Environ. Sci. Technol. 1994, 28, 1543-1549
PCB Accumulation in Lake Michigan Coho and Chinook Salmon: I ndividual-Based Models Using Allometric Relationships Craig A. Stow’ and Stephen R. Carpenter
Center for Limnology, University of Wisconsin, 680 North Park Street, Madison, Wisconsin 53706 We have developed individual-basedmodels that describe PCB accumulation and variability in Lake Michigan coho and chinook salmon. The models are based on simplified allometric relationships and incorporate a minimum of free parameters. Simulations of high and low growth rates demonstrate that salmon of a given age attain similar PCB concentrations but very different sizes, indicating that age is a better predictor of contaminant level than is size. Model results suggest that a 10-1576 reduction in PCB levels for fish of a given size can be obtained by managing for high growth rates. The models also show that prey PCB concentration strongly affects PCB levels in the salmon; however, management options for controlling prey PCBs are fairly limited and expensive. Introduction Toxic pollution in the Great Lakes is a subject of extensive study and considerable debate. Much attention focuses on PCB contamination, especially in Lake Michigan ( I ) . PCBs are considered particularly troublesome because of their extreme persistence and their tendency to bioaccumulate (2). The occurrence of PCBs in Lake Michigan sportfishes has long been known (3) and continues to be a concern because of apparent links to human health problems (4).A ban on PCBs in the 1970s resulted in an initial rapid decline in fish tissue PCB concentrations (5-3, but a more recent investigation has suggested that PCBs may be approaching constant levels (8). If future decreases in fish tissue PCB concentrations are likely to occur at negligible rates, it may be helpful to implement management practices to reduce contaminants and further limit human exposure from fish consumption. The Lake Michigan fishery is already intensively managed. The depletion of native predator fish stocks and a burgeoning alewife ( A h a pseudoharengus) population prompted extensive stocking of native trout and exotic salmon species beginning in the 1960s (9). This stocking has resulted in a successful sportfishing industry, a decrease in the nuisance alewife population, and a trophic structure currently in flux. A declining alewife population has also decreased the forage base for sportfishes and a resultant decrease in growth has been noted, particularly in chinook salmon (IO). The precarious state of the Lake Michigan fishery could be viewed as an opportunity for a modification of stocking practices to encompass a broad range of objectives. These objectives could include the stocking of species that accumulate a minimum of contamination and stocking at levels to maintain optimal growth rates. Previous research has demonstrated that different species of fish accumulate PCBs at different levels (11). For example, in Lake Michigan, estimated stable concentrations for lake trout are three to four times those for ~
* Corresponding author; e-mail address:
[email protected]. 0013-S38X/S4/0S28-1543$04.50/0
0 lSg4 American Chemlcal Society
rainbow trout and coho salmon (8). It is also known that growth rate affects contaminant levels (12),an effect often referred to as “growthdilution”. Deliberate manipulations to optimize these factors for minimal human exposure could be incorporated into an overall management strategy. To attain the objective of minimizing contaminant exposure, it will be necessary to develop an understanding of the important factors that influence fish contaminant levels. Simulation modeling is one means of exploring these factors. A number of models have appeared in the literature that explore general bioaccumulation mechanisms (12-15). Recently, individual-based models have been used as a tool to examine PCB variability in lake and rainbow trout (16,13. Individual-based models are useful for this purpose because they facilitate an investigation of factors important in determining the variability of PCB levels as well as mean or other summary measures. We present individual-based models developed to explore PCB accumulation in Lake Michigan coho (Oncorhynchus kisutch) and chinook salmon (Oncorhynychus tshawytscha). Our goal was to develop models driven, to a high degree, by available data on PCB concentration and fish size. Many simulation models assume much knowledge about the precise mechanismsgoverningsystem dynamics and require the specification of values for many unknown parameters. Frequently parameter values are estimated from laboratory or field studies, previous modeling exercises, or theoretical considerations, but in fact they are often not well known. In models with a large number of parameters there often exists a high covariance structure among the parameters such that simultaneously manipulating several parameter values results in essentially the same model predictions. Sometimes two or more parameters will not be separately