Frequency distributions of 137Cs in fish and mammal populations

Abstract

We collected fish and mammals in several radioactively contaminated locations in the Chornobyl Exclusion Zone and analyzed them for 137Cs content. Frequency distributions were built for populations of channel catfish, yellow-necked mice and bank voles. We combined our data with similar data from several other studies to demonstrate the relationship between the standard deviations and means of 137Cs of fish and mammal populations. The frequency distributions of 137Cs in populations of fish and mammals are not normal, as indicated by the strong relationship between standard deviation and mean. Distributions for mammals are more skewed than those for fish. Fish and mammals probably use their environments in fundamentally different ways. The highest concentrations and thus greatest risks are therefore confined to relatively few individuals in each population.

Full text

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Journal of
Environmental Radioactivity 61 (2002) 55–74
Frequency distributions of137Cs in fish and
mammal populations
Taras K. Oleksyka,b,*, Sergiy P. Gashchakc, Travis C. Glenna,
Charles H. Jagoea,b, John D. Pelesd, James R. Purduee, Olga
V. Tsyuskoa,b, Olexandr O. Zalisskyf, Michael H. Smitha,b
aSavannah River Ecology Laboratory, The University of Georgia’s, Drawer E, Aiken, SC 29802, USA
bInstitute of Ecology, The University of Georgia, Athens, GA 30602, USA
cInternational Radioecology Laboratory, Slavutych 07100, Ukraine
dPennsylvania State University - McKeesport, 4000 University Drive, McKeesport, PA 15132, USA
eIllinois State Museum, 1011 East Ash Street, Springfield, IL 62703, USA
fChornobyl Scientific and Technical Center for International Research, Chornobyl 07270, Ukraine
Received 13 December 2000; received in revised form 2 May 2001; accepted 17 May 2001
Abstract
We collected fish and mammals in several radioactively contaminated locations in the
Chornobyl Exclusion Zone and analyzed them for137Cs content. Frequency distributions were
built for populations of channel catfish, yellow-necked mice and bank voles. We combined our
data with similar data from several other studies to demonstrate the relationship between the
standard deviations and means of
distributions of137Cs in populations of fish and mammals are not normal, as indicated by the
strong relationship between standard deviation and mean. Distributions for mammals are
more skewed than those for fish. Fish and mammals probably use their environments in
fundamentally different ways. The highest concentrations and thus greatest risks are therefore
confined to relatively few individuals in each population. r 2002 Elsevier Science Ltd. All
rights reserved.
137Cs of fish and mammal populations. The frequency
Keywords: Radiocesium;
Chornobyl; Savannah Liver Site
137Cs; Radioactivity; Frequency distribution; Fish; Mammals; Chernobyl;
*Corresponding author. Savannah River Ecology Laboratory, The University of Georgia’s, Drawer E,
Aiken, SC 29802, USA. Tel.: +1-803-725-7283; fax: +1-803-d725-3309.
E-mail address: oleksyk@srel.edu (T.K. Oleksyk).
0265-931X/02/$-see front matter r 2002 Elsevier Science Ltd. All rights reserved.
PII: S026 5- 931X(0 1)00114 -X

