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Will Lake Michigan Lake Trout Meet the Great Lakes Strategy 2002 PCB Reduction Goal? C R A I G A . S T O W , * ,† E . C O N R A D L A M O N , ‡ SONG. S. QIAN,§ AND CANDY S. SCHRANK| Department of Environmental Health Sciences, Arnold School of Public Health, University of South Carolina, Columbia, South Carolina 29208, Department of Environmental Studies, School of the Coast and Environment, Louisiana State University, Baton Rouge, Louisiana 70803, The Cadmus Group, Inc., 6330 Quadrangle Drive, Suite 180, Chapel Hill, North Carolina 27517, and Bureau of Fisheries Management and Habitat Protection, 101 S. Webster Street, P.O. Box 7921, Madison, Wisconsin 53707-7921
The Great Lakes Strategy 2002 establishes the long-term goal that all Great Lakes fish should be safe to eat without restriction. As an indicator of progress toward that goal, the Strategy specifies that lake trout PCBs will decline 25% from 2000 to 2007. We estimated the plausibility of achieving this near-term goal by examining a time-series of Lake Michigan lake trout PCB concentrations from 1972 to 2000. We used two different Bayesian approaches, Bayesian model averaging (BMA) and dynamic linear models (DLM), to model the trajectory of these historical data and forecast concentrations through 2007. Both approaches indicate that the probability of a 25% reduction from 2000 to 2007 is negligible. The most likely lake trout PCB declines predicted by the BMA and DLM over this time period are 6.8% and 8.9%, respectively. Our results suggest that declines in lake trout PCBs will be in the range of 5-10% assuming conditions similar to recent years. This rate of decline will be difficult to discern without adequate data collection. If sufficient data are not gathered to document further declines, then the relaxation of lake trout consumption advisories is indeed a long-term prospect.
Introduction PCBs were first reported to occur at high concentrations in Great Lakes fishes in the early 1970s (1). This discovery contributed to an eventual ban on PCB manufacture and a phase-out of their use. Observable declines in Great Lakes fish PCB levels occurred through the 1980s (2, 3), but by the early 1990s these declines had slowed more than the earlier studies would have predicted (4, 5). Consequently, more than 25 years after the imposition of restrictions on PCB use and manufacture, there are fish consumption advisories recommending limited consumption, ranging from “1 meal per week” to “do not eat”, of many Great Lakes fishes, largely * Corresponding author e-mail:
[email protected]; phone: (803)7776634; fax: (803)777-3391. † University of South Carolina. ‡ Louisiana State University. § The Cadmus Group, Inc. | Bureau of Fisheries Management and Habitat Protection. 10.1021/es034610l CCC: $27.50 Published on Web 12/02/2003
2004 American Chemical Society
because of their PCB content (6). Whether or not meaningful reductions are still occurring has been an issue of some debate (7) due to the implied liabilities associated with a persistent legacy contaminant that is alleged to pose both ecological and human health risks. Recently, the U.S. EPA produced the Great Lakes Strategy 2002, which among many objectives includes “The longterm goal is to ensure that all Great Lakes fish and wildlife are safe to eat without restriction”. As an indicator of progress toward this goal the Strategy specifies that “... PCBs in whole lake trout and walleye samples will decline by 25% in the period from 2000 to 2007” (8). Herein, we examine the plausibility of this near-term goal of a 25% decline in lake trout PCBs. We provide an update of the observed trajectory of PCB concentrations in Lake Michigan lake trout (Salvelinus namaycush) with data through 2000 and use model forecasts, based on this trajectory, to estimate concentrations in 2007. Our results indicate that a 25% reduction over this time is optimistic. Thus, removing lake trout consumption advisories in Lake Michigan will indeed be a long-term prospect. Although lake trout may be a useful indicator of long-term, lake-wide, changes in PCB flows, they are not likely to reflect short-term responses to localized PCB mitigation efforts. Therefore, other indicator species that are more likely to reflect changes on smaller temporal and spatial scales should also be considered.