estimable. We sought to avoid these problems by developing relatively simple models with parameters that can be estimated from available data. The models presented specify a minimum of mechanism, but still essentially track the processes of growth and contaminant accumulation. This is not intended as a criticism of previous more complex modeling efforts, but rather as an attempt to corroborate some of the conclusions reached in these studies without overstating the information contained in the calibration data. Model Description The models consist of two functional components, an initialization that simulates stocking and a daily time component that simulates growth and net contaminant assimilation (Figure 1). Variation among individuals can be achieved in two ways, either by assigning individual differences in the stocking component or by imposing random variation in the daily time step. Assigning individual differences in the initialization results in greater variation among individuals because these differences persist throughout the simulation. Day to day variation Envlron. Scl. Technol., Vol. 28, No. 8. l S S 4
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In the second step of the daily time component, the size of each prey item is randomly chosen from a log-normal distribution. The median of the distribution is a function of predator size according to the relationship:
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where P = prey mass (kg) and 03 and 0 4 are growth calibration parameters. Because this distribution is lognormal, the mean prey size is a function of u2p, the lognormal variance (20). Therefore, u2p is also a growth calibration parameter. Values for the parameters were chosen so that prey size increases as the predator grows. The third step of the dailytime component assigns each prey a PCB concentration randomly selected from a lognormal distribution. The median of the distribution is a logistic function of prey size:
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is somewhat self-canceling and cannot effect as large a variance as specifying persistent individual differences. In the model initialization component, a cohort of fish is stocked, and individual attributes are assigned. Coho are introduced into the system in April at 30 g, and chinook are introduced in May at 4.5 g (18). Individual size variation is assumed to be small at stocking, and all individuals are initially set to the same size. Initial PCB concentrations for all individuals are set to zero. The daily time component of the model performs four steps that simulate fish growth and contaminant accumulation. Consumption, prey size, and respiration are each modeled as direct functions of body size. This is similar to the well-established bioenergetics approach (19) but is mechanistically more aggregated and requires specification of fewer parameters. The first step is a daily prey encounter rate modeled as a Poisson distribution. The probability,p, of encountering N prey is
In this expression e is the base of the natural logarithms and X is the mean and variance parameter of the Poisson distribution. The value of X on a given day is determined by the size of the predator that day according to the relationship:
where 01 and 0 2 are free parameters used to calibrate the models for growth and M is the predator mass (kg). In this way, the encounter rate changes throughout the life of the fish as the fish grows. 1544
Envlron. Scl. Technol., Vol. 28, No. 8, 1994
where PCB = prey PCB concentration (mg/kg) and 81,82, and 83 are contaminant calibration parameters. This relationship simulates the increase in prey contaminant concentration that occurs when the salmon switch from planktivory to piscivory. 8 2 is the median concentration at the lower trophic level, representative of invertebrate PCB concentrations, and 81 is the median concentration for mid-trophic prey such as alewife and bloater. 83 determines how rapidly the transition between trophic levels occurs. Again, because the distribution is lognormal, the mean of the distribution is a function of the variance, U~PCB,and the value assignedto u 2 p cis~ important in calibrating both the mean and the variance of the model. In the fourth step of the daily time component, respiration is determined, growth is calculated, and PCBs are assimilated. Respiration is calculated as
R = &MB6 where R is respiration (kg) and 0 5 and 0 6 are growth calibration parameters. The size of each fish is incremented by the difference between growth and respiration. The PCB body burden of each fish is then increased as a proportion of the prey PCB eaten that day. Model Growth Calibration. We calibrated the mean size of a cohort of individuals to track published mean size at age curves (10)for each species. To establish values for the model growth parameters that were consistent with observed growth patterns, we applied a number of constraints. The relationship
