Science of the Total Environment 496 (2014) vi–xii
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Science of the Total Environment journal homepage: www.elsevier.com/locate/scitotenv
Review
Mercury bioaccumulation factors and spurious correlations Curtis D. Pollman a, Donald M. Axelrad b,⁎ a b
Aqua Lux Lucis, Inc., 8411 NW 55th Place, Gainesville, FL, USA Florida A&M University, Institute of Public Health, 1515 South Martin Luther King Blvd, Tallahassee, FL 32307, USA
H I G H L I G H T S • • • • •
Spurious correlation is surprisingly common in studies on mercury bioaccumulation. Correlations using bioaccumulation factors (BAF), a ratio, have inherent risks. BAFs are the ratio of contaminant levels in biota to those in the water column. Misleading inferences arise when correlating BAF with its component denominator. Direct analysis of component variables is less ambiguous than BAF correlations.
a r t i c l e
i n f o
Article history: Received 26 June 2014 Received in revised form 8 July 2014 Accepted 8 July 2014 Available online 1 August 2014 Editor: J.P. Bennett Keywords: Methylmercury Aquatic ecosystems Gambusia Everglades Synthetic data
a b s t r a c t While bioaccumulation factors (BAF) – the ratio of biota contaminant concentrations (Cbiota) to aqueous phase contaminant concentrations (Cw) – are useful in evaluating the accumulation of mercury (Hg) and other contaminants for various trophic levels in aquatic ecosystems, reduction of the underlying relationship between Cbiota and Cw to a single ratio (BAF) has inherent risks, including spurious correlation. Despite a long and rich history of remonstrations in the literature, several very recent publications evaluating Hg-related BAFs have suffered from false conclusions based on spurious correlation, and thus it seems that periodic reminders of the causes and risks of these errors are required. Herein we cite examples and explanations for unsupported conclusions from publications where authors using BAF-Cw relationships fail to recognize the underlying statistical significance (or lack thereof) of direct relationships between Cw and Cbiota. This fundamental error leads to other problems, including ascribing mechanistic significance (e.g., mechanisms related to biota contaminant uptake) to “inverse” BAF-Cw relationships that reflect nothing more than regressing the log transformed inverse of Cw (i.e., negative log) against itself (i.e., positive log transformed), and using such regression models of BAF-Cw relationships that appear significant for predictive purposes, but are misleading. Spurious correlation arising in the analysis of BAF relationships can potentially appear in more subtle forms as well, including regressing variables such as dissolved organic carbon (DOC) that are correlated with Cw. We conclude that conducting a direct analysis by examining the relationship between Cbiota and Cw (or Cbiota and other variables) rather than evaluating a ratio (BAF) is less ambiguous and subject to error, more easily interpreted, and would lead to more supportable conclusions. © 2014 Elsevier B.V. All rights reserved.
Contents 1. 2. 3.
4.
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . Illustration of spurious correlation using Everglades survey data . . . . . Spurious correlation in recent literature on mercury bioaccumulation 3.1. Direct forms of spurious correlation . . . . . . . . . . . . . . 3.2. Indirect forms of spurious correlation . . . . . . . . . . . . . 3.3. Other problems related to spurious correlation . . . . . . . . . Summary and conclusions . . . . . . . . . . . . . . . . . . . . . .
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⁎ Corresponding author. Tel.: +1 850 443 4626. E-mail addresses: [email protected] (C.D. Pollman), [email protected], [email protected] (D.M. Axelrad).
http://dx.doi.org/10.1016/j.scitotenv.2014.07.050 0048-9697/© 2014 Elsevier B.V. All rights reserved.
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C.D. Pollman, D.M. Axelrad / Science of the Total Environment 496 (2014) vi–xii
Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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1. Introduction
2. Illustration of spurious correlation using Everglades survey data
In his book The Life of Reason, the philosopher George Santayana (1906) observed that “[t]hose who cannot remember the past are condemned to repeat it” — an aphorism that certainly appears to be true in aquatic ecology for the issue of spurious correlation. Spurious correlation may occur when, in the process of evaluating the relationship between variables, a common variable appears on both sides of the equation. Typically this occurs when the dependent variable comprises a ratio with the common variable, x, in the denominator, and the constructed ratio is then plotted as a function of the common variable by itself (Eq. (1)), or with the common variable appearing in the denominator of a second ratio (Eq. (2)):
We use data on Gambusia (mosquitofish) Hg concentrations and water column MeHg concentrations collected by the USEPA between 1993 and 2005 as part of their Regional Environmental Monitoring and Assessment Program (R-EMAP; Scheidt and Kalla, 2007) to illustrate some fundamental features of spurious correlation as it relates Hg BAFs in aquatic ecosystems. Our analysis has two components — first, we construct plots of the relationship between both observed Gambusia Hg concentrations and water column MeHg concentrations, and the resultant BAF values as a function of water column MeHg concentrations. The second component duplicates the analyses conducted for the observed data but uses synthesized Gambusia Hg and MeHg concentrations generated randomly with lognormal distributions that match the range of the observed distributions. The synthesized data were constructed with lognormal distributions because the observed data more closely approximate lognormal rather than normal distributions. Results for both the observed and simulated data are shown in Fig. 1. Because the observed data show only a weak correlation between Gambusia Hg and water column MeHg concentrations (r2 = 0.11 (Fig. 1a) for log-transformed concentrations), the observed and simulated results closely mimic each other. For example, because the data are lognormally distributed, the plot of observed and synthesized Gambusia Hg concentrations as a function of MeHg concentrations both have few observations where high concentrations of Gambusia Hg correspond to high concentrations of MeHg. When BAF values are plotted against MeHg concentrations, both the observed and the synthesized distributions assume a characteristic hyperbolic shape that reflects the fact that the curve is essentially a plot of the inverse of MeHg concentrations – weakly modified by Gambusia Hg concentrations – against MeHg concentrations (Fig. 1b and c). This is illustrated in Fig. 2, which superimposes the line representing the inverse of MeHg concentrations scaled by a factor ϕ comprising the geometric mean Gambusia Hg concentration (105 ng/g) multiplied by 1000 to make the units equivalent to the BAF values:
y ¼ f ðxÞ x
ð1Þ
y b ¼f : x x
ð2Þ
The difficulty is that the resultant relationship, which can appear to have clear statistical significance, is viewed as something meaningful, when in reality the relationship owes its functional and statistical significance to the common variable appearing on both sides of the equation. This problem was first identified as a concern in the biological sciences by Pearson (1897), and has long been recognized as a problem that requires attention in aquatic ecology (e.g., Kenney, 1982, Berges, 1997, Jackson and Somers, 1991, Kronmal, 1993; Krambeck, 1995; Brett, 2004; Håkanson and Stenström-Khalili, 2009; Stenström-Khalili and Håkanson, 2009). Despite such a rich history of admonitions, it seems that periodic reminders and expositions of this issue are nonetheless prudent and necessary. As we will demonstrate, we contend that spurious correlation is an issue in studies of mercury (Hg) biogeochemical cycling in aquatic ecosystems where bioaccumulation and bioconcentration factors (BAF and BCF, respectively) often are used as tools for evaluating bioaccumulation of mercury and methylmercury (MeHg) in particular. A BAF can be defined as the ratio of the concentration of a chemical contaminant in the tissue of an aquatic organism to its concentration in water, in situations where both the organism and its food are exposed to the chemical. In contrast, a BCF is the ratio of the concentration of a chemical in the tissue of an aquatic organism to its concentration in water, in situations where the organism is exposed to the chemical through the water only (US EPA, 2003). As such, Hg BAF values are constructed as the ratio of biota Hg concentrations (Cbiota) and aqueous phase concentrations of Hg (Cw): BAF ¼
Cbiota : Cw
φ¼
105 1000: Cw
ð4Þ
The asymptotic character of the curve reflects the degree to which the two variables comprising the BAF ratio are correlated. If they are highly correlated, then the resultant BAF values will vary with some error around a value that equals the slope of that relationship and that is invariant with changes in MeHg concentrations (assuming an intercept of zero). This is shown in the following two equations: Cbiota ¼ β Cw þ ε
ð5Þ
0
ð6Þ
ð3Þ 0
BAF ¼ β þ ε BCFs are constructed in an identical manner, but the ratio is typically used for primary producers because bioconcentration is defined to reflect direct uptake of the contaminant from water only, while BAFs reflect trophic transfer (dietary bioaccumulation) as well. Because methylmercury (MeHg) is the chemical species of mercury that characteristically enters the base of aquatic food webs and is involved in trophic transfer (Seixas et al. 2014), Hg BCF/BAFs typically are calculated using Cw concentrations of MeHg, although total Hg concentrations are used as well. Spurious correlation can thus arise when researchers look for relationships between BAF or BCF and Cw.
where β is the slope of the relationship between Cbiota and Cw, ε is the residual error in the model relationship, β′ is β ∗ 1000 to ensure dimensional consistency, and ε′ is ε divided by Cw ∗ 1000. When plotting BAF as a function of Cw, this “scaling” of the residual error by Cw results in greatly magnifying the effect of measurement error on calculated BAF values at the lower end of the distribution of aqueous phase contaminant concentrations. As aqueous phase concentrations increase, the relative magnitude of ε′ vis-à-vis β is reduced, and BAF values approach and then approximate β. This is shown in Fig. 3, which assumes that
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a
b
c
d
e
f
Fig. 1. Comparison of Gambusia Hg concentrations and resultant BAF relationship with water column MeHg concentrations for both observed (Everglades) and synthesized data. The synthetic data set comprises uncorrelated biota and water column MeHg concentrations to illustrate the effects of spurious correlation. Upper panels — observed Everglades data (N = 703); lower panels — synthetic data (N = 1000).