Methods PCB concentrations were measured in skin-on filets from lake trout (S. namaycush) collected by the Michigan Department of Environmental Quality and Wisconsin Department of Natural Resources from 1972 to 2000. Details of the collection, preservation, and analytical methods appear in Stow et al. (4). While the Great Lakes Strategy 2002 specifically references “whole lake trout” rather than filets, a previous analysis of Lake Michigan Coho salmon (Oncorhyncus kisutch) and rainbow trout (Oncorhyncus mykiss) revealed an approximately linear relationship between whole fish and filet PCB concentrations (9), so we believe that an analysis based on filets provides a reasonable basis for making inference about whole lake trout PCBs. We used two modeling approaches to address the question posed in the title. The two approaches are based on different assumptions, and each handled the data differently. Using parallel approaches, each with features and caveats, provides more support for the conclusions, if the results are sufficiently consistent. The first approach considers four models simultaneously. However, rather than picking the “best” of the four models and basing forecasts on that single “best-fit” model, we used Bayesian model averaging to provide a weighted average of the forecasts from all four models (10). The four models, which have been previously described in this context (4, 11), were as follows: An exponential decay model:
PCBt ) PCB0ekt +
(1)
where PCBt is the PCB concentration (mg/kg) in year t, PCB0 is the PCB concentration (mg/kg) in year t ) 0, k is the decay coefficient (yr-1), and denotes an additive normal error term with a zero mean. The implication of this model is that PCBs are continually declining, at an ever-slowing rate, toward a concentration of zero. VOL. 38, NO. 2, 2004 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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An exponential decay model with a nonzero asymptote:
PCBt ) PCB0ekt + PCBa +
(2)
where PCBa is the asymptotic PCB concentration (mg/kg). This model also implies a continual decline of PCB concentrations, at a slowing rate, but toward a positive asymptotic concentration. Implicit in this model is the idea that there are two effective PCB sources supplying the food web, one of which declines rapidly through time and one of which is relatively stable. A double exponential decay model:
PCBt ) PCB01ek1t + PCB02ek2t +
(3)
where PCB declines result from two effective sources with distinct decay coefficients, k1 and k2. This model also implies two effective PCB sources, each declining at a different rate. A mixed-order model:
PCBt ) {PCB01-φ - kt(1 - θ)}(1/1-φ) +
(4)
where PCB0 is the initial concentration, k is the reaction coefficient, and φ is the order of the reaction, and all are treated as unknowns. This model is a generalization of the exponential decay model and can accommodate declines toward zero but at rates that slow more rapidly than rates in an exponential model would. Each model was fit to 648 individual lake trout samples from the period 1974-2000. The models were fit under a natural log transformation of both sides of each equation, effectively imposing a log-normal error structure on each model. We generated posterior samples of each model’s parameter set using Markov chain Monte Carlo (MCMC) simulation (12) as implemented in WinBUGS (13). These posterior samples were used to calculate posterior probabilities for each model (14). Predictions from the four models were then combined into a Bayesian model average using the respective posterior probabilities from each model as weights in a weighted average. The second modeling approach we used, dynamic linear models (DLMs), has also been used previously in this context (15). DLMs have a flexible structure where the model parameters are allowed to change over time. All DLMs consist of an observation equation and a system equation (16). We parametrized these equations for the present study as follows:
observation equation: ln[PCB]t ) levelt + βt lengtht + νt νt ∼ N [0, Vt] (5a) system equations: levelt ) levelt-1 + growtht + ωt1 growtht ) growtht-1 + ωt2 βt ) βt-1 + ωt3
ωt1 ∼ N [0, W1] (5b) ωt2 ∼ N [0, W2]
ωt3 ∼ N [0, W3]
where ln{PCB]t is the observed ln PCB concentration at time t, levelt is the mean PCB concentration at time t, growtht is the rate of change of the level parameter (analogous to the decay rate), and βt is a length (regression) coefficient. This term is included to accommodate the fact that fish length is correlated with PCB concentration and that different sized fish have been sampled over time. νt, ωt1, ωt2, and ωt3 are normal, zero mean error terms with respective variances of Vt, W1, W2, and W3. In a static regression, every observation contains information on each parameter, while in a dynamic linear model, parameter sets for each distinct time are separate but 360
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stochastically related through the system equations. The current parameter values (at time t) are linear combinations of previous values (at time t - 1) plus a stochastic error term. DLMs are estimated sequentially moving forward in time through the data series. We make a forecast for time t based on prior knowledge of the parameters, then we observe data at time t. We update our knowledge regarding the parameters, using the likelihood of the data (given the forecast) and our prior knowledge using Bayes theorem in a process known as Bayesian learning. This posterior (updated) information regarding the parameters is “discounted” by adding a stochastic disturbance term to represent the aging of information with the passage of time. Useful discounts are generally greater than about 0.8, and discounts of 1.0 correspond to the static model (17). This discounted posterior knowledge becomes prior knowledge for time t + 1, and the process is repeated. A model is selected from the list of candidate models by conducting a model search, in which models with different structures are compared by evaluating the difference in cumulative log likelihood between competing models, called log Bayes factors (18). Full detail on the use of Bayes factors in DLM searches and discounting is available in West and Harrison (16). In this implementation, PCB concentrations and lengths were natural log transformed, and then annual means of the log-transformed data were calculated. The DLMs were fit to annual average ln[PCB] from 1972 to 2000 using Bayesian Analysis of Time Series (BATS) software (17). The series of annual average ln-transformed lengths was standardized prior to use as a predictor for annual average ln [PCB].
