U.S. Department of the Interior

U.S. Geological Survey

Scientific Investigation Report 2004-5199

Prepared in cooperation with the National Institute of Environmental Health Sciences

A Statistical Model and National Data Set for Partitioning 

Fish-Tissue Mercury Concentration Variation Between 

Spatiotemporal and Sample Characteristic Effects
A Statistical Model and National Data 

Set for Partitioning Fish-Tissue Mercury 

Concentration Variation Between 

Spatiotemporal and Sample Characteristic 

Effects

By Stephen P. Wente

Prepared in cooperation with the National Institute of Environmental Health Sciences

Scientific Investigation Report 2004-5199

U.S. Department of the Interior

U.S. Geological Survey
U.S. Department of the Interior

Gale A. Norton, Secretary

U.S. Geological Survey

Charles G. Groat, Director

U.S. Geological Survey, Reston, Virginia: 2004

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Suggested citation:

Wente, S.P., 2004, A statistical model and national data set for partitioning fish-tissue mercury concentration variation between spatiotemporal and sample characteristic effects: U.S. Geological Survey Scientific Investigation Report 

2004-5199, 15 p.
iii

Contents

Abstract ................................................................................................... 1

Introduction ............................................................................................. 1

Purpose and scope ................................................................................. 2

Acknowledgements ................................................................................. 2

Methods ................................................................................................... 2

Model description ................................................................................. 2

Model assumptions ................................................................................. 3

National fish-mercury data set .................................................................. 4

Model performance assessment .................................................................. 4

Model evaluation and applications ..................................................................... 6

Model fit ............................................................................................. 6

Fish-mercury concentration prediction ......................................................... 7

Prediction accuracy .............................................................................. 8

Model applications ................................................................................. 8

Future studies ............................................................................................. 9

Summary ................................................................................................... 9

References cited ....................................................................................... 10

Appendix ................................................................................................... 12

Figures

Figure 1. Relation of noncensored observations to predicted fish-mercury concentrations

 in log units. .................................................................................... 6

Figure 2. Predicted fish-mercury concentrations as a function of length for skin-off fillet 

cuts of 11 frequently sampled species in the upper Midwestern United States 

depicted in (a) log space, and (b) arithmetic space for a hypothetical sampling

 event .......................................................................................... 8

Tables

Table 1. Summary of fish-mercury concentration data contributions to the National Listing 

of Fish and Wildlife Advisory (NLFWA) data set (September 28, 2002 version of 

the data set) as modified for calibration of the statistical model used in this 

report. .......................................................................................... 5

Table 2. Comparison of model fit for the full and reduced fish-mercury models. .................. 7

Table 3. Likelihood ratio comparisons for the full and reduced fish-mercury models. ............ 7
iv

Conversion Factors

Multiply By To obtain

Length

inch (in.) 2.54 centimeter (cm)

mile (mi) 1.609 kilometer (km)

Area

acre 0.4047 hectare (ha)

Mass

pound, avoirdupois (lb) 0.4536 kilogram (kg) 

NOTE TO USGS USERS: Use of hectare (ha) as an alternative name for square hectometer 

(hm2) is restricted to the measurement of small land or water areas. 
ABSTRACT

Many Federal, Tribal, State, and local agencies monitor 

mercury in fish-tissue samples to identify sites with elevated 

fish-tissue mercury (fish-mercury) concentrations, track 

changes in fish-mercury concentrations over time, and produce 

fish-consumption advisories. Interpretation of such monitoring data commonly is impeded by difficulties in separating the 

effects of sample characteristics (species, tissues sampled, and 

sizes of fish) from the effects of spatial and temporal trends 

on fish-mercury concentrations. Without such a separation, 

variation in fish-mercury concentrations due to differences in 

the characteristics of samples collected over time or across 

space can be misattributed to temporal or spatial trends; and/or 

actual trends in fish-mercury concentration can be misattributed to differences in sample characteristics. This report 

describes a statistical model and national data set (31,813 

samples) for calibrating the aforementioned statistical model 

that can separate spatiotemporal and sample characteristic 

effects in fish-mercury concentration data. This model could 

be useful for evaluating spatial and temporal trends in fishmercury concentrations and developing fish-consumption 

advisories. The observed fish-mercury concentration data and 

model predictions can be accessed, displayed geospatially, and 

downloaded via the World Wide Web (http://emmma.usgs.

gov). This report and the associated web site may assist in the 

interpretation of large amounts of data from widespread fishmercury monitoring efforts.

INTRODUCTION

Mercury is a widespread environmental concern. In 

aquatic ecosystems, mercury can undergo chemical and 

biological transformations that produce methylmercury, a 

highly toxic form of mercury that is readily bioaccumulated 

and bioconcentrated in aquatic communities (Porcella, 1995). 

The major pathway by which humans are currently exposed to 

methylmercury is through consumption of fish (U.S. Environmental Protection Agency, 1997a; 1997b). Consumption 

of fish with high concentrations of methylmercury can be 

harmful to the health of both humans and wildlife (Wiener 

and others, 2002). Increased recognition of the prevalence of 

methylmercury, and its adverse health effects to humans and 

wildlife, has resulted in considerable monitoring of fish-mercury concentrations. Such monitoring is typically designed to 

serve three major purposes:

•Identifying sites with high fish-mercury concentrations 

(U.S. Environmental Protection Agency, 1993; 1995) 

(hereinafter referred to as measuring spatial variation, 

because this involves measuring variation in fish-mercury concentrations among multiple locations);

•Measuring temporal trends (hereinafter referred to as 

measuring temporal variation); and

•Developing fish-consumption advisories (U.S. Environmental Protection Agency, 1993) (fish-consumption 

advisories recommend limited fish consumption at 

specific locations where concerns exist about the health 

effects of consuming fish). 

In 2002, 45 states issued mercury-related fish-consumption advisories, which applied to a total of 12,069,319 lake 

acres and 473,186 river miles (U.S. Environmental Protection 

Agency, 2003). 

The distribution of fish-mercury concentrations within 

fish communities is complex because fish-mercury concentrations vary with a fish sample’s characteristics. Among species, 

fish-mercury concentrations tend to increase with trophic level 

(MacCrimmon and others, 1983; Suns and others, 1987; Cope 

and others, 1990; Kim and Burggraaf, 1999). Within species, 

fish-mercury concentrations typically vary with length (and 

other measures of fish size or age) (Wiener and Spry, 1996; 

Huckabee and others, 1979). Within individual fish, different 

tissues and organs have different mercury concentrations (Giblin and Massaro, 1973; Boudou and Ribeyre, 1983; Harrison 

and others, 1990), and therefore different cuts of fish (whole 

fish, skin-on fillet, skin-off fillet, as examples) are expected to 

have different fish-mercury concentrations. 

A major problem with interpreting fish-mercury monitoring data is partitioning the variation in fish-mercury concenA Statistical Model and National Data Set for Partitioning 

Fish-Tissue Mercury Concentration Variation Between 

Spatiotemporal and Sample Characteristic Effects

By Stephen P. Wente
2 A statistical model and national data set for partitioning fish-tissue mercury concentration variation

trations between spatiotemporal and sample characteristic 

effects. This problem occurs because it is commonly difficult, 

and in some cases impossible, to collect samples with consistent sample characteristics over large regions (for example, if 

no species’ range extends over the entire region of interest) 

or a variety of habitats (if no single species occurs within all 

habitats). Therefore, changes in fish-mercury concentrations 

among samples collected over time or across space may be 

due to either spatiotemporal or sample characteristic effects or 

some combination. Without a reliable method for partitioning 

fish-mercury concentration variation between these effects, 

variability in fish-mercury concentrations due to differences in 

the sample characteristics can be misattributed to temporal or 

spatial trends, or actual trends in fish-mercury concentration 

can be misattributed to differences in sample characteristics. 

To address the need for a method to partition fish-mercury 

concentrations between spatiotemporal and sample characteristic effects, the U.S. Geological Survey, in cooperation 

with the National Institute of Environmental Health Sciences, 

developed a statistical model using fish-mercury concentration 

data from the National Listing of Fish and Wildlife Advisories 

(NLFWA) data set.

