to relate Tox and biological response (i.e.,
mortality or growth retardation) of biota.
.
Overarching Conclusions







The BLM-Tox approach reasonably fits observed biological responses to metal mixtures
using a consistent set of weighting coefficients and organism-specific logistic parameters.
The composition of the metal load on the biotic ligand in metal mixtures can vary but still
produce the same biological response.
Tox incorporates the effects of solution composition and speciation (in particular,
identities and total dissolved concentrations of toxicants); affinities of toxicants for the
biotic ligand (KBL-metal); and weighting coefficients for toxicants into a single parameter.
Values of Tox do not depend on the type of organism, but rather the response of an
organism is related to Tox with increasing values of Tox producing more adverse
responses.
Organisms have different sensitivities to Tox.
Tox provides an evaluation of the relative importance of toxicants in a mixture. That
importance depends on the relative concentrations of dissolved metals in the mixture.
The relative importance of toxicants in binary or multiple metal mixtures appear to be
equal at unique dissolved metal ratios.
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Background
Our interest and collaboration in modeling the toxicity of metal mixtures followed
investigations of the speciation and bioavailability of metals and toxicity testing with trout in
stream water from the Coeur d’Alene River basin in northern Idaho, USA (Balistrieri and Blank
2008; Mebane et al. 2012). These streams contain elevated concentrations of dissolved Cd and
Zn and lower concentrations of dissolved Pb. One matched series of tests from this work was
particularly intriguing because the survival of trout at a given concentration of Zn depended on
the absence or presence of other metals (Cd and Pb) in solution; specifically, Zn alone is more
toxic than mixtures of Zn with either Cd or Pb, or in mixtures with all three metals (Zn, Cd, and
Pb) (Figure 1). Thus, survival depends on the composition of the metal mixture.
Index 6, mixture series #1 (tests 125, 136-138)
Zn
Zn+Pb
Zn+Cd
Zn+Pb+Cd
1.0
0.9
0.8
Survival
Index 6, m
1.0
0.9
0.8
0.7
0.7
0.6
0.6
0.5
Survival
0.5
0.4
0.4
0.3
0.3
0.2
0.2
0.1
0.1
0.0
0.0
0
200
400
0
Zn (µg/L)
1.0
Figure 1. Cutthroat trout survival in relation to Zn with or without secondary additions of Cd or Pb.
0.9
1.0
Secondary additions of
Cd and Pb were at about 0.6 µg/L Cd and about 100 µg/L Pb, which were about
Zn
0.5 times the expected
0.8
0.9EC50 for Cd and Pb. The apparent toxicity of Zn declined when tested in the
Zn+Pb
presence of Cd and Pb under these conditions. Error bars show ranges of responses
across replicates,
Zn+Cd
0.8
0.7
data from Mebane et al. (2012), also referred to as “Data Index 6” in this report.
Zn+Pb+Cd
0.7
0.6
Using biotic 0.6
ligand model calculations, we also looked at metal loading and speciation of
0.5
biotic ligands at 50% mortality in a series of studies that examined toxicity of metal mixtures
Survivalto
Ceriodaphnia
dubia0.5
(Cooper et al. 2009). These calculations indicated that the fraction of total 0.4
Survival
biotic ligand occupied
0.4 by metal [Σ(BLmetal/BLtotal)] and the composition (or speciation) of metal
0.3
on the biotic ligand in metal mixtures vary, but still produce the same endpoint (i.e., 50%
0.3
0.2
0.2
0.1
0.1
8
0.0
0.0
0.00
0.05
0.10
0.15
0.00
Farley et al.: Comparison of Four Modeling Approaches, File SI-3:9
mortality) (Figure 2). In other words, there is no unique lethal accumulation of metal at 50%
mortality (LA50).
This modeling-based conclusion has experimental support. In toxicity testing and
radiolabeled uptake experiments of Cd and Pb with rainbow trout, Birceanu et al. (2008) found
that there was greater Pb than Cd binding to the gill when the trout were exposed to Pb or Cd
either individually or in two-metal mixtures. Yet, despite greater loading of Pb relative to Cd and
with a Pb 96-h LC50 that is approximately 100-fold greater than that of Cd, it was clear that the
acute toxicity of Pb was substantially less than that of Cd. The LA50 for Pb was about 50% of
the measured maximal Pb-gill binding capacities (Bmax), whereas the LA50 for Cd was about
10% of the measured Bmax (Birceanu et al. 2008).
Figure 2. Variations in the sum of the fractions of total biotic ligand sites (BL total) sites occupied by metal
(BLmetal) and in the speciation of biotic ligands of C. dubia at LC50 in solutions with metal mixtures using
our multiple-toxicant BLM.
Metal loading on the biotic ligand ranges from 0.6 to 7.8% at 50% mortality, and the speciation varies
depending on the solution composition. The toxicity tests contain the following metal mixtures: tests 1-3
(Cu+Pb); test 4 (Cu+Pb+Zn); test 5 (Cu+Zn); and tests 6-7 (Pb+Zn).
The conclusion that a given biological effect, such as 50% mortality, can result from
greatly differing measured or calculated metal loading on the biotic ligand challenges a key
assumption of the toxic unit approach for predicting mixture toxicity based on additivity of
metals bound to the biotic ligand. For example, (Playle 2004) illustrated the toxic unit approach
for metal mixtures in which mortality was modeled to occur when 50% of the total binding sites
were occupied by metals. Stockdale et al (2010) devised a function called FTOX to incorporate
differences in apparent inherent toxicity of different metals, in addition to differences in metal
loading. Stockdale et al. (2010) used FTOX to predict stream benthic macroinvertebrate diversity.
In our present study, as well as recently in Balistrieri et al. (2012), we adapted their FTOX to use
with toxicity data, but because our approaches for determining metal loads on the biotic ligand
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Farley et al.: Comparison of Four Modeling Approaches, File SI-3:10
are not identical, we call our adaptation ”Tox”. Our development of Tox is primarily detailed in
Part 2.
Thus, to account for differences in solution composition, speciation of the biotic ligand,
and survival of biota in metal mixtures, a modeling approach that predicts toxicity of such
solutions should define: (1) the speciation of the biotic ligand, most likely including competition
among multiple metal toxicants at the biotic ligand; (2) a function that relates the composition of
the solution and speciation of the biotic ligand to biological response; and (3) a process for
identifying metals that are killers of aquatic organisms and those that are bystanders in metal
mixtures.
The following two major sections discuss our modeling approach for addressing these
issues and the results of our modeling efforts. The first section describes our development of
five new biotic ligand models with a common set of equilibrium constants that define
interactions among dissolved cations and a single type of biotic ligand using water quality and
toxicity data from single metal systems. We chose a biotic ligand model (BLM) approach to
evaluate loading of toxicants on the biological receptor. Although biotic ligand models have
been successfully developed to predict metal loading and acute toxicity of a single dissolved
metal to test organisms (Paquin et al. 2002), BLMs that consider competition among multiple
toxic metals (e.g., Cd, Pb, and Zn) at the biotic ligand and responses of aquatic organisms and
communities exposed to metal-mixtures are not as well developed (Playle 2004). Following the
work of Playle (2004), we integrate the five BLMs by using the common set of equilibrium
constants in a multiple-toxicant BLM.
The second section places the multiple-toxicant BLM into a larger modeling framework
for assessing toxicity of metal mixtures to aquatic organisms. The framework is discussed and
then applied to the seven data sets provided by ILZRO. The results and the insight gained from
those results are discussed for each data set.
Part 1: Developing a common set of equilibrium constants for cation-biotic
ligand interactions for use in a multiple-toxicant BLM
A key simplifying assumption of Playle’s (2004) multiple-metal modeling approach is
that there is a common mechanism of toxicity among different metals. That is, Playle (2004)
assumed that Cd, Co, Pb, Zn, Ag, and Cu all interrupted Ca homeostasis in fish, even though Ag
and Cu had been previously shown to interrupt Na homeostasis. More recent multiple metals
uptake experiments support Playle’s assumption of interacting mechanisms of uptake and
toxicity (Alsop and Wood 2011). While Cd and Zn previously have been shown to reduce Ca2+
uptake (Niyogi and Wood 2004a), Cu and Ni uptake experiments with zebrafish also decreased
Ca2+ uptake, suggesting that the epithelial transport of all these metals is through Ca2+ pathways.
The toxicity from Cd, Zn, Cu, and Ni was due to total ion loss (predominantly Na+) (Alsop and
Wood 2011). Similarly, Komjarova and Blust (2008; 2009) found that with both zebrafish and
Daphnia magna exposed to Cd, Cu, Ni, Pb and Zn, the mostly negative interactions among the
metals were those with similar interaction mechanisms among the metals and cell tissues.
Our first step in developing new single-metal BLMs with a common set of equilibrium
constants was to compile equilibrium constants (KBL-cation) for interactions among cations (H, Na,
Ca, Mg, Cd, Cu, Ni, Pb, and Zn) and biotic ligands and other BLM parameters (e.g., maximum
biotic ligand sites, lethal accumulation at 50% mortality) that were previously determined in
10
Farley et al.: Comparison of Four Modeling Approaches, File SI-3:11
single toxicant systems. Some of these equilibrium constants were estimated experimentally
through radiolabeled uptake studies (e.g., Playle et al. 1993; Alsop and Wood 2000; Niyogi et al.
2008) and others were estimated from toxicity data with cladocerans that independently varied
the concentrations of cations, such as H+, Ca2+, Mg2+, and Na+. In this approach, mortality is
assumed to result from critical levels of binding at a site of action, and the stability constants for
competing ions are calculated by assuming a linear relation between the metal concentration
causing a toxic effect and the concentration of individual competing ions (H+, Ca2+, Mg2+, and
Na+) (e.g., De Schamphelaere and Janssen 2002). These approaches provide a range of
equilibrium constants for (1) the same metal toxicant; (2) metal toxicants considered to have
similar modes of toxicity, such as Cd, Pb, and Zn that act as calcium ionoregulatory disruptors;
and (3) presumably non-toxic cations (Ca, Na, Mg) (Table 1) . However, to evaluate toxicity in
multiple toxicant systems with a single type of biotic ligand and to assess the role of competition
of multiple toxicants at the biotic ligand, a common set of equilibrium constants is needed to
describe simultaneous interactions among all cations and the biotic ligand.
11
Farley et al.: Comparison of Four Modeling Approaches, File SI-3:12
Table 1. Examples of equilibrium constants for biotic ligand-cation complexes (log KBL-cation)
The equilibrium constants are for the following reactions: BL- + cation+n = BL-cation+(n-1) and BL- + cation+n
+ H2O = BL-cationOH+(n-2) + H+.
Cd #1 Cd #2
Pb
Zn #1
Zn #2
6.7
4.
6.6
6.7
4.5
4.
3.8
3.8
Log K (BL-Mg+)
3.5
4.
3.8
Log K (BL-Na)
3.
3.5
2.
Log K (BL-H)
Log K (BL-Ca+)
Log K (BL-Cd+)
3.9
8.
Zn #3 Zn #4
Cu #1
Cu #2
6.4
5.4
6.67
4.9
3.8
3.5
4.4
2.9
3.5
Ni
6.7
5.0
3.6
4.0
4.5
3.3
3.6
4.0
4.0
2.6
3
3.0
3.5
2.91
8.6
Log K (BL-Pb+)
Playle’s
2004
Uniform
BLM #1
8.6
6.
6.0
Log K (BL-PbOH)
5.5
Log K (BL-Zn+)
5.5
-3.8
Log K (BL-ZnOH)
5.5
5.4
-3.8
-2.4
Log K (BL-Cu+)
Log K (BL-CuOH)
5.6
7.4
8.02
-1.3
0.50
7.4
4.0
Log K (BL-Ni+)
Log K (BL-NiOH)
BLtotal (nmol/gwet)
0.62
8
% DOC reactive
with metal
60% 100%
6.5
~35-60
30
50%
8.3
100%
30
30
30
100%
100
100%
30
50%
1000
100%
5
100%
Cd #1 - (Niyogi et al. 2008); Cd #2 - HydroQual unpub; Pb #1 - (Macdonald et al. 2002); Zn #1-(HydroQual 2004); Zn #2 (De
Schamphelaere and Janssen 2004a); Zn 3: (Clifford and McGeer 2009); Zn 4: (DeForest and Van Genderen 2012); Cu
#1:(USEPA 2007); Cu #2 (De Schamphelaere and Janssen 2004b); Ni #1: (Keithly et al. 2004); Uniform BLM #1 (Playle 2004).
To address this need, equilibrium constants for all biotic ligand-cation interactions were
re-evaluated using data from single metal toxicity studies on rainbow and cutthroat trout. This
effort involved (1) compiling LC50 data for single metal (Cd, Cu, Ni, Pb, and Zn) and associated
water compositions (i.e., all “default BLM” data) from USGS and previous studies (150+ tests);
(2) determining free ion activities of H, Na, Mg, Ca, Cd, Cu, Ni, Pb, and Zn for the solutions
using WHAM 7 and a constant conversion factor from dissolved organic carbon (DOC) to
dissolved organic matter (DOM); and (3) developing an interactive spreadsheet based on the
equations in De Schamphelaere and Janssen (2002) and De Schamphelaere et al. (De
Schamphelaere et al. 2002, 2003) to determine equilibrium constants for biotic ligand-cation
interactions and the fraction of biotic ligand sites occupied by metal at 50% mortality by selected
12
Farley et al.: Comparison of Four Modeling Approaches, File SI-3:13
“factors-testing” of the data and later by minimizing the difference between observed and
predicted LC50 values using SOLVER in Excel.
An important concept in the BLM approach is that the critical concentration of metal on
the biotic ligand associated with a given level of effect, e.g., LA50, should be independent of the
solution water chemistry. That is, the BLM is considered to be valid only if the LA50 values for
an organism are the same over the entire range of tested water chemistry (Di Toro et al. 2001).
Following that concept and the approach above and using toxicity tests conducted across
a range of dilution chemistries, we iteratively varied log K values to try to find a common set of
log K values that (1) gave similar LA50 values as fractions of total biotic ligand (BLtotal) for Cd,
Cu, Pb, Zn, (2) gave LA50 fractions independent of water concentrations of H, Ca, Mg, Na,
DOC, and (3) seemed plausible in relation to other experimentally derived values.
Figure 3. Zinc toxicity as LA50 values versus Ca concentrations, contrasting calculations using initial and
optimized BL-Ca log K values of 3.6 (left) and 5.0 (right). LA50 values are metal accumulations on the gill
associated with 50% mortality.
In Figure 3 we compare Zn toxicity to rainbow trout in “factors” testing, i.e., studies in
which Ca was manipulated, but most other variables were nearly constant. (In some cases, water
hardness was manipulated, so that Ca, Mg, and alkalinity were changing in unison). The datasets
were limited to tests using different solution chemistries as part of the same study or at least from
related studies conducted in the same lab to reduce the confounding influence of factors
unrelated to solution water that may affect toxicity, such as fish size or age (Chapman 1978;
Bradley and Sprague 1985; Cusimano et al. 1986; Hansen et al. 2002; Brinkman and Hansen
2004; De Schamphelaere and Janssen 2004a; Todd et al. 2009).
13
Farley et al.: Comparison of Four Modeling Approaches, File SI-3:14
log K (BL-H) =
6.7
log K (BL-Na) =
4
log K (BL-Mg) =
4.4
log K (BL-Ca) =
3.6
log K (BL-Cd) =
8.1
log K (BL-Cu) =
7.6
log K (BL-CuOH) =
0.62
log K (BL-Pb) =
6.3
log K (BL-PbOH) =
-1.3
log K (BL-Zn) =
5.6
log K (BL-ZnOH)=
-3.8
log K (BL-H) =
6.7
log K (BL-Na) =
4
log K (BL-Mg) =
4.4
log K (BL-Ca) =
5
log K (BL-Cd) =
8.1
log K (BL-Cu) =
7.6
log K (BL-CuOH) =
0.62
log K (BL-Pb) =
6.3
log K (BL-PbOH) =
-1.3
log K (BL-Zn) =
5.6
log K (BL-ZnOH)=
-3.8
Cd
Pb
Zn
Cu
Cd
Pb
Zn
Cu
Avg LA50 as
percentage of
BL-total
(BL-Me/BL-tot
14%
13%
18%
13%
Avg LA50 as
percentage of
BL-total
(BL-Me/BL-tot
4.2%
4.1%
4.1%
4.1%
CV
66%
105%
72%
85%
CV
56%
117%
77%
79%
Figure 4. Cadmium, copper, lead, and zinc toxicity as LA50 values versus dissolved Ca concentrations using
initial and optimized BL-Ca log K values of 3.6 and 5.0, respectively.
Setting the log K BL-Ca value to 5.0 minimized the slope of Ca concentration versus LA50 values and
resulted in similar LA50 values for all metals. Single metal datasets are described in the appendix.
14
Farley et al.: Comparison of Four Modeling Approaches, File SI-3:15
If the log K for BL-Ca was assumed to be 3.6, then the LA50 fractions vary from 0.05 –
0.40, a factor of 8, and increase with increasing Ca concentrations. This result is directly in
conflict with the “validity test” of Di Toro et al. (2001). When the BL-Ca log K was iteratively
increased to 5.0 using the interactive spreadsheet and holding other parameters constant, then the
pattern of increasing LA50 values with increasing Ca concentrations was largely eliminated.
In Figure 4, we move beyond these well matched tests with varying Ca and Zn
concentrations and include Cd, Cu, and Pb. When the BL-Ca log K value was set at 3.6, a similar
pattern of increasing LA50 values with Ca concentrations is apparent with average LA50 values
ranging from 13 to 18%. Changing the BL-Ca log K to 5.0 reduces the variability in LA50 with
most values between 3 and 6%. Similar sequential comparisons across tests that had specifically
varied H, Mg, Na concentrations were made with the objective of obtaining a slope of zero
across the range of test values and minimizing the average coefficient of variability (CV) of the
LA50 estimates for Cd, Cu, Pb, and Zn. The BL-Cd log K was similarly estimated.
Free metal ions (Me2+) typically are considered the toxic form of the metal (Di Toro et al.
2001), but the first hydrolysis species (MeOH+) of at least Cu, Pb, and Zn likely are also toxic
(Niyogi and Wood 2004a). To jointly optimize the log K values for biotic ligand interactions
with Me2+ and MeOH+, we also used SOLVER to minimize the CVs of the LA50 values. We
experimented using SOLVER to optimize all variables simultaneously, but this was unwieldy
because of the many constraints needed.
The first iteration of developing our new BLMs did not include Ni. However, in order to
model mixtures containing Ni, we developed a new BLM for Ni. Because of the cumulative
approach to constructing the models, we assumed that equilibrium constants for biotic ligand
interactions with several cations (H+, Na+, Mg+2, and Ca+2) that we had previously optimized in
the other BLMS could also be used in determining log K values for Ni. In other words, the only
parameters we optimized during our evaluation of Ni toxicity data were log K values for BL-Ni
and BL-NiOH (see details in Appendix 1).
A summary of reactions, log K values, and the fraction of total biotic ligand occupied by
metal in single metal toxicity experiments are summarized in Table 2.
15
Farley et al.: Comparison of Four Modeling Approaches, File SI-3:16
Table 2. Summary of reactions and associated log K values for biotic ligand (BL-) interactions with cations
determined from single metal toxicity data and used in a multiple-toxicant Biotic Ligand Model to predict
toxicity of metal mixtures. The fractions of total biotic ligand sites occupied by metal at 50% mortality
(f_50% mortality) in single metals tests also are summarized.
Constant
log K (BL-H) =
log K (BL-Na) =
log K (BL-Mg) =
log K (BL-Ca) =
log K (BL-Cd) =
log K (BL-Cu) =
log K (BL-CuOH) =
log K (BL-Ni) =
log K (BL-NiOH) =
log K (BL-Pb) =
log K (BL-PbOH) =
log K (BL-Zn) =
log K (BL-ZnOH) =
6.70
4.00
4.40
5.00
8.10
7.60
0.62
4.04
-2.58
6.30
-1.30
5.60
-3.80
Reaction
BL- + H+ = BL-H
BL- + Na+ = BL-Na
BL- + Mg+2 = BL-Mg+
BL- + Ca+2 = BL-Ca+
BL- + Cd+2 = BL-Cd+
BL- + Cu+2 = BL-Cu+
BL- + Cu+2 + H2O = BL-CuOH+ + H+
BL- + Ni+2 = BL-Ni+
BL- + Ni+2 + H2O = BL-NiOH+ + H+
BL- + Pb+2= BL-Pb+
BL- + Pb+2 + H2O = BL-PbOH+ + H+
BL- + Zn+2 = BL-Zn+
BL- + Zn+2 + H2O = BL-ZnOH+ + H+
f_50% mortality
f_50% mortality
f_50% mortality
f_50% mortality
f_50% mortality
f_50% mortality
0.035
0.027
0.113
0.014
0.015
0.019
Cd
Cu-rainbow trout
Cu-cutthroat trout
Ni
Pb
Zn
Overall our optimization approach yielded log K values for BLM calculations that are
quite similar to those previously determined by uptake experiments. In Figure 5 we compare our
equilibrium constants for cation-biotic ligand interactions with published log K values and
rainbow trout acute LC50 values. This comparison emphasizes the strong correlation between
metal binding affinities and toxicity to trout, with Ag being most toxic and Ni least toxic.
16
Farley et al.: Comparison of Four Modeling Approaches, File SI-3:17
Figure 5. Acute toxicity of metals to rainbow trout relative to the biotic ligand-metal equilibrium constants (log
K (BL-Me)) derived for the multiple-metal BLM (our study) and literature values
(Alsop and Wood 2000; Pane et al. 2003a; Rogers et al. 2003; Niyogi and Wood 2004a).
