Supplemental Information for
A test of the additivity of acute toxicity of binary-metal mixtures of Ni with Cd, Cu, and Zn to
Daphnia magna, using the inflection point of the concentration-response curves
Elizabeth M. Traudt†,*, James F. Ranville†, Samantha A. Smith†, Joseph S. Meyer†,‡
†
Department of Chemistry and Geochemistry, Colorado School of Mines, Golden, CO 80401
USA
‡
ARCADIS U.S., Inc., Lakewood, CO 80401 USA
* E-mail: etraudt@mines.edu; Telephone: (720) 839-7869; Fax: (303) 273-3629
Number of pages: 10
Number of tables: 0
Number of figures: 5
S-1
The ECxinfl approach
From individual-metal concentration-response analyses, mortality in a mixture of two
metals can be predicted based on an assumption of additive toxicity (i.e., independent action) of
the two metals. Given the concentration-response equation and fitted EC50 and slope for each
metal alone, the mortality that would be predicted to be caused by each individual metal can be
calculated for any specific concentration (C) of that metal. After predicted mortality (or survival)
is determined for each metal alone at its specified concentration in a binary mixture, the
predicted response-additive mortality is calculated using Equation S1, where SM1 and SM2 are the
survival proportion (i.e., 1 - mortality proportion) expected in exposures to Metal #1 and Metal
#2 alone, respectively.
% Mortality of Binary Mixture = [1-(SM1*SM2)]*100
Equation S1
Using this equation, if the concentration of Metal # 1 is held constant throughout an
entire series, SM1 remains constant. Meanwhile, SM2 determines the concentration-response
relationship, because the concentration of Metal # 2 increases through the metal-mixture
concentration series. However, SM2 is independent of the concentration of Metal #1. If the
toxicity of the two metals is response-additive (i.e., determined by independent toxic action of
the two metals), the concentration-response curve will have the same shape; and importantly,
50% of the residual organisms that survive the background concentration of Metal #1 will die at
the same concentration of Metal #2 regardless of the concentration of and associated mortality
caused by Metal #1. That is, higher concentrations of Metal #1 will result in a greater initial
mortality at low concentrations of Metal #2, but a specified percentage (e.g., 10%, 25% or 50%)
of the survivors will die at the at the same increased concentration of Metal #2 (Figure S1).
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Figure S1A. Hypothetical example of response-additive toxicity of 2 metals in 5 different binary
mixtures. In this example, Metal #1 was held constant at 5 different background concentrations
(represented by the 5 different colors; [Purple] < [Blue] < [Green] < [Orange] < [Red]) while
Metal #2 was increased along a concentration gradient at each background metal concentration.
Higher concentrations of Metal #1 cause higher initial mortality, but the inflection point of each
curve will occur at the same concentration of Metal #2 (at a concentration of approximately 1.6
in this example) if the toxicity of the metal mixture is response additive (see Equation S1).
Figure S1B. Probability density functions for the hypothetical examples of response-additive
toxicity in the binary-metal mixtures shown in Figure S1A. Each curve represents a separate
background concentration of Metal #1 ([Purple] < [Blue] < [Green] < [Orange] < [Red]). The
height of the curve is proportional to the slope of the same-color concentration-response curve in
Figure S1A.
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Figure S2A. Mortality in the 31 Ni-only 48-h Daphnia magna lethality tests conducted during
the 14-month study. The shaded band is the 95% confidence interval around the central-tendency
curve.
Figure S2B. Mortality in the 15 Cu-only 48-h Daphnia magna lethality tests conducted during
the 14-month study. The shaded band is the 95% confidence interval around the central-tendency
curve.
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Figure S2C. Mortality in the 7 Zn-only 48-h Daphnia magna lethality tests conducted during the
14-month study. The shaded band is the 95% confidence interval around the central-tendency
curve.
Figure S2D. Mortality in the 13 Cd-only 48-h Daphnia magna lethality tests conducted during
the 14-month study. The shaded band is the 95% confidence interval around the central-tendency
curve.
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Figure S3. Mortality across a gradient of Cd concentrations when in the presence of the constant
background concentrations of Ni shown in the legend. Dashed curves bounded by shaded bands represent
a fitted concentration-response curve (with 84% confidence intervals) to the observed toxicity data for
each background Ni concentration. The value of “n” in the legend denotes the number of toxicity tests
that were conducted at each nominal background Ni concentration.
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Figure S4A. Mortality across a gradient of Cu concentrations when in the presence of the constant
background concentrations of Ni shown in the legend. Dashed curves bounded by shaded bands represent
a fitted concentration-response curve (with 84% confidence intervals) to the observed toxicity data for
each background Ni concentration. The value of “n” in the legend denotes the number of toxicity tests
that were conducted at each nominal background Ni concentration.
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Figure S4B. Mortality across a gradient of Ni concentrations when in the presence of the constant
background concentrations of Cu shown in the legend. Dashed curves bounded by shaded bands represent
a fitted concentration-response curve (with 84% confidence intervals) to the observed toxicity data for
each background Cu concentration. The value of “n” in the legend denotes the number of toxicity tests
that were conducted at each nominal background Cu concentration.
S-8
Figure S5A. Mortality across a gradient of Zn concentrations when in the presence of the constant
background concentrations of Ni shown in the legend. Dashed curves bounded by shaded bands represent
a fitted concentration-response curve (with 84% confidence intervals) to the observed toxicity data for
each background Ni concentration. The value of “n” in the legend denotes the number of toxicity tests
that were conducted at each nominal background Ni concentration.
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Figure S5B. Mortality across a gradient of Ni concentrations when in the presence of the constant
background concentrations of Zn shown in the legend. Dashed curves bounded by shaded bands represent
a fitted concentration-response curve (with 84% confidence intervals) to the observed toxicity data for
each background Zn concentration. The value of “n” in the legend denotes the number of toxicity tests
that were conducted at each nominal background Zn concentration.
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