PURPOSE AND SCOPE

This report describes a statistical model and national fishmercury concentration data set that allow fish-mercury concentration variation to be partitioned between spatiotemporal 

and sample characteristic effects. Because this model and data 

set provide a method for partitioning fish-mercury concentration variation, this model and data set can be used to predict 

fish-mercury concentrations across a range of sample characteristics for sites and times when fish were sampled. Such 

predictions are potentially useful for calculating standardized 

fish-mercury concentrations that can be used to identify and 

measure fish-mercury concentration trends over space and 

time as well as calculating expected fish-mercury concentrations for all species and lengths of fish occurring at individual 

sites for developing site-specific fish-consumption advisories. 

The fish-mercury concentration data set contains data collected between June 22, 1977, and March 29, 2001. A rigorous assessment of the accuracy of this model’s predictions is 

beyond the scope of this report. This model is not intended for 

making predictions for sites or times that were not sampled.

This model’s predictions can be accessed, displayed 

geospatially, and downloaded via the World Wide Web (http://

emmma.usgs.gov)1

. Additionally, this web site provides tools 

for exploring spatial and temporal trends in fish-mercury concentration data and developing site-specific fish-consumption 

advisories. This report and the associated web site may assist 

in the interpretation of large amounts of data from widespread 

fish-mercury monitoring efforts.

ACKNOWLEDGMENTS

Sam Wilson and Chris Portier (National Institute of Environmental Health Sciences) and Herb Buxton, Sarah Gerould, 

Dave Krabbenhoft, and Mark Brigham of the U.S. Geological Survey were instrumental in initiating this study, and Jim 

Stark, Mark Brigham, Tom Winterstein and Rich Alexander 

of the U.S. Geological Survey provided valuable input into 

preparation of this report. The following U.S. Geological 

Survey personnel: Paul Hearn, Dave Donato, John Aguinaldo, 

Susan Price, Ovidio Rivero-Bartolomei, and Seth Tanner are 

recognized for their efforts on developing the Environmental 

Mercury Mapping, Modeling, and Analysis web site (http://

emmma.usgs.gov).

METHODS

There are essentially two ways in which spatiotemporal 

and sample characteristic effects can be misattributed to one 

another. In the first case, if a model is incapable of accurately 

describing the distribution of fish-mercury concentrations 

over space, time, and sample characteristics, then application of that model to a data set could force misattribution of 

spatiotemporal and sample characteristic effects. In the second 

case, if a model is used that can accurately describe this distribution of fish-mercury concentrations, but there are too few 

observations to properly constrain the parameter estimates, 

then the poorly constrained parameter estimates could allow 

misattribution of these effects. The analysis presented in this 

report, therefore, uses two strategies to better ensure the proper 

partitioning of these effects. The first strategy is to develop a 

model that requires as few parameter estimates as possible, 

while allowing fish-mercury concentrations to vary across 

space, time, and sample characteristics. The second strategy is 

to maximize the number of observations available for constraining this model’s parameter estimates. 

MODEL DESCRIPTION

The model presented in this report is a statistical model 

related to analysis of covariance and multiple-linear regression and is specifically designed to minimize the number of 

parameter estimates used to describe variation in fish-mercury 

concentrations due to sample characteristic effects. This model 

is similar to the equation for a line:

loge Cijk ( ) α + 1 k loge lengthijk ( + 1) βj εijk = × + +

 (1)

1

The model predictions and data set available on this web site are frequently 

updated as new observations become available. As additional observations 

are added to the data set, additional parameters typically must be added to the 

model to describe those new observations. Although this report refers specifically to the original model (4,910 parameter estimates) and data set (31,813 

observations), the conceptual informations provided in this report should aid 

in the interpretaion of the model predictions available on this web site both 

now and in the future.
where αk

 and βj are the slope and intercept, respectively, of the 

linear relation between the loge (Cijk + 1) and loge (lengthijk + 1) 

terms; 

Cijk is the fish-mercury concentration in μg Hg/kg 

(micrograms of mercury per kilogram of fish tissue) from the 

i

th sample of the jth sampling event (the term ‘sampling event’ 

refers to a collection of samples from a specific site and date) 

for the kth species and cut combination (A “cut” is the type of 

tissue sample, such as skin-off fillet.); 

αk is a set of parameters relating variation in fish-mercury concentration to fish length for each of m species and cut 

combinations of fish; 

lengthijk is the length of the i

th sample of the jth sampling 

event for the kth species (fish length is used in this model as the 

measure of fish size because length data is commonly available for fish-mercury results);

βj is a set of parameters describing variation in fish-mercury concentrations among each of n sampling events; and

εijk is an error term for the i

th sample of the jth sampling 

event for the kth species. 

Because αk and βj can take on m and n values, respectively, equation 1 describes multiple (m × n) lines in log-log 

space or, after back-transformation into arithmetic space.

Conceptually, these curves describe the mercury concentration of a particular species and cut of fish across the 

range of possible fish lengths. At a length of 0, all species are 

assumed to have a concentration of 0. At lengths greater than 

0, the fish are predicted to have positive mercury concentrations that vary according to the rate at which that species and 

cut combination’s mercury concentration changes with respect 

to fish length. Therefore, a constant of 1 is added to both the 

concentration and length variables in equation 1 to ensure the 

mercury concentration is near 0 at a length of 0. Additionally, 

if 1 is not added to length measurement, the curves will have 

the unrealistic property of crossing at length of 1 in. so that 

species that typically have higher mercury concentrations relative to other species at lengths greater than 1 in. would be predicted to have lower mercury concentrations relative to those 

same species at lengths of less that 1 in. Because concentration 

is expressed in μg Hg/kg, the concentration values typically 

are 102 to 103 times the value of this constant, and therefore, 

the predicted concentrations are relatively unaffected by inclusion of this constant.

This model is a simplified version of the ‘non-spatially 

variable’ fish-mercury model presented in Wente (1997), but 

still retains the ability to describe variation in fish-mercury 

concentrations due to spatiotemporal and sample characteristic 

effects for all of the species and cut combinations that occur 

in a given data set. It is more complex than the version of this 

model used in Watras and others (1998), which described 

fish-mercury concentration variation for only one species and 

cut of fish. All of the aforementioned models and the model 

presented in this report are specifically designed to partition 

variation in fish-mercury concentrations into variability due to 

sample characteristics and variability among sampling events. 

MODEL ASSUMPTIONS

Three major assumptions were made in designing this 

model. First, the fish-mercury concentration is linearly related 

to the size of a fish for any sample and cut combination and 

any sampling event in log-log space. Log transformation of the 

response variable was deemed necessary because the variability of the observed fish-mercury concentrations appeared to be 

directly related to the fish-mercury concentration. Log transforming the response variable stabilized the variance across 

the range of the response variable, which produces a data 

set that better meets the assumptions of regression analysis. 

Second, the variation in this relation’s slope parameters (αk) 

among sampling events is assumed to be small enough that 

each slope can be treated as a constant for all sampling events. 

Lastly, the variation in this relation’s intercept parameters (βj) 

also is assumed to be small enough that each intercept can 

be treated as a constant for all species and cut combinations 

sampled at each sampling event. These assumptions help to 

minimize the number of parameter estimates necessary to 

describe variation in fish-mercury concentrations for sample 

characteristics, which increases the ratio of the number of 

observations used to calibrate the model to the number of 

parameters estimated by the model, and reduces the uncertainty associated with each parameter estimate (assuming 

these assumptions accurately represent reality). Additionally, 

making these assumptions reduces the number of samples that 

need to be analyzed because the slope for a given species and 

cut combination does not have to be calibrated for each sampling event (this saves on analytical costs and field collection 

time). 

Because most statistical software cannot analyze models 

in the form of equation 1, the model is rewritten in a different 

form using the indicator variables, lengthk and eventj:

 

 (2)

These variables are defined as:

 if k = kl

 if k ≠ kl 

 if j = j

l

 if j = jl

 

where klis the value of k for the lth observation; and j

l

 is the 

value of j for the l

th observation. 

The lengthk term in equation 1 causes only the observations from specific species and cut combinations to be used for 

calibrating the appropriate slopes, αk. Similarly, the eventj term 

causes only the observations from specific sampling events to 

be used for calibrating the appropriate intercepts, βj. Although 

lengthk

lengthijk

0 =

Model assumptions 3

loge Cijk ( ) α + 1 k loge lengthk × ( ) + 1

βj eventj ( ) ε × ijk +

j = 1

n

+ �

k = 1

m

= �

eventj

1

0 =
4 A statistical model and national data set for partitioning fish-tissue mercury concentration variation

the notation describing the model (equations 1 and 2) is quite 

compact, the actual model can require a large number of 

parameter estimates, because the number of species and cut 

combinations (m) and number of sampling events (n) can be 

very large. Because the data set contains left-censored (below 

laboratory detection limit) values, the model is implemented 

using a SAS procedure (LIFEREG) that produces unbiased 

parameter estimates from data sets with censored observations 

(SAS, 1989). 