c cc M O T 5 where C is consumption (kg) (21) was used to bound the exponents in eqs 1and 2. Average daily consumption is proportional to the product of eqs 1and 2 so, in accordance with eq 3, the sum of 02 and 0 4 was set to 0.75. We calibrated the models so that biomass conversion efficiencies (growth/consumption) were consistent with those reported by Stewart and Ibarra (10). Conversion efficiencies of approximately 24.5 % and 23 76 were used for coho and chinook, respectively. The value of 0 4 satisfied two additional constraints. The first constraint was that prey size for coho and chinook
should increase rapidly for juvenile fish, then only slightly for adults, representing an initial shift from invertebrate prey to food in the size range of alewife and bloater. The second constraint was that 0 4 should be greater than 0.75 so that 0 2 would be negative. A negative value for 0 2 establishes an encounter rate that is higher for juvenile fish and decreases to approximately stable levels for adult predators. To accomplish both of these objectives, 0 4 was set to 0.80. The respiration exponent, 0 4 , was also set to 0.80 as a value representative of fish respiration (22). With values for the exponents set, 01,03,/35,and u2pwere manipulated until growth curves for coho and chinook were in good agreement with size at age curves presented by Stewart and Ibarra (IO). Two additional restrictions were applied for establishing these values: adult fish should be consuming an average of approximately two to four prey per day and prey size should be highly variable. Under these conditions, we set the following respective parameter values for coho and chinook: 01 = 4.2 and 3.7, 02 = 0.0265 and 0.0218,03 = 0.0076 for both, and u2p = 0.25 (0A2)and 0.1225 (0.352). These &represent coefficients of variation of approximately 0.5 and 0.35, respectively. Model Contaminant Calibration. The growthcalibrated models were calibrated to simulate the PCB: size distributions displayed in data collected by the Wisconsin Department of Natural Resources in a 1985 survey (11). We simulated asample of fish for bothspecies to approximately match the age distribution of the fish in the calibration data set. The ages of the fish in the calibration data were estimated from the date of capture and size at age curves (10). Because these data represent skin-on filets and the models represent whole-body concentrations, we multiplied all measured PCB values by 1.55 to approximately correct for the whole-body:filet fat ratio in these salmon (23). A time-series model for Lake Michigan alewife PCB concentrations (8)was used to set values that change with time for 81. 82, median values for the lower trophic level prey, were set at one-tenth the 81 values, based on data presented by Evans et al. (2). 83 and &CB were then manipulated until plots of the calibration data and the model results were comparable. All of the contaminant calibration parameters were restricted to be the same for both the coho and chinook models, to represent an essentially common prey resource. Final values used in the model for 83 and &CB were 200 and 1.5625 (1.2P), respectively. To parsimoniously achieve the observed variability in PCB concentrations, it was also necessary to assign PCB assimilation rates, 84, that varied among individuals. In the initialization component of the model, each fish is randomly assigned a value of 84 from a uniform distribution ranging from 0.1 to 0.95. The mean of this distribution is in general agreement with literature values for coho (24) and guppies (25);however, variability among individuals is not well documented in the literature. All random numbers were synthesised using algorithms from Numerical Recipes (26). Simulation Studies. We manipulated the calibrated models to examine the relative importance of various factors that influence PCB concentration and variability. To assess relative PCB variance contributions, three data sets analogous to the calibration data sets were simulated for coho and chinook. In each data set, mechanisms
responsible for inducing PCB variance were removed. In one data set, PCB assimilation variability was removed and assimilation was set to 0.525, the mean value for all individuals. In the second data set, prey PCB concentration variance was set to zero. Both assimilation variance and prey PCB variance were set to zero in the third data set. We examined the effect of growth rate on PCB concentration, as influenced by prey availability, by manipulating the value of 01,the constant in the encounter rate equation. Cohorts of 250coho and chinook were grown to maturity under three scenarios: low prey availability, calibration conditions, and conditions of high prey availability. To simulate high growth conditions, we increased 01 to 4.35 and 3.8 for coho and chinook, respectively, and low growth was achieved by setting 01to respective values of 4.05 and 3.6. These changes in 01correspond to changes in biomass conversionefficiencies of approximately f10 % from the calibration data, values consistent with those observed to occur in Lake Michigan chinook in the 1980s (10).
