JEQ Journal of Natural Resources and Life Sciences Education
HOME HELP FEEDBACK SUBSCRIPTIONS ARCHIVE SEARCH TABLE OF CONTENTS
QUICK SEARCH:   [advanced]


     

Published online 4 January 2008
Published in J Environ Qual 37:234-244 (2008)
DOI: 10.2134/jeq2007.0105
© 2008 American Society of Agronomy, Crop Science Society of America, and Soil Science Society of America
677 S. Segoe Rd., Madison, WI 53711 USA
This Article
Right arrow Abstract Freely available
Right arrow Figures Only
Right arrow Full Text (PDF) Free
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Similar articles in this journal
Right arrow Similar articles in PubMed
Right arrow Alert me to new issues of the journal
Right arrow Download to citation manager
Citing Articles
Right arrow Citing Articles via HighWire
Right arrow Citing Articles via Google Scholar
Google Scholar
Right arrow Articles by Hollister, J. W.
Right arrow Articles by Walker, H. A.
Right arrow Search for Related Content
PubMed
Right arrow PubMed Citation
Right arrow Articles by Hollister, J. W.
Right arrow Articles by Walker, H. A.
GeoRef
Right arrow GeoRef Citation
Agricola
Right arrow Articles by Hollister, J. W.
Right arrow Articles by Walker, H. A.
Related Collections
Right arrow Watershed and Landscape Processes
Right arrow Other Models

TECHNICAL REPORTS

Landscape and Watershed Processes

Predicting Estuarine Sediment Metal Concentrations and Inferred Ecological Conditions: An Information Theoretic Approach

Jeffrey W. Hollistera,*, Peter V. Augustb, John F. Paulc and Henry A. Walkerd

a USEPA, Office of Research and Development, National Health and Environmental Effects Research Laboratory, Atlantic Ecology Division, 27 Tarzwell Drive, Narragansett, RI 02882
b Univ. of Rhode Island, Dep. of Natural Resources Science, 1 Greenhouse Road, Kingston, RI 02881
c USEPA, Office of Research and Development, Mail Code B343-06, Research Triangle Park, NC 27711
d USEPA, Office of Research and Development, National Health and Environmental Effects Research Lab., Atlantic Ecology Div., 27 Tarzwell Drive, Narragansett, RI 02882

* Corresponding author (hollister.jeff{at}epa.gov).

Received for publication February 26, 2007.

   ABSTRACT
TOP
 NOTES
 ABSTRACT
INTRODUCTION
 Materials and Methods
 Results and Discussion
 Conclusions
 REFERENCES
 
Empirically derived relationships associating sediment metal concentrations with degraded ecological conditions provide important information to assess estuarine condition. Resources limit the number, magnitude, and frequency of monitoring activities to acquire these data. Models that use available information and simple statistical relationships to predict sediment metal concentrations could provide an important tool for environmental assessment. We developed 45 predictive models for the total concentrations of copper, lead, mercury, and cadmium in estuarine sediments along the Southern New England and Mid-Atlantic regions of the United States. Using information theoretic model-averaging approaches, we found total developed land and percent silt/clay of estuarine sediment were the most important variables for predicting the presence of all four metals. Estuary area, river flow, tidal range, and total agricultural land varied in their importance. The model-averaged predictions explained 78.4, 70.5, 56.4, and 50.3% of the variation for copper, lead, mercury, and cadmium, respectively. Overall prediction accuracies of selected sediment benchmark values (i.e., effects ranges) were 83.9, 84.8, 78.6, and 92.0% for copper, lead, mercury, and cadmium, respectively. Our results further support the generally accepted conclusion that sediment metal concentrations are best described by the physical characteristics of the estuarine sediment and the total amount of urban land in the contributing watershed. We demonstrated that broad-scale predictive models built from existing monitoring data with information theoretic model-averaging approaches provide valuable predictions of estuarine sediment metal concentrations and show promise for future environmental modeling efforts in other regions.