NATIONAL FISH-MERCURY DATA SET

Maximizing the number of observations available for 

constraining the model’s parameter estimates is implemented 

by calibrating the model to a large compilation of fish-mercury concentration data from State health and environmental 

agencies. This compilation is a subset of the fish-mercury 

concentration data in the NLFWA data set (U.S. Environmental Protection Agency, 2003) as received from the U.S. 

Environmental Protection Agency (USEPA) on September 28, 

2002. This NLFWA data set was comprised of fish-mercury 

analysis results for 62,314 samples collected during 9,266 

sampling events at 7,617 sites. Many samples in the NLFWA 

data set were missing important sample descriptor information (for example, species, length, or cut) or, less commonly, 

appeared to contain problematic data (lengths greatly exceeding the species’ maximum recorded length or indeterminant or 

missing sampling dates). Upon removal of these problematic 

samples, a modified version of the original NLFWA (hereinafter modified NLFWA) data set was obtained containing 31,813 

samples from 28 states (table 1). The samples in this modified 

NLFWA data set predominantly are from freshwater fish species from inland waters of the United States and were sampled 

as 7 cuts of fish (most frequently as whole fish, skin-on fillet, 

and skin-off fillet, and less frequently as carcass, eggs, liver, 

and viscera). A detailed count of the samples in the modified 

NLFWA data set by species and cut of fish is presented in the 

appendix. An updated version of the modified NLFWA data 

set (additional samples added) is available at http://emmma.

usgs.gov.

Approximately 22 percent of sites, sampling events, and 

samples are not geo-referenced with sufficient precision for 

mapping. Samples that are not geo-referenced are used in the 

model calibration and help to constrain the model’s parameter 

estimates. Observations and model predictions for sampling 

events that are not geo-referenced will not appear on, and cannot be downloaded from, the mapping portions of the associated web site. To obtain observations and predictions that are 

not precisely geo-referenced, the entire data set should be 

downloaded from the ‘Download Data sets’ section of the web 

site (http://emmma.usgs.gov). 

The modified NLFWA data set contains 1,398 left-censored observations. Left-censored observations have values 

that are less than the laboratory detection limit.

MODEL PERFORMANCE ASSESSMENT

The model’s performance is assessed using measures 

of the model’s fit to the modified NLFWA data set, magnitude of prediction error, and reliability of the separation of 

spatiotemporal from sample characteristic effects. Assessing 

the model’s fit to the modified NLFWA data set is complicated 

by the presence of left-censored, or less-than-detection-limit, 

data. For observations that have measured concentrations 

that are above the detection limit, the residual error or lackof-fit in the model’s prediction for that observation can be 

precisely measured as the difference between the observed 

and model-predicted values. Left-censored observations, 

however, are known only to be less than the detection limit 

value. Because the observed fish-mercury concentration is not 

precisely known for censored observations, it is impossible to 

precisely measure residual error or lack-of-fit in the model’s 

predictions for the censored observations. Because the 1,398 

censored observations comprise only a small proportion (4.4 

percent) of the 31,813 observations in the modified NLFWA 

data set, model fit was measured as the proportion of variation 

explained by the model for the 30,415 non-censored observations. This measure will be referred to as the pseudo-R2

 (pR2) 

and is calculated as:

pR2 1 SSE

CSS = – ----------

where SSE is the sum of squared errors for the non-censored 

log fish-mercury concentration observations; and CSS is the 

sum of squares for the non-censored log fish-mercury concentration observations corrected for the mean of the noncensored log fish-mercury concentration observations [the log 

fish-mercury concentrations are calculated as loge (μg Hg/kg 

+ 1)].

The magnitude of the model’s prediction error is estimated from the scale parameter as reported by the SAS LIFEREG procedure. A scale parameter is an unbiased estimate of 

the standard deviation of the variability left unexplained by 

the model (error) that can be used with censored data sets. It is 

analogous to the root mean square error (RMSE) reported by 

regression analysis software for non-censored data sets. Prediction error expressed as a percentage (PE) is calculated as:

PE 100 e

scale scale2

2 – -------------- � � � �

– 1 � � � � � � = ×

where scale is the scale parameter estimated by the SAS LIFEREG procedure.

The reliability of the separation of spatiotemporal from 

sample characteristic effects is assessed using a comparison of 

the full and reduced forms of the model. The reasoning behind 

this assessment is that the parameter estimates of regression 

analysis, or any type of optimization procedure, will produce 

reliable parameter estimates only if the parameter estimates 

are ‘well-constrained’ by data. The full model includes all 

variables as in equation 2 and is compared to two reduced 

forms of the full model. The first reduced model is referred 
States Sites 1 Sampling events 1 Species2 Species and cut 

combinations2

Samples1

Alabama 141 (141) 175 (175) 22 22 470 (470)

Arkansas 219( 218) 249 (248) 20 20 783 (782)

California 61 (61) 84 (84) 23 23 97 (97)

Connecticut 53 (46) 53 (46) 4 4 618 (539)

Delaware 68 (67) 75 (74) 19 25 151 (149)

Georgia 120 (92) 120 (92) 32 32 529 (385)

Illinois 1 (1) 1 (1) 1 1 1 (1)

Indiana 119 (116) 125 (122) 43 59 498 (478)

Kentucky 50 (40) 51 (41) 23 37 114 (96)

Louisiana 68 (68) 72 (72) 30 30 679 (679)

Maryland 21 (21) 22 (22) 7 7 63 (63)

Maine 125 (125) 129 (129) 13 24 354 (354)

Michigan 426 (314) 432 (319) 34 52 5,894 (4,057)

Minnesota 1,190 (1,003) 1,467 (1,246) 42 54 12,246 (10,566)

North Carolina 438 (36) 617 (36) 79 144 2,685 (78)

North Dakota 4 (1) 4 (1) 5 5 76 (3)

Nebraska 7 (6) 26 (25) 2 4 30 (29)

New Hampshire 138 (131) 158 (145) 21 30 750 (643)

New Mexico 37 (30) 44 (33) 27 28 532 (398)

New York 24 (24) 24 (24) 9 9 535 (535)

Ohio 166 (161) 166 (161) 26 33 501 (486)

Oklahoma 46 (45) 54( 52) 32 36 252 (241)

Oregon 28 (17) 34 (18) 21 25 456( 270)

Texas 27 (27) 39 (39) 14 14 45 (45)

Virginia 16 (16) 16 (16) 10 10 28 (28)

Washington 12 (12) 12 (12) 2 2 41 (41)

Wisconsin 292 (288) 334 (329) 37 54 3,349 (3,309)

West Virginia 14 (8) 14 (8) 9 9 36 (17)

Total 3,911 (3,115) 4,597 (3,570) 3

163 3

310 31,813 (24,839)

1

 Values in parentheses indicate the number of precisely geo-referenced sites, sampling events (sampling of a specific site and time), or samples.

2

 Number of unique species or species and cut combinations in a state’s data set.

3

Values indicate a national total for unique species or species and cut combinations (does not represent a cumulative sum of state totals).

Table 1. Summary of fish-mercury concentration data contributions to the National Listing of Fish and Wildlife Advisory (NLFWA) data 

set (September 28, 2002 version of the data set) as modified for calibration of the statistical model used in this report.

to as the “events only” model and omits the variables that 

describe the sample characteristic effect by omitting the term

αk loge lengthk ( × ( ) + 1 )

k = 1

m

�

from equation 2. The second is referred to as the “sample characteristics only” model and omits the variables that describe 

the spatiotemporal effect by omitting the

term from equation 2. If the full model is only marginally better at describing variability in the modified NLFWA data set 

than the events only model, then the event term is capable of 

describing most of the variability that the full model uses both 

event and sample characteristic terms to describe. Similarly, 

if the full model fits the NLFWA data only marginally better 

Model performance assessment 5

βj eventj ( ) ×

j = 1

n

�
6 A statistical model and national data set for partitioning fish-tissue mercury concentration variation

than the sample characteristics only model, then the sample 

characteristic term is capable of describing most of the variability that the full model uses both event and sample characteristic terms to describe. In both cases, the implication is 

that the full model as calibrated to the modified NLFWA data 

set is incapable of reliably separating spatiotemporal effect as 

described by the event term from sample characteristic effect 

as described by the sample characteristic term. Conversely, if 

the full model is considerably better at describing variability in 

the modified NLFWA data set than both reduced forms of the 

model, the implication is that the event and sample characteristic terms each make unique contributions to describing fishmercury concentration variation that the other term cannot. 