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1. Introduction
The frequency distribution of radionuclides within a population is often of
concern when estimating the levels of risk to the general public for a variety of
reasons. The likelihood of trophic contaminant transfer may be directly influenced
by the contaminant distribution among organisms functioning at a particular trophic
level (Pinder & Smith, 1975; H( a akanson, 1999). The chance of encountering high
concentrations of a contaminant by eating an organism is related to the form of the
contaminant’s frequency distribution, and particularly by the distribution’s mean,
variance, kurtosis and skewness. The potential for the effects of a contaminant is
often a direct function of concentration in the exposed individuals. Since
frequency distributions of contaminants are seldom normal and frequently skewed
(Dapson & Kaplan, 1975; Pinder & Smith, 1975; Ugedal, Forseth, Johnson, &
Njastad, 1995), data analyses require transformations of data or use of non-
parametric statistical methods. Finally, contaminant distributions allow inference
about the biological processes influencing the movement of contaminants within
ecosystems.
A number of studies conducted on radiocesium have reported that radiocesium is
not normally distributed among individuals of a variety of different species (Dapson
& Kaplan, 1975; Pinder & Smith, 1975; Ugedal et al., 1995). The frequency
distribution of radiocesium (137Cs) and similar contaminants is frequently skewed
and often lognormal (Federal Radiation Council, 1961; Remmenga & Whicker,
1967; Rustagi, 1964; Schubert, Brodsky, & Tyler, 1967). However, the lognormal
function is only one of a number of possible curves that could be used to describe
these distributions (Parker, Maki, & Harner, 1999). The exact mathematical form of
the distribution of137Cs is usually not known and can be difficult to determine from
its occurrence in nature. The distribution may even be the result of the interaction of
two or more distributions (Parker et al., 1999). Despite these difficulties, the study of
the distributions of
information about key factors that determine contaminant uptake and accumula-
tion.
Our general objective was to determine concentration, variation, and form
of the frequency distribution of
fish and mammals. We also examined the mathematical form of frequency
distributionsacrossindividualswithin
We tested for relationships between standard deviation and mean within
vertebrate species distributedacross
compared the overall relationship between these two moments of the frequency
distribution for fish from the Savannah River Site (SRS), SC, USA, with that for fish
samples collected in Chornobyl. In addition, we compared frequency distributions of
animal populations with the spatial distribution of radioactivity in their environ-
ment. With this information, we considered the statistical consequences for
future analysis of similar types of data on concentration of radionuclides and
the underlying physical and biological processes potentially influencing these
distributions.
137Cs among functionally different organisms may provide
137Cs in two vertebrate taxa from Chornobyl:
speciesatparticularlocations.
locationsatChornobyl. We then
T.K. Oleksyk et al. / J. Environ. Radioactivity 61 (2002) 55–7456

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2. Materials and methods
2.1. Study areas
The primary study area for this investigation was the Exclusion Zone
around Chornobyl, Ukraine approximately 120km north of the country’s
capital, Kyiv (we are using common spelling that is accepted in Ukraine (Dalton,
1999)). There have been a number of studies involving radionuclides in the
Chornobyl area since the accident in April 1986. Many studies indicate that in the
years after the Chornobyl accident, ecological processes altered the distribution of
radionuclides (Chesser et al., 1999; Ivanov et al., 1997; Jagoe et al., 1998; Medvedev,
1994; Mourad & Snell, 1987). However, the amounts of longer-lived radioisotopes
such as137Cs and90Sr around Chornobyl are still substantial, and environmental
radioactivity exceeds background levels by several orders of magnitude (Ivanov et al.,
1997).
Withinthe ChornobylExclusion
Cooling Pond (N 511200, E 291300) and Gluboke Lake (N 511270, E 301040).
The Cooling Pond is a reservoir that served as a source of cooling water for
the failed Chornobyl reactor. A substantial amount of radioactivity was released
into the Cooling Pond through a system of canals for several years after the
accident. Gluboke Lake is an old bed of the Prypiat River that had been cut
off from the main stream long before the accident. A radioactive cloud from the
reactor accident in April 1986 touched the surface of Gluboke Lake, depositing a
substantial amount of radioactivity to the site (Chesser et al., 1999). Fish were also
collected from the Kyiv Reservoir into which the Prypiat River drains (Jagoe et al.,
1998).
Mammals were collected from several contaminated sites in the Chornobyl
Exclusion Zone including Emerald Camp (N 511200, E 301080), Novoshepelichy
Forest (N 511230, E 291590), Tovsty Forest (N 511230, E 291420), and Gluboke Lake.
The first three locations have mature deciduous forests with heavy underbrush and
some standing water. At Gluboke Lake we trapped in a young deciduous forest that
replaced the pine stands that died shortly after the accident.
Data were also obtained from studies of radiocesium in fish from Steel
Creek and Pond B on the Savannah River Site (SRS) in South Carolina
(Peles,Bryan, Garten,Ribble,&Smith,
Brisbin, & Gibbons, 2000b). The radioactivity in these locations came from
reactor effluents from disassembly basins (Brisbin et al., 1974; Whicker,
Pinder, Bowling, Alberts, & Brisbin, 1989). Steel Creek is a recovering stream
with riparian vegetation succeeding from a nearly barren stream flood plain
toward a lowland hardwood forest. This situation was created by past releases of hot
water (over 701C) from two upstream reactors, which greatly extended the floodplain
from its original banks (Brisbin et al., 1974; Whicker, Pinder, Bowling, Alberts, &
Brisbin, 1990). Pond B, Par Pond and L-Lake are former cooling reservoirs for
reactors that ceased their operation between 1964 and 1985 at the SRS (Whicker
et al., 1989).
Zone,fishwere collectedfromthe
2000a;Peles,Philippi,Smith,
T.K. Oleksyk et al. / J. Environ. Radioactivity 61 (2002) 55–7457