Part 2: Assessing Toxicity and Identifying the Relative Importance of
Toxicants in Metal Mixtures
Modeling Approach
Modeling the toxicity of metal mixtures to aquatic organisms spans the gap between
measured solution composition and measured biological response to that solution. The toxicity
studies using trout and BLM calculations using the C. dubia dataset (Figure 2) suggested that a
model of a dose-response curve should (1) define the chemical speciation of the test solution and
the biological receptor and (2) provide mathematical functions that relate the chemical speciation
of the solution and biological receptor to survivability of aquatic organisms. In addition, the
results of the model fit should provide insight into the relative importance that individual metals
in a mixture play in producing toxic conditions.
17
Farley et al.: Comparison of Four Modeling Approaches, File SI-3:18
Solution
Composition
WHAM 7
Biotic Ligand Speciation
Solution Speciation
free ion activities
(H, Na, Mg, Ca, Cd, Cu, Ni, Pb, Zn)
Biotic Ligand Model
(competitive, multiple toxicant)
(fH, fCd, fCu, fNi, fPb, fZn)
Toxicity Coefficients
Tox = S(acation * fcation)
(aH, aCd, aCu, aNi, aPb, aZn )
Mortality or
Growth Retardation
cation = H, Cd, Cu, Ni, Pb, Zn
Dose-Response Equation
(Generalized Logit I)
Importance of Each Toxicant = (acation * fcation) /Tox
Figure 6.
Overview of our multiple-toxicant BLM-Tox approach.
We developed a modeling approach, called Biotic Ligand Model-Tox, to address these
issues. The primary components of the approach are illustrated in Figure 6 and include:
 Windermere Humic Aqueous Model 7 (WHAM 7), which is used to determine
the chemical speciation of the solutions (Tipping et al. 2011; Lofts 2012);
 Multiple-toxicant BLM, which was described in the previous section and is used
to define the chemical speciation of the biotic ligand in single metal solutions and
metal mixtures;
 Tox function, which “weights” the loading of hydrogen and metal toxicants on the
biotic ligand (Stockdale et al. 2010) and is used to evaluate the relative
importance of individual toxicants on overall toxicity; and
 Generalized Logit I (Scholze et al. 2001), a logistic equation that links Tox to
biological response (i.e., mortality or growth retardation).
A description of each of these components is below.
WHAM 7
WHAM 7 is a computer program that is used to determine the chemical speciation of
each solution at equilibrium (Tipping et al. 2011; Lofts 2012). The program considers both
inorganic and organic complexation with cations. Several assumptions are used in the
calculations. First, dissolved organic matter (DOM) is assumed to be 50% dissolved organic
carbon (DOC), and 10% of DOM is humic acid (HA) and 90% of DOM is fulvic acid (HA)
(Thurman 1985). Only 65% of DOC is reactive or complexes with metals, on the average
18
Farley et al.: Comparison of Four Modeling Approaches, File SI-3:19
(Bryan et al. 2002). Thus, the conversion from DOC (mg/L) to HA and FA (g/L), which are the
inputs to WHAM 7, is HA = 2*0.1*0.65*0.001*DOC and FA = 2*0.9*0.65*0.001*DOC.
Second, the solutions collected in the field are assumed to be in equilibrium with
amorphous iron and aluminum hydroxides [Fe(OH)3 and Al(OH)3]. The activity of dissolved
Al+3 is calculated using a solubility product of 108.5 at 25ºC for aluminum oxide [Al(OH)3 + 3H+
= Al+3 + 3H2O], which is corrected for temperature using an enthalpy of -107 kJ/mole (Tipping
et al. 2002; Tipping 2005). The activity of dissolved Fe+3 is determined from an empirical
equation that includes a temperature correction (Lofts et al. 2008). The calculated activities of
the free Al+3 and Fe+3 ions are inputs to WHAM 7 along with temperature, pH, and measured or
estimated concentrations of major ions (Na, K, Ca, Mg, Cl, SO4, total CO3), organic matter (HA,
FA), and minor ions (Cd, Cu, Ni, Pb, Zn) for each solution. The output of interest to this study is
the free ion activities of H, Na, Mg, Ca, Cd, Cu, Ni, Pb, and Zn in each solution.
Multiple -Toxicant BLM
The speciation of the biotic ligand in each solution is calculated using the free ion
activities of the cations (H, Na, Mg, Ca, Cd, Cu, Ni, Pb, and Zn) determined from WHAM 7, a
mass balance of total biotic ligand sites, which includes the concentrations of the free (BL-) and
complexed (BL-cation) biotic ligand, and equilibrium constants and equations for biotic ligandcation interactions (Table 2) (see appendix 2 for equations). Both competitive and noncompetitive interactions among the toxicants (Cd, Cu, Ni, Pb, and Zn) are considered. The result
of the calculations is the determination of the fraction of total biotic ligand that is complexed by
each cation (fcation = [BL-cation]/[BLtotal]) at equilibrium.
Tox
As previously indicated with the C. dubia data set (Figure 2), the amount of toxicant load
and the composition of that load on the biotic ligand can vary for the same biological endpoint.
Thus, a function is needed that weights the load so that the value of the function is the same for
different solution compositions at a given biological response. Based on the work of Stockdale
et al (2010), a function, called Tox, is defined that incorporates the load of hydrogen and metal
toxicants on the biotic ligand and their associated weighting coefficients:
Tox = S(ai * fi)
where a is an ion-specific weighting coefficient, f is the fraction of biotic ligand occupied by an
ion i, and i is H, Cd, Cu, Ni, Pb, or Zn. This function incorporates the effects of composition
(e.g., total concentrations, suites, and ratios of toxicants) and chemical speciation of the solution
on the amount, composition, and toxicity of the toxicants on the biotic ligand. It also provides an
evaluation of the relative importance (RI) of each toxicant to the Tox function:
RIi = (ai * fi)/Tox
19
Farley et al.: Comparison of Four Modeling Approaches, File SI-3:20
Generalized Logit I
Numerous versions of sigmoidal concentration-response curves, including Probit, Logit,
or Weibull functions, are used to model acute toxicity to aquatic organisms(Christensen 1984;
Scholze et al. 2001; Trögl and Benediktová 2011). A characteristic of Probit and Logit functions
is that they are symmetric relative to the median response (e.g., 50% mortality). Alternately, a
Weibull function and extended Logit functions that include a third adjustable parameter are
asymmetrical, and therefore, apply to a larger family of curves (Scholze et al. 2001) In our
modeling approach, we use the Generalized Logit I equation with three adjustable parameters
(Scholze et al. 2001):
𝐹=
1
(1 + exp[−𝑛])𝛽3
where F = biological response (i.e., fractional mortality or growth retardation), n = β1 + [β2*log
(Tox)], and β1, β2, and β3 are constants.
To summarize our approach for modeling the toxicity of metal mixtures, we developed a
common set of equilibrium constants for biotic ligand-cation interactions from single metal
toxicity studies (Part I, Table 2). These constants along with solution speciation determined by
WHAM 7 are used in a multiple-toxicant BLM to determine the speciation of biotic ligands in
solutions with metal mixtures. BLM calculations indicate that the speciation and amount of
metal on the biotic ligand in different metal mixtures can vary, but still result in the same
mortality. Thus, we define a toxicity function (Tox) that weights the loading of each metal and
hydrogen on the biotic ligand through weighting coefficients. Then, Tox is related to mortality
through a logistic equation. The primary toxicant is assessed by evaluating each term in the Tox
function. Note that in contrast to a “traditional” BLM, our multiple-toxicant BLM does not
predict toxicity or water quality criteria. It is only a tool to determine the speciation of the biotic
ligand. Tox and the logistic equation relate loading of metals and hydrogen ions to mortality,
and are used to determine the weighting coefficients and logistic parameters.
This research was presented at the 2010 SETAC meeting in Portland (Balistrieri and
Mebane 2010; Mebane et al. 2010a) and the June 2011 Metal Mixtures Workshop in Toronto.
Our approach for evaluating toxicity of metal mixtures was incorporated into a paper that was
recently published in Science of the Total Environment (Balistrieri et al. 2012)
Determination of α and β values
The unknowns are the weighting coefficients (αi) for the toxicants and three logistic
parameters (β1, β2, β3). Their values are determined by minimizing the absolute difference
between observed and predicted fractional mortality or growth retardation (F) for the data sets
using SOLVER in Excel. Toxicity data from single (if available) as well as multiple metal
solutions were included in the fit to each data set, except for Index 8 where the metal mixture
data were evaluated. We could not fit the single and multiple metal data together from Index 8,
although a fit could be obtained to each sub-index (HS6 and HS7).
Our initial hypotheses were that values of αi are intrinsic to the metal, not the organism
whereas the logistic parameters are specific to the organism. Thus, there should be a single set
of αi values for all project datasets and logistic parameters should vary among the datasets. A
sequential approach was taken in determining the weighting coefficients. Index 6 was used to
20
Farley et al.: Comparison of Four Modeling Approaches, File SI-3:21
determine αH, αCd, αPb, and αZn and the logistic parameters for that dataset. Then, those αi values
were used in Index 4 to determine αCu and the logistic parameters for that dataset. The value for
αNi was determined from Index 7 as well as the logistic parameters for that dataset. Finally, the
determined set of αi values was used to evaluate logistic parameters for Index 1, 5, 8, and 9. The
results indicate that there is a consistent set of αi values across the datasets, except for Index 5
where αCd is 1 order of magnitude lower than αCd for the other datasets (Table 3). The weighting
coefficient for hydrogen is insignificant, and the logistic parameters depend on the organism of
interest.
21
Farley et al.: Comparison of Four Modeling Approaches, File SI-3:22
Table 3. Fitting parameters (i.e., weighting coefficients (α) and logistic constants (β values) ) for Tox versus biological response, the Pearson correlation
coefficient (r) for predicted and observed biological response, the number (n) of samples included in each fit, and calculated values for Tox at 20 (Tox20) and
50 (Tox50) % biological response for the project data sets.
Index 1-Hyalella
Index 1-Mussel
Index 4-D. magna
Index 5-D. pulex
Index 6-trout
Index 7-algae
Index 8-algae-HS6
Index 8-algae-HS7
Index 8-algae
combined Index 7 & 8
Index 9-lettuce
aH
set to 0
set to 0
set to 0
set to 0
0.00
set to 0
set to 0
set to 0
set to 0
set to 0
set to 0
aCd
1.91
1.91
1.91
0.19
1.91
1.91
0.09
0.12
1.91
1.91
aCu
4.78
4.78
4.78
aNi
7.23
7.23
4.78
0.31
0.62
4.78
4.78
4.78
7.23
22.84
5.89
7.23
7.23
aPb
3.47
3.47
3.47
3.47
3.47
3.47
aZn
3.03
3.03
3.03
3.03
3.03
3.03
0.55
12.70
3.03
3.03
3.03
b1
10.00
1.28
6.59
4.82
7.28
5.45
3.26
4.56
1.01
2.37
0.00
22
b2
7.12
3.00
9.09
5.19
5.99
4.71
3.63
2.24
1.89
1.62
7.70
b3
3.88
1.01
1.03
1.97
2.84
2.74
0.83
3.26
1.57
4.28
0.34
Pearson r
0.725
0.947
0.841
0.604
0.806
0.916
0.911
0.953
0.873
0.876
0.923
n
62
40
561
101
356
33
57
57
12
46
122
Tox20
0.049
0.131
0.134
0.106
0.068
0.077
0.041
0.015
0.144
0.106
0.248
Tox50
0.067
0.378
0.190
0.173
0.100
0.128
0.107
0.040
0.597
0.410
0.572
Notes
constrained b1
constrained b2
data set used to fix a for Cu
data set used to fix a for Cd, Pb, Zn
data set used to fix a for Ni
mixtures only
Index 8 mixtures + Index 7
Farley et al.: Comparison of Four Modeling Approaches, File SI-3:23
Key Concepts of Our Modeling Approach
Several key concepts of our approach will be illustrated with a synthetic binary metal
(Cd, Zn) data set resembling Index 6. This exercise was done to gain insight into model results
while minimizing the variability of the dose-response relationships observed in many of the
project data sets. Two hundred samples, representing the range of dissolved Cd and Zn
concentrations in Index 6, were generated for waters with the major ion and DOC composition of
the South Fork Coeur d’Alene River (series 146). These samples were run through our modeling
approach using the weighting coefficients for Cd and Zn and logistic parameters for trout
determined from fitting the single and multiple metal data (i.e., loads and Tox) in the Index 6
project dataset. Single metal and binary metal mixtures were considered in the synthetic dataset
as well as competition and no competition of multiple toxicants at the biotic ligand.
The first comparison examines competition of multiple toxicants at the biotic ligand. The
loading of metal on the biotic ligand in the non-competitive case exceeds the competitive case at
fractional loadings greater than ~0.1, but only by a small amount (maximum ratio of total
toxicant load in the non-competitive to competitive cases = 1.17 at total fractional loads of 0.31
and dissolved concentrations of 22 and 3100 µg/L Cd and Zn, respectively) (Figure 7a). As
indicated by the bubble size, Cd and Zn equally contribute to the total metal load at the largest
metal loads, which is consistent with optimal conditions for competition between the metals at
the biotic ligand. In addition, mortality increases with increasing metal loads (Figure 7b). The
implication is that competition among multiple toxicants at the biotic ligand can occur, but only
at large metal loads and when toxicants equally or nearly equally contribute to that load.
However, mortality of all organisms also occurs at these large metal loads.
The specific speciation and total metal load on the biotic ligand, which are determined by
solution composition and affinity of metals for biotic ligands (i.e., KBL-metal), appear to be
important factors in determining differences in biological response between single and multiple
metal solutions (Figure 8). In the synthetic data set, the fractional metal load at 50% mortality of
trout in single metal systems is 4.6 and 3.3% for Cd and Zn, respectively. These values are
analogous to LA50 values in traditional BLMs. The fractional metal load at 50% mortality in the
mixtures is ~5.9%. This fractional load represents a combination of binding by Cd and Zn, and
is less than the sum of the loads in the individual metal solutions at 50% mortality (7.9%). In
addition, the specific combination of Cd and Zn on the biotic ligand at 50% mortality depends on
the dissolved metal ratios. As the ratio of dissolved Cd to Zn concentration increases, there is
more Cd relative to Zn bound on the biotic ligand (Figure 8b).
The main premise of the Tox approach is that variability in the amount and composition
of complexes with the biotic ligand at a given biological response is incorporated into the Tox
value. Once metal loading on the biotic ligand and weighting coefficients for each metal are
considered, then data for single and multiple metal solutions fall along a single, smooth line; that
is, Tox versus fractional biological response (Figure 9). Alternately, the same Tox value
represents a given biological response (e.g., 50% mortality) whether the solution contains single
or multiple metals. Tox at 50% mortality in the synthetic dataset is ~0.1.
The second characteristic of Tox is that it provides information on the relative importance
of toxicants in metal mixtures to the Tox value. The relative importance of metal toxicants is a
function of their identity (e.g., Cd or Cu in combination with Zn), which influences their affinity
for the biotic ligand and weighting coefficient, and solution composition, including dissolved
23
Farley et al.: Comparison of Four Modeling Approaches, File SI-3:24
metal concentrations and, particularly, the ratio of dissolved metal concentrations (Figure 9).
The synthetic dataset suggests that the relative importance of Cd or Zn to Tox is equal when
dissolved Cd to Zn concentrations ([Cd]/[Zn] in M/M) are ~ 0.003 – 0.004. Below that ratio, Zn
dominates Tox, whereas above that ratio, Cd is the dominant contributor to Tox – although each
metal plays some role in producing water quality conditions over the range of dissolved metal
ratios.
Figure 7. Comparison of total metal load on the biotic ligand considering competition and no competition
between Cd and Zn for the biotic ligand in the synthetic binary metal (Cd, Zn) data set resembling Index 6.
A) The bubble size indicates the relative importance (RI) of [BL-Cd] and [BL-Zn] to total metal load. Inset
shows deviation from 1 to 1 line; i.e., non-competitive case has greater metal load than competitive case.
Competition occurs at large metal loads that are caused by large dissolved metal concentrations, and
when each metal contributes about equally to metal load on the biotic ligand. B) The bubble size indicates
fractional mortality for fractional metal loads < 0.2.
24
Farley et al.: Comparison of Four Modeling Approaches, File SI-3:25
A
B
Figure 8. A) Total metal load on the biotic ligand for single metal (Cd or Zn) and mixtures of Cd and Zn in the
synthetic binary metal (Cd, Zn) data set resembling Index 6. B) Total and relative loads of Cd and Zn for
11 tests at ~50% mortality and associated dissolved Cd to Zn ratios in the synthetic binary metal (Cd, Zn)
data set resembling Index 6
A
B
C
Figure 9. A) Total fractional metal load on the biotic ligand for single metal (Cd or Zn) and mixtures of Cd and
Zn in the synthetic binary metal (Cd, Zn) data set resembling Index 6. B) Tox versus fractional mortality in
the synthetic data set. C) Relative importance of Cd and Zn to Tox as a function of the dissolved Cd to Zn
ratio in the mixtures in the synthetic data set.
25
Farley et al.: Comparison of Four Modeling Approaches, File SI-3:26
Model Fits and Relative Importance of Toxicants in Project Data Sets
With the key concepts in mind, we now examine the project data sets in two
complementary ways. First, a global overview is taken that looks at (1) model fits to all data in
each Index and (2) the relative importance of each toxicant in metal mixtures for each Index.
Second, the focus is on model fits and results for selected paired single and multiple metal series
in Index 4, 6, and 9.
Index 1: Hyalella azteca and fatmucket mussel tested in sediment porewaters
Index 1 contains five potential toxicants (Cd, Cu, Ni, Pb, Zn) in porewater from the TriState Mining District and 28-day survival data for two organisms (Hyalella azteca (amphipod)
and Lampsilis siliquoidea (mussel)] (Ingersoll et al. 2008). Because the solutions contain near
detection levels of dissolved sulfide concentrations and the important role that sulfide plays in
dissolved metal speciation, we spoke with the analyst (Bill Brumbaugh, USGS) on the Tri-State
project. He said that porewater did not smell of sulfide at the time of collection. This is
important because smelling sulfide is a more sensitive method than most analytical methods for
determining total concentrations of dissolved sulfide. Based on this information, we decided not
to include sulfide as a ligand in the solution speciation calculations.
Metal loads on the biotic ligand and Tox are the same for both sets of toxicity data
because these parameters only depend on solution composition, the common set of equilibrium
constants in the multiple-toxicant BLM, and the universal set of α values. The factor that differs
between the Hyalella and mussel data is the biological response of each organism to the metal
loads; i.e., the relationship between Tox and mortality as reflected in the logistic parameters.
The model fit between Tox and biological response for the mussel data is better than the fit to the
Hyalella data (Figure 10a and b), although the Pearson correlation coefficient (r) between
predicted and observed mortalities are above 0.7 (significant at the 0.01 level) for both data sets.
The range in contributions of each toxicant to Tox indicates that Cd, Cu, and Zn are
important, whereas the contributions from Ni and Pb are almost negligible (Figure 10c).
However, no pattern in the relative importance of toxicants is distinguishable in the bubble
graphs for Tox versus mortality (Figure 10a and b). For example, at the two highest Tox values
in the mussel data, either Cd or Zn is the most important contributor to Tox. On the other hand,
the relative importance of Zn and Cd plus Cu to Tox clarifies when the data are plotted versus
the ratio of dissolved molar concentrations of Cd to Zn (Figure 10d). In general, Cd and Zn are
the major players, whereas Cu has a supporting role in producing toxic conditions in the
porewater. The transition from Zn dominance to Cd plus Cu dominance occurs at a dissolved Cd
to Zn ratio of 0.002 to 0.003.
Modeling does not address sub-lethal responses
The Tox50 for these datasets was 0.07 for Hyalella and 0.38 for Lampsilis siliquoidea,
indicating that for the survival endpoint, Hyalella were considerably more sensitive in this study
than were the mussels. However, this conclusion has to be limited to the survival endpoint and
for these particular metal mixture combinations in which Zn and Cd tended to contribute most to
toxicity. We did not attempt to model sub-lethal responses because of time constraints, although
sub-lethal endpoints were available from this study for both the amphipod and mussel (length,
dry weight/individual, and total biomass) (Ingersoll et al. 2008). This is important because sublethal responses of mussels to metals begin to occur at lower concentrations than survival, and
26
Farley et al.: Comparison of Four Modeling Approaches, File SI-3:27
the relative differences between lethal and sub-lethal responses may be greater with mussels than
for amphipods. Also, mussels appear to be more sensitive to Cu than to other metals, relative to
other species (Ingersoll et al. 1998; Wang et al. 2010; Wang et al. 2011).
Figure 10. Model results for Index 1.
A) Tox versus fractional mortality for Hyalella aztca. B) Tox versus fractional mortality for mussel. C)
Relative importance of each toxicant to Tox (term = (ametal*fmetal)/Tox). D) Relative importance of Zn versus
Cd plus Cu to Tox as a function of the dissolved Cd to Zn ratio in the data set.
27
Farley et al.: Comparison of Four Modeling Approaches, File SI-3:28
Index 4: Daphnia magna with Cd, Cu, and Zn
Index 4 contains acute toxicity data for Daphnia magna in laboratory studies of paired
single (Cd, Cu, Zn) and binary (Cu plus Cd or Zn) metal exposures. All tests were conducted in
reconstituted moderately-hard water with hardness ranging from 72-103 mg/L, and with either
ambient DOC concentrations of about 0.3 mg/L or with about 3.0 mg/L DOC, added as
Suwannee River fulvic acid (Meyer et al. 2011).
Tox versus fractional mortality data were fit for the entire dataset; only the mixture data
are presented in the figures (Figure 11). The Pearson correlation coefficient (r = 0.84, n = 561)
between predicted and observed mortalities is significant at the 0.01 level, although there is large
variability in the dose-response relationship for this data set when all data rather than individual
series are examined.