We simulated the effect of high and low prey PCB concentrations by adjusting 81 to 125% and 75% of the calibration value, a range within that observed in Lake Michigan forage fishes from 1980 to 1990 (8). Cohorts of 250 coho and chinook were grown to maturity under low prey availability, calibration, and high prey PCB concentrations and were compared. The probability of exceeding the US. Food and Drug Administration 2 mg/kg action level for PCBs was estimated by simulating 1000coho and chinook under high and low growth conditions at projected stable prey concentrations (8). Simulated individuals were “capturedn at 2 kg (coho) and 4 kg (chinook) to provide a comparison of PCB concentrations in fish of a given size. Results All model output is expressed as whole-bodyconcentrations except for the verification results, which have been corrected to represent skin-on filets comparable to the verification data. The calibrated models produce concentrati0n:size plots quite similar to the calibration data (Figure 2). It should be noted that this calibration is not an attempt to match the observed data point by point but only to reproduce the distribution of the data. The models were verified by comparing predicted 1992 PCB concentrations with 1992 concentrations from empirical time-series models (8). Data sets, analogous to the calibration data sets, were generated for both coho and chinook based on projected 1992 prey PCB levels. A comparison of uncertainty bounds about the medians (Table 1)indicates that the empirical models and simulation models are in good agreement. The fitted time-series models (8) indicate a recent PCB increase has occurred in coho and chinook, possibly attributable to a change in prey. This prey shift is not incorporated in the individualbased models and may explain the slight underestimation in the 1992 predictions. Coho and chinook PCB concentration variances decreased considerably when either source of variability was removed (Table 2). The fact that the PCB variances in the calibration data sets greatly exceed the sums of the variances when the individual variance components are Environ. Scl. Technol., Vol. 28, No. 8, 1994
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Table 1. Effect of Variance Components on PCB Concentration Variancea coho
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calibration PCB variance 0.80 1.93 assimilation variance set to 0 0.26 0.81 prey PCB variance set to 0 0.17 0.39 assimilation and prey PCB 0.05 0.16 variances set to 0 a Verification results comparing the individual-based models in this study to empirical time-series models (8). The uncertainty interval is calculated as two standard error units on either side of the median. Table 2. Comparison of Predicted 1992 PCB Concentrations with Time-Series Dataa time-series models uncertainty median interval
individual-based models uncertainty median interval
0.60-1.16 0.64 0.55-0.75 1992 coho 0.78 1992 chinook 1.17 0.95-1.45 0.95 0.85-1.05 a Comparisons of simulated sample PCB variances with the assimilation variability removed, the prey PCB concentration variability removed, and both the assimilation and prey PCB concentration variabilities removed.
removed indicates that the individual components interact to produce the high observed variance in the predator species. A comparison of coho and chinook PCB concentrations resulting from simulating different growth rates shows that growth rate has very little effect on PCB concentration 1546
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Low Growth
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Flgure 3. 3. Box and whisker plots depicting PCB concentration results in three cohorts of 250 2-year-old coho and 4-year-old chinook salmon. Cohorts were grown under conditions favoring low, high, and intermediate(calibration)growth rates. Boxes represent the interquartlle range; whiskers represent extreme observations that are up to 1.5 times the interquartile range beyondthe quartiles. Observations beyond the whiskers are depicted individually. The line through the middle of each box represents the sample median, and an approximate 95% confdence intervalabout the median is depicted by the notch. Comparlng the overlap of notches between two boxes is similar to Comparing means with a two sample t-test. Sample means are depicted by an asterisk.
(Figure 3). However, fish size in these simulations is considerably affected by growth rate (Figure 4). Under high prey availability, simulated coho and chinook grow to approximately 1.5times the size that they attain under low prey availability. Viewed another way (Figure 5 ) , it is apparent that,, while growth rate does not markedly affect PCB concentration, it does affect the concentration: size relationship. In other words, under higher growth conditions a given size fish is likely to be less contaminated than the same size fish grown under low growth conditions. Under high growth conditions, the probability that a 2-kg coho will be below the 2 mg/kg FDA action level is approximately 80 % compared to approximately 60 76 under low growth conditions (Figure 6). For a 4-kg chinook, the respective probabilities are approximately 55% and45%. Prey PCB concentration has a pronounced affect on predator contaminant concentration (Figure 7). Manipulating prey concentrations by h25 % results in comparable changes in both the mean and the median predator concentrations. Predator PCB variance also increases with increased prey PCB levels, because the prey concentration is modeled to be log-normal.