Abbreviations: AIC, Akaike Information Criteria • EMAP-E, EPA's Environmental Monitoring and Assessment Program-Estuaries component • ER, effects range • ERL, effects range low • ERM, effects range median • MAIA, Mid-Atlantic Integrated Assessment • NCPDI, National Coastal Pollution Discharge Inventory


   INTRODUCTION
TOP
 NOTES
 ABSTRACT
 INTRODUCTION
Materials and Methods
 Results and Discussion
 Conclusions
 REFERENCES
 
THE demand for food, timber, recreational opportunities, and housing in the Northeastern and Mid-Atlantic coast of the USA has had a lasting impact on the spatial patterns of the coastal landscape, which in turn has affected ecological processes and conditions (Forman and Godron, 1986; Forman, 1995; Turner, 1989). Point and nonpoint pollution resulting from these anthropogenic land uses has added sediments, nutrients, pesticides, and toxic metals to fresh, salt, and estuarine waterways (Basnyat et al., 1999; Novotny and Olem, 1994; USEPA, 1995). For instance, industrial and commercial land uses are known to be important sources of lead, copper, and zinc (Sonzogni et al., 1980). Our knowledge of these inputs and their impacts is largely due to environmental monitoring efforts, which are necessary to identify degraded and threatened waterways, to measure changes in condition, and to assess the success of mitigation or restoration activities. For example, the EPA's Environmental Monitoring and Assessment Program–Estuaries component (EMAP-E) provides quantitative data on the status and changing condition of our nation's estuaries (USEPA, 1999). One challenge of large-scale monitoring efforts, such as EMAP-E, is that it is impossible to monitor all estuaries all the time. Establishing the relationship between estuarine condition and landscape structure is important because it allows for the prediction of estuarine condition in estuaries that have not been monitored.

Turner et al. (2001) discuss several studies that have modeled the relationships between landscape structure and eutrophication and pollution of freshwater systems; however, a review of the literature reveals that less work has been done in estuarine systems. Comeleo et al. (1996) and Paul et al. (2002) have explored these relationships in small estuarine systems of the Mid-Atlantic region. Using the Chesapeake Bay Watershed Pilot Project land cover data set and the U.S. Geologic Survey's Land Use Data Analysis data set, respectively, they found relationships between several measures of landscape composition (percent forest and percent urban) and sediment contamination. Additionally, across the northeastern USA, urban land uses near sampling stations have been linked to a variety of measures of estuarine condition (Dauer et al., 2000; Hale et al., 2004). The results from these prior studies show that it is possible to develop predictive models of the ecological condition of estuarine waters; however, associations between sediment condition and upstream land use are complex; therefore, a large number of predictive models is possible.

In any study with many competing models, the methods used are often as interesting as the science underlying the models. Paul et al. (2002), as well as many of the previously cited studies of sediment contamination in estuaries, used standard parametric model selection techniques, which have generated useful results and demonstrate a powerful means for creating predictive models. For these methods to remain robust, several assumptions must be met (equality of variances, multivariate normality, and linearity), and the data must be replicated (Carpenter, 1990; Reckhow, 1990; Zar, 1999). Due to practical and logistical limitations, these assumptions are rarely satisfied with broad-scale environmental data, and thus the results of statistical tests may be questionable, and hypothesis-based model selection can be logically difficult (Anderson et al., 2000; Nester, 1996; Reckhow, 1990).

Some alternatives to traditional parametric model selection include hierarchical Bayesian modeling and information theoretic approaches. Bayesian modeling methods have been successfully used in estuarine water quality monitoring (Borsuk et al., 2001; Borsuk et al., 2004) and promise to be powerful analytical tools. However, Bayesian methods are technically and mathematically demanding and therefore are not fully accessible by the scientific community (Burnham and Anderson, 2002). Information theoretic approaches are seeing wider use in ecology and environmental science partly because they provide a feasible alternative to Bayesian approaches and are easily implemented (Burnham and Anderson, 2002; Johnson and Omland, 2004; Richards, 2005).

The objectives of our study are twofold: (i) to identify a simple set of readily available measures of watershed condition that can be used to predict estuarine sediment metal concentration and (ii) to use information theoretic multi-model inference methods described by Burnham and Anderson (2002) to advance the modeling described in Paul et al. (2002). Our general modeling approach follows the recommendations of the National Research Council of avoiding reliance on expensive, complex mechanistic models in favor of cheaper, simpler, statistical models (Reckhow et al., 2001).