This data set clearly illustrates that biological response may be the same despite
differences in the speciation of the biotic ligand. For example, at 20% mortality, there are tests
where Cd, Cu, or Zn is the primary metal contributing to Tox (Figure 11a). Similar observations
are apparent at other mortality levels.
When the relative importance of each toxicant in the binary mixtures is plotted versus the
dissolved metal ratio, the relative importance of the metals to toxicity is equal (i.e., each
contributes 50%) when [Cu]/[Cd] = 20-30 and [Cu]/[Zn] = 0.04-0.05 (Figure 11b and c). Cd or
Zn is the primary contributor to Tox for metal ratios below those values, whereas Cu is the most
important toxicant at ratios above those values.
28
Farley et al.: Comparison of Four Modeling Approaches, File SI-3:29
Figure 11. Model results for Index 4.
A) Tox versus fractional mortality for Daphnia magna in binary metal mixtures (Cu+Cd or Cu+Zn). B)
Relative importance of Cu versus Cd to Tox as a function of the dissolved Cu to Cd ratio in the data set.
C) Relative importance of Cu versus Zn to Tox as a function of the dissolved Cu to Zn ratio in the data set.
Index 4: Focus
We selected several concurrent test series to more closely examine the responses of
Daphnia magna to Cu, Cd, and Zn, and our BLM-Tox model behavior. The test series shown
were selected to contrast different responses occurring from different combinations of the same
metals, and that each had a good mix of partial responses in both the individual and mixture
exposures. We also include some illustrations of the classic concentration-addition, toxic unit
approach (Sprague 1970) to evaluating mixture toxicity in contrast with the BLM-Tox modeling
approach in Appendix 3.
29
Farley et al.: Comparison of Four Modeling Approaches, File SI-3:30
The comparisons are illustrated in a series of figures that all follow the same format. The
top rows show metal concentrations in water overlain by the observed mortalities and mortalities
predicted by our BLM-Tox model; the middle rows show cumulative metals loading on the
biotic ligand as a fraction of total binding sites, overlain by observed and predicted mortalities,
and the bottom rows show the Tox values with observed and predicted mortalities. Error bars
show response ranges across replicates (Figure 12).
The apparent exposure strategy in Index 4 was to first determine the expected Cd, Cu,
and Zn concentrations that would likely result in partial toxicity in a series of single metals tests.
Then concurrent single and binary Cu+Cd and Cu+Zn mixture toxicity tests were conducted
where one metal was held constant at a concentration expected to cause partial kills, and the
second metal was “titrated” into it using geometrically increasing concentrations in the usual
manner.
Copper and cadmium - In test series Cu-Cd#12, Cd was titrated into a constant 40 µg/L
Cu solution (Figure 12). For a given load or Tox value, the Cd+Cu mixtures were more toxic
than individual metals. The BLM-Tox model predictions were mostly similar to observations
except “Mix2” where effects were under-predicted. EC50s in the concurrent single metal test
were estimated to be about 6.8 and 77µg/L for Cd and Zn, respectively, with DOC
concentrations of about 2.8 mg/L.
In Series Cu-Cd #16, #17, and #19, the above dosing regime was reversed with Cu
titrated into constant Cd concentrations of about 5, 9, and 14 µg/L, respectively (Figures 13, 14,
15). In contrast to series Cu-Cd#12 in which Cd was added to Cu, mortality tended to decline
with increasing Cu concentrations in series Cu-Cd#17 for a given load or Tox value to a point
and then increased in the highest treatment. The observed Cu responses were consistent in these
three series, but Cd responses were more variable. The BLM-Tox model predicted Cu toxicity
well for the most part, whereas mortality due to Cd was either under- or over-predicted because
of the drift in the apparent sensitivity of the Daphnia magna to Cd in series Cu-Cd#17 as
compared to Cu-Cd#12. EC50 values in the Cu-Cd#16 Cd and Cu tests were about 4.8 and 99
µg/L, respectively; EC50 values in Cu-Cd#17 were about 15 µg/L Cd and 119 µg/L Cu; and
EC50 values for the Cu-Cd#19 Cd and Cu tests were about 8.1 and 116 µg/L, respectively. DOC
concentrations were about 3.4 mg/L in all three series.
The most striking result of test series Cu-Cd #’s 16,17, and 19 is that addition of Cu to a
baseline Cd concentration was expected to cause moderate to severe mortality (5, 9, or 15 µg/L
Cd), but observations indicated that mortalities tended to decline. While responses in individual
tests could be highly variable, the three series taken together provide persuasive evidence of
reduced Cd mortality with Cu additions. While not illustrated here, responses from three
additional series in which Cu was added to higher Cd baseline concentrations (11-27 µg/L Cd)
generally supported this interpretation. These reductions in toxicity were not predicted by our
BLM-Tox model or by the sum of metal loading on the biotic ligand. Poor predictions of
reductions in mortality occur despite the fact that our BLM loading model includes direct
competition between Cu and Cd for binding sites on the biotic ligand. Thus, we cannot attribute
the apparent reductions in Cd toxicity from Cu additions by direct competition between Cu and
Cd for binding sites on the biotic ligand. This is treated in more detail in the section,
Competition of multiple toxicants at the biotic ligand. While our present evaluations do not
necessarily suggest an alternative explanation, it is intriguing that Komjarova and Blust (2008)
measured decreased Cu uptake in Daphnia magna when Cd was present. They also noted that
these negative interactions could not be explained exclusively by direct competition for the
30
Farley et al.: Comparison of Four Modeling Approaches, File SI-3:31
binding sites on the cell membrane, although they did not explain how this was deduced.
Because uptake rates are sometimes associated with differences in sensitivity to metals toxicity
(Niyogi and Wood 2004a; Niyogi and Wood 2004b), examining links between metal uptake rates
and biological response seems like a useful line of further inquiry.
Copper and zinc – Two Cu and Zn exposure scenarios are considered in detail. First, Cu
was titrated into solutions with constant Zn concentrations (Cu-Zn #3, Figure 16), and second,
Zn was titrated into solutions with constant Cu concentrations (Cu-Zn #7, Figure 17). In series
Cu-Zn #3, Cu toxicity and toxicity of the Cu-Zn mixtures were predicted well by the BLM-Tox
model. Zn toxicity was substantially under-predicted (Figure 16). For a given metal load or Tox
value, Cu+Zn mixtures tended to have slightly higher mortalities than Cu alone. Sensitivity of
Daphnia magna to Cu in series Cu-Zn #3 was similar to that in the Cu-Cd series discussed
earlier, with an EC50 value of about 116 µg/L in water with DOC concentrations of about 3.0
mg/L. The Zn EC50 value was about 490 µg/L.
In the Cu-Zn test series #7, observed mortalities for Daphnia magna tended to be more
severe in the mixtures than for similar metal loads or Tox values in the single metal tests (Figure
17). Mortalities were substantially under-predicted for all mixture tests, and for exposures at low
Cu concentrations. Zn toxicity was predicted accurately at the 50% mortality level, but was
under-predicted at lower exposures. The Cu EC50 was about 14 µg/L and the Zn EC50 was
about 930 µg/L. The low Cu EC50 cannot be easily compared with other Cu tests because DOC
was only about 0.3 mg/L in this test series, and the other Cu tests conducted at low DOC were
not ideal for estimating EC50s because of control mortalities or limited partial kills.
31
Farley et al.: Comparison of Four Modeling Approaches, File SI-3:32
A. Concentrations of metals in water and predicted and observed mortalities
100
300
1.0
90
90
250
80
Cd
Cd
(µg/L)
(µg/L)
Cd (µg/L)
Cu (µg/L)
Predicted mortality
Observed mortality
100
0.8
70
60
0.6
150
1.0
200
80
0.8
70
150
60
100
90
0.8
70
200
50
80
1.0
200
0.6
150
60
0.6
50
50
100
100
40
0.4
100
30
20
40
0.4
10
50
20
0.2
0.0
0
Cd 1
Cd 2
Cd 3
Cd 4
Cd 5
Cd 6
0
0
Cu 1
Cd treatments
20
50
0.2
0
0.0
10
10
0
Cu 2
Cu 3
Cu 4
Cu 5
0.0
0
Cu 6
Mix 1
Mix 2
Mix 3
Mix 4
Mix 5
Mix 6
Cd + 40 µg/L Cu
Cu treatments
B. Accumulation of metals on biotic ligands and predicted and observed mortalities
0.7
1.0
0.6
0.8
0.5
BLMetal
BLTotal
0.14
0.12
0.10
0.6
0.4
0.3
0.4
0.2
1.0
BL-Cu/BLtot
BL-Cd/BLtot
Predicted mortality
Observed mortality
0.0
0.8
0.5
0.6
0.4
0.6
0.3
0.4
0.08
0.4
0.06
0.0
0.00
0.2
0.1
0.0
0.0
Mix 1 Mix 2 Mix 3 Mix 4 Mix 5 Mix 6
Cu 1 Cu 2 Cu 3 Cu 4 Cu 5 Cu 6
Cd treatments
Mortality
0.2
0.2
0.02
Cd 1 Cd 2 Cd 3 Cd 4 Cd 5 Cd 6
1.0
0.8
0.04
0.0
0.7
0.6
0.2
0.1
Cd + 40 µg/L Cu
Cu treatments
C. TOX values and predicted and observed mortalities
1.2
1.0
1.1
1.0
1.0
0.8
0.9
0.8
0.9
0.8
0.6
0.7
0.6
TOX
1.2
1.1
0.5
0.4
0.4
TOX fm Cu
TOX fm Cd
Predicted mortality
Observed mortality
1.0
0.8
0.2
0.2
0.5
0.5
0.4
0.0
Cd 1 Cd 2 Cd 3 Cd 4 Cd 5 Cd 6
Cd treatments
0.6
0.7
0.6
Mortality
0.4
0.4
0.3
0.3
0.2
0.2
0.2
0.1
0.1
0.0
0.8
0.9
0.6
0.2
0.1
1.0
1.1
0.8
0.6
0.7
1.2
1.0
0.4
0.3
Mortality
0.4
30
30
0.2
50
40
Cu
(µg/L)
0.0
0.0
Cu 1 Cu 2 Cu 3 Cu 4 Cu 5 Cu 6
Cu treatments
0.0
0.0
Mix 1 Mix 2 Mix 3 Mix 4 Mix 5 Mix 6
Cd + 40 µg/L Cu
Figure 12. D. magna mortalities following exposures to Cd + constant Cu (Index 4, series Cu-Cd #12).
In this mixture series Cd was titrated into 40 µg/L Cu solution. Error bars show response ranges across replicates.
32
Farley et al.: Comparison of Four Modeling Approaches, File SI-3:33
A. Concentrations of metals in water and predicted and observed mortalities
120
300
1.0
Cd (µg/L)
Cu (µg/L)
Predicted mortality
Observed mortality
16
100
14
250
14
0.8
12
1.0
200
0.8
12
150
150
200
10
0.6
Cd
(µg/L) 8
1.0
200
14
0.8
12
16
150
10
0.6
10
0.6
8
8
100
100
0.4
6
100
4
0.2
50
2
0.4
6
4
50
4
0.2
0.0
0
Cd 1
Cd 2
Cd 3
Cd 4
Cd 5
Cd 6
Mortality
0.4
50
0.2
0
0.0
2
2
0
6
Cu
(µg/L)
0
0
Cu 1
Cu 2
Cu 3
Cd
Cu 4
Cu 5
0.0
0
Cu 6
Mix 1
Mix 2
Mix 3
Mix 4
Mix 5
Mix 6
Cu + 5 µg/L Cd
Cu
B. Accumulation of metals on biotic ligands and predicted and observed mortalities
0.6
0.5
1.0
0.12
0.8
0.12
0.10
0.10
BLMetal
BLTotal
0.14
0.6
0.08
0.06
0.4
0.04
1.0
BL-Cu/BLtot
BL-Cd/BLtot
Predicted mortality
Observed mortality
0.8
0.6
0.08
0.4
0.06
0.2
0.02
0.0
Cd 1 Cd 2 Cd 3 Cd 4 Cd 5 Cd 6
0.0
0.00
0.6
0.08
Mortality
0.4
0.06
0.2
0.02
0.0
0.00
Mix 1 Mix 2 Mix 3 Mix 4 Mix 5 Mix 6
Cu 1 Cu 2 Cu 3 Cu 4 Cu 5 Cu 6
Cd
0.8
0.04
0.04
0.00
0.12
0.10
0.2
0.02
1.0
0.14
Cu + 5 µg/L Cd
Cu
C. TOX values and predicted and observed mortalities
1.2
0.5
1.0
0.8
0.4
0.8
0.3
0.6
0.3
0.6
0.4
0.2
0.4
0.2
0.4
0.2
0.1
0.2
0.1
0.2
0.0
0.0
1.0
0.5
0.8
0.4
0.6
1.0
0.4
TOX fm Cu
TOX fm Cd
Predicted mortality
Observed mortality
1.0
0.3
Mortality
TOX
0.2
0.1
0.0
0.0
Cd 1 Cd 2 Cd 3 Cd 4 Cd 5 Cd 6
Cd
Figure 13.
0.0
Cu 1 Cu 2 Cu 3 Cu 4 Cu 5 Cu 6
Cu
0.0
Mix 1 Mix 2 Mix 3 Mix 4 Mix 5 Mix 6
Cu + 5 µg/L Cd
D. magna mortalities following exposures to Cd and Cu, where Cu was titrated into constant 5 µg/L Cd (Index 4, series Cu-Cd #16).
33
Farley et al.: Comparison of Four Modeling Approaches, File SI-3:34
A. Concentrations of metals in water and predicted and observed mortalities
16
300
14
1.0
Cd (µg/L)
Cu (µg/L)
Predicted mortality
Observed mortality
16
14
250
0.8
12
1.0
200
0.8
12
150
150
200
Cd 10
(µg/L) 8
1.0
200
14
0.8
12
16
0.6
150
10
0.6
10
0.6
8
8
100
100
0.4
6
100
4
0.2
50
2
0.4
6
4
50
4
0.2
0.0
0
Cd 1
Cd 2
Cd 3
Cd 4
Cd 5
Cd 6
0
0
Cu 1
Cd treatments
Mortality
0.4
50
0.2
0
0.0
2
2
0
6
Cu
(µg/L)
Cu 2
Cu 3
Cu 4
Cu 5
0.0
0
Cu 6
Mix 1
Mix 2
Mix 3
Mix 4
Mix 5
Mix 6
Cu + 9 µg/L Cd
Cu treatments
B. Accumulation of metals on biotic ligands and predicted and observed mortalities
1.0
0.14
0.12
0.8
0.12
0.10
0.10
0.6
BLMetal
BLTotal
0.14
0.08
0.4
0.06
1.0
BL-Cu/BLtot
BL-Cd/BLtot
Predicted mortality
Observed mortality
0.8
0.6
0.08
0.4
0.06
0.2
0.02
0.0
0.00
Cd 1 Cd 2 Cd 3 Cd 4 Cd 5 Cd 6
0.0
0.00
0.6
0.08
Mortality
0.4
0.06
0.2
0.02
0.0
0.00
Mix 1 Mix 2 Mix 3 Mix 4 Mix 5 Mix 6
Cu 1 Cu 2 Cu 3 Cu 4 Cu 5 Cu 6
Cd treatments
0.8
0.04
0.2
0.02
0.12
0.10
0.04
0.04
1.0
0.14
Cu + 9 µg/L Cd
Cu treatments
C. TOX values and predicted and observed mortalities
TOX
0.5
1.0
0.8
0.4
0.8
0.3
0.6
0.3
0.6
0.4
0.2
0.4
0.2
0.4
0.2
0.1
0.2
0.1
0.2
0.0
0.0
0.5
1.0
0.5
0.4
0.8
0.4
0.3
0.6
0.2
0.1
TOX fm Cu
TOX fm Cd
Predicted mortality
Observed mortality
1.0
Mortality
0.0
0.0
Cd 1 Cd 2 Cd 3 Cd 4 Cd 5 Cd 6
Cd treatments
0.0
Cu 1 Cu 2 Cu 3 Cu 4 Cu 5 Cu 6
Cu treatments
0.0
Mix 1 Mix 2 Mix 3 Mix 4 Mix 5 Mix 6
Cu + 9 µg/L Cd
Figure 14. D. magna mortalities following exposures to Cd and Cu, where Cu was titrated into constant 9 µg/L Cd.
For a given load or Tox value, observed mortality tended to decline with increasing Cu concentrations in the mixture, to a point. The BLM-Tox model predicted
Cu toxicity very well but over-predicted mortality in Cd solutions and in the mixtures. Data from Index 4, test series Cu-Cd #17 with water hardness about 80
mg/L and DOC about 3.4 mg/L.
34
Farley et al.: Comparison of Four Modeling Approaches, File SI-3:35
A. Concentrations of metals in water and predicted and observed mortalities
130
300
120
250
20
200
15
150
1.0
14
0.8
Cd
(µg/L)
Cd (µg/L)
Cu (µg/L)
Predicted mortality
Observed mortality
16
1.0
200
1.0
200
14
0.8
12
16
0.8
12
150
150
0.6
10
0.6
10
0.6
8
8
100
100
0.4
10
100
5
50
0.2
0.4
6
4
50
4
0.2
0.0
0
Cd 1
Cd 2
Cd 3
Cd 4
Cd 5
Cd 6
0
0
Cu 1
Cd treatments
Mortality
0.4
50
0.2
0
0.0
2
2
0
6
Cu
(µg/L)
Cu 2
Cu 3
Cu 4
Cu 5
0.0
0
Cu 6
Mix 1
Mix 2
Mix 3
Mix 4
Mix 5
Mix 6
Cu + 13 µg/L Cd
Cu treatments
B. Accumulation of metals on biotic ligands and predicted and observed mortalities
0.20
0.7
1.0
0.6
0.8
BLMetal
BLTotal
0.15
0.16
BL-Cu/BLtot
BL-Cd/BLtot
Predicted mortality
Observed mortality
1.0
0.20
1.0
0.8
0.16
0.8
0.6
0.12
0.6
0.12
0.6
0.4
0.08
0.4
0.08
0.4
0.2
0.04
0.2
0.04
0.2
0.0
0.00
Mortality
0.10
0.05
0.0
0.00
Cd 1 Cd 2 Cd 3 Cd 4 Cd 5 Cd 6
0.00
Cd treatments
0.0
Mix 1 Mix 2 Mix 3 Mix 4 Mix 5 Mix 6
Cu 1 Cu 2 Cu 3 Cu 4 Cu 5 Cu 6
Cu + 13 µg/L Cd
Cu treatments
C. TOX values and predicted and observed mortalities
1.2
1.0
1.1
0.7
0.6
0.8
1.0
0.5
0.25
0.6
TOX fm Cu
TOX fm Cd
Predicted mortality
Observed mortality
1.0
0.7
1.0
0.6
0.8
0.8
0.5
0.4
0.6
0.3
0.4
0.4
0.6
0.3
0.4
Mortality
0.20
TOX
0.4
0.15
0.2
0.2
0.10
0.2
0.0
0.00
Cd 1 Cd 2 Cd 3 Cd 4 Cd 5 Cd 6
Cd treatments
0.2
0.2
0.1
0.1
0.05
0.0
0.0
Cu 1 Cu 2 Cu 3 Cu 4 Cu 5 Cu 6
Cu treatments
0.0
0.0
Mix 1 Mix 2 Mix 3 Mix 4 Mix 5 Mix 6
Cu + 13 µg/L Cd
Figure 15. D. magna mortalities following exposures to Cd and Cu, individually and in mixtures, similar to the previous example (i.e., Cu-Cd #17).
Mortalities were highly variable in some tests, but again a pattern of declining mortalities was seen when Cu was added to the base Cd concentration, that by
itself was highly toxic. The BLM-Tox model predicted mortality well in the single metals exposures but predicted the toxicity of the mixture to progressively
increase. Data from Index 4, test series Cu-Cd #19 with water hardness about 80 mg/L and DOC about 3.4 mg/L.