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Figure5. Mean PCB concentration vs mean fish mass from simulations of three cohorts of 250 2-year-old coho and 4-year-old chinook salmon. Cohorts were grown under Conditions favoring low, high, and intermediate (calibration) growth rates.
Previous models for estimating contaminant concentrations in aquatic biota have spanned a range of complexity. Simple linear relationships (27,28)have illuminated broad underlying factors responsible for observed contaminant concentrations, and complexmechanistic models (13)have detailed specific processes that influence contaminant levels. For prediction purposes, however, models of intermediate complexity generally provide the least uncertainty (29). The inclusion of many parameters in a model, the values of which are not well known and that may be highly correlated, inflates prediction variance. Our models describe a minimum of detail, but based on the calibration and verification results appear to capture the essence of PCB accumulation dynamics. To match the high degree of PCB concentration variability in the calibration data, it was necessary to impose variability at two places in the accumulation dynamics. We chose to do this by giving the prey highly variable PCB concentrations and by giving individuals in the predator population different PCB assimilation rates. Various other strategies were tried in the model development, but no others matched the calibration data variance. The imposition of day to day rather than individually specific variability in PCB assimilation, for example, was not effective in establishing a simulated population of high variability. This result is consistent with conclusions reached by Madenjian et al. (16). In their analysis, however, PCB variability was increased by simulating lake trout that fed on differentiallycontaminated prey populations. For lake
trout this may be reasonable because trout tend to be relatively stationary, but coho and chinook generally move about the lake. Availabledatacannot distinguish between these potential mechanisms, spatial variability and assimilation variability, and it is possible that both mechanisms operate in Lake Michigan. It is not reasonable to use either high assimilation or prey variance alone to generate the highPCB concentration variance in the calibration data. Because these two variance sources have an interactive effect (Table 2), unrealistic values would have to be used to duplicate the calibration data. It would be necessary to assign PCB assimilation values outside of the realistic range of &loo%, or the prey PCB concentration variance would have to be much greater than 1.5625 (1.252), the value used in the model. This variance corresponds to a coefficient of variation of approximately 1.9, and it is unlikely that true population values are much higher than this. If either of the mechanisms we have used to achieve a high PCB variance are incorrect or too variable, then something else must be occurring. That cohorts grown under different growth conditions achieve similar contaminant concentrations but very different sizes indicates that age rather than size is more important in determining contaminant levels. This may also be a source of contaminant at size variability that is not explicitly included in our models. The models were growth calibrated to match average size at age growth data (10). Unfortunately, variability about these averagevalues Environ. Sci. Technol., Vol. 25,No. 8, 1994
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is not well established. Catch records provide some evidence for upper sizes of these fish (30), but lower size ranges for a given age fish are not well documented. We used published upper size ranges to constrain growth variability in the coho and chinook simulations. However, if growth is actually more variable than we allowed in the models or if the true size at age distribution is heavily skewed to the left, then individual growth variability may be more important in determining contaminantvariability than our models indicate. In other words, it is possible that the coho and chinook populations actually contain a relatively high proportion of older, slow growing fish that account for some of the high concentration at size variability found in the calibration data. That prey PCB levels strongly affect coho and chinook PCB concentrations is no surprise, particularly in the context of these models where consumption was the only means by which the predators encountered PCBs. We modeled accumulation this way because, while there may be some disagreement (13),current evidence favors prey consumption as the mechanism of primary importance for PCB uptake (31). Other recent modeling efforts (16) have included direct uptake and internal metabolism as very minor components of overall accumulation dynamics. Using the length-weight calibration data, it is not possible to assign separate values to all of these mechanisms, so the most parsimonious approach was to model accumula1548
Envlron. Scl. Technol., Vol. 28, No. 8, 1994
Low' Prey Concentration
High' Prey Concentration
Flgure 7. Box and whisker plots depicting PCB concentration simulation results in three cohorts of 250 2-year-old coho and 4-year-old chinook salmon. Cohorts were grown under conditions of low, high, and intermediate (caiibration) prey PCB concentration levels. Boxes represent the interquartile range; whiskers represent extreme observations that are up to 1.5 times the interquartile range beyondthe quartiles. Observations beyond the whiskers are depicted individually. The line through the middle of each box represents the sample median, and an approximate 95 % confidence interval about the median is depicted by the notch. Comparing the overlap of notches between two boxes is similar to comparing means with a two sample t-test. Sample means are depicted by an asterisk.