Cbiota is a highly correlated function (in this case, r2 = 0.96) of Cw, and with β = 300. This is also in contrast with the scenario where Cbiota and Cw are weakly correlated or uncorrelated — in this case BAF approaches zero as Cw increases (Fig. 1b and e). It is also worthwhile noting that, when Cbiota and Cw are uncorrelated, the magnitude of the correlation between BAF and Cw is a function of the relative differences in standard deviations (i.e., coefficients of variation or CV) for the variables Cbiota and Cw (Kenney, 1991). For example, if the CVs are identical, the coefficient of determination (r2) between
BAF and Cw will approximate 0.5. The larger the CV of Cw relative to Cbiota, the more the variance in BAF reflects the variance in Cw, and the more closely the BAF-Cw relationship functionally approximates the curve defined by 1/Cw (and thus the stronger the negative correlation). Likewise, as CVbiota increasingly exceeds CVw, the weaker the correlation between BAF and Cw, and the relationship increasingly approximates the distribution of Cbiota divided by a constant (mean Cw). In many aquatic ecosystems, the CV for aqueous MeHg concentrations well exceeds that for biota Hg concentrations – for example, the ratio of CVbiota to CVw in Florida aquatic ecosystems ranges from 1.6 for the Everglades to 3.2 for streams (N = 130 streams; data from Pollman (2012)) – making Hg-related BAF-Cw relationships particularly susceptible to strong, spurious inverse correlations. 3. Spurious correlation in recent literature on mercury bioaccumulation 3.1. Direct forms of spurious correlation
Fig. 2. Observed BAF for Everglades Gambusia as a function of observed water column MeHg concentrations. Superimposed on the plot (red curve) is the inverse of MeHg concentrations multiplied by a numerator constant – the observed geometric mean Gambusia concentration – plotted against MeHg.
Several papers over the past decade or so have examined variations in Hg BAF or BCF values and have emphasized the importance of the “inverse” relationship between these ratios and the aqueous phase concentration of the Hg species (total Hg or MeHg) while failing to explicitly recognize that the inverse relationship is simply spurious correlation. This includes McGeer et al. (2003) and DeForest et al. (2007), who evaluated the relationships between BAFs and exposure concentrations (both log-transformed) for numerous species in part to illustrate that a fundamental and implicit aspect of a robust BAF necessary for hazard assessment – viz., that BAF remains constant over a range of conditions and be independent of exposure – is often violated for a number of trace elements, including Hg. In both studies linear regression fit statistics were used to establish the importance of the “inverse” relationship. DeForest et al. (2007) conclude that “multiple mechanisms” (e.g., active regulation of uptake, uptake kinetics) were
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a
b
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c
Fig. 3. Comparison of biota Hg concentrations and resultant BAF relationship with water column MeHg concentrations for a synthesized data set where biota Hg concentrations are strongly correlated (r2 = 0.96) with water column MeHg concentrations (N = 1000). Panel a = direct plot of Cbiota vs. Cw.; panel b — linear plot of BAF vs. Cw; and panel c — log–log plot of BAF vs. Cw.
potentially responsible when “statistically significant” inverse relationships were observed between BAF and Cw. As we have demonstrated in our analysis of Everglades and synthesized bioaccumulation data, however, we assert that the statistical significance of the “inverse” relationship identified by DeForest et al. (2007) simply reflects that they are fundamentally regressing the negative of log Cw against log Cw and that the underlying relationship between Cbiota and Cw for many of the organisms evaluated by DeForest et al. (2007) is weak or non-existent. It is this latter point that should be of interest to researchers, and we contend that DeForest et al. (2007) should be asking that question more directly. An interesting aspect to this question relates to whether the lack of a clear relationship between Cbiota and Cw represents mechanisms governing Hg bioaccumulation that relates to direct cellular processes such as saturable uptake kinetics or active regulation as suggested by DeForest et al. (2007), or whether the real relationship between Cbiota and Cw is obscured because of the confounding influence of other variables not included in the analysis. Returning to the Everglades Gambusia data as an example, recall that a simple model of (log-transformed) Gambusia Hg as a function of MeHg yields a rather weak relationship (r2 = 0.11). The standardized β coefficient, which describes the response of the dependent variable standardized with unit variance to a one standard deviation change in the independent variable, equals 0.36. If we include other variables in the model such as DOC and sulfate that also influence Gambusia Hg concentrations significantly, the relationship that emerges between MeHg and Gambusia Hg concentrations is stronger statistically, and more important with respect to influencing Gambusia Hg concentrations (standardized β coefficient equal to 0.53). It is interesting to note that DeForest et al. (2007) recognize that the absence of the inverse relationship can reflect bioaccumulation at a rate proportional to the exposure concentration. However, they also suggest that the absence of the inverse relationship may simply be an artifact of the data collected. In reality, and as we have demonstrated through simulation exercises and algebraically, the converse is likely true. If the BCF-contaminant water concentration relationship is insignificant over a reasonable range of contaminant water concentrations, then the direct relationship between biota and aquatic contaminant concentrations must be statistically significant and strong. Another example where lack of a relationship between Cbiota and Cw was seen to reflect mechanisms of Hg bioaccumulation is that of Southworth et al. (2004), who measured aqueous MeHg and total Hg, along with fish tissue mercury concentrations from 28 sites in 13 streams in Tennessee, North Carolina, Virginia, and Kentucky. BAF values for fish were constructed based on both aqueous total and MeHg concentrations, and the relationships between these BAFs and aqueous MeHg and total Hg were evaluated to determine the efficacy of using a single BAF to describe Hg bioaccumulation. Southworth et al. (2004) found that the MeHg-based BAF regressed against aqueous
MeHg concentrations essentially showed no relationship, while the total Hg-based BAF was inversely correlated with aqueous total Hg. In addition, Southworth et al. (2004) regressed the percentage of aqueous total Hg comprised by MeHg against aqueous total Hg and observed that the relationship was negative and significant. Based on these three sets of results, Southworth et al. (2004) concluded that the negative association of BAF with aqueous total Hg reflected relatively lower MeHg concentrations as total Hg concentrations increased, presumably because of substrate saturation kinetics. Southworth et al. (2004), however, compounded the problem of spurious correlation related to BAFaqueous concentration regression by introducing a second spurious relationship — viz. the inverse relationship between MeHg as a percentage of total Hg in water, and total Hg in water, to help interpret the BAF results. More specifically, a close examination of their data shows no significant correlation between MeHg and total Hg concentrations in water (r2 = 0.032; p = 0.365). We thus submit that (1) the lack of correlation and relatively tight distribution of MeHg-based BAF with aqueous MeHg reflects the fact that fish Hg concentrations in the systems studied by Southworth et al. (2004), are indeed linearly related to aqueous MeHg concentrations; (2) the inverse relationship between percent MeHg and total Hg in water cannot be used to support their notion of substrate saturation limiting MeHg production; and (3) the negative relationship between total Hg-based BAF and aqueous total Hg cannot be interpreted to reflect the supposed percent MeHg — total Hg in water relationship, and that the negative BAF relationship is simply spurious correlation. More simply stated, fish tissue Hg concentrations in the systems studied by Southworth et al. (2004) are related to aqueous MeHg concentrations, but not to aqueous total Hg concentrations. A very recent example of spurious correlation in the interpretation of variations in Hg BAF/BCF is Bergman and Bump (2014a). Bergman and Bump (2014a) analyzed Hg bioaccumulation in moose and beaver (Alces alces and Castor canadensis, respectively) resulting from foraging on macrophytes which had bioconcentrated Hg. As part of their analysis, Bergman and Bump (2014a) computed bioconcentration factors (BCFs) for two macrophyte species, Nuphar variegata and Utricularia vulgaris, as the ratio of wet weight macrophyte MeHg concentration to the MeHg concentration measured in the water column. Bergman and Bump (2014a) then plotted BCF for MeHg for both macrophyte species as a function of the water column MeHg concentration and, noting an inverse relationship between BCFwater and Cwater, then fit separate two-parameter exponential equations for each macrophyte species. Bergman and Bump (2014a) provide coefficients of determination for each of the two models (r2 = 0.78 and 0.84 for U. vulgaris and N. variegata, respectively) and corresponding p values to support the statistical significance of the models. Bergman and Bump (2014a) then proceeded to conclude that the “pattern of MeHg bioconcentration from water to plants suggests that as MeHg decreases in water, plant MeHg BCFs increase nonlinearly.”