   Materials and Methods
TOP
 NOTES
 ABSTRACT
 INTRODUCTION
 Materials and Methods
Results and Discussion
 Conclusions
 REFERENCES
 
Study Area and Data
Our study area encompasses the United States' Atlantic Coast from southern New England to the southeastern USA (Fig. 1 ). We used the U.S. Environmental Protection Agency's EMAP-E and Mid-Atlantic Integrated Assessment (MAIA) data to characterize estuary condition and characteristics, the National Coastal Pollution Discharge Inventory (NCPDI) for information on point sources of metal inputs, the National Land Cover Dataset to estimate all land use/land cover area, and the United States Geological Survey river gauge data and the National Oceanic and Atmospheric Administration tide gauge data to estimate estuarine hydrology. In addition to these datasets, we used the National Elevation Dataset to delineate watersheds for estuarine sampling sites. Our final dataset consisted of 112 EMAP sampling stations. These stations were in estuaries with sufficient coastal relief to automatically delineate watersheds and were not flagged as questionable by the quality assurance, quality control codes in EMAP-E. Further detail on the data acquisition, compilation, filtering, and manipulation procedures used to synthesize the many datasets used in this study are briefly discussed later in this section and in greater detail in Hollister (2004) and Hollister et al. (2004). An important caveat is that one of the driving forces behind this project was to develop a methodology that could be easily and quickly repeated; therefore, we used only public domain data so that these methods could be extended to other regions of the country with few requirements for additional data collection.


Figure 1
View larger version (21K):
[in this window]
[in a new window]

  		Fig. 1. Map of study area with locations of EPA's Environmental Monitoring and Assessment Program-Estuaries sampling stations used to generate models (n = 112).

 
Sediment Metal Concentrations
We built models to predict the concentration of cadmium, copper, mercury, and lead in estuarine sediments. We focused on these metals for various reasons. First, because this effort was in part a methods exploration, we wanted a dependent variable that would facilitate predictions. Total metals in estuarine sediments are known to be strongly related to land use (e.g., Comeleo et al., 1996; Paul et al., 2002), and the four individual metals we used have shown the strongest individual relationships with developed land in coastal watersheds (Hollister et al., 2007). Beyond mere statistical considerations, metals in general are known to come from mostly anthropogenic sources, represent long-term impacts, and are associated with degraded biological condition (Cochran et al., 1998; Kim et al., 2000; Sonzogni et al., 1980). We recognize that using sediment metal concentrations does not result in a true or "best" measure of estuarine condition because it ignores other mechanisms for degradation (e.g., hypoxia, other toxics, degraded habitat). However, the models developed with these four metals as dependent variables has utility because they predict values that are closely associated with anthropogenic impacts, have links to existing broad-scale data sets, and build on findings of previous studies (Comeleo et al., 1996; Hollister et al., 2007; Paul et al., 2002).

Modeling Approach and Model Development
We used an information theoretic approach for our model development and assessment. These approaches are free from the assumptions required for hypothesis-based model selection and thus are a better choice with environmental data that rarely meet the classic assumptions. However, information theoretic approaches are designed for model selection and multi-model averaging and do not introduce new methodologies for parameter estimation (i.e., parameters may be estimated with maximum likelihood or ordinary least squares); therefore, the assumptions of the models and parameter estimation (i.e., for linear models—linearity, normality and equality of variance in residuals, etc.) must hold true.

Information theoretic approaches, unlike standard regression model selection methods, do not rely on p values to measure the quality of a model. Instead, they attempt to directly estimate effects and effects sizes of a "set of candidate models" developed a priori through the use of Akaike Information Criteria (AIC) (Burnham and Anderson, 2002). The values of the Akaike Information Criteria are unitless and can be converted to AIC differences, which is the difference between the AIC of a given model and the minimum AIC of the candidate set (Eq. [1]).

Formula 1[1]
The {Delta}i is converted to the Akaike weight wi (Eq. [2]) and is directly interpreted as the probability that the model is the best model out of the candidate set.

Formula 2[2]
For details of these equations, see Burnham and Anderson (2002).