Results The BMA-generated posterior probabilities for models 1-4 were 6.76 × 10-9, 4.56 × 10-1, 2.52 × 10-2, and 5.19 × 10-1, respectively. Thus, forecasts from the BMA are most heavily influenced by models 2 and 4. The influence of model 1, the exponential decay model, is negligible. Visually, it appears that lake trout PCBs began to deviate from an exponential decay (model 1, which is linear in the ln metric) in about 1990 (Figure 1). Of the four component models, only model 1 predicts a significant future concentration decline (Figure 2). The smoothed DLM level parameter provides a similar retrospective inference, indicating that declines were slowing by the early 1990s (Figure 3). The estimated growth parameter continues to approach zero, an indication that the rate of decline continues to slow (Figure 4). Both the BMA and DLM results indicate that a 25% PCB concentration decline from 2000 to 2007 is unlikely (Figure 5). The BMA predicts that the most likely result by 2007 is a 6.8% decline and that the probability of a 25% decline is almost zero (Figure 5). Approximately 15% of the area of this probability density function is above zero, indicating the possibility that no measurable improvement will occur by 2007. The DLM predicts even less chance of a 25% decline than does the BMA. The most likely change by 2007 according to DLM results is an 8.9% PCB concentration decline (Figure 5).
Discussion Using several models and modeling approaches simultaneously is a means of ensuring that inferences are not completely contingent on the idiosyncrasies of one particular method. The BMA and the DLM generate different kinds of output, providing complementary interpretations and insights. We also handled the data differently with each approach, using individual observations in the BMA and
FIGURE 1. Lake Michigan Lake Trout PCB concentration vs time with model 1 (dotted red), model 2 (dashed green), model 3 (dashed dark blue), model 4 (dashed light blue), and BMA (solid black) depicted. Vertical dashed lines depict 90% credible intervals for each model through 2008.
FIGURE 2. Expanded view of BMA forecasts with results expressed as a fraction of the 2000 PCB modeled value. Vertical lines depict 90% credible intervals. annual averages in the DLM. In this case, both approaches indicate that a decline as large as 25% by 2007 is unlikely. Each approach has some relative advantages and disadvantages. The DLM has an evolving structure that allows for a parsimonious representation of models 1-4 and, thus, is more flexible. Information from the more distant past is more heavily discounted in predicting the future. It also accommodates fish size and compounds uncertainty at each future time step. Alternatively, the BMA is based on models with a fixed structure through time, which is likely to result in more accurate prediction, if that structure closely reflects reality. Additionally, forecasts are based on all of the data, not just the most recent data. Therefore the BMA will be less sensitive to short-term deviations from a long-term pattern or unusual observations in a particular year. Thus, the BMA and DLM have complementary features, so that when they are used in concert in an ongoing assessment they can help
to distinguish between real changes from an underlying process and short-term anomalies. The results from the BMA are consistent with previous conclusions, using data only through 1994, indicating that ongoing PCB concentration declines are minor. Stow et al. (11) found model 2 to provide the best fit to data through 1994, suggesting a slowing decline to a positive asymptote. In the strictest sense, this result does not mean that concentrations are “stable”, but from a practical standpoint, it means that future declines will likely be so slight that they will have little practical significance. We note some differences between the forecasting model of Lamon et al. (15) and the model identified in this update. Lamon et al. (15) used lake trout PCB data through 1994 and did not use length as a regressor, and evidence in the data through 1994 favored a trend discount of 0.85. The present model uses data through 2000, which supports a trend VOL. 38, NO. 2, 2004 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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FIGURE 3. Average annual lake trout PCB concentration vs time with the smoothed level parameter and a 90% credible interval from the dynamic linear model.