This would indicate the modified NLFWA data set does constrain the event and sample characteristic parameter estimates 

and, therefore, provides evidence that the model is separating 

spatiotemporal and sample characteristic effects. 

The fit of the full and reduced forms of the model to the 

modified NLFWA data set will be compared by calculating 

values of pR2

, scale parameter, prediction error, and the Akaike 

Information Criterion (AIC) for the full and both reduced 

forms of the model. The AIC is an adjustment of the log likelihood calculated as:

AIC = –2log L + 2p

where log L is the log-likelihood and p is the number of 

parameters estimated for a specific model. However, a better 

fit is always expected for a linear model that includes additional variables such as the full model in comparison to the 

reduced models that include fewer variables. Therefore, a 

statistical test, called a likelihood ratio comparison, is used to 

determine whether the fit of the full model is significantly better than the fit of the reduced models after accounting for the 

difference in the number of variables included in each model. 

In the likelihood ratio comparison tests, a value calculated as 2 

times the difference in AIC of the full and one of the reduced 

models, is compared to a chi-square distribution. The number 

of degrees of freedom for the test is the difference in number 

of parameters estimated by the full model and the reduced 

model being compared.

MODEL EVALUATION AND 

APPLICATIONS

Calibration of the model presented in this report requires 

one αk parameter estimate for each of the m species and cut 

combinations and one ßj parameter estimate for each of the 

n sampling events in the modified NLFWA data set. The 

modified NLFWA data set described in this report contains 

observations from 310 species and cut combinations and 4,597 

sampling events (table 1). The statistical model described in 

this report, therefore, uses 310 species and cut parameter estimates (αk

) and 4,597 sampling event parameter estimates (ßj) 

for a total of 4,907 parameter estimates. 

MODEL FIT

As with all models, the familiar statement, “all models 

are wrong: some models are useful” (Box, 1979) applies. 

This model is based on a simplified conceptualization of how 

fish-mercury concentrations are distributed. The distribution 

of fish-mercury concentrations will vary with the structure of 

the aquatic food web during a particular event (Cabana and 

Rasmussen, 1994). This implies that the model assumption 

of common slopes (αk) for all sampling events and common 

intercepts (βj) within each sampling event is ‘wrong’ to some 

degree. This model, however, does fit the non-censored portions of the modified NLFWA data set well (pR2

 = 0.82, fig. 

1). The model, therefore, can be thought of as a good approximation of reality and the simplifying assumption of similar 

food web structure at all sampling events is probably not 

unwarranted because actual differences in food web structure 

between sampling events must rarely be large. 

Figure 1. Relation of noncensored observations to predicted 

fish-mercury concentrations in log units. 

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The fit of the full model and both reduced models to the 

modified NLFWA data set is compared in table 2. The larger 

pR2 value and smaller values for scale parameter, prediction 

error, and AIC for the full model indicate that the full model 

fits the modified NLFWA data set much better than either of 

the reduced models. In table 3, the likelihood ratio comparison 

tests indicate the better model fit of the full model as compared to that of the reduced models is statistically significant 

after accounting for the difference in number of variables in 

each model. These results provide evidence that, in general, 

the modified NLFWA data set constrains the models’ parameter estimates such that neither spatiotemporal nor sample 

characteristic effect variables alone are able to fit the variability in the data that the other effect’s variables are able to fit. 

Therefore in general, the full model as calibrated to the modi-
fied NLFWA data set separates spatiotemporal and sample 

characteristic effects. However, not all parameter estimates are 

equally constrained. It is likely that parameter estimates for 

species and cut combinations that were rarely sampled during 

events where other more frequently sampled species and cut 

combinations were collected do not separate spatiotemporal 

and sample characteristic effects well. Similarly, event parameter estimates that are based solely on data from rare species 

and cut combinations may also misattribute spatiotemporal 

and sample characteristic effects. A more rigorous assessment 

of the accuracy of this model’s estimation of fish-mercury concentrations, or predictions, is beyond the scope of this report.

FISH-MERCURY CONCENTRATION PREDICTION

The statistical model presented in this report represents 

an attempt to provide a realistic description of the distribution 

of fish-mercury concentrations across space, time, and sample 

characteristics using as few parameter estimates as possible 

to describe variation in fish-mercury concentrations across 

sample characteristics. To predict fish-mercury concentration 

in log units for a specific species and cut combination and 

length of fish, equation 1 is simplified as:

 loge(Cpred + 1) = αk × loge(lengthpred + 1) + βj (3)

where Cpred is a fish-mercury concentration prediction in units 

of μg Hg/kg; 

αk is a parameter estimate from equation 2 for a specific 

species and cut combination for any of the 310 species and cut 

combinations in the modified NLFWA data set; 

lengthpred is any desired fish length (in inches); and

βj is a parameter estimate from equation 2 for any specific 

sampling event of the 4,957 sampling events in the modified 

NLFWA data set. In log-log space, equation 3 is the equation 

of a straight line with slope of αk and an intercept of βj. It is 

used to graph the lines in figures 2a and 2c.

To predict fish-mercury concentration in arithmetic units 

for a specific species and cut combination and length of fish, 

equation 3 can be transformed into:

Cpred e αk loge × lengthpred ( + 1) β + j ( ) = – 1 

 (4)

Equation 4 is used to graph the curves in figures 2b and 

2d. The simplicity of this model’s description of fish-mercury 

variation across sample characteristics is demonstrated in 

figure 2a, which depicts fish-mercury concentration predictions for a single hypothetical sampling event. Theoretically, 

one line could be predicted for each of the 310 combinations 

of species and cut occurring in the modified NLFWA data set. 

For clarity of presentation, only concentration predictions for 

skin-off fillet samples of 11 species are depicted throughout 

figure 2. Each line is depicted for the range of fish lengths 

sampled from that species in the modified NLFWA data set. 

The predictions in figure 2a also are shown in concentration 

and length units in figure 2b. Comparison of figures 2a and 2b 

shows how small variations of slope in log-log space (figure 

2a) can describe variation in the rate of mercury accumulation 

(per unit of fish length) across multiple species and lengths of 

fish (figure 2b). 

Different sampling events have different intercepts as 

depicted in the log-log graph of figure 2c. This figure presents 

predictions for the same species and cut combinations of fish 

at two sampling events with one-half (blue lines) and twice 

(red lines) the fish-mercury concentrations depicted in figure 

2a. Notice that each line in figure 2a has two corresponding 

parallel lines (one blue and one red) in figure 2c. Similarly, 

lines for the same species and cut at any other sampling event 

also would be parallel. Similar to the relation between figures 

2a and 2b, figure 2d shows the predictions of figure 2c transformed into concentration and length units. Figure 2d shows 

how changes in the intercepts in figure 2c (the corresponding 

red and blue lines in figure 2c differ by a constant in log-log 

space) translate into multiplicative changes in fish-mercury 

concentration between sampling events (the corresponding red 

and blue curves in figure 2d differ by a multiplication factor in 

arithmetic space). 

Models pR2 Scale parameter Prediction error (%) AIC

Full 0.82 0.41 38.2 42,742

Events Only .60 .61 52.9 67,342

Sample Characteristics Only .41 .76 60.3 72,922

Table 2. Comparison of model fit for the full and reduced fish-mercury models.

Model comparison Change in AIC Degrees of freedom P-value

Full and events only 24,600 310 < 0.0001

Full and sample characteristics only 30,180 4,596 < .0001

Table 3. Likelihood ratio comparisons for the full and reduced fish-mercury models.