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2.2. Sample collection and analysis for137Cs
A total of 345 individuals of nine species of fish and 493 individuals of five
mammalian species were collected in five different locations within and near the
Chornobyl Exclusion Zone in Ukraine (Table 1). Additional data from studies of fish
on the SRS were also used (Table 1). Three sample sets including channel catfish
(Ictarulus punctatus) from Chornobyl Cooling Reservoir, yellow-necked mouse
(Apodemus flavicollis) from Tovsty Forest and bank vole (Clethrionomys glareolus)
from Tovsty Forest were large enough (N ¼ 150; 65, and 65, respectively) to present
their frequency distributions (Fig. 1a, c and d). We also present a distribution of
137Cs in dry muscle of Micropterus salmoides from the SRS (Fig. 1b). The original
sources for fish data from the SRS (summarized in Table 1) are given in Peles et al.
(2000a,b).
Muscle was sampled from the hind leg in mammals. In fish, a small piece of muscle
was cut out of the side between lateral line and dorsal fin. Tissues were dried at 50oC
and weighed. Muscle weights averaged 0.6270.44g dry weight in mammals and
1.4770.23g in fish. Confidence intervals are given 71 standard deviation (S) except
as indicated otherwise. Radiocesium in the individual muscles was measured using a
Minaxig-5000 (Packard, Meriden, CT, USA) automatic gamma counter with an NaI
detector. Fish from SRS collected in 1998–1999 were assayed using a germanium
detector (Peles et al., 2000a,b). Data from low-activity standards with the same
geometry as the samples were used to calculate detector efficiency. Counting times
were adjusted to produce confidence intervals whose width was less than 5% of the
average background levels and were made long enough to ensure that there were no
values below the background level since using negative values would bias the
analyses (Newman, Dixon, Looney, & Pinder, 1989). Background count rates were
determined for every eight vials and background levels were subtracted from the
individual counts in the same batch. Detection limits were calculated according to
Currie (1968).
2.3. Statistical analysis
Statistical analyses were performed using SAS v.8.1 software (SAS, 1999). The
mean, variance (S2), and standard deviation (S) were calculated for every sample set
with more than six individuals. The four moments of each distribution, which
included mean, S;S2; and coefficients of skewness (G1) and kurtosis (G2) were
calculated for samples with more than 30 individuals. Linear regressions were
calculated for the relationships between the standard deviation and mean for each
sample set of mammals and fish separately using the maximum likelihood method
(SAS, 1999). Regressions were forced through the origin, and the slope is an estimate
of the average coefficient of variation under this restriction. Pearson product-
moment correlation coefficients for these regressions were also calculated, and plots
of the residuals were examined for trends and other indications of a non-normal
distribution. Results of statistical tests were considered significant when pp0:05 and
highly significant when pp0:01:
T.K. Oleksyk et al. / J. Environ. Radioactivity 61 (2002) 55–7458