FIGURE 4. Estimated growth parameter and 90% credible interval vs time from the dynamic linear model. discount of 0.8. This difference indicates that the more recent tribution that represents our knowledge of the growth data has given us less confidence in the trend, that it is parameter through 2000 indicates only 2.1:1 odds that this changing more rapidly now than in 1994. A more rapid change rate of change is still negative. A similar distribution derived in model parameters over time is accounted for in a DLM from the Lamon et al. (15) model indicates that as of 1994, by a reduction in memory (a lower discount rate). The odds were 40.8:1 that the rate of change was negative. This underlying, retrospective level of the time series (Figure 3), difference is, in part, due to the addition of length as a along with the associated rate of change in this level (Figure predictor variable in the model. Systematic differences over 4), indicate that the decreases in lake trout PCB concentration time in the size of the fish analyzed are accommodated by have slowed considerably since 1994. The probability disthis inclusion. 362
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investment that will provide valuable information to guide ongoing decision-making in an adaptive management framework.
Acknowledgments The Wisconsin Department of Natural Resources and the Michigan Department of Environmental Quality provided lake trout PCB concentration data. We thank Steve Carpenter, Jim Kitchell, and Tara Stow for reviewing early versions of this manuscript.
Literature Cited
FIGURE 5. Probability density functions depicting the relative likelihood of the percent PCB change from 2000 to 2007, based on the Bayesian model averaging and dynamic linear model results. The possibility that Great Lakes fish PCB concentrations might initially decline and then stabilize was suggested more than 10 years before stabilization started to become apparent (19). Recent data confirm that declines have slowed much more than would have been predicted by earlier assessments (2, 3). At current sampling rates, it is difficult to statistically discern if any further decline is occurring at all. A previous analysis pointed out that hundreds of individual fish would need to be analyzed to detect PCB concentration changes at reasonable total error (the sum of a type 1 and type 2 error) rates (4). This sample size could be lowered if sampling is stratified to reduce some components of variability (20) or if individual fish are composited before analysis. However, compositing results in considerable information loss, and documenting the sources of individual variability is particularly useful for updating fish consumption advisories and documenting hotspots where fish may have higher contaminant levels. The various objectives of a fish contaminantmonitoring program invite a coordinated, well-planned program that is adequately funded to meet all the objectives. While lake trout are a native species and may be a compelling indicator of lake conditions, they are relatively long-lived and sequester an estimated 80% of their dietary PCB intake (21). Thus, the lag between improvements in ambient PCB levels and any resultant concentration changes that occur in lake trout PCBs will be relatively long. Consideration should be given to incorporating a suite of indicators, including species that are relatively short-lived and thus are more likely to reveal short-term PCB changes. When data were available only into the early 1990s, the argument for a slowing PCB decline may have been debatable. But the accumulating evidence does not support rapid future improvement. Both the BMA and the DLM provide evidence that near-term future PCB declines will be small. In a classical statistical context, neither the percent reduction predicted by the BMA (Figure 5) or the most current growth parameter estimate of the DLM (Figure 4) would be considered “significantly different from zero”. The reason for such slow declines is unclear; PCBs stored in near-surface sediments may supply a relatively stable food web input, or perhaps PCBs are efficiently recycled within the biota of the food web. Further research directed at this question is likely to provide interesting insights. Our two models, alongside the 25% reduction goal presented in the Great Lake Strategy 2002, present alternative testable hypotheses that can be either verified or nullified with adequate data collection through 2007. Collecting sufficient data over this time is a relatively inexpensive
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Received for review June 16, 2003. Revised manuscript received October 2, 2003. Accepted October 23, 2003. ES034610L
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