Development of our set of candidate models was based on the published literature and current scientific understanding of the effects of human impact on estuarine sediment metal concentrations. We followed common practice and developed a general global model of the system and created alternative models as nested subsets of the global model (Burnham and Anderson, 2002). The parameters were estimated using ordinary least squares, specifically with the "glm" function in R version 1.9.1 (R Development Core Team, 2004). For any of the candidate models to provide a reasonable linear fit, the global model must be assessed for linearity and the residuals examined for homoscedasticity and normality. Adjusted R2 values were examined for each of the four global models (Cu, Pb, Hg, and Cd). Residuals were examined for homoscedasticity with Levene's test on the median of the residuals and a Shapiro-Wilk's test was used to assess normality (Brown and Forsythe, 1974; Zar, 1999). Standard transformations of the dependent and independent variables were explored to resolve problems with the residuals and fit, and the transformations used were determined by residual analysis and ease of interpretation of the final model. Following these procedures, we log transformed Cu and Pb. We used a log transformation of the form ln(Metal + k) and followed suggestions in Zar (1999) to use k = 1. When we followed these suggestions, the log transformations for Hg and Cd still resulted in a highly non-normal univariate distribution. Power transformations for Hg (Hg0.2) and Cd (Cd0.3) more closely approximated a normal distribution. Smaller values of k (e.g., 0.1, 0.5, etc.) in the log transformation begin to approximate a normal distribution, but the univariate distributions are still slightly non-normal; however, for Cd, a transformation of ln(Cd + 0.1) resulted in normally distributed residuals of the global model. The resulting predictions from a log-transformed global model, using ln(Cd + 0.1), are very similar to predictions from the global model with a power transformation of Cd0.3. In this case we defer to the suggestion in Zar (1999) and only considered using log transformations of the form ln(metal + 1) and thus favor the power transformations over log transformations with different values of k for Cd and Hg.

Several other factors were taken into consideration when developing the set of candidate models. First, the number of parameters in any given model should not be more that one tenth of the sample size (in our case no more than 11 parameters). Second, a combination of observational studies and critical a priori examination of potential variables should be used when selecting parameters (Burnham and Anderson, 2002). Based on these guidelines, we examined 19 potential independent variables (Table 1 ). The process of a priori model development resulted in the inclusion of seven of these independent variables in the final modeling, and data were collected for only these seven variables (Table 1). The other 12 potential variables were excluded from further consideration for various reasons. Prior studies determined that cadmium was most strongly related to urban lands within the drainage basin and within 2.5 km of sampling stations, whereas copper and mercury showed the strongest relationship at 10 km and lead at 7.5 km (Hollister et al., 2007). Developed and agricultural area estimates and total annual point source loadings for each metal were calculated with these empirically derived distance-limited watersheds (2.5 km for cadmium, 7.5 km for lead, and 10 km for copper and mercury). Although the NCPDI, EMAP-E, and the MAIA data cover different temporal extents (the NCPDI is from 1991 and prior, and EMAP-E and MAIA range in date from 1990 to 1997), it was assumed that the point-loading estimate from 1991 would adequately represent total point sources for all years. The total estuarine area and sediment grain size (i.e., silt/clay percentage) were taken directly from the EMAP-E dataset. Estuarine hydrology was included in the models as freshwater inflow and tidal range. Freshwater inflow and tidal range were estimated from the closest USGS-monitored river or NOAA tide gauge. River gauges were limited to those that fell within the sampling station's drainage area. Data for each of these variables (Table 1) were compiled from 112 EMAP-E and MAIA sampling stations (for details see Hollister, 2004).


View this table:
[in this window]
[in a new window]

  		Table 1. Predictor variables examined during a priori modeling process. All variables are included here to highlight breadth of variables considered during the modeling a priori process. We collected data and modeled only variables labeled below as "Included."

 
We examined the final 45 models (Table 2 ) for major violations of multiple linear regression assumptions. An important caveat to our effort is that the primary goal of this analysis is the development of predictive models of estuarine sediment metal concentrations and not necessarily the identification of the mechanisms driving estuarine sediment contamination. Any conclusions regarding the underlying processes and mechanisms should be considered the result of a largely exploratory and not confirmatory analysis.


View this table:
[in this window]
[in a new window]

  		Table 2. Specification for the 45 models examined in this study with the associated Akaike weights (w). Transformations of the dependent variable were used to account for heteroscedasticity in the residuals. Only models with a w >0 are included.