35
Farley et al.: Comparison of Four Modeling Approaches, File SI-3:36
A. Concentrations of metals in water and predicted and observed mortalities
Zn (µg/L)
Cu (µg/L)
Predicted mortality (fraction)
Observed mortality (fraction)
1000
900
250
1000
1000
1.0
200
800
0.8
200
800
600
150
100
150
300
0.6
50
0.2
100
0.4
50
0
Zn 1
Zn 2
Zn 3
Zn 4
Zn 5
0.0
0.4
50
0.2
200
600
0
Cu 1
Cu 2
Zn treatments
Cu 3
Cu 4
Cu 5
0
0.0
Cu 6
150
400
200
100
0
Zn 6
1.0
0.8
Cu
(µg/L)
0.6
Mortality
100
0.4
50
0.2
0
0.0
300
200
0.2
100
0
100
800
300
200
100
0.6
500
400
300
200
150
500
400
0.4
250
700
600
500
400
1000
900
0.8
700
600
0.6
500
1.0
200
0.8
700
700
250
900
900
800
Zn
(µg/L)
250
1.0
100
Mix 1
Mix 2
Mix 3
Mix 4
Mix 5
Mix 6
0.0
0
0
Cu treatments
Mix 1
Mix 2
Mix 3
Mix 4
Mix 5
Mix 6
Cu + 330 µg/L Zn
Cu + 216 µg/L Zn
B. Accumulation of metals on biotic ligands and predicted and observed mortalities
0.20
0.16
BLMetal
BLTotal
Predicted mortality
Observed mortality
BL-Cu/BLtot
BL-Zn/BLtot
0.20
1.0
0.20
1.0
0.20
1.0
0.16
0.8
0.16
0.8
0.16
0.8
1.0
0.8
0.12
0.6
0.12
0.6
0.12
0.6
0.12
0.6
0.08
0.4
0.08
0.4
0.08
0.4
0.08
0.4
0.04
0.2
0.04
0.2
0.04
0.2
0.04
0.2
0.0
0.00
0.0
0.00
Mortality
0.0
0.00
Zn 1 Zn 2 Zn 3 Zn 4 Zn 5 Zn 6
0.00
Zn treatments
Cu + 330 µg/L Zn
Cu + 216 µg/L Zn
Cu treatments
0.0
Mix 1 Mix 2 Mix 3 Mix 4 Mix 5 Mix 6
Mix 1 Mix 2 Mix 3 Mix 4 Mix 5 Mix 6
Cu 1 Cu 2 Cu 3 Cu 4 Cu 5 Cu 6
C. TOX values and predicted and observed mortalities
1.0
0.9
0.8
Predicted mortality
Observed mortality
TOX fm Cu
TOX fm Zn
1.0
0.8
0.6
0.5
0.8
0.8
0.8
0.4
0.3
0.6
0.2
0.1
0.4
0.0
Zn 1 Zn 2 Zn 3 Zn 4 Zn 5 Zn 6
Zn treatments
0.4
0.3
0.2
0.2
0.1
0.0
0.0
0.0
Cu 1 Cu 2 Cu 3 Cu 4 Cu 5 Cu 6
Mix 1 Mix 2 Mix 3 Mix 4 Mix 5 Mix 6
Cu treatments
0.8
0.6
0.6
Mortality
0.4
0.4
0.3
0.2
0.2
0.0
0.8
0.5
0.4
0.1
0.0
0.6
0.5
0.4
1.0
0.9
0.7
0.6
0.6
0.3
0.2
0.8
0.7
0.5
0.4
1.0
0.9
0.7
0.6
1.0
1.0
1.0
0.9
0.7
TOX
1.0
Cu + 216 µg/L Zn
0.2
0.2
0.1
0.0
0.0
Mix 1 Mix 2 Mix 3 Mix 4 Mix 5 Mix 6
Cu + 330 µg/L Zn
Figure 16. D. magna mortalities following exposures to Zn and Cu, with copper titrated onto two fixed Zn exposures.
For both Cu+Zn mixture scenarios, mortalities occurring at a given load or TOX value tended to be greater than for similar loads or Tox values in single Cu
exposures. The BLM-Tox model substantially under-predicted mortality in Zn solutions, but did very well with the Cu solutions and Cu+Zn mixtures. Data from
Index 4, test series Cu-Zn #3.
36
Farley et al.: Comparison of Four Modeling Approaches, File SI-3:37
A. Concentrations of metals in water and predicted and observed mortalities
Zn (µg/L)
Cu (µg/L)
Predicted mortality (fraction)
Observed mortality (fraction)
1000
250
1000
1000
1.0
200
800
0.8
80
800
600
150
100
60
300
0.6
50
0.2
40
0.4
20
0
Zn 1
Zn 2
Zn 3
Zn 4
Zn 5
0.0
0.6
100
0.4
50
0.2
0
0.0
600
0
Cu 1
Cu 2
Zn treatments
Cu 3
Cu 4
Cu 5
0
0.0
Cu 6
150
400
200
100
0
Zn 6
1.0
200
0.8
Cu
(µg/L)
0.6
Mortality
100
0.4
50
0.2
0
0.0
300
200
0.2
100
0
150
300
200
100
800
500
400
300
200
250
900
500
400
0.4
1000
0.8
700
600
500
400
1.0
700
600
0.6
500
200
0.8
700
700
250
900
900
800
Zn
(µg/L)
100
1.0
900
100
Mix 1
Mix 2
Mix 3
Mix 4
Mix 5
Mix 6
0
Mix 2
Mix 3
Mix 4
Mix 5
Mix 6
Zn + 21 µg/L Cu
Zn + 14 µg/L Cu
Cu treatments
Mix 1
B. Accumulation of metals on biotic ligands and predicted and observed mortalities
Predicted mortality
Observed mortality
0.20
BLMetal
BLTotal
Predicted mortality
Observed mortality
BL-Cu/BLtot
BL-Zn/BLtot
0.20
1.0
0.20
1.0
0.20
1.0
0.16
0.8
0.16
0.8
0.16
0.8
1.0
0.16
0.8
0.12
0.6
0.12
0.6
0.12
0.6
0.12
0.6
0.08
0.4
0.08
0.4
0.08
0.4
0.08
0.4
0.04
0.2
0.04
0.2
0.04
0.2
0.04
0.2
0.0
0.00
0.0
0.00
Mortality
0.0
0.00
Zn 1 Zn 2 Zn 3 Zn 4 Zn 5 Zn 6
0.00
Zn treatments
0.0
Mix 1 Mix 2 Mix 3 Mix 4 Mix 5 Mix 6
Mix 1 Mix 2 Mix 3 Mix 4 Mix 5 Mix 6
Cu 1 Cu 2 Cu 3 Cu 4 Cu 5 Cu 6
Zn + 21 µg/L Cu
Zn + 14 µg/L Cu
Cu treatments
C. TOX values and predicted and observed mortalities
1.0
0.9
0.8
Predicted mortality
Observed mortality
TOX fm Cu
TOX fm Zn
1.0
0.8
0.6
0.5
0.8
0.8
0.8
0.4
0.3
0.6
0.1
0.4
0.0
Zn 1 Zn 2 Zn 3 Zn 4 Zn 5 Zn 6
Zn treatments
0.4
0.2
0.2
0.1
0.0
0.0
0.0
Mix 1 Mix 2 Mix 3 Mix 4 Mix 5 Mix 6
Cu treatments
0.6
0.6
Mortality
0.4
0.4
0.2
0.2
0.1
0.0
Cu 1 Cu 2 Cu 3 Cu 4 Cu 5 Cu 6
0.8
0.3
0.3
0.2
0.2
0.8
0.5
0.4
0.1
0.0
0.6
0.5
0.4
1.0
0.9
0.7
0.6
0.6
0.3
0.2
0.2
0.8
0.7
0.5
0.4
1.0
0.9
0.7
0.6
1.0
1.0
1.0
0.9
0.7
TOX
1.0
Zn + 14 µg/L Cu
0.0
0.0
Mix 1 Mix 2 Mix 3 Mix 4 Mix 5 Mix 6
Zn + 21 µg/L Cu
Figure 17. D. magna mortalities following exposures to Zn titrated into constant Cu concentrations.
Predicted mortalities tended to be more severe in the mixtures than for similar concentrations, loads or Tox values in the single metals tests. In marked contrast
to an earlier series where titrating Cu into Cd tended to reduce mortalities (tests Cu-Cd#17 and #19). Data from Index 4, test series Cu-Zn #7 with water
hardness about 90 mg/L and DOC about 0.3 mg/L.
37
Farley et al.: Comparison of Four Modeling Approaches, File SI-3:38
Index 5: Daphnia pulex with Cd and Zn
Index 5 contains survival data for Daphnia pulex in laboratory studies of paired single
metal and metal mixtures containing As, Cd, and Zn. The dataset included both results from tests
published by Shaw et al (2006) as well as additional, unpublished data. Solution water
chemistries were not measured, but were estimated from the recipe for the growth medium used
(i.e., Kilham et al. 1998). We only considered Cd and Zn data in our modeling efforts and
estimated detection levels of dissolved metal (0.1 and 10 µg/L for Cd and Zn, respectively) for
tests with zero metal concentrations. The compositions are nominal, and we suspect that the
estimates for dissolved Cd concentrations maybe too large.
All single and multiple metal tests were included in the Tox versus mortality fit, but only
data for the mixtures are presented in the figures (Figure 18). The Pearson correlation
coefficient between predicted and observed mortalities is 0.60 (n = 101), which is significant at
the 0.01 level.
These experiments were done for a range of dissolved Cd to Zn concentrations where Cd
is the major contributor to Tox. By including estimates for detection level metals in the no metal
tests, the relative importance of the metals to Tox is equal at an estimated ratio of 0.02 to 0.03 for
dissolved Cd to Zn concentrations.
Figure 18. Model results for Index 5.
A) Tox versus fractional mortality for Daphnia pulex in binary metal mixtures (Cd+Zn). B) Relative
importance of Cd versus Zn to Tox as a function of the dissolved Cd to Zn ratio in the data set.
38
Farley et al.: Comparison of Four Modeling Approaches, File SI-3:39
Index 6: Cutthroat and Rainbow Trout with Cd, Pb, and Zn
Index 6 examines the toxicity of Cd, Pb, and Zn to cutthroat and rainbow trout in spiked and
ambient dilutions of natural waters from the Coeur d’Alene River basin (Mebane et al. 2012).
There are paired single and metal mixture toxicity tests.
Figure 19. Model results for Index 6.
A) Tox versus fractional mortality for rainbow and cutthroat trout for tests with multiple metals. B) Relative
importance of each toxicant to Tox (term = (ametal*fmetal)/Tox). C) Relative importance of Cd versus Zn plus
Pb to Tox as a function of the dissolved Cd to Zn ratio in the data set.
39
Farley et al.: Comparison of Four Modeling Approaches, File SI-3:40
All single metal and mixture data were fit, but only data from the mixtures is presented in
the figures (Figure 19). The Pearson correlation coefficient between predicted and observed
mortalities is 0.81 (n = 356), which is significant at the 0.01 level.
Each of the metals was a major contributor to Tox in several or many tests, although the
primary contributors were Cd and Zn. The relative importance of Cd and Pb plus Zn is equal at
[Cd]/[Zn] (M/M) = 0.003-0.004. Many test solutions had metal ratios where the relative
importance of Cd and Zn (plus Pb) to Tox is about equal.
Index 6: Focus
The model fits for four series of matched single metal and metal mixtures were examined
in detail. In these series, the tests were conducted in test waters with matched chemistries, and
the tests were either concurrent or nearly so. The evaluations of tests that were not concurrent
were constrained to those conducted within two weeks of each other and fish sizes, which can
influence sensitivity, were nearly identical
Series #1 Four tests with rainbow trout with varying Zn concentrations were conducted,
in which Cd, Pb, or Cd+Pb were added at nearly constant concentrations that were expected to be
about half of their EC50s (Figure 20). Half of the EC50 value was expected to be a
concentration close to the thresholds for the onset of mortalities. Index 6’s “Series #1”, consisted
of tests #125, 136-138, using 0.66g fish with water hardness about 65 mg/L and DOC about 0.6
mg/L (Mebane et al. 2012).
For a given total metal load on the biotic ligand or a given Tox value, the Zn+Cd, Zn+Pb,
or Zn+Cd+Pb mixtures all had fewer mortalities than Zn alone (Figure 20). The BLM-Tox
model under-predicted Zn mortality, predicted Zn+Pb well, and over-predicted Zn toxicity when
Cd was present. BLM-Tox did not predict the observed reduced toxicity of mixtures (Figure
20).
Series #2 – Cutthroat trout were tested with Pb and Zn, individually and in a constant
ratio exposure (Figure 21). “Series 2” tests were conducted in very soft water, total hardness
about 12 mg/L as CaCO3 and DOC was about 0.2 mg/L (Tests 89, 128, 139, Index 6). Trout
mortalities were predicted well by BLM-Tox across all tests. Mortality at a given Tox value
appears roughly similar whether Tox was made up of a single metal or a Pb+Zn mixture.
Series #3 – Rainbow trout were exposed to Cd, Zn, and a constant ratio Cd+Zn mixture
(Figure 22). BLM-Tox predicted mortalities very well across the range of Zn exposures, but
severely under-predicted one Cd treatment (30% mortality predicted, 80% observed). In the
mixtures, predicted mortalities tracked the general pattern of observed mortality, but consistently
over-predicted mortalities. For a given Tox value or biotic ligand load, mortalities were more
severe in the single metals exposures than in the mixtures. For example, a Tox value of about
0.08 in the Cd exposure corresponded with 80% mortalities, Tox of about 0.08 in the Zn
exposure corresponded with 40% mortalities, and Tox of about 0.08 in the Cd+Zn mixture
corresponded with 5% mortalities (Figure 22 C).
Series #4 – Rainbow trout were exposed to two mixtures of Cd, Pb, and Zn that targeted
the U.S. EPA’s aquatic life acute criteria values (“EPA”) and a set of prospective site-specific
criteria (Mebane et al. 2012). Single metals tests were also conducted (Figure 23). Although the
criteria were presumed to be “safe” from an individual metal view, metal combinations killed
53% and 96% of the trout. Tox tended to under-predict both Cd and Zn toxicity, but predicted
the mixture toxicity well. In Index 4, Series 4, a given Tox value was associated with higher
40
Farley et al.: Comparison of Four Modeling Approaches, File SI-3:41
mortalities in single metal exposures than in a mixture. A cumulative Tox value of about 0.08
was associated with 80% mortality in the Cd only test, 93% mortality in the Zn only test, but
only 53% in the Cd+Pb+Zn test (Figure 23).
41
Farley et al.: Comparison of Four Modeling Approaches, File SI-3:42
A. Concentrations of metals in water and predicted and observed mortalities
500
500
1.0
2.0
400
2.0
0.8
0.8
300
0.6
200
0.4
100
0.2
0
0.0
0.5
0.5
Zn 1
Zn3
Zn 2
Zn 4
0.0
Mix 2
Mix 1
Mix 4
Mix 3
100
0.2
0
0.0
0.8
1.0
400
0.8
1.5
0.6
1.0
300
1.0
200
0.4
200
100
0.2 0.5
100
0
0.0 0.0
0.5
0.0
Mix 2
Mix 1
Zn + 0.7 µg/L Cd
Zn exposures
500
2.0
300
1.0
0.4
1.0
1.5
0.6
200
500
400
1.5
300
1.0
0.0
1.0
2.0
400
1.5
Cd
(µg/L)
Cd (µg/L)
Zn (µg/L)
Pb (µg/L)
Predicted mortality (fraction)
Observed mortality (fraction)
Mix 3
Mix 4
Zn + 120 µg/L Pb
Mix 2
Mix 1
Mix 3
0.6
Zn
or Pb
(µg/L)
Mortality
0.4
0.2
0.0
0
Mix 4
Zn + 0.7 µg/L Cd + 120 µg/L
B. Accumulation of metals on biotic ligands and predicted and observed mortalities
BL-Pb/BLtot
BL-Cd/BLtot
BL-Zn/BLtot
Predicted mortality
Observed mortality
0.14
0.14
1.0
0.12
0.14
1.0
0.12
0.8
0.10
BLMetal
BLTotal
0.14
0.12
0.8
0.6
0.06
0.4
0.10
0.6
0.08
0.06
0.4
0.06
0.02
0.02
0.0
0.00
Zn 1
Zn3
Zn 2
0.00
Zn 4
0.4
0.00
Mix 4
Mix 3
Zn + 0.7 µg/L Cd
Zn
0.6
0.06
0.4
Mortality
0.04
0.2
0.0
Mix 2
0.08
0.2
0.02
0.0
0.00
0.02
Mix 1
0.8
0.04
0.2
0.2
1.0
0.6
0.08
0.04
0.04
0.10
0.8
0.10
0.08
0.12
1.0
Mix 1
Mix 2
Mix 3
Mix 4
0.0
Mix 1
Mix 2
Mix 3
Mix 4
Zn + 0.7 µg/L Cd + 120 µg/L
Zn + 120 µg/L Pb
C. TOX values and predicted and observed mortalities
0.30
0.30
0.4
0.10
0.05
0.00
Zn 1
Zn 2
Zn3
Zn 4
0.05
0.0
0.00
0.2
0.10
Mix 3
0.2
0.05
0.0
Mix 2
Mortality
0.4
0.4
0.10
Mix 1
0.6
0.15
0.4
0.10
0.2
0.8
0.6
0.15
0.15
0.15
1.0
0.20
0.6
0.6
TOX
0.8
0.20
0.20
TOX fm Pb
TOX fm Cd
TOX fm Zn
Predicted mortality
Observed mortality
0.30
0.25
0.8
0.8
0.20
1.0
0.25
0.25
0.25
0.30
1.0
1.0
0.00
Mix 4
0.0
Mix 1
Mix 2
Mix 3
Zn + 120 µg/L Pb
Zn + 0.7 µg/L Cd
Mix 4
0.2
0.05
0.00
0.0
Mix 1
Mix 2
Mix 3
Mix 4
Zn + 0.7 µg/L Cd + 120 µg/L
Figure 20. Rainbow trout mortalities with varying Zn, with Cd and or Pb nearly constant at about half their expected EC50s (Index 6, “Series 1).
Metals mixtures containing zinc were consistently less toxic than were similar zinc concentrations singly. BLM-Tox predicted mortality reasonably well, although
the model did not predict the observed reduced toxicity of mixtures. Data from Index 6, mixture “Series #1”, tests 125, 136-138, using 0.66g fish with water
hardness about 65 mg/L and DOC about 0.6 mg/L.
42
Farley et al.: Comparison of Four Modeling Approaches, File SI-3:43
A. Concentrations of metals in water and predicted and observed mortalities
Pb (µg/L)
Zn (µg/L)
Predicted mortality
Observed mortality
200
1.0
200
0.8
150
150
0.8
150
100
100
Pb
(µg/L)
0.6
0.6
100
100
0.6
Zn
(µg/L)
100
0.4
0.4
50
0.2
0.2
0.0
0
Pb 1
Pb 2
Pb 3
Pb 4
Pb 5
Pb 6
0
Pb 7
0
Zn 1
Pb exposures
Zn 2
Zn 3
Zn 4
Zn 5
Mortality
0.4
50
50
50
1.0
200
0.8
150
150
1.0
0.0
50
0.2
0
0.0
0
Mix 1
Zn 6
Mix 2
Mix 3
Mix 4
Mix 5
Mix 6
Pb+Zn treatments
Zn treatments
B. Accumulation of metals on biotic ligands and predicted and observed mortalities
0.14
0.14
1.0
0.12
0.12
0.8
0.10
0.10
BLMetal
BLTotal
0.6
0.08
0.06
1.0
BL-Zn/BLtot
BL-Pb/BLtot
Predicted mortality
Observed mortality
0.8
0.6
0.4
0.2
0.02
0.0
0.00
0.0
0.00
Pb 1 Pb 2 Pb 3 Pb 4 Pb 5 Pb 6 Pb 7
0.08
0.6
0.06
0.4
0.2
0.02
0.0
0.00
Mix 1 Mix 2 Mix 3 Mix 4 Mix 5 Mix 6
Zn 1 Zn 2 Zn 3 Zn 4 Zn 5 Zn 6
Pb exposures
Mortality
0.04
0.04
0.2
0.02
0.8
0.10
0.06
0.04
1.0
0.12
0.08
0.4
0.14
Pb + Zn treatments
Zn treatments
C. TOX values and predicted and observed mortalities
0.30
1.0
0.25
0.8
0.20
0.30
0.25
0.20
TOX fm Zn
TOX fm Pb
Predicted mortality
Observed mortality
0.6
0.15
1.0
0.20
0.10
0.2
0.05
0.0
Pb 1 Pb 2 Pb 3 Pb 4 Pb 5 Pb 6 Pb 7
Pb exposures
Mortality
0.4
0.4
0.2
0.00
0.6
0.15
0.10
0.05
0.8
0.8
0.6
0.4
0.10
1.0
0.25
0.15
TOX
0.30
0.0
0.00
Zn 1 Zn 2 Zn 3 Zn 4 Zn 5 Zn 6
Zn treatments
0.2
0.05
0.0
0.00
Mix 1 Mix 2 Mix 3 Mix 4 Mix 5
Cd+Zn treatments
Figure 21. Cutthroat trout mortalities with Pb and Zn in mixtures where both increased proportionally (Index 6, Series 2.)
The BLM-Tox model predicted both single metal and mixture exposures very well. Data from Index 6, "Series 2", tests 89, 128, and 139, using 0.3g fish with
water hardness about 12 mg/L and DOC about 0.2 mg/L.
43
Farley et al.: Comparison of Four Modeling Approaches, File SI-3:44
A. Concentrations of metals in water and predicted and observed mortalities
300
Cd (µg/L)
Zn (µg/L)
Predicted mortality
Observed mortality
1.0
2.0
2.0
250
0.8
1.5
Cd
(µg/L)
300
0.8
0.2
50
0.0
0
Cd 3
Cd 4
0.6
150
1.0
0.4
0.5
50
0.0
Cd 5
0
Zn 1
Zn 2
Cd treatments
Zn3
Zn 4
Zn
(µg/L)
Mortality
0.4
100
100
0.5
Cd 2
200
0.6
0.4
Cd 1
0.8
1.5
150
1.0
100
0.0
250
200
0.6
150
1.0
1.0
2.0
1.5
200
300
1.0
250
0.2
0.0
0.5
50
0.0
0.0
0
Mix 1
Zn 5
Mix 2
Mix 3
Mix 4
0.2
Mix 5
Cd+Zn treatments
Zn treatments
B. Accumulation of metals on biotic ligands and predicted and observed mortalities
0.14
0.14
1.0
0.12
0.12
0.8
0.10
BLMetal
BLTotal
0.08
0.6
0.06
0.4
0.10
1.0
BL-Zn/BLtot
BL-Cd/BLtot
Predicted mortality
Observed mortality
0.8
0.08
0.6
0.06
0.4
0.0
Cd 1
Cd 2
Cd 3
Cd 4
Cd 5
0.08
0.6
0.06
0.4
Mortality
0.04
0.2
0.02
0.00
0.8
0.10
0.2
0.02
1.0
0.12
0.04
0.04
0.14
0.0
0.00
Zn 1
Cd treatments
Zn 2
Zn3
Zn 4
0.2
0.02
0.0
0.00
Cd 1
Zn 5
Cd 2
Cd 3
Cd 4
Cd 5
Cd + Zn treatments
Zn treatments
C. TOX values and predicted and observed mortalities
0.30
1.0
0.25
0.8
0.20
0.30
0.25
0.20
1.0
TOX fm Zn
TOX fm Cd
Predicted mortality
Observed mortality
0.20
0.10
0.2
0.05
0.0
Cd 1
Cd 2
Cd 3
Cd 4
Cd treatments
Cd 5
0.4
0.4
0.10
0.00
Mortality
0.15
0.2
0.05
0.6
0.6
0.4
0.10
0.8
0.8
0.15
TOX
1.0
0.25
0.6
0.15
0.30
0.0
0.00
Zn 1
Zn 2
Zn3
Zn 4
Zn treatments
Zn 5
0.2
0.05
0.0
0.00
Mix 1 Mix 2 Mix 3 Mix 4 Mix 5
Cd+Zn treatments
Figure 22. Rainbow trout mortalities with Cd and Zn in mixtures where both increased proportionally (Index 6, "Series 3“)
For a given load or Tox value, the Cd+Zn mixtures were consistently less toxic than single metals exposures. BLM-Tox predicted Zn mortalities very closely, but
under-predicted mortality in Cd solutions and over-predicted mortality in mixtures. Data from Index 6, "Series 3", tests 14, 105, and 150.