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In reality, and not surprisingly based on our earlier simulation analyses, this nonlinear relationship noted by Bergman and Bump (2014a) was simply a spurious correlation resulting from their exponential model including Cw as both dependent and independent variables in the equation. Indeed, if we assume that plant MeHg concentrations are constant and thus not related to aqueous MeHg concentrations, we can produce a model of the same form and nearly identical fit and fit statistics as Bergman and Bump's (2014a) model. This is shown in Fig. 4 for N. variegata (r 2 = 0.88, p b 0.0001). In other words, we can create essentially the same inverse relationship between BCFwater and C water as observed by Bergman and Bump (2014a) simply by plotting the inverse of Cwater as a function of itself. Thus, all that their model is telling us is the obvious: that there is an exponential decay in the inverse of MeHg as the concentration of MeHg is increased! We should note that Bergman and Bump subsequently recognized the inherent problems with this aspect of their paper and have published a corrigendum acknowledging the spurious correlation (Bergman and Bump, 2014b). 3.2. Indirect forms of spurious correlation Spurious correlation also can arise subtly when BAF dynamics are examined with respect to other variables. When a seemingly independent variable z is regressed against a ratio, any resultant correlation may reflect simply a correlation of z with one of the individual terms in the ratio, and not a meaningful relationship with the ratio itself. For example, Rolfhus et al. (2011) found that concentrations of dissolved organic carbon (DOC) were negatively correlated with seston and zooplankton BAF values (r2 = 0.46 and 0.26, respectively) for a series of lakes and experimental systems in the Upper Midwest and southern Ontario, including Lake Superior. Their conclusion was that the negative relationship was consistent with the fact that DOC competitively binds Hg relative to particles at higher DOC concentrations. However, DOC was also correlated with MeHg, and the correlation is stronger (r2 = 0.69). Thus, while we agree that higher DOC concentrations can limit the bioavailability of MeHg for uptake, we contend that the possibility of spurious correlation in the BAF regression limits the ability to draw supportable conclusions, and that direct analyses of the multivariate relationship between
Fig. 4. MeHg BCF for N. variegata plotted against water column MeHg concentration. The plot compares the predicted relationship obtained from Bergman and Bump's (2014a) BCF model for N. variegata with a model fitted with hypothetical data holding N. variegata MeHg concentrations constant over the same range of observed MeHg concentrations.
zooplankton or seston MeHg concentrations and DOC and aqueous MeHg concentrations would be more appropriate. 3.3. Other problems related to spurious correlation One highly misleading and troubling aspect of spurious correlation as it relates to Hg BAF factors is the idea that statistical models constructed from regression analysis of variations in BAF to variations in Cw can be used to predict biota Hg concentrations as a function of a specified water column Hg concentration. We cite Deforest et al. (2007) as a clear example of this problem. DeForest et al. (2007) use log-linear regression models constructed from BAF-Cw relationships to first estimate the BAF that corresponds to a specified value for Cw; this estimated BAF value is then used to estimate Cbiota. The problem of course is spurious correlation that results in a regression model that is largely capturing variations in the negative log of Cw, and does a poor job of capturing the variations in Cbiota. As a result, the BAF model itself has virtually no value in predicting tissue concentrations. We can illustrate this problem using data for N. variegata and water column concentrations of MeHg abstracted from Bergman and Bump (2014a,b) (Fig. 5a). Using these data, we can fit a log–log model that explains 88% of the variance in BCF values — which on the surface most would agree is a good model fit (Fig. 5b). But does the model provide any meaningful information that justifies its use? Fig. 6 shows the comparison between observed and “back-predicted” values for both N. variegata and water column MeHg concentrations (all log10 transformed), and the observed and predicted values for BCF (also log10 transformed). As the plots illustrate, the BCF model captures and is driven by the variance in water column MeHg concentrations, and the degree that the variance in BCF is explained is very nearly the same as the correlation between observed and predicted water column MeHg concentrations. We can better understand why this is so by examining the contributions of Cbiota and Cw to the total variance in the log-transformed BCF values used to fit the model. The variance of log10 BCF is 0.181, while the variances for aqueous MeHg and for N. variegata MeHg concentrations (also log10 transformed) are 0.176 and 0.022 respectively. Assuming normality and independence between Cbiota and Cw, the variance in the log10 BCF value is the sum of the two component variances (that the two terms do not add up identically to 0.181 reflects the fact that the variables are not normally distributed and that Cbiota and Cw are very weakly correlated). The BAF model thus fails miserably to predict reasonably accurate N. variegata MeHg concentrations (Fig. 6b). As a point of fact, the model fails because it produces precisely the same predictions for the log-transformed biota tissue MeHg concentrations as one would produce from modeling tissue concentrations directly as a function of water column MeHg concentrations. Because that underlying, fundamental relationship (Fig. 5a) is weak and insignificant, the ability of the BAF model to predict variations in biota MeHg is identically weak and insignificant. Restated, because the fit statistics are inflated by the spurious correlation, the BAF model masks the strength of the real, underlying relationship between biota MeHg and water column concentrations of MeHg. As a result, the BAF model tells us nothing that is useful, the fitted equation serves no meaningful purpose, and the model has the very real risk of being misused or misinterpreted. A final concern about the use of BAF as a metric in evaluating Hg bioaccumulation in aquatic ecosystems is that the concept of BAF has the inherent risk of confusing researchers who do not critically understand the implications of BAF as a ratio. An example of misinterpreting BAF values is a recent paper by Julian (2013) in which he examined Hg bioaccumulation and BAF in particular in the Florida Everglades. In his analysis, Julian (2013) notes regional differences in BAF values for Gambusia and assumes that lower BAF levels likely reflect inefficiencies in MeHg production. The inference in his analysis is that lower BAF values are the product of lower MeHg concentrations. In reality, and as we have shown, because fish tissue Hg concentrations are only
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a
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b
Fig. 5. Plot of macrophyte N. variegata MeHg concentrations (ng g−1 wet weight) as a function of water column MeHg concentrations (panel a) and resultant BCF-MeHg relationship (panel b). Data from Bergman and Bump (2014b).
weakly correlated with MeHg in the Everglades, spurious correlation results in a strong negative relationship between BAF and MeHg. Thus the regions in the Everglades where BAF values are lower actually have higher MeHg concentrations (Pollman and Axelrad, in press). In this case, using BAF by itself to draw conclusions about underlying relationships regarding mercury methylation rather than examining the variables directly leads to the wrong conclusion. 4. Summary and conclusions While BAF/BCF values can certainly be useful, particularly in the context of evaluating Hg bioaccumulation within a given aquatic ecosystem, reduction of the underlying relationship between biota and aqueous phase Hg concentrations to a single ratio has inherent risks, including spurious correlation. If the ratio is presented as a constant, then this implies that biota tissue Hg concentrations increase linearly with aqueous phase Hg concentrations. For this ratio thus to be unambiguous and fully meaningful, the direct relationship between untransformed biota and aqueous phase Hg concentrations needs to be not only statistically significant and linear, but the intercept also needs to be zero (see Jackson and Somers, 1991). Non-zero intercepts can arise, for example, because biota tissue concentrations typically reflect an integrated MeHg signal over time. Aqueous phase concentrations of MeHg characteristically are far more dynamic than biota concentrations, and thus may not adequately represent the true signal contributing to biota concentrations, particularly if only a few measurements of aqueous MeHg over time are used to construct the ratio. In part because of this source of bias, and because of other confounding factors, USEPA (2010) has recommended using BAF values to set water quality criteria only on a site-specific basis, and abandoned the idea of setting a nationwide BAF-based MeHg criterion (USEPA, 2001).