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Table 1
Means, standard deviations (S), variance (S2), sample sizes (N) and sources of data
Taxa YearLocation SpeciesNMeanSS2
Fish
Fish
Fish
Fish
Fish
Fish
Fish
1974
1981
1999
1993
1999
1993
1993
Steel Creeka
Steel Creeka
Gluboke Lakeb
Cooling Pondc
Gluboke Lakeb
Kyiv Reservoirc
Cooling Pond
Channelc
Cooling Pondb
Cooling Pondc
Steel Creeka
Steel Creeka
Steel Creeka
L-Laked
Par Pondd
Par Pondd
Pond Be
Pond Bd
Pond Bd
Steel Creeka
Steel Creeka
Cooling Pondc
Kyiv Reservoirc
Gluboke Lakeb
Emerald Campb
Gluboke Lakeb
Novoshepelichy
Forestryb
Tovsty Forestb
Emerald Campb
Gluboke Lakeb
Novoshepelichy
Forestryb
Tovsty Forestb
Gluboke Lakeb
Emerald Campb
Novoshepelichy
Forestryb
Emerald Campb
Gluboke Lakeb
Novoshepelichy
Forestryb
Aphredoderus sayanus
Aphredoderus sayanus
Carassius auratus
Carassius carassius
Carassius carassius
Carassius carassius
Cyprinus carpio
146
47
32
6.11
1.93
11.69
25.39
12.10
1.27
97.79
2.78
0.77
2.63
11.61
3.76
0.31
18.34
7.71
0.59
6.90
9 134.89
14.13
0.09
336.26
21
14
22
Fish
Fish
Fish
Fish
Fish
Fish
Fish
Fish
Fish
Fish
Fish
Fish
Fish
Fish
Fish
Mammal
Mammal
Mammal
Mammal
1999
1993
1981
1981
1981
1998
1999
1998
1973
1998
1999
1981
1981
1993
1993
1998
1999
1998
1999
Ictalurus punctatus
Ictalurus punctatus
Lepomis auritus
Lepomis gulosus
Lepomis punctatus
Micropterus salmoides
Micropterus salmoides
Micropterus salmoides
Micropterus salmoides
Micropterus salmoides
Micropterus salmoides
Micropterus salmoides
Notropis cummingsae
Rutilus rutilus
Tinca tinca
Apodemus agrarius
Apodemus flavicollis
Apodemus flavicollis
Apodemus flavicollis
150
35
45
5.15
39.23
1.72
3.04
1.85
0.07
1.18
1.09
36.65
11.63
12.04
4.62
2.19
8.39
1.72
352.11
29.07
1175.75
319.78
1.18
8.83
0.63
1.34
0.70
0.03
0.22
0.20
7.38
2.27
2.51
1.64
1.23
1.36
0.49
1.38
77.94
0.39
1.80
0.49
0.00
0.05
0.04
54.50
5.16
6.31
2.70
1.52
1.84
0.24
9
49
64
120
33
588
99
37
53
57
8
54
24
33
24
33
410.94
68.05
833.18
292.98
168870.90
4631.41
694191.94
85834.68
Mammal
Mammal
Mammal
Mammal
1997
1999
1998
1999
Apodemus flavicollis
Clethrionomys glareolus
Clethrionomys glareolus
Clethrionomys glareolus
65
47
40
61
37.56
125.51
1159.46
1627.58
38.30
253.95
894.72
2122.73
1467.11
64488.76
800532.47
4506000.62
Mammal
Mammal
Mammal
Mammal
1998
1998
1999
1999
Clethrionomys glareolus
Microtus spp
Muscardinus avellanarius
Muscardinus avellanarius
65
24
8
25
56.59
1420.97
23.67
279.85
73.77
2656.00
26.35
275.33
5442.10
7054359.35
694.49
75807.67
Mammal
Mammal
Mammal
1999
1998
1999
Sorex araneus
Sorex araneus
Sorex araneus
812.52
259.15
155.29
11.78
338.57
201.93
138.68
13
23
114629.93
40775.91
aPeles et al. (2000a).
bThis study.
cJagoe et al. (1998).
dPeles (unpublished data).
ePeles et al. (2000b).
T.K. Oleksyk et al. / J. Environ. Radioactivity 61 (2002) 55–7459