Fish mercury concentration prediction 7
8 A statistical model and national data set for partitioning fish-tissue mercury concentration variation

PREDICTION ACCURACY

Measures of model fit like the pR2 (or R2) do not directly 

indicate how well this model will perform its intended 

applications. This is because the applications for which the 

model is intended commonly require predictions for sample 

characteristics that were not sampled at the actual sampling 

events, while measures of model fit only indicate how well the 

model’s predictions match the observations that were actually 

sampled. For example, measuring spatial and temporal variation requires converting between the samples collected during 

each sampling event and a standardized sample that may 

have been collected during few of the actual sampling events. 

Similarly, development of fish-consumption advisories would 

be greatly facilitated by the ability to estimate concentrations 

for fish that likely occur at a site, but were not sampled during 

the sampling event for that site. Because estimating fish-mercury concentrations for samples that were not included in the 

calibration data set is less accurate than estimates for samples 

included in the calibration data set, the ability of the model to 

predict the fish-mercury concentrations needed for the model’s 

intended applications will be less accurate than the pR2 measure indicates. 

A reduction in prediction accuracy will be especially 

acute for predictions based on species and cut combination parameter estimates (αk

), or sampling event parameter 

estimates (βj), that are poorly constrained. Therefore, users of 

predictions from this model should determine how well each 

parameter estimate is constrained. The appendix provides sample counts for individual species and cut combinations1

 , which 

indicates species and cut parameter estimates (αk) that are well 

constrained (high numbers of samples) and poorly constrained 

(low numbers of samples). A similar table for sampling event 

parameter estimates (βj) was judged to be too long for inclusion in this report and would need constant revision as new 

sampling events are added to the data set. Therefore, users are 

encouraged to download the current data set from the web site, 

sort the data set by sampling event code, and judge the quality of the model prediction based on the number of samples 

collected for an event as well as the number of samples in the 

data set for each of the species and cut combinations collected 

during that sampling event.

MODEL APPLICATIONS

Using the model’s predictions to assess spatial and 

temporal variation and develop site-specific fish-consumption advisories is accomplished by setting one or two of the 

three variables in equation 4 to appropriate constants and 

varying the remaining variable(s). In this way, spatial and 

temporal variability can be assessed by setting αk to a specific 

or ‘standardized’ species and cut combination, length of fish 

(length pred) to a constant value, and varying the sampling event 

(βj). For example, temporal variability is depicted by displaying standardized fish-mercury concentrations for sampling 

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Figure 2. Predicted fish-mercury concentrations as a function of length for skin-off fillet cuts of 11 frequently sampled species in the 

upper Midwestern United States depicted in (a) log space, and (b) arithmetic space for a hypothetical sampling event; (c) and (d) are 

similar but compare two hypothetical sampling events with high (red lines) and low (blue lines) fish-mercury concentrations.

1

 This data set is correct as of September 28, 2002. The NLFWA data set 

often is updated. The most recent version of the data set is at http://emmma.

usgs.gov
events from the same site across time. Spatial variability is 

depicted by displaying standardized fish-mercury concentrations for sampling events from a small period of time (the 

same year, for example) for the sites that were sampled within 

that time period. Site-specific fish-consumption advisories can 

be developed by predicting fish-mercury concentrations for 

multiple species, lengths, and cuts of fish (if necessary) for the 

most recent sampling event at the site of interest. To accomplish this, βj

 is held constant while αk and lengthpred are varied 

for all the species and cut combinations and lengths of fish of 

interest at that site (similar to figure 2b). Consumption advisories can then be developed for the species, lengths, and cuts of 

fish that have predicted concentrations that exceed the concentrations of concern for the specific group of fish consumers. 

The shape of the curves as depicted in figure 2b can be 

used to estimate important bio-physical parameters describing the net accumulation of mercury as a fish grows in length. 

Also, the relative differences between these curves describe 

which sizes and species of fish typically are safer to eat with 

respect to fish-mercury ingestion concerns. Even if fish-mercury concentrations have never been measured at a site, or 

for a particular species at a site, a fish consumer can reduce 

potential mercury exposure by choosing to consume sizes and 

species of fish that are expected to have lower fish-mercury 

concentrations according to the relations described by the 

model.

FUTURE STUDIES

The model and data set presented in this report could 

form the basis for many important research products. A brief 

listing might include:

• Producing a continuous coverage of local fish-mercury 

temporal trend estimates. The model presented in this report 

is specifically designed to require as few parameter estimates 

as possible to describe the variation of fish-mercury concentrations with sample characteristics. The model’s description 

of spatial and temporal variation, however, requires a large 

number of parameter estimates. Future versions of this model 

could be designed to reduce the number of parameter estimates used to describe temporal and spatial variation using 

geostatistical methods similar to the ‘spatially variable’ model 

of Wente (1997). Such methods could produce local estimates 

of temporal variation over large regions based on the average 

temporal variation observed at nearby fish-mercury sampling 

sites.

• Prediction uncertainty estimates. Determining the 

accuracy of individual model predictions is difficult because 

the number of fish in a composite fish sample often was not 

compiled into the NLFWA data set. Compositing a number 

of nearly identical fish together into a sample will produce a 

more accurate estimate of the mean fish-mercury concentration than will a sample comprised of a single fish. Obtaining 

this information in future updates to this data set would allow 

better estimates of prediction accuracy to be given for individual model predictions and aid in estimating transformation 

bias correction factors.

• Identifying factors that cause spatiotemporal variation 

in fish-mercury concentrations. Spatiotemporal variation only 

is described by the model in this report rather than attributed 

to any specific cause (for example, changes in methylation 

efficiency or mercury loadings). The spatiotemporal variation described by this model, however, can be used to formulate hypotheses regarding the factors causing this variation. 

Additionally, after collecting data on the hypothesized causal 

factors, a variation of the model and data set could be used to 

test these hypotheses.

• Estimating human health effects from fish consumption. An individual’s exposure to fish-mercury is largely 

determined by that individual’s fish-consumption patterns and 

the concentration of mercury in the fish that the individual 

consumes. Because fish-consumption patterns are highly variable, better estimates of a local population’s exposure risk may 

be obtained by simulating the local variation in consumption 

habits (based on fish-consumption survey data) and the local 

fish-mercury concentrations (as estimated from the model and 

modified NLFWA data set in this report). Such simulations 

could be run over large regions to identify which locales have 

the largest proportions of their populations at risk of adverse 

affects from methylmercury exposure. 

• Optimization of regulatory strategies for reducing 

fish-mercury concentrations. Reducing fish-mercury concentrations over large regions will likely be expensive. It may be 

beneficial to test different regulatory strategies or combinations of regulatory strategies through models to optimize a 

final remediation strategy before implementation. 

SUMMARY

Many Federal, Tribal, State, and local agencies monitor 

mercury in fish-tissue samples to identify sites with elevated 

fish-tissue mercury (fish-mercury) concentrations, track 

changes in fish-mercury concentrations over time, and produce 

fish-consumption advisories. The fish-mercury concentration 

data sets generated by these monitoring programs often contain data from samples with differing characteristics (species, 

cuts, and sizes of fish) as well as from different locations and 

dates of sampling. Interpreting such data sets can be difficult 

because spatiotemporal trends in fish-mercury concentrations 

can be difficult to reliably separate from the effect of sample 

characteristics on fish-mercury concentrations. Without such 

a separation, variation in fish-mercury concentrations due to 

differences in the characteristics of samples collected over 

time or across space can be misattributed to temporal or spatial 

trends; and/or actual trends in fish-mercury concentration can 

be misattributed to differences in sample characteristics.

This report describes a statistical model capable of 

partitioning variation in fish-mercury concentrations into 

Summary 9
10 A statistical model and national data set for partitioning fish-tissue mercury concentration variation

spatiotemporal and sample characteristic effects and a large 

(31,813 samples) national compilation of fish-mercury data 

that can be used to calibrate and constrain the parameter estimates of this model. Calibration of this model was performed 

using a method that produces unbiased parameter estimates 

from fish-mercury concentration data sets containing left-censored (less than laboratory detection limit) observations. The 

model’s performance was evaluated using measures of model 

fit, prediction error, Akaike Information Criterion, and likelihood ratio comparisons. These measures provided evidence 

that, in general, the model as calibrated to a national fishmercury data set is capable of separating spatiotemporal and 

sample characteristic effects.

The observed fish-mercury concentration data and model 

predictions can be accessed, displayed geospatially, and downloaded via the World Wide Web (http://emmma.usgs.gov). 

This web site also provides tools for exploring spatial and temporal trends in fish-mercury concentration data and developing 

site-specific fish-consumption advisories for mercury. 