 
Multimodel Inference
From the set of 45 parameterized candidate models, we created functions in R version 1.9.1 and calculated the AIC (output from "glm" function), AICc (an adjustment to AIC for small samples), AIC {Delta}i, and AIC wi (R Development Core Team, 2004). In a model selection framework, it is possible to interpret wi as the probability that a given model is best; therefore, the objective is to identify and select the model with the highest wi. However, were a single "best" model to be used to make inferences, those inferences would be conditional on that single model and would require the explicit consideration of model selection uncertainty. If it is not clear which of the models from the set of candidate models is "best" as measured by wi (i.e., wi >0.9 for any given model), then that single "best" model is unlikely to provide reliable predictions because of a high degree of uncertainty. Instead of relying on a single "best" model, we used an information theoretic–based model averaging approach (Burnham and Anderson, 2002). Each of the candidate models were weighted by its Akaike weight and combined into a single, averaged model. This was accomplished by generating weighted parameter estimates (i.e., parameter estimate multiplied by wi then summed across all models) for each parameter and making an "averaged" prediction from the combined model (Burnham and Anderson, 2002). Model averaging is appropriate when the primary goal is prediction (Burnham and Anderson, 2002). We did not include the 31 models that had an Akaike wi of essentially zero (i.e., <0.0001) in the calculation of the model averaged parameter estimates. We assessed prediction accuracy from the averaged model by the mean absolute error (MAE) and by the percent of the total range of observed values (MAE/[max. metal conc. – min. metal conc.]); however, the ecological and biological relevance of these concentrations is not readily apparent from the raw numbers, and further investigation is often required.

One method to describe metal concentrations in terms that are ecologically relevant is to use the effects range (ER) (Long et al., 1995). The ER is one way (of many) that relates biological condition to sediment metal concentration. The effects range low (ERL) and the effects range median (ERM) may be used to rank the concentration into a low (below ERL), medium (between ERL and ERM), or high (i.e., above ERM) potential for producing a biological impact. We converted the predicted values to an ER ranking for two reasons. First, we wanted to provide a rough test of the ability of these models to accurately predict estuarine condition. We converted each of the predicted values to a low, medium, or high level of impact based on the ER ranking and calculated the accuracy of these predictions with the use of a 3 x 3 error matrix similar to those used to assess the accuracy of thematic spatial data (Congalton and Green, 1999). Second, predicting a transformed (i.e., log or power transformed) concentration requires a back transformation to the original units, which may introduce a bias. However, it is our opinion that this bias is relatively small and would not affect our final conclusions. The impact of bias is further diluted when using a range of concentrations, like the ER rankings. We have not corrected for this bias in our back transformations.

These approaches are an improvement on past modeling (e.g., Comeleo et al., 1996; Paul et al., 2002) because they allow predictions based on multiple models, not just on a single, selected "best" model. The resulting predictions more robustly infer ecological condition of estuarine sediments by accounting for model selection uncertainty. This is an improvement because no longer is a single model, whose selection will likely vary as a result of the specific data used for parameterization, used to make predictions. In theory the model-averaged prediction accounts for this uncertainty (Burnham and Anderson, 2002). Although comparing information theoretic methods with more traditional methods (e.g., stepwise selection) might prove useful, other investigators have done similar comparisons, and repeating those here is beyond the scope of this study (Burnham and Anderson, 2002). We rely on their findings that multi-model inference is an improvement on standard stepwise model selection.


   Results and Discussion
TOP
 NOTES
 ABSTRACT
 INTRODUCTION
 Materials and Methods
 Results and Discussion
Conclusions
 REFERENCES
 
Descriptive Statistics and Effects Range Values of Actual Sediment Metal Concentrations
Many of the variables were positively skewed; in particular, the four dependent variables (Cu, Cd, Hg, Pb) showed fairly dramatic positive skewness, indicating that high concentrations were rare (Table 3 ). Similarly, the distribution of the ER values indicates that for this sample of estuaries, highly affected sediments are rare. For copper, 74% of the samples had a low potential for biological impact, and 26% had a medium risk of biological impact. None of the samples had a high potential for biological impact for copper. Lead showed a similar pattern, with 74% low, 24% medium, and 2% with a high potential. Mercury had 69% low, 24% medium, and 7% high; cadmium had 89% low, 11% medium, and no high rankings.


View this table:
[in this window]
[in a new window]

  		Table 3. Descriptive statistics of untransformed dependent variables and independent variables. Units reported are units native to the datasets.

 
Model Results
To determine if transformations were needed and if the set of independent variables was reasonable, the general fit of the global model was assessed, and the residuals were examined for homogeneity of variance and normality. Although statistically significant, the nontransformed global models had adjusted R2 values that were relatively low (0.23–0.55), had skewed residuals, and had residual plots indicating heteroscedasticity. In all cases, transforming the dependent variables increased the adjusted R2 and removed heteroscedasticity; however, the residuals were still significantly non-normal (Table 4 ). Although transformations (log and square root) of many of the independent variables improved normality and made marginal improvements in the adjusted R2, they would have added considerable complexity in the interpretation of the final models. Regression is fairly robust to deviations from normality in the residuals as long as the residuals are also homoscedastic (González and Auda, 2002). Therefore, we only transformed the dependent variables.