a
b
We have cited McGeer et al. (2003) and DeForest et al. (2007) as examples of spurious correlation arising from comparing variations in Hg BAF values to variations in aqueous MeHg concentrations. In both cases, the analyses that lead to spurious correlation were motivated by a cognition of fundamental problems in the application of Hg BAF values to hazard assessment and setting water quality criteria in particular. While we do not disagree with their criticisms of such uses of BAF, our contention is that their analyses should have been conducted by directly examining the relationship between biota Hg and aqueous phase Hg concentrations. Such an analysis then can be used to unambiguously comment on, for example, when the development of a water quality concentration criterion for MeHg is supportable. Restated, the use of BAF values to set water quality criteria should be examined with a jaundiced eye not because regressing BAF against aqueous MeHg often leads to “statistically significant” inverse relationships – those relationships are seen clearly as the product of spurious correlation – but rather because the underlying relationship of the variable of most critical importance with respect to risk – the biota Hg concentration – with aqueous MeHg concentrations is often statistically weak or nonexistent. Such direct analyses offer a number of critical advantages, including evaluating the functional form and robustness of the Hg biota concentration — Hg aqueous concentration relationship, assessing whether the data characteristics match the underlying assumptions of the statistical model used to evaluate the relationship, and ascribing uncertainty to predictions. It is often tempting to clean up messy bivariate relationships by constructing ratios and then conducting the analysis with the common variable on both sides of the equation. Any gains from such practices are highly questionable, and it is hard to conceive when the practice yields any useful information that justifies its use in favor of conducting a more direct analysis. Nonetheless the problem of spurious correlation, as
c
Fig. 6. Plots of observed vs. predicted BCF values (panel a), observed vs. predicted tissue MeHg concentrations (log10 transformed; panel b), and observed vs. predicted water column MeHg concentrations (log10 transformed; panel c) for the macrophyte N. variegata. Predictions are based on the BCF vs. MeHg regression model shown in Fig. 5 (panel b).
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Neyman (1972) stated forty plus years ago, “ha(s) been ruining empirical statistical research from time immemorial” and continues to be persistent to this day. Acknowledgments The authors wish to acknowledge James Bennett, Co-Editor-in-Chief of STOTEN, for encouraging us to take our original manuscript, which was submitted as a letter to the editor commenting on a paper published in STOTEN, and develop it into an independent scientific commentary. The authors also wish to thank Pete Kalla and Dan Scheidt of the US EPA for making the Everglades R-EMAP data accessible. References Berges JA. Ratio, regression statistics, and “spurious” correlation. Limnol Oceanogr 1997; 42(5):1006–7. http://dx.doi.org/10.4319/lo.1997.42.5.1006. Bergman BG, Bump JK. Mercury in aquatic forage of large herbivores: impact of environmental conditions, assessment of health threats, and implications for transfer across ecosystem compartments. Sci Total Environ 2014a;479–480:66–76. http://dx.doi. org/10.1016/j.scitotenv.2014a.01.102. Bergman BG, Bump JK. Corrigendum to “Mercury in aquatic forage of large herbivores: Impact of environmental conditions, assessment of health threats, and implications for transfer across ecosystem compartments”. Sci Total Environ 2014b;479–480: 66–76. Sci Total Environ 493 2014b 1128 http://dx.doi.org/10.1016/j.scitotenv.2014. 05.103. Brett MT. When is a correlation between non-independent variables “spurious”? Nordic Soc Oikos 2004;105(3):647–56. http://dx.doi.org/10.1111/j.0030-1299.12777.x. DeForest DK, Brix KV, Adams WJ. Assessing metal bioaccumulation in aquatic environments: the inverse relationship between bioaccumulation factors, trophic transfer factors and exposure concentration. Aqua\t Toxicol 2007;84:236–46. http://dx.doi. org/10.1016/j.aquatox.2007.02.022. Jackson DA, Somers KM. The spectre of “spurious” correlations. Oecologia 1991;86(1): 147–51. http://dx.doi.org/10.1007/BF00317404. Julian P. Mercury bio-concentration factor in mosquito fish (Gambusia spp.) in the Florida Everglades. Bull Environ Contam Toxicol 2013;90:329–32. http://dx.doi.org/10.1007/ s00128-012-0939-6. Håkanson L, Stenström-Khalili MI. Uncertainties in data and spurious correlations related to the Redfield ratio. Int Rev Hydrobiol 2009;94:338–51. http://dx.doi.org/10.1002/ iroh.200811110. Kenney BA. Beware of spurious self-correlations! Water Resour Res 1982;18:1041–8. http://dx.doi.org/10.1029/WR018i004p01041. Kenney BA. Comment on ‘Some misconceptions about the spurious correlation problem in the ecological literature’ by Y.T. Prairie and D.F. Bird. Oecologia 1991;86:152.
Krambeck H-J. Application and abuse of statistical methods in mathematical modelling in limnology. Ecol Model 1995;78:7–15. http://dx.doi.org/10.1016/0304-3800(94) 00113-V. Kronmal RA. Spurious correlation and the fallacy of the ratio standard revisited. J R Stat Soc A Stat Soc 1993;156(3):379–92. http://dx.doi.org/10.2307/2983064. McGeer JC, Brix KV, Skeaff JM, DeForest DK, Brigham SI, Adams WJ, et al. Inverse relationship between bioconcentration factor and exposure concentration for metals: implications for hazard assessment of metals in the aquatic environment. Environ Toxicol Chem 2003;22(5):1017–37. http://dx.doi.org/10.1002/etc.5620220509. Neyman J. Epilogue of the health-pollution conference. In: Le Cam LM, Neyman J, Scott EL, editors. Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability. Berkeley, CA: University of California Press; 1972. p. 575–87. Pearson K. Mathematical contributions to the theory of evolution — on a form of spurious correlation which may arise when indices are used in the measurement of organs. Proc Roy Soc London 1897;60:489–98. http://dx.doi.org/10.1098/rspl.1896.0076. Pollman CD. Integrated report on aquatic modeling. Final reported submitted to the Florida Department of Environmental Protection, Tallahassee, FL. Gainesville, FL: Aqua Lux Lucis, Inc.; 2012. Pollman CD, Axelrad DM. Mercury bioaccumulation and bioaccumulation factors for Everglades mosquitofish as related to sulfate: a reanalysis of Julian II. Bull Environ Contam Toxicol 2014. [in press]. Rolfhus KR, Hall BD, Monson BA, Paterson MJ, Jeremiason JD. Assessment of mercury bioaccumulation within the pelagic food web of lakes in the western Great Lakes region. Ecotoxicology 2011;20:1520–9. http://dx.doi.org/10.1007/s10646-011-0733-y. Santayana G. The life of reason: reason in common sense. New York: Charles Scribner's Sons; 1906. Scheidt DJ, Kalla PI. Everglades ecosystem assessment: water management and quality, eutrophication, mercury contamination, soils and habitat: monitoring for adaptive management: a R-EMAP status report. Athens, GA: USEPA Region 4; 2007. [EPA 904-R-07-001. 98 pp. http://www.epa.gov/region4/sesd/reports/epa904r07001/ epa904r07001.pdf]. Seixas TG, Moreira I, Siciliano S, Olaf Malm O, Kehrig HA. Differences in methylmercury and inorganic mercury biomagnification in a tropical marine food web. Bull Environ Contam Toxicol 2014;92:274–8. http://dx.doi.org/10.1007/s00128-014-1208-7. Southworth GR, Peterson MJ, Bogle MA. Bioaccumulation factors for mercury in fish. Environ Pract 2004;6:135–43. http://dx.doi.org/10.1017/S1466046604000249. Stenström-Khalili MI, Håkanson L. Variations and spurious correlations related to DIN, DIP, TN, TP, DIN/DIP and TN/TP in lakes, rivers, and marine systems. Open Mar Biol J 2009;3:28–35. http://dx.doi.org/10.2174/1874450800903010028. USEPA. Water quality criterion for the protection of human health: methylmercury. EPA823-R-01-0012001. Washington, DC: U.S. Environmental Protection Agency, Office of Water; 2001. USEPA. Methodology for deriving ambient water quality criteria for the protection of human health (2000). EPA-822-R-03-030. Technical support documentDevelopment of National Bioaccumulation FactorsWashington, DC: U.S. Environmental Protection Agency, Office of Water; 2003. USEPA. Guidance for implementing the January 2001 methylmercury water quality criterion. EPA 823-R-09-002 Washington, DC, 2010: U.S. Environmental Protection Agency, Office of Water; 2009.