REFERENCES CITED

Boudou, A. and Ribeyre, F., 1983, Contamination of aquatic 

biocenoses by mercury compounds—An experimental 

ecotoxicological approach, in Nriagu, J.O., ed., Aquatic 

Toxicology: John Wiley and Sons, New York, p. 73-116.

Box, G.E.P., 1979, Robustness in the strategy of scientific 

model building, in Launer R.L., and Wilkinson, G.N. , eds., 

Robustness in statistics: Academic Press, New York, 202 p. 

Cabana, G., and Rasmussen, J.B., 1994, Modeling food chain 

structure and contaminant bioaccumulation using stable 

nitrogen isotopes: Nature, v. 372, p. 255-257.

Cope, W.G., Wiener, J.G., and Rada, R.G., 1990, Mercury 

accumulation in yellow perch in Wisconsin seepage lakes—

Relation to lake characteristics: Environmental Toxicology 

and Chemistry, no. 9, p. 931-940.

Giblin F.J., and Massaro, E.J., 1973, Pharmacodynamics of 

methyl mercury in the rainbow trout (Salmo gairdneri)—

Tissue uptake, distribution and excretion: Toxicololgy and 

Applied Pharmacology, no. 24, p 81-91.

Harrison, S.E., Klaverkamp, J.F., and Hesslein, R.H., 1990, 

Fates of metal radiotracers added to a whole lake—Accumulation in fathead minnow (Pimephales promelas) and 

lake trout (Salvelinus namaycush): Water, Air, and Soil Pollution, no. 52, p. 277-293.

Huckabee, J.W., Elwood, J.W., and Hildebrand, S.G., 1979, 

Accumulation of mercury in freshwater biota, in Nriagu, 

J.O., ed., Biogeochemistry of Mercury in the Environment: 

Elsevier/North-Holland Biomedical Press, New York, p. 

277-302.

Kim, J.P., and Burggraaf, S., 1999, Mercury bioaccumulation 

in rainbow trout (Oncorhynchus mykiss) and the trout food 

web in lakes Okareka, Okaro, Tarawera, Rotomahana and 

Rotorua, New Zealand: Water, Air, and Soil Pollution, no. 

115, p. 535-546.

MacCrimmon, H.R., Wren, C.D., and Gots, B.L., 1983, Mercury uptake by lake trout, Salvelinus namaycush, relative to 

age growth, and diet in Tadenac Lake with comparative data 

from other Precambrian Shield Lakes: Canadian Journal of 

Fisheries and Aquatic Sciences, no. 40, p. 114-120.

Porcella, D.B., 1995, Aquatic biogeochemistry and mercury 

cycling model (MCM), in National Forum on Mercury in 

Fish Proceedings, U.S. Environmental Protection Agency, 

Office of Water, EPA 823-R-95-002, 211p.

SAS (SAS Institute Inc.), 1989, SAS/STAT User’s Guide v. 2, 

version 6, 4th ed., SAS Institute Inc., Cary, NC. 795 p.

Suns, K., Hitchin, G., Loescher, B., Pastorek, E., and Pearce, 

R., 1987, Metal accumulations in fishes from MuskokaHaliburton lakes in Ontario (1978-1984): Ontario Ministry 

of the Environment, Rexdale, Ontario, and p. 38.

U.S. Environmental Protection Agency, 1993, Guidance for 

assessing chemical contaminant data for use in fish advisories, vol. I: Fish sampling and analysis, 2nd ed.: U.S. 

Environmental Protection Agency, Office of Water, EPA 

823-R-95-007, Variously paged.

U.S. Environmental Protection Agency, 1995, Guidance for 

assessing chemical contaminant data for use in fish advisories, vol. II: Risk assessment and fish-consumption limits: 

U.S Environmental Protection Agency, Office of Water, 

EPA 823-B-94-004, Variously paged.

U.S. Environmental Protection Agency, 1997a, Mercury study 

report to congress, vol. III: An assessment of exposure from 

anthropogenic mercury emissions in the United States: U.S. 

Environmental Protection Agency, Office of Air Quality 

Planning & Standards and Office of Research and Development, EPA-452/R-96-001, Variously paged.

U.S. Environmental Protection Agency, 1997b, Mercury 

study report to congress, vol. VII: Characterization of 

human health and wildlife risks from mercury exposure in 

the United States: U.S. Environmental Protection Agency, 

Office of Air Quality Planning & Standards and Office of 

Research and Development, EPA-452/R-97-009, Variously 

paged.

U.S. Environmental Protection Agency, 2003, Update—

National listing of fish and wildlife advisories: U.S. Environmental Protection Agency, Office of Water, EPA-823-F003. 6 p.
Watras, C.J., Back, R.C., Halvorsen, S., Hudson, R.J.M., 

Morrison, K.A., and Wente, S.P., 1998, Bioaccumulation 

of mercury in pelagic freshwater food webs: Science of the 

Total Environment, v. 219, no. 2-3, p. 183-208.

Wente, S.P., 1997, A spatially and temporally variable model 

of mercury concentrations in aquatic communities with 

applications to public health protection and water quality 

assessment, Purdue University: West Lafayette, Ind., Ph.D. 

dissertation, 132 p.

Wiener, J.G., Krabbenhoft, D.P., Heinz, G.H., and Scheuham-

mer, A.M., 2002, Ecotoxicology of Mercury, in Hoffman, 

D.J., Rattner, B.A., Burton, G.A., and Cairns, J., Handbook 

of Toxicology, 2 ed.: CRC Press, 1344 p.

Wiener, J.G., and Spry, D.J., 1996, Toxicological significance 

of mercury in freshwater fish, in Beyer, W.N., Heinz, G.H., 

and Redmon-Norwood, A.W., eds., Environmental Con

-

taminants in Wildlife—Interpreting Tissue Concentrations: 

Lewis Publ., Boca Raton, Fla., p. 297-339. 

References 11
12 A statistical model and national data set for partitioning fish-tissue mercury concentration variation

Sample counts by cut of fish 

Species and common names Length 

range 

(in.)

Whole 

fish

Skin-on 

fillet

Skin-off 

fillet

Other 

cuts

Total

Achiridae

Trinectes maculatus (Bloch & Schneider, 1801), Hogchoker 5.5 - 8.9 3 1 4

Acipenseridae

Acipenser fulvescens Rafinesque, 1817, Lake sturgeon 12.3 - 68.1 5 2 7

A. oxyrinchus oxyrinchus Mitchill, 1815, Atlantic sturgeon 8.2 - 20.0 3 3

Scaphirhynchus platorynchus (Rafinesque, 1820), Shovelnose sturgeon 30.9 1 1

Amiidae

Amia calva Linnaeus 1766, Bowfin 8.9 - 28.0 44 5 46 95

Anguillidae

Anguilla rostrata (Lesueur, 1817), American eel 1.5 - 30.5 28 4 3 35

Ariidae

Bagre marinus (Mitchill, 1815), Gafftopsail Sea Catfish 18.8 1 1

Batrachoididae

Opsanus tau (Linnaeus, 1766), Oyster toadfish 6.3 - 11.6 1 1 2

Catostomidae

Carpiodes carpio (Rafinesque, 1820), River carpsucker 10.1 - 21.6 6 22 28

C. cyprinus (Lesueur, 1817), Quillback 7.0 - 17.8 1 17 18

C. velifer (Rafinesque, 1820), Highfin carpsucker 11.5 1 1

Catostomus catostomus catostomus (Forster, 1773), Longnose sucker 13.2 - 22.3 14 12 26