44
Farley et al.: Comparison of Four Modeling Approaches, File SI-3:45
A. Concentrations of metals in water and predicted and observed mortalities
300
300
1.0
2.0
2.0
250
0.8
0.8
1.5
200
0.2
0.0
Cd 1
Cd 2
Cd 3
Cd 4
Cd 5
0.0
0
250
50
Zn 1
Zn 2
Zn3
Zn 4
Zn 5
0
200
0.6
0.6
150
1.0
0.4
0.5
50
0.0
0.0
Pb 1
Pb 2
Zn
Cd
0.8
1.5
100
0.2
1.0
250
150
0.4
0.5
300
0.8
1.0
100
0.0
1.0
2.0
0.6
0.4
50
300
200
150
1.0
100
0.5
1.5
200
0.6
150
1.0
1.0
2.0
250
1.5
Cd (µg/L)
Zn (µg/L)
Pb (µg/L)
Predicted mortality (fraction)
Observed mortality (fraction)
Pb 3
Pb 4
Pb 5
0
100
0.2
Zn
or Pb
(µg/L)
0.5
50
0.0
0.0
Control
Pb
EPA
0
SSC
Mortality
0.4
0.2
0.0
Cd+Pb+Zn
B. Accumulation of metals on biotic ligands and predicted and observed mortalities
BLMetal
BLTotal
0.20
1.0
0.20
1.0
0.20
0.16
0.8
0.16
0.8
0.16
Predicted mortality
Observed mortality
0.20
1.0
0.16
0.8
0.6
0.12
0.6
0.08
0.4
0.04
0.2
1.0
0.8
BL-Cd/BLtot
BL-Pb/BLtot
BL-Zn/BLtot
0.12
0.6
0.12
0.6
0.12
0.08
0.4
0.08
0.4
0.08
0.4
0.04
0.2
0.04
0.2
0.04
0.2
0.00
0.0
0.00
0.0
0.00
0.0
Cd 1
Cd 2
Cd 3
Cd 4
Cd 5
Zn 1
Cd
Zn 2
Zn3
Zn 4
Mortality
Zn 5
Pb 1
Pb 2
Pb 3
Pb 4
0.00
Pb
Zn
0.0
Control
EPA
SSC
Cd+Pb+Zn
C. TOX values and predicted and observed mortalities
0.30
0.20
1.0
0.25
0.16
0.20
1.0
0.16
0.8
0.6
0.12
0.6
0.08
0.4
0.08
0.4
0.04
0.2
0.04
0.2
0.0
0.00
0.20
1.0
Predicted mortality
Observed mortality
TOX fm Zn
TOX fm Pb
TOX fm Cd
0.8
0.16
0.8
0.20
0.6
0.12
0.6
0.12
0.15
0.4
0.08
0.4
0.10
0.04
0.2
0.05
0.0
0.00
0.00
Cd 1
Cd 2
Cd 3
Cd
Cd 4
Cd 5
0.2
0.0
Zn 1
Zn 2
Zn3
Zn 4
0.00
Zn 5
Zn
Pb 1
Pb 2
Pb 3
Pb
Pb 4
Pb 5
1.0
0.8
Mortality
0.0
Control
EPA
SSC
Cd+Pb+Zn
Figure 23. Rainbow trout mortalities with Cd, Pb, or Zn in mixtures targeting USEPA Aquatic Life Criteria (EPA) or prospective site-specific criteria (SSC)
(Index 6, "Series 4“). Toxicity tended to be under-predicted in individual Cd and Zn exposures, and accurately predicted in the mixtures. For a given load or Tox
value, the toxicity of the Cd+Pb+Zn mixtures were roughly similar to the sum of single metals exposures. Index 6, "Series 4", is tests 14, 60, 109, 131, and 132.
45
Farley et al.: Comparison of Four Modeling Approaches, File SI-3:46
Index 7: Green algae with Cd, Cu, Ni, Pb, and Zn, using field collected water
Index 7 examines the effects of metals (As, Cd, Cu, Ni, Pb, Zn) on the growth rate of
Pseudokirchneriella subcapitata (freshwater green algae) in field samples (Bass et al. 2008).
Our multiple-toxicant BLM does not include As and, therefore, we did not include As in our
modeling efforts.
The model fit is very good with a Pearson correlation coefficient between predicted and
observed growth retardation of 0.92 (n = 33); although fractional growth retardation above 20%
is only observed for six samples (Figure 24a). Of those tests, the dominant contributor to Tox
includes both Cd and Zn.
The relative importance of Cd, Cu, and Zn to Tox is greater than the contributions from
Ni and Pb (> 70% versus < 15%) within the data set (Figure 24b). The critical [Cd]/[Zn] ratio
where the contributions of Zn and Cd plus Cu are equal is 0.002-0.003. Cd is generally more
important than Cu in contributing to Tox (Figure 24c).
46
Farley et al.: Comparison of Four Modeling Approaches, File SI-3:47
A
B
C
Figure 24. Model results for Index 7.
A) Tox versus fractional growth retardation for algae in field samples. B) Relative importance of each
toxicant to Tox (term = (ametal*fmetal)/Tox). C) Relative importance of Zn versus Cd plus Cu to Tox as a
function of the dissolved Cd to Zn ratio in the data set.
Index 8: Green algae with Cd, Cu, Ni, Zn, laboratory waters
Index 8 examines the effects of metals (Cd, Cu, Ni, Zn) on the growth rate of
Pseudokirchneriella subcapitata (freshwater green algae) (Bass et al. 2008). Two of the more
pristine water samples (HS6 and HS7) with different pH (5.5 and 8.4) and hardness (5.8 and 95
mg/L CaCO3) from the field study of Index 7 were spiked with increasing concentrations of
single metals and metal mixtures.
47
Farley et al.: Comparison of Four Modeling Approaches, File SI-3:48
Following our modeling approach, values of α determined from Indexes 4, 6 and 7 were
used to model all of the data in Index 8. Some of the data in each set of tests could be reasonably
fit, but data for other metals did not collapse into a good relationship between Tox and fractional
growth retardation (Figure 25a and b). It was possible to get good fits (Pearson correlation
coefficients > 0.9, n = 57) by adjusting all α and β values and modeling each water type
separately (Figure 25c and d; Table 3), but that approach does not provide a global or universal
set of α values or is consistent with our modeling scheme. In addition, values of α for Ni and Zn
for the individual fits greatly varied between the two data sets (i.e., αNi = 23 or 5.9, αZn = 0.55 or
13 for HS6 and HS7, respectively).
The mixture data in Index 8 were fit separately from the single metal data using the
universal set of α values, and this fit resulted in a reasonable correlation between predicted and
observed growth retardation (r = 0.87, r = 12) (Figure 26a). Because the waters and algae in
Index 8 came from field samples in Index 7, the fit from all mixture data for tests in Index 7 and
8 also was examined. The data for HS7 (dominated by Cu) versus HS6 (dominated by Cd) is a
better fit with the Index 7 mixtures, although a good correlation is observed for all of the
combined data sets (r = 0.88, n = 46) (Figure 26a) .
Ranges in the relative importance of each toxicant to Tox in the Index 8 mixture data
indicate the dominance of Cd and Cu over Pb, Ni, and Zn (Figure 26b). Although the plot of the
relative importance of Cd compared with the sum of Cu, Ni, and Zn to Tox as a function of
dissolved Cu to Cd ratios is not as good as other data sets, it does suggest that their relative
importance to Tox is equal for dissolved metal ratios of about 10-20 (Figure 26c). The
difference in dominance among the metals to Tox between Index 7 and 8 is due to manipulation
of metal concentrations and ratios in Index 8.
48
Farley et al.: Comparison of Four Modeling Approaches, File SI-3:49
A
B
C
aCd =
aCu =
aNi =
aPb =
aZn =
D
global
1.9
4.8
7.2
3.5
3
HS6
0.08
0.31
23
--0.55
HS7
0.12
0.62
5.9
--13
Figure 25. Model results for Index 8.
Tox versus fractional growth retardation for algae in spiked field sample HS6 (A) or HS7 (B) using global
set of α values. Tox versus fractional growth retardation for algae in field sample HS7 (C) or HS7 (D)
using best fit α values.
49
Farley et al.: Comparison of Four Modeling Approaches, File SI-3:50
A
B
C
Figure 26. Model results for Index 8 with comparison to Index 7.
A) Tox versus fractional growth inhibition for algae from Index 7 and for algae in Index 8 only for tests with
spiked multiple metals. B) Relative importance of each toxicant to Tox (term = (ametal*fmetal)/Tox) for Index
8. C) Relative importance of Cd versus Cu+Ni+Zn to Tox as a function of the dissolved Cu to Cd ratio in
Index 8.
Index 9: Lettuce with Cu and Zn in hydroponic exposures
Index 9 examines the toxicity of Ag, Cu, and Zn to root growth in lettuce (Lactuca
sativa) in hydroponic experiments (Le et al. 2013). Because our BLM does not include Ag, we
only fit the Cu and Zn data. Metal data were given as free ion activities, and WHAM 7
calculated the total dissolved concentrations in equilibrium with those free ion activities. Total
dissolved concentrations of Cu and Zn were very large in these experiments with maximum
concentrations of 48 mg/L Cu and 1 g/L Zn. Thermodynamic calculations indicate super
saturation with metal hydroxide and metal carbonate phases in some solutions. However,
precipitation of these phases was not considered in the model fits.
The entire data set was used to obtain the fit, but only the mixture data are presented in
the figures. The model fit of Tox versus fractional growth retardation is very good with a
50
Farley et al.: Comparison of Four Modeling Approaches, File SI-3:51
Pearson correlation coefficient of 0.92 (n = 122) (Figure 27a). Both Cu and Zn can dominate the
Tox term at a given biological response.
The relative importance of Cu or Zn to Tox ranges from near zero to 100% (Figure 27b).
The dissolved Cu to Zn ratio where the relative importance of Cu and Zn to Tox is equal is about
0.08.
Index 9: Focus
Index 9’s Cu and Zn tests with lettuce included an exposure design where the plants were
grown in solutions in which Zn was titrated into a baseline Cu concentration. This scheme was
repeated several times with increasing Cu concentrations. Two of these mixture exposures,
together with the single metal exposures, are examined in Figure 28. Both single metal and
mixture exposures were mostly predicted reasonably well by BLM-Tox. One exception is the
Zn+1000 µg/L Cu mixture exposure in which the predicted response is 10% baseline inhibition,
but about 40% was observed.
One quirk of how these data were reported is important for interpreting these results. The
control exposures have about a 20% “inhibition” prior to the addition of any metals. This
baseline occurs because rather than reporting % inhibition as a reduction in growth from
controls, % inhibition was calculated and reported as a reduction from the highest growth
measured in any exposure in the experiment, which happened to be a low Cu exposure (the
single point with a fractional growth reduction of 0, Figure 27A). Whether this was a hormetic
response because control plants were truly Cu or Zn deficient or just variability is probably not
important for the data interpretation here. However, the fact that about a 20% “inhibition”
equates to “no toxic effect” should be kept in mind.
51
Farley et al.: Comparison of Four Modeling Approaches, File SI-3:52
Figure 27. Model results for Index 9.
A) Tox versus fractional growth retardation for lettuce in binary metal mixtures (Cu+Zn). B) Relative importance of Cu versus Zn to Tox as a function of the dissolved
Cu to Zn ratio in the data set.
52
Farley et al.: Comparison of Four Modeling Approaches, File SI-3:53
A. Concentrations of metals in water and predicted and observed mortalities
Zn (µg/L)
Cu (µg/L)
Predicted inhibition (fraction)
Observed inhibition (fraction)
1,000,000
100,000
1,000,000
100,000
10,000
1.0
1,000,000
100,000
100,000
100,000
10,000
0.8
1,000
1,000
100
1,000
10
10
0.2
10
1
1
0.0
1
Zn1 Zn2 Zn3 Zn4 Zn5 Zn6 Zn7 Zn8 Zn9 Zn10 Zn11
0.8
0.6
0.4
10
0.2
10
Cu1
Cu2
Zn treatments
Cu3
Cu4
Cu5
Cu6
Cu7
1
0.0
1
Cu8
1.0
10,000
0.8
1,000
0.6
Cu
(µg/L) Inhibition
1,000
100
100
100
100,000
100,000
1,000
0.4
1,000,000
10,000
0.6
1,000
100
1.0
10,000
0.6
1,000
10,000
0.8
10,000
10,000
100,000
1.0
0.4
100
0.4
10
0.2
1
0.0
100
100
Mix1 Mix2 Mix3 Mix4 Mix5 Mix6 Mix7
10
0.2
10
1
0.0
1
Cu treatments
Mix1 Mix2 Mix3 Mix4 Mix5 Mix6 Mix7
Zn + 1000 g/L Cu
Zn + 500 g/L Cu
B. Accumulation of metals on biotic ligands and predicted and observed mortalities
Predicted inhibition
Observed inhibition
1.0
BLMetal
BLTotal
Predicted inhibition
Observed inhibition
BL-Cu/BLtot
BL-Zn/BLtot
1.0
1.0
1.0
1.0
1.0
1.0
0.8
0.8
0.8
0.8
0.8
0.8
1.0
0.8
0.8
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.0
0.0
0.0
0.0
Inhibition
0.0
0.0
Zn1 Zn2 Zn3 Zn4 Zn5 Zn6 Zn7 Zn8 Zn9 Zn10Zn11
0.0
Cu1
Zn treatments
Cu2
Cu3
Cu4
Cu5
Cu6
Cu7
Predicted inhibition
Observed inhibition
TOX fm Cu
TOX fm Zn
2.5
2.0
TOX
1.0
3.0
1.0
3.0
1.0
0.8
2.5
0.8
2.5
0.8
0.6
1.5
2.0
0.6
1.5
0.0
Zn1 Zn2 Zn3 Zn4 Zn5 Zn6 Zn7 Zn8 Zn9 Zn10Zn11
Zn treatments
0.0
Cu1 Cu2 Cu3 Cu4 Cu5 Cu6 Cu7 Cu8
0.6
Inhibition
0.4
1.0
0.2
0.2
0.5
0.0
0.0
Mix1 Mix2 Mix3 Mix4 Mix5 Mix6 Mix7
Zn + 500 g/L Cu
Cu treatments
0.8
0.4
0.5
0.0
2.5
1.5
0.2
0.5
1.0
0.6
1.0
0.2
0.0
2.0
0.4
1.0
3.0
2.0
1.5
0.4
1.0
0.5
Zn + 1000 g/L Cu
Zn + 500 g/L Cu
Cu treatments
C. TOX values and predicted and observed mortalities
3.0
0.0
Mix1 Mix2 Mix3 Mix4 Mix5 Mix6 Mix7
Mix1 Mix2 Mix3 Mix4 Mix5 Mix6 Mix7
Cu8
0.0
0.0
Mix1Mix2Mix3Mix4Mix5Mix6Mix7
Zn + 1000 g/L Cu
Figure 28. Growth inhibition in lettuce following hydroponic exposures to Zn and Cu.
These tests targeted very large exposure concentrations, although Zn concentrations were unmeasured and thus actual exposures are uncertain, especially at
implausibly high (g/L) concentrations. Nevertheless, the BLM-Tox model tended to do well predicting the growth inhibition of roots.
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Farley et al.: Comparison of Four Modeling Approaches, File SI-3:54
Competition of multiple toxicants at the biotic ligand
The total amount of toxicant bound by the biotic ligand potentially can be less if
competition among multiple toxicants (e.g., Cd and Zn) at the biotic ligand is included in
speciation calculations. The effects of competition on total metal loads can be evaluated by
using our common set of equilibrium constants that define interactions of all cations (non-toxic
as well as toxic) at a single type of biotic ligand. For non-competitive cases, metal loading is
determined by adding the loads calculated by considering that each dissolved metal in a mixture
is present as a single metal. Both competitive and non-competitive biotic ligand speciation
calculations were run for mixtures in Index 4, 6, and 9.
The ratio of non-competitive to competitive total metal load for the Cu plus Cd mixtures
in Index 4 ranged from 1.00 to 1.16, whereas the same ratio for the Cu plus Zn mixtures in Index
4 varied from 1.00 to 1.07. The relatively low ratios suggest that competition among the
toxicants for the biotic ligand in these mixtures is not that important; i.e., there is little difference
in loads between competitive and non-competitive cases for many samples. The bubble graphs
for the mixtures in Index 4 illustrate the relative importance of each metal to the total metal load
in the competitive case (Figure 29a and b), and indicate that a single metal (Cd for the Cu plus
Cd mixture and Cu for the Cu plus Zn mixtures) dominates the total metal load at the larger
loads. For these tests, dissolved concentrations of Cd (or Cu) exceed that of Cu (or Zn).
Because the load is comprised basically of one metal at larger loads, little competition is
expected or observed.
The picture changes for Index 6 (Figure 29c). The ratio of metal loads (sum of Cd, Pb,
and Zn) in the non-competitive to competitive cases ranges from 1.00 to 1.51. The bubble graph
for this index indicates that competition is important when Cd and Zn contribute equally to total
metal load at larger loads. Many of the tests in this Index were near the ratio of dissolved Cd to
Zn concentrations where Cd and Zn equally contribute to total metal loads and Tox (Figure 19 in
Index 6 discussion).
Likewise, the speciation calculations for Index 9 also suggest competition (Figure 29d).
The ratio of total metal load for the non-competitive to competitive cases in the mixtures ranges
from 1.00 to 1.27. At the larger metal loads, the tests that deviate from the 1 to 1 line are those
where Cu and Zn contribute more equally to the total metal load.
Metal loads on the biotic ligand for the competitive and non-competitive cases also can
be examined in terms of mortality or growth retardation (Figure 30). In this figure, the bubble
size represents the observed fractional biological response. Competition among multiple
toxicants occurs at total metal loads that typically result in very adverse biological impacts
(100% mortality or growth retardation).
This analysis suggests that competition among multiple toxicants for the biotic ligand can
be important at larger metal loads, which occur at larger dissolved metal concentrations, and
when multiple toxicants contribute nearly equally to the total metal load on the biotic ligand.
Many of the tests in the project data set were run at elevated dissolved concentrations of multiple
metals that result in large metal loads and competition on the biotic ligand. However, these
conditions also result in adverse impacts to biota and may not be realistic for most natural
environments.
54
Farley et al.: Comparison of Four Modeling Approaches, File SI-3:55
B.
A.
C.
D.
Figure 29. Comparison of total metal load on the biotic ligand considering competition and no competition,
using actual data from Indexes 4, 6, and 9.
Competition occurs at large metal loads that are caused by large dissolved metal concentrations. The
bubble size represents the relative importance (RI) of a metal to the total metal load.
55
Farley et al.: Comparison of Four Modeling Approaches, File SI-3:56
Figure 30. The fraction of total biotic ligand sites occupied by metal for the competitive and non-competitive
cases for Index 4, 6, and 9.
The bubbles represent fractional mortality or growth retardation and vary from 0 to 1. The inset for Index 6
is for fractional biotic ligand loads < 0.2.
Tox50
The model fits for each data set can be used to determine values of Tox at any level of
biological response (F) (Scholze et al. 2001) The equation is:
𝑇𝑜𝑥 = 10
−ln(𝐾)−𝛽1
(
)
𝛽2
where K = (1/F)1/β3 -1. Values of Tox at 50% biological response (Tox50) were determined
using the logistic parameters for each type of organism in the project data sets (Table 3). The
56
Farley et al.: Comparison of Four Modeling Approaches, File SI-3:57
results of this analysis provide information on the relative sensitivities of the studied organisms.
Values of Tox50 indicate that the most sensitive organism is Hyalella followed by trout, daphnia
and mussel with intermediate sensitivity, whereas algae and lettuce are the least sensitive (Figure
31). This comparison is to illustrate the utility of using Tox in a manner analogous to EC10s and
EC50s, and is not true comparison of the inherent sensitivity of the organisms to metals toxicity.
The datasets modeled are mostly short-term exposures, and for the longer term response data for
Hyalella and mussel we did not attempt to include sub-lethal responses in our modeling (see
Modeling focused on lethal responses).
less
sensitive
more
sensitive
Figure 31.
Tox at 50% mortality or growth retardation (Tox50) for organisms in the project data sets.