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Review
Mercury bioaccumulation factors and spurious correlations Curtis D. Pollman a, Donald M. Axelrad b,⁎ a b
Aqua Lux Lucis, Inc., 8411 NW 55th Place, Gainesville, FL, USA Florida A&M University, Institute of Public Health, 1515 South Martin Luther King Blvd, Tallahassee, FL 32307, USA
H I G H L I G H T S • • • • •
Spurious correlation is surprisingly common in studies on mercury bioaccumulation. Correlations using bioaccumulation factors (BAF), a ratio, have inherent risks. BAFs are the ratio of contaminant levels in biota to those in the water column. Misleading inferences arise when correlating BAF with its component denominator. Direct analysis of component variables is less ambiguous than BAF correlations.
a r t i c l e
i n f o
Article history: Received 26 June 2014 Received in revised form 8 July 2014 Accepted 8 July 2014 Available online 1 August 2014 Editor: J.P. Bennett Keywords: Methylmercury Aquatic ecosystems Gambusia Everglades Synthetic data
a b s t r a c t While bioaccumulation factors (BAF) – the ratio of biota contaminant concentrations (Cbiota) to aqueous phase contaminant concentrations (Cw) – are useful in evaluating the accumulation of mercury (Hg) and other contaminants for various trophic levels in aquatic ecosystems, reduction of the underlying relationship between Cbiota and Cw to a single ratio (BAF) has inherent risks, including spurious correlation. Despite a long and rich history of remonstrations in the literature, several very recent publications evaluating Hg-related BAFs have suffered from false conclusions based on spurious correlation, and thus it seems that periodic reminders of the causes and risks of these errors are required. Herein we cite examples and explanations for unsupported conclusions from publications where authors using BAF-Cw relationships fail to recognize the underlying statistical significance (or lack thereof) of direct relationships between Cw and Cbiota. This fundamental error leads to other problems, including ascribing mechanistic significance (e.g., mechanisms related to biota contaminant uptake) to “inverse” BAF-Cw relationships that reflect nothing more than regressing the log transformed inverse of Cw (i.e., negative log) against itself (i.e., positive log transformed), and using such regression models of BAF-Cw relationships that appear significant for predictive purposes, but are misleading. Spurious correlation arising in the analysis of BAF relationships can potentially appear in more subtle forms as well, including regressing variables such as dissolved organic carbon (DOC) that are correlated with Cw. We conclude that conducting a direct analysis by examining the relationship between Cbiota and Cw (or Cbiota and other variables) rather than evaluating a ratio (BAF) is less ambiguous and subject to error, more easily interpreted, and would lead to more supportable conclusions. © 2014 Elsevier B.V. All rights reserved.
Contents 1. 2. 3.
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Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . Illustration of spurious correlation using Everglades survey data . . . . . Spurious correlation in recent literature on mercury bioaccumulation 3.1. Direct forms of spurious correlation . . . . . . . . . . . . . . 3.2. Indirect forms of spurious correlation . . . . . . . . . . . . . 3.3. Other problems related to spurious correlation . . . . . . . . . Summary and conclusions . . . . . . . . . . . . . . . . . . . . . .
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⁎ Corresponding author. Tel.: +1 850 443 4626. E-mail addresses: [email protected] (C.D. Pollman), [email protected], [email protected] (D.M. Axelrad).
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Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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1. Introduction
2. Illustration of spurious correlation using Everglades survey data
In his book The Life of Reason, the philosopher George Santayana (1906) observed that “[t]hose who cannot remember the past are condemned to repeat it” — an aphorism that certainly appears to be true in aquatic ecology for the issue of spurious correlation. Spurious correlation may occur when, in the process of evaluating the relationship between variables, a common variable appears on both sides of the equation. Typically this occurs when the dependent variable comprises a ratio with the common variable, x, in the denominator, and the constructed ratio is then plotted as a function of the common variable by itself (Eq. (1)), or with the common variable appearing in the denominator of a second ratio (Eq. (2)):
We use data on Gambusia (mosquitofish) Hg concentrations and water column MeHg concentrations collected by the USEPA between 1993 and 2005 as part of their Regional Environmental Monitoring and Assessment Program (R-EMAP; Scheidt and Kalla, 2007) to illustrate some fundamental features of spurious correlation as it relates Hg BAFs in aquatic ecosystems. Our analysis has two components — first, we construct plots of the relationship between both observed Gambusia Hg concentrations and water column MeHg concentrations, and the resultant BAF values as a function of water column MeHg concentrations. The second component duplicates the analyses conducted for the observed data but uses synthesized Gambusia Hg and MeHg concentrations generated randomly with lognormal distributions that match the range of the observed distributions. The synthesized data were constructed with lognormal distributions because the observed data more closely approximate lognormal rather than normal distributions. Results for both the observed and simulated data are shown in Fig. 1. Because the observed data show only a weak correlation between Gambusia Hg and water column MeHg concentrations (r2 = 0.11 (Fig. 1a) for log-transformed concentrations), the observed and simulated results closely mimic each other. For example, because the data are lognormally distributed, the plot of observed and synthesized Gambusia Hg concentrations as a function of MeHg concentrations both have few observations where high concentrations of Gambusia Hg correspond to high concentrations of MeHg. When BAF values are plotted against MeHg concentrations, both the observed and the synthesized distributions assume a characteristic hyperbolic shape that reflects the fact that the curve is essentially a plot of the inverse of MeHg concentrations – weakly modified by Gambusia Hg concentrations – against MeHg concentrations (Fig. 1b and c). This is illustrated in Fig. 2, which superimposes the line representing the inverse of MeHg concentrations scaled by a factor ϕ comprising the geometric mean Gambusia Hg concentration (105 ng/g) multiplied by 1000 to make the units equivalent to the BAF values:
y ¼ f ðxÞ x
ð1Þ
y b ¼f : x x
ð2Þ
The difficulty is that the resultant relationship, which can appear to have clear statistical significance, is viewed as something meaningful, when in reality the relationship owes its functional and statistical significance to the common variable appearing on both sides of the equation. This problem was first identified as a concern in the biological sciences by Pearson (1897), and has long been recognized as a problem that requires attention in aquatic ecology (e.g., Kenney, 1982, Berges, 1997, Jackson and Somers, 1991, Kronmal, 1993; Krambeck, 1995; Brett, 2004; Håkanson and Stenström-Khalili, 2009; Stenström-Khalili and Håkanson, 2009). Despite such a rich history of admonitions, it seems that periodic reminders and expositions of this issue are nonetheless prudent and necessary. As we will demonstrate, we contend that spurious correlation is an issue in studies of mercury (Hg) biogeochemical cycling in aquatic ecosystems where bioaccumulation and bioconcentration factors (BAF and BCF, respectively) often are used as tools for evaluating bioaccumulation of mercury and methylmercury (MeHg) in particular. A BAF can be defined as the ratio of the concentration of a chemical contaminant in the tissue of an aquatic organism to its concentration in water, in situations where both the organism and its food are exposed to the chemical. In contrast, a BCF is the ratio of the concentration of a chemical in the tissue of an aquatic organism to its concentration in water, in situations where the organism is exposed to the chemical through the water only (US EPA, 2003). As such, Hg BAF values are constructed as the ratio of biota Hg concentrations (Cbiota) and aqueous phase concentrations of Hg (Cw): BAF ¼
Cbiota : Cw
φ¼
105 1000: Cw
ð4Þ
The asymptotic character of the curve reflects the degree to which the two variables comprising the BAF ratio are correlated. If they are highly correlated, then the resultant BAF values will vary with some error around a value that equals the slope of that relationship and that is invariant with changes in MeHg concentrations (assuming an intercept of zero). This is shown in the following two equations: Cbiota ¼ β Cw þ ε
ð5Þ
0
ð6Þ
ð3Þ 0
BAF ¼ β þ ε BCFs are constructed in an identical manner, but the ratio is typically used for primary producers because bioconcentration is defined to reflect direct uptake of the contaminant from water only, while BAFs reflect trophic transfer (dietary bioaccumulation) as well. Because methylmercury (MeHg) is the chemical species of mercury that characteristically enters the base of aquatic food webs and is involved in trophic transfer (Seixas et al. 2014), Hg BCF/BAFs typically are calculated using Cw concentrations of MeHg, although total Hg concentrations are used as well. Spurious correlation can thus arise when researchers look for relationships between BAF or BCF and Cw.
where β is the slope of the relationship between Cbiota and Cw, ε is the residual error in the model relationship, β′ is β ∗ 1000 to ensure dimensional consistency, and ε′ is ε divided by Cw ∗ 1000. When plotting BAF as a function of Cw, this “scaling” of the residual error by Cw results in greatly magnifying the effect of measurement error on calculated BAF values at the lower end of the distribution of aqueous phase contaminant concentrations. As aqueous phase concentrations increase, the relative magnitude of ε′ vis-à-vis β is reduced, and BAF values approach and then approximate β. This is shown in Fig. 3, which assumes that
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a
b
c
d
e
f
Fig. 1. Comparison of Gambusia Hg concentrations and resultant BAF relationship with water column MeHg concentrations for both observed (Everglades) and synthesized data. The synthetic data set comprises uncorrelated biota and water column MeHg concentrations to illustrate the effects of spurious correlation. Upper panels — observed Everglades data (N = 703); lower panels — synthetic data (N = 1000).