View this table:
[in this window]
[in a new window]

  		Table 4. Global model residual analysis statistics for the untransformed and transformed dependent variables.

 
The adjusted R2 of the 45 models ranged from 0 to 0.79. The wi for each model ranged from essentially 0 (i.e., <0.0001) to 0.409 (Table 2). Only the 14 models with wi >0.0001 are reported. These were the same models across all metals and were those that contained parameters for total hectares of urban land and the percent of silt/clay in the sediment (Table 5 ). The ranking varied for each metal, and the adjusted R2 for models without these variables was substantially lower. This result corroborates several prior studies and suggests that the total amount of urban land is a useful predictor of sediment metal concentrations and that the physical conditions of sediments are important in determining contaminant concentration (Kennish, 1986; Novotny and Olem, 1994; Paul et al., 2002). Beyond urban land and percent silt/clay, there was variation in the importance of the remaining variables, and it was not readily apparent which were the most important, except area of the estuary for cadmium. Area of the estuary was added to the models as a surrogate for atmospheric deposition, which is a known source of the metals we modeled (e.g., Kim et al., 2000; Sabin et al., 2005). However, much of the true variation is unlikely to be captured by a simple measure such as estuarine area because it does not account for variations in deposition caused by precipitation or distance from source (Cochran et al., 1998; Friedland et al., 1986; Kim et al., 2000), nor does it account for changes in the metals as they enter into and are transported in the estuarine environments (Sadiq, 1992). These factors, along with other variables not included in our models (e.g., wetlands), contribute to the uncertainty in the importance of the other variables and the relatively low percent of variation explained for cadmium and mercury.


View this table:
[in this window]
[in a new window]

  		Table 5. Model results and Akaike Information Criteria (AIC) statistics for ln(Cu + 1), ln(Pb + 1), Hg0.2, and Cd0.3. Only the models with an AIC w >0 are included and are ordered by the magnitude of w.

 
Model Averaging and Prediction Accuracy
The model-averaged adjusted R2 values for the copper, lead, mercury, and cadmium models are 0.784, 0.705, 0.564, and 0.503, respectively; the model-averaged SEs of the residuals are 0.604, 0.540, 0.161, and 0.242, respectively (Table 6 ). Tests of the assumptions (i.e., homoscedasticity and normality of residuals) for the model-averaged residuals are nearly identical to those of the global models and thus are not presented. Because the averaged models account for model selection uncertainty, the adjusted R2 for the averaged models is lower than that for the individual "best" model. This is a benefit because inferences based on the averaged model are more stable than those based on a single "best" model, even if that "best" model has a higher adjusted R2 (Burnham and Anderson, 2002). In cases where wi is not high (i.e., >0.9), model selection uncertainty likely plays a role, and model averaging should be used (Burnham and Anderson, 2002). This was this case with our models because the highest wi was only 0.3, indicating that given another dataset, a different "best" model could be selected; thus, model selection uncertainty is quite high, and model averaging is necessary in our case. This fact suggests an improvement over past studies (e.g., Comeleo et al., 1996; Paul et al., 2002), where only a single best model was identified by traditional means.


View this table:
[in this window]
[in a new window]

  		Table 6. Model averaged parameter estimates and parameter SEs averaged from all models with wi >0.0001. These parameters constitute the final averaged model and may be directly used to predict concentrations of the metals.

 
Overall the averaged models do a fairly good job at predicting the actual metal concentrations and the ER values (Table 7 and Fig. 2 ). However, on average, estimates of copper are 1.61 µg g–1 greater than the actual concentration. Lead is underestimated by 2.23 µg g–1, mercury is underestimated by 0.042 µg g–1, and cadmium is underestimated by 0.14 µg g–1. As a percentage of the total range of observed values, copper is overestimated by only 0.61%. Lead is underestimated by 0.68%, mercury by 1.28%, and cadmium by 2.13%. These patterns of over- and underestimation are also borne out by comparing predicted versus observed plots (Fig. 2). For instance, cadmium has more points above the perfect agreement line, indicating more transformed predictions lower than the expected transformed values.