tion as a function of prey consumption only, recognizing that the assimilation rates used represent effective net assimilation. Growth dilution is a term loosely applied in contaminant dynamics to imply that faster growing organisms accumulate contaminants at lower levels than comparable slower growing organisms. However, these simulations demonstrate that fish grown under different growth scenarios assume similar PCB concentrations at the same age. The faster growing fish simply get bigger. This might appear as an effective decrease in PCB levels because comparable sized fish will be less contaminated under faster growth conditions, but the overall population concentration is not strongly affected. Growth dilution can, however, be translated into management practices that lower human exposure from fish consumption. Advisories warning against the consumption of fish over a certain size become increasingly 2ffective if fish below that size are less contaminated. In addition, the presence of a greater proportion of larger fish become important as more trophies in the sportfish industry. Alternatively, the maximum advised consumption size could be raised if large fish were less contaminated.
The projected decreases in PCB concentrations that can be achieved by managing for higher fish growth rates are fairly modest (Figure 6). The probability of falling below the FDA action level increases by approximately 15-20% for coho and 10-15% for chinook. However, the cost of this management alternative is relatively low. Permitting depleted prey stocks to recover by decreasing the rate of salmon stocking is an inexpensive option, especially if anglers have access to alternative quarry such as rainbow and brown trout. Other remediation techniques for reducing PCB levels, such as dredging contaminated sediments, are relatively expensive, present an ultimate disposal problem, and the benefit in terms of a reduction in fish contaminant levels is difficult to estimate accurately. The importance of prey PCB levels in determining sportfish PCB concentrations raises the question of whether or not effective management steps can be taken to further reduce PCBs in the prey stocks. In Lake Michigan, this question is particularly complex because of the transitional state of the food web. The welldocumented decline in the favored alewife forage base during the 1980s has been accompanied by a substantial increase in the native bloater chub (Coregonus hoyi) population (32),a potential alternate prey. Alewife and bloater chub feed in somewhat different spatial niches (33), and a switch to the consumption of bloaters may require a modification in forage behavior with a resultant change in consumption and growth energetics. The net affect of these simultaneous changes, and the degree to which they can be deliberately manipulated by management practices is yet to be resolved. Acknowledgments
This work was funded by the University of Wisconsin Sea Grant Institute under grants from the National Sea Grant College Program, National Oceanic and Atmospheric Administration, U.S. Department of Commerce, and the State of Wisconsin: Federal Grant NA9OAA-DSG469, Project RIMW-41. Literature Cited (1) Simmons, M. S. In Toxic Contaminants in the Great Lakes; Nriagu, J. O., Simmons, M. S., Eds.; Wiley: New York, 1984; pp 287-309. (2) Evans, M. S.; Noguchi, G. E.; Rice, C. P. Arch. Environ. Contam. Toxicol. 1991, 20, 87-93. (3) Veith, G. D. Pestic. Monit. J. 1975, 9, 21-29. (4) Jacobson, J. L.; Jacobson, S. W.; Humphrey, H. E. B. J. Pediatr. 1990, 116, 38-45. (5) Devault, D. S.; Willford, W. A.; Hesselberg, R. J. EPA 905/ 3-85-001. Government Printing Office: Washington, DC, 1985.