Cbiota is a highly correlated function (in this case, r2 = 0.96) of Cw, and with β = 300. This is also in contrast with the scenario where Cbiota and Cw are weakly correlated or uncorrelated — in this case BAF approaches zero as Cw increases (Fig. 1b and e). It is also worthwhile noting that, when Cbiota and Cw are uncorrelated, the magnitude of the correlation between BAF and Cw is a function of the relative differences in standard deviations (i.e., coefficients of variation or CV) for the variables Cbiota and Cw (Kenney, 1991). For example, if the CVs are identical, the coefficient of determination (r2) between
BAF and Cw will approximate 0.5. The larger the CV of Cw relative to Cbiota, the more the variance in BAF reflects the variance in Cw, and the more closely the BAF-Cw relationship functionally approximates the curve defined by 1/Cw (and thus the stronger the negative correlation). Likewise, as CVbiota increasingly exceeds CVw, the weaker the correlation between BAF and Cw, and the relationship increasingly approximates the distribution of Cbiota divided by a constant (mean Cw). In many aquatic ecosystems, the CV for aqueous MeHg concentrations well exceeds that for biota Hg concentrations – for example, the ratio of CVbiota to CVw in Florida aquatic ecosystems ranges from 1.6 for the Everglades to 3.2 for streams (N = 130 streams; data from Pollman (2012)) – making Hg-related BAF-Cw relationships particularly susceptible to strong, spurious inverse correlations. 3. Spurious correlation in recent literature on mercury bioaccumulation 3.1. Direct forms of spurious correlation
Fig. 2. Observed BAF for Everglades Gambusia as a function of observed water column MeHg concentrations. Superimposed on the plot (red curve) is the inverse of MeHg concentrations multiplied by a numerator constant – the observed geometric mean Gambusia concentration – plotted against MeHg.
Several papers over the past decade or so have examined variations in Hg BAF or BCF values and have emphasized the importance of the “inverse” relationship between these ratios and the aqueous phase concentration of the Hg species (total Hg or MeHg) while failing to explicitly recognize that the inverse relationship is simply spurious correlation. This includes McGeer et al. (2003) and DeForest et al. (2007), who evaluated the relationships between BAFs and exposure concentrations (both log-transformed) for numerous species in part to illustrate that a fundamental and implicit aspect of a robust BAF necessary for hazard assessment – viz., that BAF remains constant over a range of conditions and be independent of exposure – is often violated for a number of trace elements, including Hg. In both studies linear regression fit statistics were used to establish the importance of the “inverse” relationship. DeForest et al. (2007) conclude that “multiple mechanisms” (e.g., active regulation of uptake, uptake kinetics) were
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b
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c
Fig. 3. Comparison of biota Hg concentrations and resultant BAF relationship with water column MeHg concentrations for a synthesized data set where biota Hg concentrations are strongly correlated (r2 = 0.96) with water column MeHg concentrations (N = 1000). Panel a = direct plot of Cbiota vs. Cw.; panel b — linear plot of BAF vs. Cw; and panel c — log–log plot of BAF vs. Cw.
potentially responsible when “statistically significant” inverse relationships were observed between BAF and Cw. As we have demonstrated in our analysis of Everglades and synthesized bioaccumulation data, however, we assert that the statistical significance of the “inverse” relationship identified by DeForest et al. (2007) simply reflects that they are fundamentally regressing the negative of log Cw against log Cw and that the underlying relationship between Cbiota and Cw for many of the organisms evaluated by DeForest et al. (2007) is weak or non-existent. It is this latter point that should be of interest to researchers, and we contend that DeForest et al. (2007) should be asking that question more directly. An interesting aspect to this question relates to whether the lack of a clear relationship between Cbiota and Cw represents mechanisms governing Hg bioaccumulation that relates to direct cellular processes such as saturable uptake kinetics or active regulation as suggested by DeForest et al. (2007), or whether the real relationship between Cbiota and Cw is obscured because of the confounding influence of other variables not included in the analysis. Returning to the Everglades Gambusia data as an example, recall that a simple model of (log-transformed) Gambusia Hg as a function of MeHg yields a rather weak relationship (r2 = 0.11). The standardized β coefficient, which describes the response of the dependent variable standardized with unit variance to a one standard deviation change in the independent variable, equals 0.36. If we include other variables in the model such as DOC and sulfate that also influence Gambusia Hg concentrations significantly, the relationship that emerges between MeHg and Gambusia Hg concentrations is stronger statistically, and more important with respect to influencing Gambusia Hg concentrations (standardized β coefficient equal to 0.53). It is interesting to note that DeForest et al. (2007) recognize that the absence of the inverse relationship can reflect bioaccumulation at a rate proportional to the exposure concentration. However, they also suggest that the absence of the inverse relationship may simply be an artifact of the data collected. In reality, and as we have demonstrated through simulation exercises and algebraically, the converse is likely true. If the BCF-contaminant water concentration relationship is insignificant over a reasonable range of contaminant water concentrations, then the direct relationship between biota and aquatic contaminant concentrations must be statistically significant and strong. Another example where lack of a relationship between Cbiota and Cw was seen to reflect mechanisms of Hg bioaccumulation is that of Southworth et al. (2004), who measured aqueous MeHg and total Hg, along with fish tissue mercury concentrations from 28 sites in 13 streams in Tennessee, North Carolina, Virginia, and Kentucky. BAF values for fish were constructed based on both aqueous total and MeHg concentrations, and the relationships between these BAFs and aqueous MeHg and total Hg were evaluated to determine the efficacy of using a single BAF to describe Hg bioaccumulation. Southworth et al. (2004) found that the MeHg-based BAF regressed against aqueous
MeHg concentrations essentially showed no relationship, while the total Hg-based BAF was inversely correlated with aqueous total Hg. In addition, Southworth et al. (2004) regressed the percentage of aqueous total Hg comprised by MeHg against aqueous total Hg and observed that the relationship was negative and significant. Based on these three sets of results, Southworth et al. (2004) concluded that the negative association of BAF with aqueous total Hg reflected relatively lower MeHg concentrations as total Hg concentrations increased, presumably because of substrate saturation kinetics. Southworth et al. (2004), however, compounded the problem of spurious correlation related to BAFaqueous concentration regression by introducing a second spurious relationship — viz. the inverse relationship between MeHg as a percentage of total Hg in water, and total Hg in water, to help interpret the BAF results. More specifically, a close examination of their data shows no significant correlation between MeHg and total Hg concentrations in water (r2 = 0.032; p = 0.365). We thus submit that (1) the lack of correlation and relatively tight distribution of MeHg-based BAF with aqueous MeHg reflects the fact that fish Hg concentrations in the systems studied by Southworth et al. (2004), are indeed linearly related to aqueous MeHg concentrations; (2) the inverse relationship between percent MeHg and total Hg in water cannot be used to support their notion of substrate saturation limiting MeHg production; and (3) the negative relationship between total Hg-based BAF and aqueous total Hg cannot be interpreted to reflect the supposed percent MeHg — total Hg in water relationship, and that the negative BAF relationship is simply spurious correlation. More simply stated, fish tissue Hg concentrations in the systems studied by Southworth et al. (2004) are related to aqueous MeHg concentrations, but not to aqueous total Hg concentrations. A very recent example of spurious correlation in the interpretation of variations in Hg BAF/BCF is Bergman and Bump (2014a). Bergman and Bump (2014a) analyzed Hg bioaccumulation in moose and beaver (Alces alces and Castor canadensis, respectively) resulting from foraging on macrophytes which had bioconcentrated Hg. As part of their analysis, Bergman and Bump (2014a) computed bioconcentration factors (BCFs) for two macrophyte species, Nuphar variegata and Utricularia vulgaris, as the ratio of wet weight macrophyte MeHg concentration to the MeHg concentration measured in the water column. Bergman and Bump (2014a) then plotted BCF for MeHg for both macrophyte species as a function of the water column MeHg concentration and, noting an inverse relationship between BCFwater and Cwater, then fit separate two-parameter exponential equations for each macrophyte species. Bergman and Bump (2014a) provide coefficients of determination for each of the two models (r2 = 0.78 and 0.84 for U. vulgaris and N. variegata, respectively) and corresponding p values to support the statistical significance of the models. Bergman and Bump (2014a) then proceeded to conclude that the “pattern of MeHg bioconcentration from water to plants suggests that as MeHg decreases in water, plant MeHg BCFs increase nonlinearly.”