Dissolved metal ratios
Dissolved metal ratios play a key role in determining the relative loading of the biotic
ligand by multiple toxicants. This loading is incorporated into Tox along with weighting
coefficients, and then an evaluation is made of the relative importance of toxicants in metal
mixtures. Ratios of dissolved Cu to Cd, Cu to Zn, and Cd to Zn where the relative importance of
toxicants in binary mixtures or one toxicant to the sum of other toxicants in multiple metal
mixtures is equal are summarized in Table 4 for the project data sets. Although this set of
57
Farley et al.: Comparison of Four Modeling Approaches, File SI-3:58
combined results is small and Index 5 is an exception, it appears that the relative importance of
toxicants is equal at critical dissolved molar metal ratios, which are [Cu]/[Cd] ~20, [Cu]/[Zn]
~0.06, and [Cd]/[Zn] ~ 0.003. At values greater than these ratios, the metal in the numerator
(and its less dominant associates) are the dominant contributors to Tox, whereas at values less
than the ratios, the metal in the denominator (and its less dominant associates) are the dominant
contributors to Tox.
Table 4. Summary of the values of dissolved metal ratios where the relative importance of toxicants to Tox
is equal in the project data sets.
[Cu]/[Cd] [Cu]/[Zn]
[Cd]/[Zn]
(M/M)
(M/M)
(M/M)
Index 4 20 - 30
Index 8 10 - 20
Index 4
0.04 - 0.05
Index 9
0.08
Index 1
0.002 - 0.003
Index 5
0.02 - 0.03
Index 6
0.003 - 0.004
Index 7
0.002 - 0.003
Pre-Workshop Conclusions







The BLM-Tox approach reasonably fit observed biological responses to metal mixtures
using a common set of weighting coefficients and organism-specific logistic parameters.
The composition of the metal load on the biotic ligand in metal mixtures can vary but still
produce the same biological response.
Tox incorporates the effects of solution composition and speciation (in particular,
identities and total dissolved concentrations of toxicants); affinities of toxicants for the
biotic ligand (KBL-metal); and weighting coefficients for toxicants into a single parameter.
Values of Tox do not depend on the type of organism, but rather the response of an
organism is related to Tox with increasing values of Tox producing more adverse
responses.
Organisms have different sensitivities to Tox.
Tox provides an evaluation of the relative importance of toxicants in a mixture. That
importance depends on the ratio of dissolved metal concentrations in the mixture.
The relative importance of toxicants in binary or multiple metal mixtures appears to be
equal at unique dissolved metal ratios
The set of equilibrium constants for cation interactions with the biotic ligand as well as α
and β values are not unique. For example, the LC50 data for Ni could be fit equally well by two
different sets of constants describing Ni-biotic ligand interactions, which is similar to the
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Farley et al.: Comparison of Four Modeling Approaches, File SI-3:59
modeling results of Kozlova et al. (2009). An alternate set of weighting coefficients and logistic
parameters also were obtained, but those values appear to be consistent as a set.
The BLM-Tox approach predicts that increasing loads of single or multiple toxicants
results in greater adverse impacts to biota. Potential ways to predict decreasing adverse impacts
with increasing loads (as observed in Index 4) using the BLM-Tox approach are to have negative
weighting coefficients, different log K values that result in greater competition of toxicants, or
multiple biotic ligand sites.
The perception that competition plays an important role in metal mixtures is valid, but
only at large dissolved metal concentrations, large loads of toxicants on the biotic ligand, and
dissolved metal ratios that result in nearly equal loading of multiple toxicants.
An equilibrium approach for describing toxicity in metal mixtures probably does not
adequately represent true metal interactions with biota. Biota can regulate their processes or
have feedback mechanisms and kinetics may play an important role in metal uptake (Slaveykova
and Wilkinson 2005; Komjarova and Blust 2009; Chen et al. 2010). However, despite the
complexities and range of organisms in the project datasets, the equilibrium BLM-Tox approach
did fit the data very well.
This modeling project involved bridging the gap between two measurable parameters –
solution composition and biological response. Different model constructs can be developed to
bridge that gap. Presumably, they can provide equally good fits to biological responses.
However, there are no data to validate the intermediate steps – particularly, the amount and
composition of the load of toxicants on the biota. Future work could focus on determining such
information, which (perhaps) can assist in differentiating among approaches for determining
toxicity of metal mixtures.
Post-workshop thoughts regarding modeling metal mixtures
First, we thought the interchange of ideas at the workshop was exceptionally valuable,
and we greatly appreciated the discussions. We grouped some of our thoughts into three general
lessons learned. These in turn lead us to some thoughts for improving our understanding and
modeling of metals mixture toxicity.
1. All of the models presented at the workshop included an approach for predicting metal
accumulation at the biotic ligand, i.e., either applying some form of a “traditional” biotic
ligand model or using humic acid as an analog for biological receptors. Yet there was no
comparison among the models of those predictions, which likely varied both in amount
and composition of metal accumulation. Furthermore, there was no metric to verify that
prediction of accumulation because the data sets for modeling (and data sets, in general)
only contained two measurable parameters – water composition and biological endpoints
(survival or growth). However, there are a few data sets in the literature that report
accumulation of metal on fish gills. We recognize that these measurements may be
difficult to interpret; in particular, separating background and metal accumulated above
background concentrations, comparing stable and radio-labeled metal accumulations.
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Farley et al.: Comparison of Four Modeling Approaches, File SI-3:60
Similarly, correlations between predictions of accumulation at the biotic ligand and
measurements from field collected invertebrates could be informative. These too have
complications, since field collections reflect indefinite metals exposures and measured
residues are influenced by homeostasis mechanisms and diet in addition to the water
composition. Nevertheless, it seems that more consideration of accumulation data as an
intermediate metric could provide some sense whether model predictions are reasonable.
2. Several of the supplied data sets had series where the metal mixtures indicated less than
additive toxicity. Our single site biotic ligand model approach was not able to properly
predict biological endpoints when metal mixtures resulted in less than additive toxicity.
Thus, a model that includes multiple types of biotic ligands may be needed to properly
describe competition of metals and predict less than additive toxicity. The downside of
including multiple types of biotic ligands with different associated functions (e.g., toxic
versus non-toxic sites of action) is an increase in adjustable model parameters.
3. The third lesson of the workshop is the need to better bridge the gaps among solution
geochemistry, biological function, and toxicity in the modeling approach – although the
extent to which this is accomplished depends on the goal of the model. The scientific
community is good at describing the speciation of many metals in solution, and is making
gains in describing and modeling biological function in certain organisms. These
approaches strive to incorporate our fundamental understanding of chemical and
biological processes into the model. In contrast, models of hardness-based water quality
criteria that are used in the regulatory arena are based on empirical relationships with
limited incorporation of process-understanding. The biotic ligand model is a hybrid. The
BLM assumes that a biological receptor is analogous to another ligand in solution and
that metal accumulation on that biotic ligand directly relates to toxicity. Thus, it uses
basic understanding and models of chemical speciation as well as empirical relationships
between accumulation on that ligand (i.e., LA50) and toxicity (i.e., LC50). Although
biotic ligand models do a reasonably good job of setting water quality criteria, they likely
are poor representations of actual biological function. Again, it is important to define the
goal of the model.
We have explored several avenues since the workshop. First, we initially reconsidered Cd
binding affinity because of difficulty in modeling mixtures containing Cd. In particular, there
were discussions that the stability constants we and others had used for Cd were stronger than
those for Cu, which would not have been expected based on metal-ligand solution binding. This
phenomenon has long been recognized with the differences between metal binding to a living gill
and organic acids attributed to active Ca transport and ionic mimicry in the former (Playle et al.
1993). We briefly explored whether in contrast to using stability constants derived from
empirical fitting to toxicity tests, stability constants correlated with ion characteristics, a covalent
index (Veltman et al. 2010) would provide reasonable accumulations predictions with field
collected invertebrate tissue residues (Fig 45). Second, we considered that the biological
receptor has two types of biotic ligands – one site with limited binding capacity and another site
with larger capacity. Third, we adjusted binding constants for Cd, Pb, and Zn associations with
biotic ligands and the maximum capacities of the two ligand sites to fit accumulation data of
metals on fish gills from the studies of Birceanu et al. (2008) and Todd et al. (2009). During this
fitting, we assumed that the values of binding constants for the formation of H, Na, Ca, and Mg
complexes with biotic ligands were the same for the two types of sites and equivalent to the
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Farley et al.: Comparison of Four Modeling Approaches, File SI-3:61
constants for fish in Veltman et al. (2010). The observations and model fits are presented in
Figures 46-48. The results indicate that the binding constant for Cd on site 1 is larger than on
site 2, whereas the reverse is true for Pb. There is no difference in affinity between the two
binding sites for Zn. And, the capacity of site 2 is about 20 times that of site 1. Next, we reexamined a “less than additive” series from Index 6 using the new log K values, maximum
capacities for the two types of sites, and our BLM-Tox approach. The results are promising
(Figure 49). Future work will fit Cu accumulation data on fish gills, re-visit our modeling of the
fish toxicity data of Nimick et al., (Nimick et al. 2007; Balistrieri et al. 2012) and evaluate
whether this new approach is transferable to other organisms and metal mixtures.
A.
B.
Figure 45. Measured and modeled accumulation of Cd, Cu, and Zn with the mayfly Rhithrogena sp. tissue
residues collected from Colorado, USA streams (Schmidt et al. 2011). At left (A), the WHAM 7
model was used with measured stream water chemistry treating all DOC as fulvic acid and
assuming that invertebrate body burdens can be represented as humic acid (after Stockdale et al.
2010). At right (B), a BLM was used in the same manner as described earlier, except that earlier
we used log KBL-Me constants that were optimized from single metals toxicity test data (Fig. 43).
Here we used Veltman et al.’s (2010) mean KBL-Me constants for fish for Ca, Mg, Na, Cd, Cu, and
Zn. In Veltman et al.’s set of constants, the KBL-Cd constant is intermediate to Cu and Zn, whereas
in our pre-workshop version of a multiple-metals BLM, our KBL-Cd constant was higher than that for
Cu (Table 2).
Both approaches yielded modeled accumulations that were correlated with measured Rhithrogena
values, however the absolute values of modeled loads differed greatly. The WHAM 7 modeled
loads on humic acid were around two orders of magnitude lower than the BLM modeled loads.
The comparison was limited here to Rhithrogena because metals efflux is particularly inefficient for
this genus, making it less capable of regulating metals burdens (Buchwalter et al. 2008). The
correlation between BLM-fractional load predictions and measured Rhithrogena tissue residues
was much stronger using the present approach (R2 = 0.86, pooling the three metals) than that from
our earlier optimization approach (R2 = 0.17, for Rhithrogena results in Figure 43).
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Farley et al.: Comparison of Four Modeling Approaches, File SI-3:62
Figure 46. Model fits using two biotic ligand binding sites
and observed accumulation on rainbow trout
gills following short-term, single-metals
exposures to Pb and Cd. Consistent with
Birceanu et al. (2008) results, we considered
that the biological receptor has two types of
biotic ligands – one site with limited binding
capacity and another site with larger capacity.
We adjusted the Cd and Pb biotic ligand
binding constants and the maximum
capacities of the two ligand sites to fit the
measured metals accumulations on fish gills.
This modeling approach reproduced the
observed patterns of Cd and Pb accumulation
on trout gills well.
The results indicated that with Pb, site 2 accounted for all of the modeled accumulation (A), whereas with
Cd at low concentrations (B), most accumulation could be attributed to site 1. However at high Cd
concentrations (C), site 1 was saturated and site 2 accounted for further accumulation. Figures correspond
to Birceanu et al.’s Figure 1.
62
Farley et al.: Comparison of Four Modeling Approaches, File SI-3:63
A.
B.
Figure 47. Model fits using two biotic ligand binding sites and observed accumulation on rainbow trout gills
following short-term exposures to Pb and Cd mixtures. Figures correspond to Birceanu et al.’s
Figure 2.
Figure 48. Model fits using two biotic ligand binding sites and observed accumulation on rainbow trout gills
following short-term exposures to Zn alone. The affinities were the same between the two
binding sites for Zn. Figure corresponds to Todd et al.’s (2009) Figure 3.b.
63
Farley et al.: Comparison of Four Modeling Approaches, File SI-3:64
A.
B.
Figure 49. Modeling a “less than additive” mixture toxicity scenario, redux: The “Index 6, Series 1” data are
a set of toxicity tests where cutthroat trout were exposed to varying concentrations of Zn alone,
or to varying concentrations of Zn as mixtures with Cd or Pb also present with concentrations
close to half their respective EC50s (our Figure 1). At left (A), the observed mortalities
(symbols joined by dashed lines) are plotted against the predicted toxicity (solid lines) from the
same 1-site BLM-Tox model as we used in the pre-workshop modeling approach. At right (B),
the modeled mortalities using the 2-site BLM approach with the conditional binding affinity and
capacity constants estimated from the Cd, Pb, and Zn rainbow trout gill accumulation studies
(Figures 46-48) are compared with the observed mortalities.
The 1-site BLM failed to reproduce the observed reductions in toxicity of the mixtures
compared to Zn alone (A., see also our Figure 20). In contrast, the 2-site BLM could reproduce
both the single metal Zn mortalities and the reduced mortalities in the mixture exposures quite
well.
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Farley et al.: Comparison of Four Modeling Approaches, File SI-3:65
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Appendices
Appendix 1: Developing the Unified individual BLMs
Testing the robustness and generality of the single-metal BLMs with different organisms and diverse
waters
To further evaluate the realism of our new BLMs, we extended the predictions of LA50s to
dissolved total metals concentrations (LC50s) that can be directly compared with empirical EC50
estimates. We calculated species mean critical accumulation values as the geometric mean of all LA50s
for a species. We followed the approach of De Schamphelaere and Janssen (2002) to make these
calculations, using their Equation 7. These model comparisons are usually called “predicted versus
observed” or “predicted vs. measured” comparisons, although we used the phrase “predicted versus
empirical” because EC50s are not observable or measureable data, but rather model fits themselves.
For the comparisons, we evaluated our new BLMs with three tests of model performance: (1)
the ideal model has the slope of a simple regression close to 1, (2) the R-square coefficient of
determination is close to 1, and (3) the prediction values fall close to the 1:1 line of perfect agreement.
In practice, a more achievable standard is if the model predictions are not obviously skewed, and if the
great majority of predictions fall within a factor of 2 of the line of perfect agreement (Santore et al.
2001).
Where available, we also compare our model predictions to published models for the metal. Our
objective was that the performance of the new BLMs should not be substantively worse than previous
published BLMs for that metal. While there have been previously developed BLMs that were calibrated
using multiple species across many studies (HydroQual 2004; DeForest and Van Genderen 2012), most
commonly BLMs have been calibrated using data from a single species, and often from a single study.
Conceptually, a BLM based on data from a single species or especially a single study should, for the
dataset or organism, handily outperform a BLM derived with data from multiple metals, datasets, and
different species. However, models developed from a single dataset are vulnerable to over-fitting, and
may lack generality.
Zinc
Our initial model comparisons with Zn toxicity datasets were limited to 96-h tests with rainbow
and cutthroat trout (Oncorhynchus mykiss and O. clarki). Tests were further constrained to those that
used early juvenile life stages, that is, fish that were free swimming and feeding but were still in their
first few months of life, weighing about 2g or less. Datasets meeting these criteria included a study of
the effects of modifying Ca, Mg, Na, and pH in artificial waters on the acute and chronic toxicity of zinc
to juvenile rainbow trout (De Schamphelaere and Janssen 2004a), studies of the effects of modifying
water hardness and or pH by blending natural well waters with RO water or adding strong acids
(Chapman 1978; Cusimano et al. 1986; Stratus 1999; Hansen et al. 2002; Brinkman and Hansen 2004;
Todd et al. 2009), and a study adding Zn to stream waters that had a natural range of ionic strength but
low DOC (Mebane et al. 2012). Hansen et al (2002) and Stratus (1999) report the same tests, but they
are referenced to both sources since their journal article only reported 120-h LC50s and summaries of
test water chemistries. We estimated 96-hour LC50s from their raw data appendices using EPA’s
Toxicity Relationship Assessment Program (Erickson 2010).
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Our BLM performed reasonably well with all datasets, with the predicted and empirical 96-h
EC50s being highly correlated (R2 = 0.86). Only a slight bias is obvious in the predictions, with our
new BLM tending toward under-prediction of toxicity (that is, predicting higher that the empirical
EC50s) at the low range of EC50s. The lowest EC50s, which tended to be over-predicted, occurred in
test waters with very soft water (Figure 32a). The problem that Zn was more toxic than predicted in
dilute waters cannot simply be attributed to BLM calibration, because fish living in very dilute
freshwaters without the presence of elevated metals may undergo changes that make them become more
sensitive to later metal stress (Mebane et al. 2010b). It seems plausible that Zn was more toxic than
predicted in very soft waters because of osmoregulatory stress from low ionic strength water and
variations in Zn concentrations, with complex physiological and compensation responses by fish
(Hogstrand et al. 1998). These physiological changes in very soft water are unaccounted for in our
BLM, and to our knowledge, any other released BLMs.
Also of note are the good predictions of the influence of pH on Zn toxicity to rainbow trout
(plotted as blue diamonds, Figure 32a). There is an unexpected plateau in predictions of the Hansen
data at about 100 µg/L (plotted as red circles, Figure 32a). This plateau is from testing fish of different
sizes that turn out to have different sensitivities; swim-up fry become more sensitive as they get larger.
Since the tests were in almost identical dilution water, the model of course predicts nearly identical
results for tests with nearly identical waters. Mebane et al. (2012) encountered the same problem with
Zn sensitivity being dependent on fish size, which introduces much scatter into their dataset as well
(plotted as black circles, Figure 32a).
In contrast, De Schamphelaere & Janssen’s (2004a) rainbow trout Zn BLM works reasonably
well with the data from which it was developed, but toxicity is greatly under-predicted, by a factor of 10
or more, for the more sensitive measured LC50s, which tend to be from low Ca waters. Also of note are
the very poor predictions of the varying pH test series (plotted as blue diamonds, Figure 32b).
Opposite of this bias pattern, the HydroQual (2004) BLM developed from multiple species
predicts reasonably well the samples for which Zn would be highly toxic (the low Ca tests), but greatly
over-predict toxicity as Ca concentrations rise (Figure 32c). Predictions with pH are at least trending in
the correct direction, but toxicity at high pH was strongly under-predicted.
The final comparison between empirical and predicted Zn toxicity shown here is with Daphnia
pulex, tested in artificial waters that were manipulated to vary pH, Ca, Mg, Na, and natural organic
matter (NOM) (Clifford and McGeer 2009). Our BLM performed as well as did the Clifford and
McGeer (2009) BLM, which was specifically fit to their data with linear R2 of 0.83 and 0.80, and slopes
of 0.89 and 0.85 for our model and Clifford and McGeer’s model, respectively. Curiously, while pH
had a pronounced influence on Zn toxicity to rainbow trout, it had little influence on Zn toxicity to
Daphnia pulex (Figure 32d).
Overall, the performance of our BLM with these datasets performed at least as well as did
previous published BLMs for Zn.
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A. Uniform BLM: Zn and trout
B. De Schamphelaere and Janssen 2004 BLM:
Zn and trout
D. Uniform BLM: Zn and Daphnia pulex,
data from Clifford and McGeer 2009
C. HydroQual 2004 BLM: Zn and trout
Figure 32. Zinc predicted and empirical acute EC50s with rainbow and cutthroat trout:
(A) using our uniform BLM), (B) the same tests using De Schamphelaere and Janssen’s(2004a) BLM, and (C)
using HydroQual’s (2004) Zn BLM, and (D) our uniform BLM using Daphnia pulex data from Clifford and McGeer
(2009). Other data sources: (Stratus 1999; Hansen et al. 2002; Brinkman and Hansen 2004; Todd et al. 2009;
Mebane et al. 2012).
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Cadmium
Similar to Zn, our BLM evaluations with Cd were focused on trout tests and Clifford and
McGeer’s (2010) Daphnia pulex study that was parallel to their Zn study. Both the datasets and the
modeling results for Cd were similar to those for Zn.
We think that our BLM model worked very well with the Cd data over the range of available
data, including reasonable predictions with high and very low Ca waters and high and low pH (Figure
33a). As with Zn, there is a plateau in our model predictions at about 0.8 µg/L with the Hansen data
(plotted as red circles, Figure 33a) that reflects a Cd sensitivity dependency on fish size, where the
rainbow trout became more sensitive with increasing size.
The model of Niyogi et al (2008) worked very well with the tests at the high range of the EC50s
where Cd was relatively less toxic because of higher Ca or DOC concentrations in the dilution water.
However, their model did not perform as well at the low range of the data because of low Ca
concentrations, and their model, which did not include a BL-H term (Table 1), did not work at all with
changing pH (Figure 33b).
A non-referenced Cd BLM is included within HydroQual, Inc. (2007) BLM software. This
model also performed reasonably well, and the pH series is trending in the correct direction.
Overall, the performance of our BLM with these datasets performed at least as well as did
previous published BLMs for Cd.
Lead
Compared with Zn and Cd, and as follows, Cu, much fewer data are available with Pb (Figure
34). Most recent BLM calibration studies used “factors testing” designs in which one key water
parameter is varied while attempting to keep other parameters constant. No such studies have been
reported with rainbow trout although extensive factors testing has been reported using the fathead
minnow, Pimephales promelas (Grosell et al. 2006; Mager et al. 2010). Similar to Zn and Cd tests,
Mebane et al. (2012) tested Pb toxicity to trout by adding Pb to stream waters that had a natural range of
ionic strength, but low DOC. These data provide information on the performance of our BLM with Pb
in natural waters.
We calibrated our BL-Pb parameters using the series of tests of different factors with varying Ca
and humic acid concentrations, and acute and chronic exposures with varying pH (Grosell et al. 2006;
Mager et al. 2010). Applying the model to Mebane et al.’s data with cutthroat trout, mayflies, black
flies, and snails worked reasonably well (Figure 34). The rainbow trout empirical EC50s from Mebane
et al.’s (2012) testing were highly variable, with tests straddling both sides of the factor of two
prediction interval. This variability was correlated with differences in the size of the tested fish, with
the swim-up fry apparently becoming less resistant as they got older during their first months of life
(Mebane et al. 2012).