View this table:
[in this window]
[in a new window]

  		Table 7. Error matrices comparing effects ranges (ER) predictions to actual ER. The ER rankings were converted from the back-transformed model averaged predictions of sediment metal concentration.

 

Figure 2
View larger version (19K):
[in this window]
[in a new window]

  		Fig. 2. Scatterplot of predicted vs. observed copper, lead, mercury, and cadmium sediment concentrations. Predictions were made from averaged models. The lines represents perfect agreement between predicted and observed values (y = 1x + 0). Values above the line indicate sampling points with potentially enriched concentrations.

 
Prediction accuracies of the ER rankings were 78.6% for mercury, approximately 84% for copper and lead, and 92.0% for cadmium (Table 7). In general, the models correctly predicted low rankings, with most misclassification occurring in the predictions of medium and high conditions, and one of the low predictions was misclassified as high, lending further credibility to the model predictions. Additionally, omission errors (i.e., Type II errors) were generally lower than commission errors (i.e., Type I errors) for the low ranking. This was reversed for the medium ranking because the models more often classified actual medium rankings as low or high. It is important to use some caution when evaluating class-specific measures of accuracy in an error matrix because they only show the probability of correct classification. Often it is more interesting to evaluate what types of misclassifications are occurring. This information is contained in the commission (Type I) and omission (Type II) errors (Table 7). Omission errors indicate the probability that the model incorrectly classified an estuary that was actually low as medium or high. Commission errors are the inverse of this and indicate that the model incorrectly classifies an estuary that is actually medium or high as low. Using these models in a screening framework (see Screening Models) highlights the importance of commission error because high commission error results in potentially degraded estuaries being missed and not examined when in fact they should be. Because a certain degree of error is unavoidable, it is necessary to determine what level of commission error is unacceptable when using predictive models such as these. Making this determination is not straightforward and must be done on a case-by-case basis.

Screening Models
Ours and similar models may be used in a screening process. Model predictions provide a mechanism to limit estuaries included in a monitoring sampling scheme to make better use of environmental monitoring resources and to focus data collection in estuaries that are most likely imperiled. For example, our models use independent variables that have little value in a management context (i.e., it is largely impossible to reduce overall urban land or alter silt/clay content of the sediment), and modeling metals with these variables predicts ambient sediment metal concentrations. Estuaries with sediment metal concentrations greater than predicted could be considered elevated. These are identified by plotting predicted values on the x axis and observed values on the y axis with a line representing perfect agreement (Fig. 2). Points that fall above the line indicate estuaries with sediment metal concentrations higher than expected by the model. It is these points that might be of most interest in a management setting (e.g., the enriched sampling points might have point sources of metals that are not currently known), and managers can focus remediation activities where they may have the most impact.

Comments on the Information Theoretic Approach
A number of modeling and model selection methodologies exist that accommodate messy data (i.e., the type of data commonly used in environmental applications). These include, among others, computer intensive methods (e.g., Monte Carlo simulation), information theoretic approaches, and Hierarchical Bayesian methods (Burnham and Anderson, 2002; Reckhow, 1990). Most of these approaches are somewhat recent to ecology and environmental science, and it is not necessarily clear under which conditions one method is superior. Some (e.g., many of the Bayesian methods) can be difficult to implement without a great deal of statistical expertise and custom programming. The information theoretic approaches are based on similar principles as the Bayesian approaches but are much easier to implement. They provide an estimate of a model's suitability relative to competing models, no arbitrary probability of acceptance or rejection is required (e.g., a p value <0.05), and the importance of a given model or set of models is left up to the interpretation of the analyst.

Environmental scientists and ecologists must decide to use the traditional methods that have known shortcomings for many environmental applications or to implement more contemporary methods (i.e., information theoretic approaches) that hold promise as an improvement on traditional null hypothesis–based model selection methods. This is especially the case when scientists are developing and evaluating multiple plausible hypotheses (Johnson and Omland, 2004; Richards, 2005). Studies such as ours and others (e.g., Johnson and Omland, 2004; Richards, 2005) suggest that until superior methods are developed or current debates are resolved (e.g., Burnham and Anderson, 2004; Link and Barker, 2006), it seems wise to choose the best available model selection and prediction methodology that can also be readily implemented. We believe that information theoretic approaches are such a method. They represent a step forward in the analysis of environmental data and advance how we model the relationship between human activities and the many aspects of ecological condition.