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In reality, and not surprisingly based on our earlier simulation analyses, this nonlinear relationship noted by Bergman and Bump (2014a) was simply a spurious correlation resulting from their exponential model including Cw as both dependent and independent variables in the equation. Indeed, if we assume that plant MeHg concentrations are constant and thus not related to aqueous MeHg concentrations, we can produce a model of the same form and nearly identical fit and fit statistics as Bergman and Bump's (2014a) model. This is shown in Fig. 4 for N. variegata (r 2 = 0.88, p b 0.0001). In other words, we can create essentially the same inverse relationship between BCFwater and C water as observed by Bergman and Bump (2014a) simply by plotting the inverse of Cwater as a function of itself. Thus, all that their model is telling us is the obvious: that there is an exponential decay in the inverse of MeHg as the concentration of MeHg is increased! We should note that Bergman and Bump subsequently recognized the inherent problems with this aspect of their paper and have published a corrigendum acknowledging the spurious correlation (Bergman and Bump, 2014b). 3.2. Indirect forms of spurious correlation Spurious correlation also can arise subtly when BAF dynamics are examined with respect to other variables. When a seemingly independent variable z is regressed against a ratio, any resultant correlation may reflect simply a correlation of z with one of the individual terms in the ratio, and not a meaningful relationship with the ratio itself. For example, Rolfhus et al. (2011) found that concentrations of dissolved organic carbon (DOC) were negatively correlated with seston and zooplankton BAF values (r2 = 0.46 and 0.26, respectively) for a series of lakes and experimental systems in the Upper Midwest and southern Ontario, including Lake Superior. Their conclusion was that the negative relationship was consistent with the fact that DOC competitively binds Hg relative to particles at higher DOC concentrations. However, DOC was also correlated with MeHg, and the correlation is stronger (r2 = 0.69). Thus, while we agree that higher DOC concentrations can limit the bioavailability of MeHg for uptake, we contend that the possibility of spurious correlation in the BAF regression limits the ability to draw supportable conclusions, and that direct analyses of the multivariate relationship between
Fig. 4. MeHg BCF for N. variegata plotted against water column MeHg concentration. The plot compares the predicted relationship obtained from Bergman and Bump's (2014a) BCF model for N. variegata with a model fitted with hypothetical data holding N. variegata MeHg concentrations constant over the same range of observed MeHg concentrations.
zooplankton or seston MeHg concentrations and DOC and aqueous MeHg concentrations would be more appropriate. 3.3. Other problems related to spurious correlation One highly misleading and troubling aspect of spurious correlation as it relates to Hg BAF factors is the idea that statistical models constructed from regression analysis of variations in BAF to variations in Cw can be used to predict biota Hg concentrations as a function of a specified water column Hg concentration. We cite Deforest et al. (2007) as a clear example of this problem. DeForest et al. (2007) use log-linear regression models constructed from BAF-Cw relationships to first estimate the BAF that corresponds to a specified value for Cw; this estimated BAF value is then used to estimate Cbiota. The problem of course is spurious correlation that results in a regression model that is largely capturing variations in the negative log of Cw, and does a poor job of capturing the variations in Cbiota. As a result, the BAF model itself has virtually no value in predicting tissue concentrations. We can illustrate this problem using data for N. variegata and water column concentrations of MeHg abstracted from Bergman and Bump (2014a,b) (Fig. 5a). Using these data, we can fit a log–log model that explains 88% of the variance in BCF values — which on the surface most would agree is a good model fit (Fig. 5b). But does the model provide any meaningful information that justifies its use? Fig. 6 shows the comparison between observed and “back-predicted” values for both N. variegata and water column MeHg concentrations (all log10 transformed), and the observed and predicted values for BCF (also log10 transformed). As the plots illustrate, the BCF model captures and is driven by the variance in water column MeHg concentrations, and the degree that the variance in BCF is explained is very nearly the same as the correlation between observed and predicted water column MeHg concentrations. We can better understand why this is so by examining the contributions of Cbiota and Cw to the total variance in the log-transformed BCF values used to fit the model. The variance of log10 BCF is 0.181, while the variances for aqueous MeHg and for N. variegata MeHg concentrations (also log10 transformed) are 0.176 and 0.022 respectively. Assuming normality and independence between Cbiota and Cw, the variance in the log10 BCF value is the sum of the two component variances (that the two terms do not add up identically to 0.181 reflects the fact that the variables are not normally distributed and that Cbiota and Cw are very weakly correlated). The BAF model thus fails miserably to predict reasonably accurate N. variegata MeHg concentrations (Fig. 6b). As a point of fact, the model fails because it produces precisely the same predictions for the log-transformed biota tissue MeHg concentrations as one would produce from modeling tissue concentrations directly as a function of water column MeHg concentrations. Because that underlying, fundamental relationship (Fig. 5a) is weak and insignificant, the ability of the BAF model to predict variations in biota MeHg is identically weak and insignificant. Restated, because the fit statistics are inflated by the spurious correlation, the BAF model masks the strength of the real, underlying relationship between biota MeHg and water column concentrations of MeHg. As a result, the BAF model tells us nothing that is useful, the fitted equation serves no meaningful purpose, and the model has the very real risk of being misused or misinterpreted. A final concern about the use of BAF as a metric in evaluating Hg bioaccumulation in aquatic ecosystems is that the concept of BAF has the inherent risk of confusing researchers who do not critically understand the implications of BAF as a ratio. An example of misinterpreting BAF values is a recent paper by Julian (2013) in which he examined Hg bioaccumulation and BAF in particular in the Florida Everglades. In his analysis, Julian (2013) notes regional differences in BAF values for Gambusia and assumes that lower BAF levels likely reflect inefficiencies in MeHg production. The inference in his analysis is that lower BAF values are the product of lower MeHg concentrations. In reality, and as we have shown, because fish tissue Hg concentrations are only
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Fig. 5. Plot of macrophyte N. variegata MeHg concentrations (ng g−1 wet weight) as a function of water column MeHg concentrations (panel a) and resultant BCF-MeHg relationship (panel b). Data from Bergman and Bump (2014b).
weakly correlated with MeHg in the Everglades, spurious correlation results in a strong negative relationship between BAF and MeHg. Thus the regions in the Everglades where BAF values are lower actually have higher MeHg concentrations (Pollman and Axelrad, in press). In this case, using BAF by itself to draw conclusions about underlying relationships regarding mercury methylation rather than examining the variables directly leads to the wrong conclusion. 4. Summary and conclusions While BAF/BCF values can certainly be useful, particularly in the context of evaluating Hg bioaccumulation within a given aquatic ecosystem, reduction of the underlying relationship between biota and aqueous phase Hg concentrations to a single ratio has inherent risks, including spurious correlation. If the ratio is presented as a constant, then this implies that biota tissue Hg concentrations increase linearly with aqueous phase Hg concentrations. For this ratio thus to be unambiguous and fully meaningful, the direct relationship between untransformed biota and aqueous phase Hg concentrations needs to be not only statistically significant and linear, but the intercept also needs to be zero (see Jackson and Somers, 1991). Non-zero intercepts can arise, for example, because biota tissue concentrations typically reflect an integrated MeHg signal over time. Aqueous phase concentrations of MeHg characteristically are far more dynamic than biota concentrations, and thus may not adequately represent the true signal contributing to biota concentrations, particularly if only a few measurements of aqueous MeHg over time are used to construct the ratio. In part because of this source of bias, and because of other confounding factors, USEPA (2010) has recommended using BAF values to set water quality criteria only on a site-specific basis, and abandoned the idea of setting a nationwide BAF-based MeHg criterion (USEPA, 2001).