More factors testing data with fathead minnows and Ceriodaphnia dubia have recently become
available (Parametrix 2010; Esbaugh et al. 2011; Mager et al. 2011; Esbaugh et al. 2012). However, we
have not had an opportunity to go back and compare the performance of our BLM with those datasets.
In 2010 Robert Santore and Adam Ryan at HydroQual generously shared an unreleased Pb BLM they
were developing. While the testing with their unreleased model is not shown in Figure 34, its
performance with these datasets was comparable to that of our BLM.
Overall, the limited data reviewed supported the use of our BLM for Pb.
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Farley et al.: Comparison of Four Modeling Approaches, File SI-3:80
Figure 33. Cadmium predicted and empirical acute EC50s with rainbow and cutthroat trout:
(A) using our BLM, (B) the same tests using Niyogi et al.’s (2008) BLM, and (C) using HydroQual’s unpublished Cd
BLM, and (D) our BLM using Daphnia pulex data from Clifford and McGeer’s (2010). Other data from: (Chapman
1978; Cusimano et al. 1986; Stratus 1999; Hansen et al. 2002; Besser et al. 2007; Mebane et al. 2012).
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Farley et al.: Comparison of Four Modeling Approaches, File SI-3:81
A. Uniform BLM: Pb and fish
B. Uniform BLM: Pb and invertebrates
Suspect
value
Figure 34. Lead predicted and empirical acute and chronic effects with fish:
(A) using our BLM, and (B) acute Pb tests using invertebrates with our BLM (Grosell et al. 2006; Birceanu et al.
2008; Mager et al. 2010; Mebane et al. 2012)
Copper
The performance of our BLM with copper is reviewed more extensively than for other metals.
This is because much more data are available with Cu than other metals and because of contrary results
between datasets, especially between rainbow trout and some fathead minnow datasets with pH.
Previous BLMs with Cu are more mature than with other metals, and comparisons focus on the BLM
incorporated by USEPA (USEPA 2007) into its regulatory Cu criteria. The USEPA Cu criteria BLM in
turn is refined from Di Toro et al.’s (2001) and Santore et al’s (2001) BLM.
Trout tests with major ions
Several rich datasets were reviewed of cutthroat or rainbow trout responses to Cu in waters with
varying ionic content. Chakoumakos et al. (1979) tested cutthroat trout with Cu in spring waters that
were manipulated to provide a range of alkalinities and pH, and differing Ca and Mg concentrations.
We think our BLM handled these data very well, with an overall R2 coefficient of determination of 0.78
between our model predictions and the empirical results. The tests were conducted over a 3-month
period and as the fish grew during the holding period, differences in size of tested fish likely introduced
variability into the empirical results. When predicted and empirical results are compared among
concurrent tests using the same sized fish, the correlations were nearly perfect with R2 coefficients
ranging from 0.92 to 1.00 (Figure 35a). The predictions from USEPA (2007) BLM were almost as
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Farley et al.: Comparison of Four Modeling Approaches, File SI-3:82
good, with an overall R2 of 0.72 and for the individual series, R2 coefficients ranged from 0.68 to 0.99
(Figure 35b).
The relative influence of either Ca or Mg on Cu toxicity to rainbow trout was investigated by
Welsh et al (2000; 2001) and Naddy et al (2002). Both studies concocted solution waters with a
common total hardness as CaCO3 but were composed of different ratios of Ca and Mg. Generally, Ca
tended to reduce copper toxicity in DOC-free solutions, but Mg had little or no influence on copper
toxicity in rainbow trout or fathead minnows (although Mg did mitigate Cu toxicity in Daphnia magna)
(De Schamphelaere and Janssen 2002; Naddy et al. 2002).
Our BLM at least predicted copper LC50s to trend in the same direction as the empirical LC50s
from these tests with differing Ca and Mg ratios, although the regression slopes were all appreciably
lower than 1.0 (Figure 35c). In contrast, the USEPA (2007) BLM “flatlined” the predictions for these
tests, predicting nearly identical LC50s for the tests with differing Ca and Mg concentrations (Figure
35d). This result occurs because the BL-Ca and BL-Mg log K values in the USEPA (2007) BLM are
identical, implying they are equally important competitors for binding sites on the gill. This is clearly
not the case for rainbow trout.
Copper and pH
We examined the influence of varying pH on Cu toxicity to rainbow trout from three studies.
Stratus Consulting (1996, 1998) tested the toxicity of copper to rainbow trout in a series of tests in lab
and natural waters (Sacramento River, CA, USA) in which they amended pH in low or high Ca waters.
DOC ranged from about 0.1 to 2 mg/L in the lab and natural waters. Ng et al. (2010) tested the toxicity
of Cu to rainbow trout in soft water with pH ranging from 5 to 8.5 in 30-d exposures, and Cusimano et
al. (1986) tested the toxicity of Cu to rainbow trout in soft water with pH ranging from 4.7 to 7. Tests
were grouped by common Ca concentrations for the comparisons.
The predicted LC50s for tests varying pH in lab or river waters matched our predictions very
well (Figure 36a), which was not wholly surprising since these tests were among those used to calibrate
our model. Likewise, the Cusimano pH series was also used to calibrate the pH response in our BLM
and these empirical LC50s were also predicted well by our model (Figure 36d). The Ng 30-d tests were
not used in our model calibration, which was limited to 96-hr test data, but these empirical test results
were also predicted well by our model (Figure 36c). In contrast, the USEPA (2007) BLM predicted
much more pronounced decreases in Cu toxicity with increasing pH than were actually observed with
rainbow trout in any of these three series.
These results with rainbow trout and pH and the corresponding excellent performance of our
BLM and the poor performance of the USEPA (2007) with these datasets are sharply reversed with
fathead minnows tested with Cu across a pH range of 6 to 9 (Figure 37a). These data are from Erickson
et al.’s (1987; 1996) series of about 150 fathead minnow experiments with Cu under a wide variety of
solution water chemistries. In their pH test series, Cu toxicity was consistently reduced at pH values
greater than 7.5 (Figure 37a). This empirical pattern was not at all reflected in predictions using our
BLM, but was matched very closely by the USEPA (2007) predictions (Figure 37b). This agreement
between the Erickson empirical results and the USEPA (2007) BLM predictions was expected because
the Erickson data were used to calibrate USEPA (2007) BLM.
82
Cu, major ions, and trout
Farley et al.: Comparison of Four Modeling Approaches, File SI-3:83
A. Uniform BLM: Cu, major ions and
cutthroat trout
C. Uniform BLM: Cu, major ions and rainbow
trout
B. USEPA 2007 BLM: Cu, major ions and
cutthroat trout
D. USEPA 2007 BLM: Cu, major ions and
rainbow trout
Figure 35. Copper predicted and empirical trout LC50s with varying major ions:
(A) our BLM, and (B) the same data with the USEPA (2007) BLM; (C) rainbow trout LC50s with varying major ions
and our BLM; (D) the same data with the USEPA (2007) BLM. (Chakoumakos et al. 1979; Welsh et al. 2000;
Welsh et al. 2001; Naddy et al. 2002)
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Farley et al.: Comparison of Four Modeling Approaches, File SI-3:84
Cu, pH and trout
B. USEPA 2007 BLM: Cu and paired rainbow
trout tests at pH 6 or 8 in different lab or river
waters (Stratus 1996, 1998)
A. Uniform BLM: Cu and paired rainbow trout
tests at pH 6 or 8 in different lab or river
waters (Stratus 1996, 1998)
C. Copper, rainbow trout 30-d tests with
varying pH, and our Uniform and USEPA
2007 BLMs (Ng et al. 2010)
D. Copper, rainbow trout 96-h tests with
varying pH, and our Uniform and USEPA
2007 BLMs (Cusimano et al. 1986)
Rainbow trout copper 168h LC50s, across pH gradient, Cusimano et al 1986
Cusimano empirical
Cu LC50s (µg/L)
40
35
Cusimano 2007 BLM
parameters
30
Cusimano - uniform
parameters
25
20
15
10
5
0
4.0
5.0
6.0
pH
Figure 36. Copper empirical and predicted LC50s from rainbow trout tests with varying pH
(Cusimano et al. 1986; Stratus 1996, 1998; Ng et al. 2010)
84
7.0
8.0
Farley et al.: Comparison of Four Modeling Approaches, File SI-3:85
A. Uniform BLM: Cu and fathead minnow
LC50s obtained over a pH range and
otherwise constant conditions (Erickson
1987,1996)
B. USEPA 2007 BLM: Cu and fathead
minnow LC50s obtained over a pH range
and otherwise constant conditions (Erickson
1987,1996)
A. Uniform BLM: Cu and fathead minnow
LC50s obtained over a pH range and
otherwise constant conditions (Sciera et al
2004)
B. USEPA 2007 BLM: Cu and fathead minnow
LC50s obtained over a pH range and otherwise
constant conditions (Sciera et al 2004)
Figure 37. Copper empirical and predicted LC50s from fathead minnow tests with varying pH
(Erickson et al. 1987; Erickson et al. 1996; Sciera et al. 2004).
The apparently contradictory story of rainbow trout and fathead minnow responses is further
complicated by a series of tests by Sciera et al (2004). Sciera and her colleagues used a factors testing
study design comparable to Erickson’s wherein waters with a constant Ca content were pH adjusted by
adding HCl or NaOH. However, unlike Erickson’s results, raising the pH from about 7.3 to 8 resulted in
only small increases in the Cu LC50s. Our BLM tracked the general patterns of these responses
reasonably well, except for the very soft water series with only 2 mg/L Ca, for which our model
predicted a decrease in Cu toxicity from pH 6.0 to 7.3 when none was observed. The USEPA (2007)
matched the empirical results for the highest Ca water (8 mg/L) from pH 6 to 7.3, but every other
transition from low to higher pH, Cu toxicity was predicted to decrease more than was observed.
Fathead minnows
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The preceding string of comparisons of Cu toxicity as modified by pH showed that in different,
closely matched test series, contradictory response patterns have occurred between rainbow trout and
fathead minnow tests. Even among factors testing studies with fathead minnows, markedly different
patterns arise from tests across similar pH ranges at overlapping Ca concentrations (Figure 37). These
different patterns elude simple explanations, but emphasize an important limitation to our goal of
developing a highly generalized BLM: if fundamentally different biological responses result from
similar water chemistry conditions, no water chemistry based model is going to be able to predict these
different biological responses.
Next, we move from comparing species test series with fathead minnows and Cu to more general
comparisons of predicted and empirical LC50s from large fathead minnow datasets developed over a
wide range of water chemistry conditions (Figure 38). Erickson et al. (1987; 1996) reported 150 test
results of Cu toxicity to fathead minnows from many different water chemistry combinations in addition
to the pH experiments previously presented (Figure 37). Other tested factors included Ca, Mg, Na, K,
alkalinity, and humic acid in both flow-through or static exposures (Figure 38a). This is the dataset
used by Santore et al. (2001) to calibrate the Cu BLM that was later refined and used to establish
USEPA’s national aquatic life criteria for Cu (USEPA 2007). As did Santore et al. (2001), tests with
added K are excluded from the analyses because, independent of Cu, elevated K appears to be toxic to
fathead minnows. Data are segregated by whether flow-through or static exposures were used because
the exposure method also influences test results. Flow-through tests with limited contact time between
Cu and solution, such as the ~45 minute volume replacement used by Erickson et al., will not have
reached equilibrium with humic acid, leaving more Cu bioavailable than if equilibrium had been
reached (Santore et al. 2001). In contrast, in static tests with no or limited water replacement, DOC may
increase over the test duration reducing copper toxicity (Welsh et al. 2008). Thus, we segregate, but
retain, both test types in our analyses.
In contrast to the performance of our BLM with Erickson’s pH series (not correlated), when
compared to the larger dataset, our BLM predictions are highly correlated with their empirical LC50s,
with R2 0.58 to 0.91 for the static and flow-through tests, respectively (Figure 38a). Particularly with
the static dataset that make up the majority of the data, our predictions are more ragged and correlations
are weaker than those obtained with the USEPA (2007) BLM (R2 of 0.77 and 0.90 for the static and
flow-through tests respectively (Figure 38b). This suggests that while our BLM may handle certain pH
transitions poorly, overall for most water chemistry combinations in this dataset, our BLM performed
adequately.
Four other large studies of Cu toxicity to fathead minnows under a wide variety of water
chemistry conditions were evaluated with our BLM (Figure 38c). Ryan et al. (2004) reported 30 tests
with different natural DOC sources and amounts, all in reconstituted moderately hard water (hardness
about 90 mg/L). Sciera et al. (Sciera et al. 2004) reported 39 tests of various combinations of water
hardness, pH, and DOC, all in reconstituted waters, emphasizing soft water conditions (hardness was
<50 mg/L). Van Genderen et al (2005) reported 81 tests conducted using both low-hardness natural
waters from coastal South Carolina, USA and reconstituted waters, with hardness ranging from 4 to 122
mg/L CaCO3, pH ranging from 6 to 8, and DOC ranging from 0.4 to 13 mg/L. Welsh et al (1993; 1996)
reported 38 tests with fathead minnows and Cu conducted in natural lake waters from the Canadian
Shield region of Ontario, Canada. The lakes were all soft water and moderately acidic with DOC
ranging from 0.4 to 16 mg/L. Hardness ranged from only 7 to 20 mg/L and pH from 55 to 7.2.
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A. Uniform BLM: Cu and fathead minnow LC50s
obtained over a wide range of ionic composition,
pH, and DOC concentration (Erickson
1987,1996)
B. USEPA 2007 BLM: with the same data as
plot “A”
D. USEPA 2007 BLM with same data as plot
“C”
C. Uniform BLM: Cu and fathead minnow
LC50s obtained from soft or hardwater tests
with varying DOC concentrations and or pH
and ionic compositions
Figure 38. Copper predicted and empirical LC50s from large fathead minnow datasets developed over a wide range
of water chemistry conditions
(Erickson et al. 1987; Welsh et al. 1993; Erickson et al. 1996; Welsh et al. 1996; Ryan et al. 2004; Sciera et al.
2004; Van Genderen et al. 2005)
Considering these four large datasets with fathead minnows tested in diverse natural and
laboratory soft and hard waters water, we see the data sets for the three soft water studies grouped
together (open symbols) and the fish used in the hard water study were dramatically more resistant
(solid symbols) (Figure 38c). Because of this dichotomy, our BLM tended to under-predict toxicity in
very soft water and over-predict in hard water, i.e., predicted LC50s tended to be too high in soft water
and too low in hard water tests. The USEPA (2007) BLM was similar in this regard, although the under
predictions in soft water were more severe and the fit in the hard water tests was very good (Figure
38d).
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The soft water problem
The problem with the BLMs under-predicting Cu toxicity to fish in very soft water (Figure 38c)
appears systematic and is consistent with similar observations noted earlier in the Cadmium Toxicity
Tests and Zinc Toxicity Tests sections. This limitation to the BLM predictions goes beyond getting the
competition terms correct for Ca, Na, and Cu or other metals at the biotic ligand. Rather it is related to
changes that the fish undergo that are independent of metals exposure (Taylor et al. 2000; Van
Genderen et al. 2008; Mebane et al. 2010b). In very soft waters without elevated metals, fish have
increased energy requirements for respiratory gas transfer across the gill and to counter passive diffusive
losses of Ca and Na from their bodies (Wendelaar Bonga and Lock 2008). Conceptually, these increased
efflux rates in soft water could be incorporated into a biodynamic model adjusted to Ca levels in the
ambient water (Veltman et al. 2010). However, such a model, especially if extended to multiple metals,
seems likely to be overwhelmingly complex, which would limit its generality and utility. A more
pragmatic solution might be to empirically reduce the LA50s of organisms in soft water by regression
analysis (Paquin et al. 2011). Such an adjustment could be thought of as an extension of the common
BLM practice of adjusting LA50s to fit observed sensitivities of organisms.
Because we did not have empirical soft water adjustments to metals other than copper, and
because we did not wish to add more complexity to our modeling approach, we decided to accept this
potential bias in Cu predictions in soft water from our BLM. In general, although our BLM did not work
well for every fathead minnow dataset, on the whole we thought the predictions seemed acceptable.
Invertebrates
Because our multiple-toxicant BLM was calibrated from rainbow trout data, whether it was
suitable for use with invertebrates was uncertain. Separate Cu BLMs have been developed for fish and
invertebrates (Daphnia magna), where the latter has been argued to be more appropriate for use with
invertebrates (Niyogi and Wood 2004a). Thus we analyzed several datasets in diverse waters with our
BLM. All datasets analyzed used cladocerans, Daphnia magna or Ceriodaphnia dubia.
GLEC (2006) tested the acute toxicity of Ceriodaphnia dubia to Cu using a wide variety of
natural waters collected from the southern boreal forests in the Upper Peninsula of Michigan, USA.
Water hardness ranged from 17 to 213 mg/L and DOC ranged from <1 – 30 mg/L. We think our BLM
performed quite well with these data with reasonably accurate predictions and little obvious bias (Figure
39a and b).
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Farley et al.: Comparison of Four Modeling Approaches, File SI-3:89
A. Uniform BLM: Cu and Ceriodaphnia dubia tested in
natural waters with a wide range of DOC and
hardness, and pH (GLEC 2006)
B. USEPA 2007 BLM predictions with the same data
as plot “A”
C. Uniform BLM: Cu 48-h tests with Daphnia magna in
diverse Chilean waters (Villavicencio et al 2005)
D. USEPA 2007 BLM predictions with the same data
as plot “C”
E. Uniform BLM: Cu 48-h tests with Daphnia magna in
waters with varying pH, hardness and DOC
concentrations (Ryan et al 2009)
Figure 39.
F. USEPA 2007 BLM predictions with the same data
as plot “E”
Copper predicted and empirical EC50s from cladocerans in diverse waters.
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Farley et al.: Comparison of Four Modeling Approaches, File SI-3:90
Villavicencio et al. (2005) tested the acute toxicity of Cu to different daphnids across a range of
natural waters in Chile. The natural waters included high Ca and low DOC waters from rivers in arid
north central Chile; low Ca and low DOC from mountain rivers and lakes, and lakes with high DOC.
We think our BLM predicted these empirical data exceptionally well, as did the USEPA (2007) BLM
(Figure 39c and d).
Ryan et al (2009) tested the influence of different water chemistry factors on Cu toxicity to
Daphnia magna, with varying Ca, pH, and DOC in soft waters. Their study design was analogous to the
fathead minnow studies by Sciera et al. (2004). Again we thought that our BLM did very well with test
data from these diverse waters, except perhaps for a couple of tests with artificial water and no added
DOM (Figure 39d and e).
While most of our calibration or validation datasets involved acute data, environmental
exposures are probably more commonly long-term, low level exposures. Thus, we also tried to evaluate
chronic test data when available. One major study was De Schamphelaere and Janssen’s (2004b) testing
and modeling the chronic (21-d) toxicity of Daphnia magna in natural waters collected from The
Netherlands and Belgium, and amended by varying DOM and inorganic factors. They found their
chronic effects were not predicted well by a previously developed acute Daphnia magna BLM, and
developed their “Model 3’ that was the best model fit specifically to the dataset. Applying our BLM to
their chronic Daphnia no-observed effect concentrations (NOECs), our model did almost as well as
“Model 3” (Figures 40a and b).
A. Uniform BLM
B. “Model 3”, De
Schamphelaere &
Janssen (2004b)
C. USEPA (2007)
BLM
Figure 40. Copper predicted and empirical 21-day NOECs with Daphnia magna
(De Schamphelaere and Janssen 2004b).
These various Cu toxicity datasets with invertebrates represented diverse water types. However
all comparisons were based on daphnids, which begs the question whether other freshwater
invertebrates would respond similarly. We note that Wang et al. (2009; 2011) were able to predict acute
and chronic Cu toxicity to juvenile freshwater mussels using the USEPA (2007) BLM, as was acute Cu
toxicity to the amphipod Hyalella azteca (C. Mebane, unpublished data).
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In summary, we note that in the analyses presented in this study, our BLM mostly performed on
par with the USEPA (2007) Cu BLM. We think that these various datasets, each of which were large
and obtained from diverse water chemistries, amply support the use of our BLM with Cu.
Nickel
Our initial development of new BLMs for single metals did not include Ni. Because this model
was added after the other metal BLMs had been developed, we assumed that the biotic ligand binding
constants that we had previously optimized for nontoxic cations could also be used to evaluate Ni
toxicity (i.e., BL-H, BL-Ca, BL-Mg, and BL-Na). Thus, we only optimized log K values for BL-Ni and
BL-NiOH in developing the new Ni BLM.
This approach probably pushes the limits of our BLM approach for several reasons. First, until
recently Ni has had much less research interest than more toxic metals such as Cu or Cd (Pyle and
Couture 2011). The burst of recent research findings indicate different organisms have different modes
of toxicity and model parameters such as Mg may have markedly different influence on Ni toxicity for
different organisms. Something as fundamental as the mechanism of Ni toxicity to aquatic organisms
seems to vary with organism. The fundamental concept of the BLM approach to predicting metals
toxicity is that ionoregulatory function may be disrupted by trace metals (Di Toro et al. 2001; Paquin et
al. 2011). Yet, with rainbow trout exposed to Ni concentrations far higher than those expected in aquatic
ecosystems, Ni was found to be a respiratory toxicant, not an ionoregulatory toxicant. However, Ni has
subsequently been shown to be a ionoregulatory toxicant with zebrafish, with a common mechanism of
toxicity with the other metals included in our BLM evaluations: Cd, Cu, Pb, and Zn (Alsop and Wood
2011). Further, nickel has also been shown to be an ionoregulatory toxicant to Daphnia magna
impairing Mg2+ uptake, which results in a net decrease of whole bodyMg2+ (Pane et al. 2003b).