   Conclusions
TOP
 NOTES
 ABSTRACT
 INTRODUCTION
 Materials and Methods
 Results and Discussion
 Conclusions
REFERENCES
 
There is a long history in ecological research of linking human activities on land to water quality, with much of the original work conducted in freshwater systems. Only recently have efforts extended into estuaries and coastal waters. Our research builds on the estuarine studies of Comeleo et al. (1996) and Paul et al. (2002) by expanding the geographic extent, by updating the datasets used, and, perhaps most importantly, by adopting and demonstrating the use of information theoretic approaches in broad-scale modeling of estuarine condition. Our conclusions from this work are:

  1. Information theoretic approaches are relatively straightforward and easy to implement in a standard linear modeling application.
  2. Consistent with prior studies, total area of urban land and the percent silt/clay in estuarine sediments were extremely important in describing the variation in estuarine sediment metal concentrations.
  3. Averaged models using total urban land, total agricultural land, percent silt/clay of estuarine sediments, estimated tidal range, estimated freshwater input, area of the estuary, and known point sources correctly predict the effects range ranking in approximately 80% of estuaries.


   ACKNOWLEDGMENTS
 
We thank Stephen Hale, Anne Kuhn, Diane Nacci, and all anonymous reviewers of this manuscript for their time and effort. Your thoughtful comments greatly improved our final product. We also thank the University of Rhode Island, the US Environmental Protection Agency, Rhode Island Natural History Survey, and the Rhode Island Chapter of Surfrider who provided funds and/or facilities for the successful completion of this project. JWH was initially partially supported through USEPA Cooperative Agreement CT825802, Brian D. Melzian, Project Officer. The research described in this paper has been funded in part by the US Environmental Protection Agency. This paper has not been subjected to Agency review. Therefore, it does not necessary reflect the views of the Agency. Mention of trade names or commercial products does not constitute endorsement or recommendation for use. This is contribution number AED-07-013 of the Atlantic Ecology Division, Office of Research and Development, National Health and Environmental Effects Research Laboratory.


   NOTES
TOP
 NOTES
ABSTRACT
 INTRODUCTION
 Materials and Methods
 Results and Discussion
 Conclusions
 REFERENCES
 
All rights reserved. No part of this periodical may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage and retrieval system, without permission in writing from the publisher.


   REFERENCES
TOP
 NOTES
 ABSTRACT
 INTRODUCTION
 Materials and Methods
 Results and Discussion
 Conclusions
 REFERENCES
 




This article has been cited by other articles:


Home page
 ANN OCCUP HYGHome page
J. Lavoue and P. O. Droz
Multimodel Inference and Multimodel Averaging in Empirical Modeling of Occupational Exposure Levels
Ann. Hyg., March 1, 2009; 53(2): 173 - 180.
[Abstract] [Full Text] [PDF]

Home page
 J. Environ. Qual.Home page
J. W. Hollister, H. A. Walker, and J. F. Paul
CProb: A Computational Tool for Conducting Conditional Probability Analysis
J. Environ. Qual., October 23, 2008; 37(6): 2392 - 2396.
[Abstract] [Full Text] [PDF]

This Article
Right arrow Abstract Freely available
Right arrow Figures Only
Right arrow Full Text (PDF) Free
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Similar articles in this journal
Right arrow Similar articles in PubMed
Right arrow Alert me to new issues of the journal
Right arrow Download to citation manager
Citing Articles
Right arrow Citing Articles via HighWire
Right arrow Citing Articles via Google Scholar
Google Scholar
Right arrow Articles by Hollister, J. W.
Right arrow Articles by Walker, H. A.
Right arrow Search for Related Content
PubMed
Right arrow PubMed Citation
Right arrow Articles by Hollister, J. W.
Right arrow Articles by Walker, H. A.
GeoRef
Right arrow GeoRef Citation
Agricola
Right arrow Articles by Hollister, J. W.
Right arrow Articles by Walker, H. A.
Related Collections
Right arrow Watershed and Landscape Processes
Right arrow Other Models

HOME HELP FEEDBACK SUBSCRIPTIONS ARCHIVE SEARCH TABLE OF CONTENTS
The SCI Journals Agronomy Journal Crop Science
Journal of Natural Resources
and Life Sciences Education		 Vadose Zone Journal
Soil Science Society of America Journal Journal of Plant Registrations The Plant Genome