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We have cited McGeer et al. (2003) and DeForest et al. (2007) as examples of spurious correlation arising from comparing variations in Hg BAF values to variations in aqueous MeHg concentrations. In both cases, the analyses that lead to spurious correlation were motivated by a cognition of fundamental problems in the application of Hg BAF values to hazard assessment and setting water quality criteria in particular. While we do not disagree with their criticisms of such uses of BAF, our contention is that their analyses should have been conducted by directly examining the relationship between biota Hg and aqueous phase Hg concentrations. Such an analysis then can be used to unambiguously comment on, for example, when the development of a water quality concentration criterion for MeHg is supportable. Restated, the use of BAF values to set water quality criteria should be examined with a jaundiced eye not because regressing BAF against aqueous MeHg often leads to “statistically significant” inverse relationships – those relationships are seen clearly as the product of spurious correlation – but rather because the underlying relationship of the variable of most critical importance with respect to risk – the biota Hg concentration – with aqueous MeHg concentrations is often statistically weak or nonexistent. Such direct analyses offer a number of critical advantages, including evaluating the functional form and robustness of the Hg biota concentration — Hg aqueous concentration relationship, assessing whether the data characteristics match the underlying assumptions of the statistical model used to evaluate the relationship, and ascribing uncertainty to predictions. It is often tempting to clean up messy bivariate relationships by constructing ratios and then conducting the analysis with the common variable on both sides of the equation. Any gains from such practices are highly questionable, and it is hard to conceive when the practice yields any useful information that justifies its use in favor of conducting a more direct analysis. Nonetheless the problem of spurious correlation, as
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Fig. 6. Plots of observed vs. predicted BCF values (panel a), observed vs. predicted tissue MeHg concentrations (log10 transformed; panel b), and observed vs. predicted water column MeHg concentrations (log10 transformed; panel c) for the macrophyte N. variegata. Predictions are based on the BCF vs. MeHg regression model shown in Fig. 5 (panel b).
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Neyman (1972) stated forty plus years ago, “ha(s) been ruining empirical statistical research from time immemorial” and continues to be persistent to this day. Acknowledgments The authors wish to acknowledge James Bennett, Co-Editor-in-Chief of STOTEN, for encouraging us to take our original manuscript, which was submitted as a letter to the editor commenting on a paper published in STOTEN, and develop it into an independent scientific commentary. The authors also wish to thank Pete Kalla and Dan Scheidt of the US EPA for making the Everglades R-EMAP data accessible. References Berges JA. Ratio, regression statistics, and “spurious” correlation. Limnol Oceanogr 1997; 42(5):1006–7. http://dx.doi.org/10.4319/lo.1997.42.5.1006. Bergman BG, Bump JK. Mercury in aquatic forage of large herbivores: impact of environmental conditions, assessment of health threats, and implications for transfer across ecosystem compartments. Sci Total Environ 2014a;479–480:66–76. http://dx.doi. org/10.1016/j.scitotenv.2014a.01.102. Bergman BG, Bump JK. Corrigendum to “Mercury in aquatic forage of large herbivores: Impact of environmental conditions, assessment of health threats, and implications for transfer across ecosystem compartments”. Sci Total Environ 2014b;479–480: 66–76. Sci Total Environ 493 2014b 1128 http://dx.doi.org/10.1016/j.scitotenv.2014. 05.103. Brett MT. When is a correlation between non-independent variables “spurious”? Nordic Soc Oikos 2004;105(3):647–56. http://dx.doi.org/10.1111/j.0030-1299.12777.x. DeForest DK, Brix KV, Adams WJ. Assessing metal bioaccumulation in aquatic environments: the inverse relationship between bioaccumulation factors, trophic transfer factors and exposure concentration. Aqua\t Toxicol 2007;84:236–46. http://dx.doi. org/10.1016/j.aquatox.2007.02.022. Jackson DA, Somers KM. The spectre of “spurious” correlations. Oecologia 1991;86(1): 147–51. http://dx.doi.org/10.1007/BF00317404. Julian P. Mercury bio-concentration factor in mosquito fish (Gambusia spp.) in the Florida Everglades. Bull Environ Contam Toxicol 2013;90:329–32. http://dx.doi.org/10.1007/ s00128-012-0939-6. Håkanson L, Stenström-Khalili MI. Uncertainties in data and spurious correlations related to the Redfield ratio. Int Rev Hydrobiol 2009;94:338–51. http://dx.doi.org/10.1002/ iroh.200811110. Kenney BA. Beware of spurious self-correlations! Water Resour Res 1982;18:1041–8. http://dx.doi.org/10.1029/WR018i004p01041. Kenney BA. Comment on ‘Some misconceptions about the spurious correlation problem in the ecological literature’ by Y.T. Prairie and D.F. Bird. Oecologia 1991;86:152.
Krambeck H-J. Application and abuse of statistical methods in mathematical modelling in limnology. Ecol Model 1995;78:7–15. http://dx.doi.org/10.1016/0304-3800(94) 00113-V. Kronmal RA. Spurious correlation and the fallacy of the ratio standard revisited. J R Stat Soc A Stat Soc 1993;156(3):379–92. http://dx.doi.org/10.2307/2983064. McGeer JC, Brix KV, Skeaff JM, DeForest DK, Brigham SI, Adams WJ, et al. Inverse relationship between bioconcentration factor and exposure concentration for metals: implications for hazard assessment of metals in the aquatic environment. Environ Toxicol Chem 2003;22(5):1017–37. http://dx.doi.org/10.1002/etc.5620220509. Neyman J. Epilogue of the health-pollution conference. In: Le Cam LM, Neyman J, Scott EL, editors. Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability. Berkeley, CA: University of California Press; 1972. p. 575–87. Pearson K. Mathematical contributions to the theory of evolution — on a form of spurious correlation which may arise when indices are used in the measurement of organs. Proc Roy Soc London 1897;60:489–98. http://dx.doi.org/10.1098/rspl.1896.0076. Pollman CD. Integrated report on aquatic modeling. Final reported submitted to the Florida Department of Environmental Protection, Tallahassee, FL. Gainesville, FL: Aqua Lux Lucis, Inc.; 2012. Pollman CD, Axelrad DM. Mercury bioaccumulation and bioaccumulation factors for Everglades mosquitofish as related to sulfate: a reanalysis of Julian II. Bull Environ Contam Toxicol 2014. [in press]. Rolfhus KR, Hall BD, Monson BA, Paterson MJ, Jeremiason JD. Assessment of mercury bioaccumulation within the pelagic food web of lakes in the western Great Lakes region. Ecotoxicology 2011;20:1520–9. http://dx.doi.org/10.1007/s10646-011-0733-y. Santayana G. The life of reason: reason in common sense. New York: Charles Scribner's Sons; 1906. Scheidt DJ, Kalla PI. Everglades ecosystem assessment: water management and quality, eutrophication, mercury contamination, soils and habitat: monitoring for adaptive management: a R-EMAP status report. Athens, GA: USEPA Region 4; 2007. [EPA 904-R-07-001. 98 pp. http://www.epa.gov/region4/sesd/reports/epa904r07001/ epa904r07001.pdf]. Seixas TG, Moreira I, Siciliano S, Olaf Malm O, Kehrig HA. Differences in methylmercury and inorganic mercury biomagnification in a tropical marine food web. Bull Environ Contam Toxicol 2014;92:274–8. http://dx.doi.org/10.1007/s00128-014-1208-7. Southworth GR, Peterson MJ, Bogle MA. Bioaccumulation factors for mercury in fish. Environ Pract 2004;6:135–43. http://dx.doi.org/10.1017/S1466046604000249. Stenström-Khalili MI, Håkanson L. Variations and spurious correlations related to DIN, DIP, TN, TP, DIN/DIP and TN/TP in lakes, rivers, and marine systems. Open Mar Biol J 2009;3:28–35. http://dx.doi.org/10.2174/1874450800903010028. USEPA. Water quality criterion for the protection of human health: methylmercury. EPA823-R-01-0012001. Washington, DC: U.S. Environmental Protection Agency, Office of Water; 2001. USEPA. Methodology for deriving ambient water quality criteria for the protection of human health (2000). EPA-822-R-03-030. Technical support documentDevelopment of National Bioaccumulation FactorsWashington, DC: U.S. Environmental Protection Agency, Office of Water; 2003. USEPA. Guidance for implementing the January 2001 methylmercury water quality criterion. EPA 823-R-09-002 Washington, DC, 2010: U.S. Environmental Protection Agency, Office of Water; 2009.