C. commersonnii (Lacepède, 1803), White sucker 1.9 - 23.0 174 1,131 74 1,379

C. macrocheilus Girard, 1856, Largescale sucker 12.1 - 23.3 43 43

C. santaanae (Snyder, 1908), Santa Ana sucker 1.3 1 1

Cycleptus elongatus (Lesueur, 1817), Blue sucker 23.6 1 1

Cyprinella lutrensis (Baird & Girard, 1853), Red shiner 2.1 - 2.5 19 19

Erimyzon oblongus (Mitchill, 1814), Creek chubsucker 5.3 - 14.0 31 1 32

E. sucetta (Lacepède, 1803), Lake chubsucker 7.2 1 1

Gila bicolor (Girard, 1856), Tui chub 1.8 - 11.0 6 4 10

G. orcuttii (Eigenmann & Eigenmann, 1890), Arroyo chub 2.5 - 3.1 6 6

Hypentelium etowanum (Jordan, 1877), Alabama hog sucker 4.9 - 6.6 4 4

H. nigricans (Lesueur, 1817), Northern hog sucker 4.9 - 13.8 21 14 35

Ictiobus bubalus (Rafinesque, 1818), Smallmouth buffalo 13.4 - 32.7 7 33 25 65

I. cyprinellus (Valenciennes, 1844), Bigmouth buffalo 11.4 - 28.7 1 37 25 63

I. niger (Rafinesque, 1819), Black buffalo 20.7 1 1

Minytrema melanops (Rafinesque, 1820), Spotted sucker 11.2 - 23.5 13 19 23 55

Moxostoma anisurum (Rafinesque, 1820), Silver redhorse 9.7 - 23.5 14 19 33

M. carinatum (Cope, 1870), River redhorse 11.3 - 24.6 1 4 6 11

M. duquesnii (Lesueur, 1817), Black redhorse 11.4 - 17.6 10 20 30

M. erythrurum (Rafinesque, 1818), Golden redhorse 10.1 - 22.3 5 29 1 35

M. macrolepidotum (Lesueur, 1817), Shorthead redhorse 8.5 - 24.9 7 42 49

M. poecilurum (Jordan, 1877), Blacktail redhorse 10.1 - 15.4 5 5

M. valenciennesi Jordan, 1885, Greater redhorse 13.2 - 21.5 15 3 18

Scartomyzon rupiscartes (Jordan & Jenkins, 1889), Striped jumprock 6.8 - 7.2 1 1 2

Centrarchidae

Ambloplites rupestris (Rafinesque, 1817), Rock bass 2.4 - 11.9 18 319 47 384

Centrarchus macropterus (Lacepède, 1801), Flier 3.6 - 7.2 7 3 10

Enneacanthus gloriosus (Holbrook, 1855), Bluespotted sunfish 5.9 - 7.8 4 4

Lepomis auritus (Linnaeus, 1758), Redbreast sunfish 3.0 - 9.0 5 10 15

L. cyanellus Rafinesque, 1819, Green sunfish 2.1 - 9.4 36 30 4 70

L. gibbosus (Linnaeus, 1758), Pumpkinseed 3.3 - 9.5 40 81 121

L. gulosus (Cuvier, 1829), Warmouth 4.2 - 26.0 14 34 4 52

L. macrochirus Rafinesque, 1819, Bluegill 1.9 - 15.0 114 984 98 1,196

L. megalotis (Rafinesque, 1820), Longear sunfish 2.5 - 7.3 25 9 34

L. microlophus (Günther, 1859), Redear sunfish 4.3 - 11.1 14 112 28 154

Appendix 1. Sample characteristics (species, length, and cut of fish) of fish-mercury analysis results included in the modified National 

Listing of Fish and Wildlife Advisory (NLFWA) data set (September 28, 2002, version of the data set). 
Sample counts by cut of fish 

Species and common names Length 

range 

(in.)

Whole 

fish

Skin-on 

fillet

Skin-off 

fillet

Other 

cuts

Total

L. punctatus (Valenciennes, 1831), Spotted sunfish 10.8 1 1

Micropterus cataractae Williams & Burgess, 1999, Shoal bass 9.4 - 13.4 3 3

M. coosae Hubbs & Bailey, 1940, Redeye bass 9.4 - 10.6 3 3

M. dolomieu Lacepède, 1802, Smallmouth bass 3.0 - 19.7 36 757 145 938

M. punctulatus (Rafinesque, 1819), Spotted bass 4.3 - 19.1 4 52 99 155

M. salmoides (Lacepède, 1802), Largemouth bass 0.9 - 32.4 214 1,408 1,754 5 3,381

Pomoxis annularis Rafinesque, 1818, White crappie 3.1 - 27.0 68 169 97 2 336

P. nigromaculatus (Lesueur, 1829), Black crappie 3.6 - 14.1 25 733 86 844

Perca flavescens (Mitchill, 1814), Yellow perch 1.9 - 17.7 183 1,230 451 1,864

Sander canadensis (Griffith & Smith, 1834), Sauger 1.4 - 24.8 108 108

S. vitreus (Mitchill, 1818), Walleye 6.8 - 31.4 145 5,733 204 20 6,102

S. vitreus × S. canadensis, Saugeye 10.9 - 21.3 9 2 11

Clupeidae

Alosa chrysochloris (Rafinesque, 1820), Skipjack shad 14.3 1 1

A. mediocris (Mitchill, 1814), Hickory shad 11.0 - 15.9 3 3

A. pseudoharengus (Wilson, 1811), Alewife 3.6 - 11.2 18 1 3 22

A. sapidissima (Wilson, 1811), American shad 8.6 - 16.7 5 5

Brevoortia tyrannus (Latrobe, 1802), Atlantic menhaden 5.1 - 36.3 7 5 12

Dorosoma cepedianum (Lesueur 1818), American gizzard shad 2.0 - 16.1 97 33 34 164

D. petenense (Günther, 1867), Threadfin shad 2.9 1 1

Cottidae

Cottus asper Richardson, 1836, Prickly sculpin 3.0 - 3.7 3 3

C. cognatus Richardson, 1836, Slimy sculpin 2.4 - 3.0 3 3

C. gulosus (Girard, 1854), Riffle sculpin 3.4 - 3.5 2 2

Leptocottus armatus Girard, 1854, Pacific staghorn sculpin 2.8 1 1

Triglopsis thompsonii Girard, 1851, Deepwater sculpin 2.5 1 1

Cyprinidae

Acrocheilus alutaceus Agassiz & Pickering, 1855, Chiselmouth 3.4 - 3.6 3 3

Campostoma anomalum (Rafinesque, 1820), Central stoneroller 5.4 - 6.1 3 3

C. pauciradii Burr & Cashner, 1983, Bluefin stoneroller 5.1 1 1

Carassius auratus auratus (Linnaeus, 1758), Goldfish 6.0 - 10.9 6 6 1 13

Clinostomus funduloides Girard, 1856, Rosyside dace 3.0 - 3.3 2 1 3

Ctenopharyngodon idella (Valenciennes, 1844), Grass carp 20.9 1 1

Cyprinus carpio carpio Linnaeus, 1758, Common carp 2.6 - 37.8 340 1,003 927 4 2,274

Hesperoleucus symmetricus (Baird & Girard, 1854), California roach 3.6 1 1

Hybognathus placitus Girard, 1856, Plains minnow 1.0 - 2.5 2 2

Lavinia exilicauda Baird & Girard, 1854, Hitch 3.0 - 3.6 2 2

Nocomis leptocephalus (Girard, 1856), Bluehead chub 2.4 - 8.9 42 4 46

N. micropogon (Cope, 1865), River chub 5.6 - 5.8 2 2

Notemigonus crysoleucas (Mitchill, 1814), Golden shiner 3.3 - 9.7 22 2 24

Phoxinus erythrogaster (Rafinesque, 1820), Southern redbelly dace 5.6 1 1

Pimephales promelas Rafinesque, 1820, Fathead minnow 1.6 - 2.7 14 14

Ptychocheilus oregonensis (Richardson, 1836), Northern pikeminnow 3.8 - 15.6 1 1 2

Rhinichthys cataractae (Valenciennes, 1842), Longnose dace 6.9 - 9.3 5 5

R. osculus (Girard, 1856), Speckled dace 2.8 - 3.7 4 4

Semotilus atromaculatus (Mitchill, 1818), Creek chub 3.6 - 9.0 30 30

S. corporalis (Mitchill, 1817), Fallfish 5.9 - 6.3 2 2

S. lumbee Snelson & Suttkus, 1978, Sandhills chub 6.5 - 6.5 2 2

Embiotocidae

Rhacochilus toxotes Agassiz, 1854, Rubberlip seaperch 8.2 1 1

Esocidae

Esox americanus americanus Gmelin, 1789, Redfin pickerel 6.2 - 9.7 7 2 9

E. lucius Linnaeus 1758, Northern pike 1.0 - 44.1 249 4,582 590 5,421

E. masquinongy Mitchill, 1824, Muskellunge 18.2 - 47.9 49 49

E. masquinongy × E. lucius, Tiger Muskellunge 27.4 - 30.9 4 4

E. niger Lesueur, 1818, Chain pickerel 3.8 - 26.1 29 44 66 139

Appendix 13
14 A statistical model and national data set for partitioning fish-tissue mercury concentration variation

Sample counts by cut of fish 

Species and common names Length 

range 

(in.)