A second fundamental assumption of the BLM approach is that the parameters that describe
interactions between cations (Ca2+, Mg2+, Na+ and H+) and the toxic free metal ions are constant across
organisms, and that among species only the intrinsic sensitivity varies (Di Toro et al. 2001; Paquin et al.
2011). The evidence for this is also equivocal. With fish and daphnids, increasing either water hardness
or Ca and Mg individually appears to mitigate Ni toxicity, with Ca generally providing a stronger
protective effect (Lind et al. 1978; Meyer et al. 1999; Deleebeeck et al. 2007a; Deleebeeck et al. 2007b;
Meyer et al. 2007; Kozlova et al. 2009). These findings are consistent with the structure of our BLM
(Table 2). However, with the single-cell green algae Pseudokirchneriella subcapitata, also known as
Selenastrum capricornutum, www.itis.gov), increased Mg strongly reduced Ni toxicity, but Ca had little
effect. With pH, the influence on Ni toxicity is also variable, with reports that increasing pH resulted in
increased toxicity of Ni to fish (Schubauer-Berigan et al. 1993; Deleebeeck et al. 2007a), or decreased
toxicity of Ni to fish (Pyle et al. 2002). Thus, at the outset it was not clear that our BLM (or any single
BLM) could be applied across algae, invertebrates, and fish.
Candidate data sources for modeling were sought that tested Ni toxicity across a range of
solution chemistries and that fully reported necessary biological and chemical data. Data sets used in
modeling were sub-acute rainbow trout tested across a range of pH, Ca, Mg, and DOC concentrations in
artificial and natural waters in ~17 day exposures (Deleebeeck et al. 2007a), acute Daphnia magna tests
similarly conducted in artificial and natural waters (Deleebeeck et al. 2008a), chronic Daphnia magna
tests similarly conducted in artificial and natural waters (Deleebeeck et al. 2008b), green algae growth
tests in artificial and natural waters (Deleebeeck et al. 2009b), acute and chronic tests with wild
cladocerans and green microalgae collected from Swedish lakes (Deleebeeck et al. 2007b; Deleebeeck
et al. 2009a), and chronic Ceriodaphnia dubia in artificial waters from two studies (Keithly et al. 2004;
De Schamphelaere et al. 2006, citing Wirtz et al. 2004). Unused data included studies that varied
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solution waters, but full measured BLM water chemistry parameters were not readily available (Lind et
al. 1978; Meyer et al. 1999; Pyle et al. 2002; Hoang et al. 2004). Some studies measured and reported
all necessary chemistry to evaluate in a BLM context but were not very useful to calibrate a BLM
because tests were conducted in a single type of solution chemistry (Nebeker et al. 1985; Brix et al.
2004; Besser et al. 2011). Two studies that would have been useful for calibration or validation of the Ni
modeling were reviewed while we were writing the report and we intend to add them later. Kozlova et
al.’s (2009) factors testing with Daphnia magna would have been a useful calibration dataset.
Schlekat’s et al. (2010) study of Ni toxicity to six species in five different natural waters would have
been a good validation check.
To obtain BL-Ni and BL-NiOH binding affinity constants, the fractions of biotic ligand bound
by each cation were calculated in an interactive Excel spread sheet following Appendix 2. The log K
values for BL-H, BL-Ca, BL-Mg, and BL-Na were carried forward from other metals. We used the
Solver optimization add-in for Microsoft Excel (http://www.solver.com/) to calculate the log K (BL-Ni)
and log K (BL-NiOH) values by minimizing differences between predicted and empirical LC50s using
the rainbow trout data of Deleebeeck et al. (2007a). Using the rainbow trout data to define the binding
constants in preference to other Ni data was a judgment based on two reasons. First, our review of the
literature mentioned above indicated diverse responses by different organisms to factors modifying Ni
toxicity making it unlikely that we could find good universal solutions, and second, to be consistent
with our approach with other metals for which we used trout data preferentially.
Specifically, using Solver we set the objective to find the minimum difference between the
average predicted and observed LC50s by adjusting all combinations of (1) log K (BL-Ni), (2) log K
(BL-NiOH), and (3) the f_50% mortality (fraction of the BL occupied at 50% mortality effectively, the
LA50). Both of the Solver global optimization algorithms were used and produced similar results, the
generalized reduced gradient (GRG) nonlinear method for smooth nonlinear problems, and the
Evolutionary algorithm for problems that are assumed to be non-smooth. With the GRG nonlinear
method, 1000 iterations were used with 100 restarts to reduce the likelihood that Solver would only find
a local vs. global optimum. Constraints imposed were that log K (BL-Ni) had to be between 2 and 10,
and f_50% mortality had to be between 0 and 1. Then using the solution from minimizing the average
differences between the predicted and observed LC50s as initial values, the process was repeated setting
the goal to obtain a slope of 1.0 between the predicted and observed LC50s.
The results of these steps were a log K (BL-Ni) of 4.04, log K (BL-NiOH) -2.58, and an f50 of
0.012. The other datasets were optimized using these binding constants and only using Solver to find the
best f_50% mortality. Curiously, depending on initial conditions, Solver also found a very different
solutions that worked almost equally well with all datasets (log K (BL-Ni) of 6.16, log K (BL-NiOH) 0.84 , and an f50 of 0.477) While mathematically these two solutions were almost equivalent, we chose
the first set because the lower log K (BL-Ni) of 4.04 was within the range of values determined by
others, e.g., 4.0 to 4.68 (Keithly et al. 2004; Kozlova et al. 2009), and it preserved the rank order
correspondence of increasing log K (BL-Metal) with increasing toxicity of the metal (Figure 6; Niyogi
and Wood 2004a). Also, a 50% fractional mortality occurring only when almost 50% of the total biotic
ligand binding sites are filled (f_50% mortality of 0.477) is far greater than that obtained for other metals
which usually predicted 50% mortality to occur when less than 5% of total binding sites were filled.
Obviously, this selection of which parameter set to use was a judgment call on our part that
illustrates an unsettling aspect of our and most BLM related models that are developed from toxicity
data. Only the solution chemistries and the biological endpoints are measured, and all the intermediate
steps are constructs. Thus, BLMs generally and our BLM, in particular, suffer from the fact that there
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are non-unique solutions that may be about mathematically equivalent, but imply different underlying
chemical or biological mechanisms or interpretation of model results.
Considering the model datasets specifically, our BLM parameters predicted LC50s for trout that
were strongly correlated with empirical LC50s in test series that varied pH and Ca. Correlations were
still reasonably strong with the Mg series (r2 =0.40), but not at all with the field validation series
(Figure 41a).
Daphnia magna (acute) patterns between predicted and empirical LC50s are almost reversed
from those with the rainbow trout. The strongest correlations were with the Mg and field validation
series, and pH and Ca (the strongest correlates with rainbow trout) were minimally correlated (Figure
41b). However, if the toxicity test in 5 mM Ca (total hardness 525 mg/L CaCO3) were excluded, then
the correlation would be reasonably good (r2 = 0.52). Deleebeeck et al (2008a) noted that above 3 mM
Ca or Mg, further increases in concentrations did not result in further decreases in toxicity, and excluded
these data from their model development.
Daphnia magna (chronic) predicted EC50s were strongly correlated with the pH, Ca, Mg and
field validation test series (r2 0.54 to 0.92, Figure 41c). These strong patterns with the chronic test are
additionally curious because the model predictions fit the empirical data far better than for the acute
Daphnia magna data. This is unexpected because most BLMs, including ours, have mostly been
developed from acute datasets (Niyogi and Wood 2004a). In their critical review of the BLM,
Slaveykova and Wilkinson (2005) argued that the fundamental theory and critical assumptions implicit
to BLM are unrealistic and contradicted when extrapolated from acute to chronic settings.
The green algae model predictions have yet another strikingly different response pattern. pH
and Ca tests were highly correlated with predictions, but the slopes of the predicted responses were far
steeper than occurred with the empirical data (Figure 42a). Magnesium tests predictions and
observations of growth inhibition were well correlated. This stands to reason, assuming that Ni acts as
an ionoregulatory toxicant to algae, similarly as it does with Daphnia magna. Magnesium deficiency in
plants impairs photosynthesis because Mg must be incorporated into the chlorophyll molecule before
chlorophyll is effective at gathering light for photosynthetic carbon reduction (Wilkinson et al. 1990).
Wild cladocerans and green microalgae responses to acute and chronic Ni exposures were all
predicted exceptionally well by our BLM (Figure 42b). It is interesting that the green microalgae
Desmodesmus sp. growth inhibition predictions were in such good agreement with the empirical results
yet the (Pseudokirchneriella/Selenastrum) growth inhibition predictions were generally poor (Figure
42a). Likewise, in the acute testing with daphnids, the wild, Swedish daphnid responses were predicted
well but the cultured Daphnia magna responses not so well (Figures 41b and 42b).
Chronic Ceriodaphnia dubia responses were predicted well from the Keithley et al.dataset, but
not so well with the Wirtz et al. dataset (Figure 42c). Of note is that the two test results with the worst
predictions in the Wirtz data were conducted in test waters with alkaline waters. (The Wirtz data
included tests in natural waters of low alkalinity, but we excluded them from our evaluation because we
noticed that Cu and Zn were elevated in the natural waters, 7 to 27 µg/L Cu and 3 to 11 µg/L Zn, and
could confound interpretation of Ni toxicity (De Schamphelaere et al. 2006).) Others had noted a
dichotomy in the Ca and Ni toxicity relations in soft or hard water that could not easily be modeled
together. Calcium apparently provides a relatively greater protective effect from Ni toxicity in soft
waters than harder water (Deleebeeck et al. 2007b; Kozlova et al. 2009).
Overall, the performance of our BLM with these datasets indicated that we could reasonably
apply a single Ni BLM to various species.
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Rainbow trout, ~17-d EC50s, Deleebeeck et al. (2007a)
A.
Ppredicted LC50 Ni (µg/L)
10,000
Rainbow trout f_50% mortality = 0.012
1,000
pH series
Slope
r2
2.33
0.98
Ca series
1.36
0.67
Mg Series
0.27
0.40
Field validation
0.13
0.03
100
100
1,000
10,000
Observed LC50 Ni (µg/L)
B.
Daphnia magna, acute
f_50% mortality = 0.012
C.
Slope
r2
-2.38
0.05
0.79
0.10
0.97
0.46
3.52
0.11
0.71
0.52
Daphnia magna, chronic
f_50% mortality = 0.00031
Slope r2
Figure 41.
Nickel predicted and empirical effects for rainbow trout and Daphnia magna.
94
3.08
0.54
2.57
0.87
0.53
0.92
0.47
0.66
Farley et al.: Comparison of Four Modeling Approaches, File SI-3:95
A.
r2
Slope
Green algae, 72-h growth inhibition
3.19
0.76
14.1
0.80
0.67
0.58
0.37
0.25
f_50% effect = 0.00031
B.
f_50% effect = 0.00031
Slope
r2
f_50% effect
0.79
0.70
0.0077
0.85
0.95
0.0005
0.80
0.84
0.0067
C.
7-d 50% inhibition, lowest endpoint
Slope
f_50% effect = 0.00009
0.26
r2
0.14
f_50% effect = 0.00004
Slope
0.49
r2
Low alkalinity
0.63
Figure 42. Nickel predicted and empirical EC50s for (A) cultured green algae Pseudokirchneriella subcapitata, (B)
field collected green microalgae and field collected Ceriodaphnia quadrangula and (C) chronic Ceriodaphnia
dubia exposures
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Comparisons of benthic invertebrate tissue residues and predicted metal loading using our multipletoxicant BLM and evaluation of the diversity of benthic invertebrate communities using the BLM-Tox
approach
Metal tissue residues in aquatic insects in streams
Schmidt et al. (2011) analyzed tissue residues from three species of aquatic insects collected
from streams in Colorado, USA. Stream water chemistry was collected once and analyzed for all
needed BLM parameters. The three aquatic insect taxa studied, the mayflies Rhithrogena spp. and
Drunella spp. and the caddisfly Arctopsyche grandis, are expected to accumulate metals such that loads
are Rhithrogena > Drunella > Arctopsyche because of their relative abilities to eliminate metals
(Rhithrogena < Drunella < Arctopsyche) (Buchwalter et al. 2008). The streams studied reflected leastdisturbed reference streams, streams with naturally elevated metals, and streams influenced by mining
disturbances. Schmidt et al.’s (2011) interpretation focused on zinc, although Cd and Cu were also
elevated in some streams (90th percentile concentrations were Cd 0.83, Cu 17, and Zn 209 µg/L;
maximum concentrations Cd 7.9, Cu 935, and Zn 1790 µg/L). Arctopsyche were metals tolerant, and
populations were not at all limited by zinc. In contrast, declines in Rhithrogena and Drunella
populations were suggested to begin at very low Zn concentrations, 4 and 7 µg/L respectively (Schmidt
et al. 2011).
Comparing the predicted fractions of the biotic ligand for Cd, Cu, and Zn to the measured
accumulated metals shows that the BLM predicted accumulations had some correlation with measured
accumulations (Figure 43). Correlations were strongest with Zn for all three taxa (ignoring r2 of 0.91
with Cu and Rhithrogena because it was highly leveraged by a single value), and correlations for all
three metals were strongest in Rhithrogena.
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Cd
Cu
Zn
10000
A. Arctopsyche grandis (n=48)
1000
Figure 43. Correlations
between tissue
residues of Cd, Cu,
and Zn measured in
three stream
invertebrate species
collected from
Colorado, USA
streams and predicted
metal loading on the
biotic ligand.
Data from Schmidt
et al (2011).
Cd r2 = 0.04
Cu r2 = 0.25
Zn r2 = 0.34
100
Tissue 10
metal
(mg/kg dw)
1
0.1
0.01
1E-6
1E-5
1E-4
1E-3
0.01
0.1
1
BL-Me/BL-Tot
10,000
B. Drunella doddsi (n=58)
1,000
Cd r2 = 0.09
Cu r2 = 0.25
Zn r2 = 0.33
100
Tissue 10
metal
(mg/kg dw)
1
Cd
Cu
Zn
0.1
0.01
1E-6
1E-5
1E-4
1E-3
0.01
0.1
1
BL-Me/BL-Tot
10,000
1,000
Cd
Cu
Zn
C. Rhithrogena sp. (n=14)
Cd r2 = 0.21
Cu r2 = 0.91
Zn r2 = 0.41
100
Tissue
metal
(mg/kg dw)
10
1
0.1
0.01
1E-6
1E-5
1E-4
1E-3
BL-Me/BL-Tot
97
0.01
0.1
1
Farley et al.: Comparison of Four Modeling Approaches, File SI-3:98
With Zn, the correlations between BLM predicted accumulations and measured accumulations
were somewhat similar with r2 values between 0.33 and 0.41. Still, more than half of the variability in
measured accumulations was not “explained” by our BLM. This unexplained portion presumably could
be related to factors such as (1) limitations in the general BLM concept, (2) inaccuracies in our BLM,
(3) aquatic organisms are not passive biotic ligands, but have mechanisms to regulate essential trace
metals to avoid deficiency or overload, (4) insects get much or most of their metals exposure through
their diet than directly through the water in time-dependent, chronic exposures, (5) one-time sampling
may not be representative of antecedent conditions, and (6) measurement error. Considering this host of
potentially confounding factors, the fact that there was any correlation between modeled and observed
accumulations was somewhat encouraging.
Stream aquatic insect diversity predicted from BLM-Tox
Previous approaches have used quantile regression and toxic units (Schmidt et al. 2010) or
quantile regression and FTOX (Stockdale et al. 2010) to assess water quality impacts to benthic
invertebrate communities. We used the Schmidt et al. (2011) data set to illustrate the application of our
BLM-Tox approach to these field samples. Water composition was used to calculate solution and biotic
ligand speciation, Tox was calculated, and the relationship between Tox and the Ephemeroptera,
Plecoptera and Trichoptera (EPT) richness index was determined. The weighting coefficients
determined in the project data sets were used. The EPT richness index is used to assess water quality
and its effect on the diversity of aquatic invertebrates in ecosystems.
We were able to successfully model the macroinvertebrate data (Figure 44). Our results indicate
that EPT richness is high at low values of Tox, begins to decrease at Tox ~ .02, and then levels off at
Tox ~ 0.4. The midpoint between high and low diversity occurs at Tox = 0.069. Cd, Cu, and Zn are
important contributors to Tox in this dataset. The relative importance of the metals to Tox again varies
with metal ratios.
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Figure 44. Relationships between species richness of EPT aquatic insects collected from Colorado, USA streams and
water chemistry and relative importance of metals to toxicity using the BLM-Tox approach. Aquatic insect
occurrences and stream chemistry data are from Schmidt et al. (2010).
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Appendix 2 - Calculation of the speciation of the biotic ligand
Calculation of the speciation of the biotic ligand (i.e., fraction of biotic ligand bound by each cation)
Nomenclature
( ) = activity
[ ] = concentration
BL- = biotic ligand
cat+n = cation, including H+, Na+, Mg+2, Ca+2, Cd+2, Cu+2, Ni+2, Pb+2, and Zn+2
fcat = [BL-cat+(n-1)]/BLtotal = fraction of total biotic ligand bound by cat+n
fcatOH = [BL-catOH+(n-2)]/[BLtotal] = fraction of total biotic ligand bound by catOH+(n-1)
Equilibrium reactions and constants
BL- + cat+n = BL-cat+(n-1)
BL- + cat+n + H2O = BL-catOH+(n-2) + H+
Kcat = [BL-cat+(n-1)]/([BL-](cat+n))
KcatOH = [BL-catOH+(n-2)](H+)/([BL-](cat+n))
Re-arrange:
[BL-cat+(n-1)] = Kcat [BL-](cat+n)
[BL-catOH+(n-2)] = KcatOH [BL-](cat+n)/(H+)
Mass balance on biotic ligand
[BLtotal] = [BL-] + S[BL-cat+(n-1)] + S[BL-catOH+(n-2)]
Substitute and re-arrange:
[BLtotal] = [BL-] (1 + S Kcat (cat+n) + SKcatOH (cat+n)/(H+))
Define:
C = (1 + S Kcat (cat+n) + SKcatOH (cat+n)/(H+))
(C is a constant for given solution speciation and BLM equilibrium constants)
Then re-arrange:
1/C = [BL-]/[BLtotal] = f BL- (fraction of total biotic ligand as BL-)
Calculate fractional speciation of biotic ligand
f BL-cat = [BL-cat+(n-1)]/[BLtotal] = Kcat (cat+n)/C
f BL-catOH = [BL-catOH+(n-2)]/[BLtotal] = KcatOH (cat+n)/((H+)C)
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Appendix 3: Illustrations of the concentration-addition toxic unit and the BLM-Tox approaches to evaluating mixture toxicity
Selected comparisons of concentration-based Toxic Unit (TU), additive approach to evaluating mixture toxicity, observed
mortalities (black circles) vs. the fractional mortalities predicted by BLM-Tox model (white circles). Observed mortalities at 1.0
Toxic Unit implies additive toxicity of the mixture components, >50% mortality at 1 TU indicates greater than additive toxicity, and
<50% mortality indicates less than additive toxicity. Toxic Units were defined from the matched single metal test for each mixture
test.
Daphnia magna
Conclusion:
Mixture toxicity was
less than additive in
this test, based on
exposures #2-5
having <50%
mortality at >1 TU.
Conclusion:
Mixture toxicity
was greater
than additive
in this test,
based on
exposure #2
having nearly
100% mortality
at 1 TU.
Daphnia magna
Daphnia magna
Daphnia magna
Conclusion:
Mixture toxicity was
less than additive in
this test, based on
exposures #4-6
having <50%
mortality at TUs near
or >1.
Appendices-101
Conclusion:
Mixture toxicity was
about additive in
exposure #2 and
much less than
additive in
exposures #3-6
which had <50%
mortality at TUs >1.
Farley et al.: Comparison of Four Modeling Approaches, File SI-3:102
Daphnia magna
Daphnia magna
Conclusion:
Mixture toxicity was
less than additive in
exposure #2 having
<50% mortality at >1
TU. Other exposures
were ambiguous re
concentration
additivity.
Conclusion: Mixture
toxicity was probably
greater than additive
in this test, based on
exposure #2 having
~60 to 90% mortality
at TUs of about 1.1 to
1.3.
Daphnia magna
Daphnia magna
Conclusion:
Exposure #2
suggests roughly
additive toxicity,
however mixture
exposure #1 was
actually solely Cu,
with 25% observed at an exposure concentration that happened to
be the same as the 50% mortality concentration from the
concurrent Cu test. This intra-batch variability cautions against
making too strong of conclusions from any single experiment.
Appendices-102
Conclusion: No conclusions on concentration additivity are
possible from this test series because of high mortalities in all
mixture exposures, which were all dosed at >1 TU.
Farley et al.: Comparison of Four Modeling Approaches, File SI-3:103
Rainbow trout
Cutthroat trout
Conclusion:
Mixture toxicity could
be considered
roughly additive
because exposures
3 and 4 bracket 1
TU and bracket 50%
mortality
Conclusion: Mixture
toxicity was
consistently less than
additive in this series
since <50% mortality
occurred in all
mixtures with >1 TU
Rainbow trout
Conclusion:
Exposures #3
and #4 suggest
less than additive
toxicity, based on
low mortality in
exposure #3 at
close to 1 TU and
because in
exposure #4, 1.75
TUs resulted in
only 60%
mortality.
Rainbow trout
Conclusion: Toxicities appear less than additive on a
concentration basis, because 1.85 TUs in exposure #2 only
produced 53% mortality.
Appendices-103