(6) Devault, D. S.;Clark, J. M.; Garet, L.; Weishaar, J. J.Great Lakes Res. 1988, 14, 23-33. (7) Hesselberg, R. J.; Hickey, J. P.; Nortrup, D. A.; Willford, W. A. J. Great Lakes Res. 1990, 16, 121-129. (8) Stow, C. A.; Carpenter, S. R.; Eby, L. A.; Amrhein, J. F.; Hesselberg, R. J. Ecol. Appl., (in press). (9) Emery, L. Technical Report No. 45. Great Lakes Fishery Commission, 1985. (10) Stewart, D. J.;Ibarra, M. Can. J.Fish. Aquat. Sci. 1991,48, 909-922. (11) Masnado, R. G. Fish Management Report 132. Bureau of Fish Management, Wisconsin Department of Natural Resources, 1987. (12) Thomann, R. V. Environ. Sci. Technol. 1989,23,699-707. (13) Barber, M. C.; Suarez, L. A.; Lassiter, R. R. Can. J. Fish. Aquat. Sei. 1991,48, 318-337. (14) Thomann, R. V.; Connolly, J. P.; Parkerton, T. F. Environ. Toxicol. Chem. 1992, 11, 615-629. (15) Gobas, F. A. P. C. Ecol. Modell. 1993, 69, 1-17. (16) Madenjian, C. P.; Carpenter, S. R.; Eck, G. W.; Miller, M. A. Can. J. Fish. Aquat. Sci. 1993, 50,97-109. (17) Madenjian, C. P.; Carpenter, S. R.; Rand, P. S. Can. J.Fish. Aquat. Sci., in press. (18) Stewart, D. J.; Kitchell, J. F.; Crowder, L. B. Trans. Am. Fish. SOC.1981, 110, 751-763. (19) Hewett, S. W.; Johnson, B. L. WIS-SG-92-250. University of Wisconsin Sea Grant Institute, 1992. (20) Crow, E. L.; Shimizu, K. Lognormal Distributions Theory and Applications; Marcel Dekker: New York, 1988;pp 9-10, (21) Peters, R. H. The Ecological Implications of Body Size; Cambridge University Press: New York, 1983;pp 100-146. (22) Weatherley, A. H.; Gill, H. S. The Biology of Fish Growth; Academic Press: New York, 1987; pp 80-82. (23) Rottiers, D. V.; Tucker, R. M. Tech. Pap. U.S. Fish Wildl. Serv. 1982, No. 108. (24) Gruger, E. H.; Karrick, N. L.; Davidson, A. I.; Hruby, T. Environ. Sci. Technol. 1975, 9, 121-126. (25) Opperhuizen, A; Schrap, S. M. Chemosphere 1988,17,253262. (26) Press, W. H.; Teukolsky, S. A.; Vetterling, W. T.;Flannery, B. P. Numerical Recipes in C,2nd ed., Cambridge University Press: New York, 1992. (27) Mackay, D. Environ. Sci. Technol. 1982, 16, 274-278. (28) Schuurmann, G.; Klein, W. Chemosphere 1988,17, 15511574. (29) Walters, C. Adaptive Management of Renewable Resources; Macmillan Publishing Company: New York, 1986;pp 188190. (30) Hansen, M. J. Fish Management Report 126. Bureau of Fish Management, Wisconsin Department of Natural Resources, 1986. (31) Rasmussen, J. B.; Rowan, D. J.; Lean, D. R S.; Carey, J. H. Can. J.Fish. Aquat. Sei. 1990, 47, 2030-2038. (32) Brown, E. H.; Argyle, R. L.; Payne, N. R.; Holey, M. E. Can. J.Fish. Aquat. Sci. 1987, 44 (Suppl. 2), 371-383. (33) Crowder, L. B.; Binkowski, F. P. Environ. Biol. Fishes 1983, 2, 105-113.
Received for review January 26, 1994. Revised manuscript received April 25, 1994. Accepted May 10, 1994." 0 Abstract published in Advance ACS Abstracts, June 1, 1994.
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