Whole 

fish

Skin-on 

fillet

Skin-off 

fillet

Other 

cuts

Total

Fundulidae

Fundulus parvipinnis Girard, 1854, California killifish 2.0 - 2.5 4 4

F. zebrinus Jordan & Gilbert, 1883, Plains killifish 1.5 - 1.5 2 2

Gasterosteidae

Gasterosteus aculeatus aculeatus Linnaeus, 1758, 

Three-spined stickleback

1.8 - 2.2 12 12

Gobiidae

Acanthogobius flavimanus (Temminck & Schlegel, 1845), 

Yellowfin goby

14.7 1 1

Gillichthys mirabilis Cooper, 1864, Longjaw mudsucker 2.5 - 3.2 6 6

Hiodontidae

Hiodon alosoides (Rafinesque, 1819), Goldeye 13.6 1 1

Ictaluridae

Ameiurus brunneus (Jordan, 1877), Snail bullhead 5.3 - 11.9 5 2 7

A. catus (Linnaeus, 1758), White Catfish 7.7 - 23.5 3 13 16

A. melas (Rafinesque, 1820), Black bullhead 5.0 - 15.0 9 34 94 137

A. natalis (Lesueur, 1819), Yellow bullhead 4.5 - 13.8 37 35 77 149

A. nebulosus (Lesueur, 1819), Brown bullhead 6.7 - 15.6 32 59 69 160

A. platycephalus (Girard, 1859), Flat bullhead 4.7 - 12.8 14 10 24

Ictalurus furcatus (Valenciennes, 1840), Blue catfish 10.8 - 40.0 2 86 88

I. punctatus (Rafinesque, 1818), Channel catfish 3.6 - 39.4 171 25 964 2 1,162

Noturus insignis (Richardson, 1836), Margined madtom 3.9 - 6.2 3 3

Pylodictis olivaris (Rafinesque, 1818), Flathead catfish 8.9 - 39.3 6 149 155

Lepisosteidae

Lepisosteus oculatus Winchell 1864, Spotted gar 19.4 - 28.2 1 8 9

L. osseus (Linnaeus, 1758), Longnose gar 19.3 - 43.5 61 10 2 2 75

L. platostomus Rafinesque, 1820, Shortnose gar 22.2 - 27.3 1 4 5

Lotidae

Lota lota (Linnaeus, 1758), Burbot 12.1 - 28.9 22 19 41

Moronidae

Morone americana (Gmelin, 1789), White perch 4.3 - 14.8 45 61 38 1 145

M. chrysops (Rafinesque, 1820), White bass 4.7 - 18.2 8 125 62 195

M. saxatilus (Walbaum, 1792), Striped Sea-bass 10.4 - 35.9 24 40 2 17 83

Mugilidae

Mugil cephalus Linnaeus, 1758, Flathead mullet 9.9 - 16.0 14 17 31

Osmeridae

Osmerus mordax mordax (Mitchill, 1814), Atlantic rainbow smelt 3.0 - 21.3 100 125 225

Spirinchus thaleichthys (Ayres, 1860), Longfin smelt 3.2 1 1

Paralichthyidae

Paralichthys dentatus (Linnaeus, 1766), Summer flounder 13.0 - 14.2 1 3 4

P. lethostigma Jordan & Gilbert, 1884, Southern flounder 7.1 - 16.2 2 18 2 22

Percidae

Etheostoma whipplii (Girard, 1859), Redfin darter 6.4 - 7.4 6 6

Pleuronectidae

Hippoglossoides platessoides (Fabricius, 1780), American plaice 7.0 - 12.0 4 4

Poeciliidae

Gambusia affinis (Baird & Girard, 1853), Mosquitofish 1.7 - 2.1 4 4

Poecilia latipinna (Lesueur, 1821), Sailfin molly 2.2 - 3.0 2 2

Polyodontidae

Polyodon spathula (Walbaum 1792), Paddlefish 32.0 1 1

Pomatomidae

Pomatomus saltatrix (Linnaeus, 1766), Bluefish 9.4 - 19.1 1 8 9

Salmonidae

Coregonus artedi Lesueur, 1818, Cisco 7.7 - 19.8 10 130 39 179

C. clupeaformis (Mitchill, 1818), Lake whitefish 10.2 - 26.4 224 224
Sample counts by cut of fish 

Species and common names Length 

range 

(in.)

Whole 

fish

Skin-on 

fillet

Skin-off 

fillet

Other 

cuts

Total

C. hoyi (Milner, 1874), Bloater 9.8 - 11.3 2 2

Oncorhynchus clarki clarki (Richardson, 1836), Cutthroat trout 7.1 - 12.0 12 12

O. clarki clarki (Richardson, 1836), Cutthroat trout (listed as Snake 

river cutthroat trout)

17.5 - 19.5 2 2

O. kisutch (Walbaum, 1792), Coho salmon 4.9 - 26.0 55 55

O. mykiss (Walbaum, 1792), Rainbow trout 2.7 - 31.1 12 248 12 272

O. nerka (Walbaum, 1792), Sockeye salmon (listed as Kokanee 

salmon)

7.3 - 18.1 21 21

O. nerka (Walbaum, 1792), Sockeye salmon (listed as Sockeye salmon) 10.4 - 15.0 37 37

O. tshawytscha (Walbaum, 1792), Chinook salmon 10.5 - 37.9 72 10 82

Salmo salar Linnaeus, 1758, Atlantic salmon (listed as Atlantic 

salmon)

6.9 - 21.3 5 3 7 15

S. salar Linnaeus, 1758, Atlantic salmon (listed as Ouananiche) 13.3 - 19.7 12 4 14 30

S. trutta trutta Linnaeus, 1758, Sea trout 5.2 - 28.4 19 259 16 294

Salvelinus confluentus (Suckley, 1859), Bull trout 17.7 - 20.9 3 3

S. fontinalis (Mitchill, 1814), Brook trout 4.3 - 19.9 32 130 52 214

S. namaycush (Walbaum, 1792), Lake trout 7.4 - 37.2 8 820 14 842

Sciaenidae

Aplodinotus grunniens Rafinesque, 1819, Freshwater Drum 5.1 - 25.6 4 116 94 214

Bairdiella chrysoura (Lacepède, 1802), Silver croaker 7.5 - 7.7 2 2

Cynoscion regalis (Bloch & Schneider, 1801), Gray weakfish 12.3 - 17.3 6 6

Micropogonias undulatus (Linnaeus, 1766), Atlantic croaker 6.1 - 13.2 1 16 17

Pogonias cromis (Linnaeus, 1766), Black drum 18.9 - 21.9 2 2

Sciaenops ocellatus (Linnaeus, 1766), Red drum 12.4 - 26.9 4 4 3 11

Scombridae

Scomberomorus maculatus (Mitchill, 1815), Spanish mackerel 11.8 - 15.6 4 1 5

Sparidae

Archosargus probatocephalus (Walbaum, 1792), Sheepshead seabream 11.7 - 18.4 4 4

Lagodon rhomboides (Linnaeus, 1766), Pinfish 5.6 - 8.7 1 5 6

Synodontidae

Synodus foetens (Linnaeus, 1766), Inshore lizardfish 12.3 1 1

Triakidae

Mustelus canis (Mitchill, 1815), Dusky smooth-hound 24.0 1 1

Zoarcidae

Zoarces americanus (Bloch & Schneider, 1801), Ocean pout 11.7 - 14.7 3 3

Species names as recorded in the modified NLFWA that could not be identified to a specific species

Cusk 5.7 - 18.3 1 3 4

Papio (three species have this common name in the U.S.) 5.1 - 6.8 7 7

Siscowet trout 14.8 - 30.9 19 175 194

Splake trout 4.6 - 28.8 8 60 68

Spotted sea trout 11.4 - 19.7 1 6 7 14

Total 3,016 21,968 6,774 55 31,813

Appendix 15
Wente—A Statistical Model and National Data Set for Partitioning Fish-Tissue Mercury Concentration Variation Between Spatiotemporal and Sample Characteristic Effects—Scientific Investigation Report 2004-5199

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