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The normal, lognormal, exponential and two-parameter Weibull models were used
to fit the data as in Pinder and Smith (1975). The Anderson–Darling (A–D) test
(Stephens, 1974) was used to determine whether certain distributional models fit the
data. The A–D test is a modification of the Kolmogorov-Smirnov (K–S) test that
gives more weight to the tails of the distribution than the K–S test. The K–S test is
distribution free in the sense that the critical values do not depend on the specific
distribution being tested. The A–D test requires the use of the specific distribution in
calculating critical values. This yields a more sensitive test although critical values
must be calculated for each distribution.
The expected values for G1 and G2 for a normal distribution are both zero.
Negative G1values (left skewed) occur when the distribution of values tends to tail
off below the mean (more values than would be expected with a normal distribution
with a similar variance), while positive values (right skewed) indicate tailing above
the mean. Negative G2values occur when there are more values in the tails about the
Fig. 1. The frequency distributions of137Cs for the following: (a) Channel catfish (Ictarulus punctatus)
from the Cooling Reservoir at Chornobyl. (b) Largemouth bass (Micropterus salmoides) from Par Pond on
the Savannah River site. There was no significant difference between the distribution of137Cs in this
sample and a normal distribution (p > 0:05). (c) Yellow-necked mice (Apodemus flavicollis) from the
Tovsty Forest located within the 30-km Exclusion Zone. (d) Bank voles (Clethrionomys glareolus) from
Tovsty Forest. Estimates of distributional parameters for each of the above are given in Table 2.
T.K. Oleksyk et al. / J. Environ. Radioactivity 61 (2002) 55–74 60

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mean (platykurtotic), and positive G2values occur when values are more clustered
about the mean (leptokurtotic) than in a normal distribution with a similar variance
(Snedecor & Cochran, 1981). Another way of looking at the distribution is to
examine the ratio of variance to mean. For example, if the distribution were Poisson,
then a ratio of 1 would be expected (Parker et al., 1999). Normal distributions are
characterized by two independent parameters, their mean and variance. There
should be no relationship between the variance and mean for normal distributions. If
data from the samples were not normally distributed but skewed to some degree
(e.g., lognormal, exponential, etc.), they should fit a regression line with a slope
significantly different from zero. This relationship should no longer exist after an
appropriate transformation (log transformation in our case) is applied to the raw
data.
2.4. Assessing the spatial distribution of radioactivity
To assess the spatial distribution of radiation in the terrestrial environment of the
Exclusion Zone, we used thermo-luminescent dosimeters (LiF; Mg, Ti; TLD-100,
Bicron RMP, Solon, OH, USA) encapsulated in polyethylene vials. The TLDs were
primed at 4001C for 1h and then held at 1001C for 4h. Sixteen TLDs were left at the
laboratory in the United States to serve as a control (Control SREL). Thirty-two
TLDs stayed at the laboratory in Chornobyl (Control Chornobyl). The rest of the
TLDs were placed along the trapping lines every 10m at some of our study locations
within the Exclusion Zone. We placed 20 or more TLDs for the duration of 14 days
at each site. Dosimeters were collected, brought back to the USA and read using a
Solon-Harshaw QS 3500 TLD reader. A sub-set of TLDs was irradiated using a well-
characterized radiation source at the Center for Applied Isotope Studies, University
of Georgia, to serve as calibration standards. We calculated four moments of the
distributions for the remaining dosimeter sets the same way as for the mammal and
fish samples.
We used gamma exposure rate data determined with scintollometers as described
in Gladden, Brown, Smith, and Towns (1985) to calculate mean exposure rate at
ground level and standard deviations for each of the 32 transects extending laterally
across Steel Creek. Determinations were taken every 5m, and the number of
determinations per transect varied from 9 to 196 for a total of 1362 determinations.
The raw data that were used are given in Smith, Sharitz, and Gladden (1981, Table
VII. C-l). Regressions using the mean and standard deviation for each transect were
forced through the origin.
3. Results
3.1. Anderson–Darling tests for single population samples of fish an mammals
Frequency distributions for
lognormal (Fig. 1a and b, Table 2). Data from the largest sample of fish used in this
137Cs in most fish species appear to be normal or
T.K. Oleksyk et al. / J. Environ. Radioactivity 61 (2002) 55–7461

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Table 2
The coefficients of skewness (G1) and kurtosis (G2) for samples greater than 30 individuals and a comparison of each sample distribution to four model
distributions according to the Anderson–Darling test
Taxa YearLocationSpeciesNG1a
G2a
NormalLognormalExponential Weibull
Fish
Fish
Fish
Fish
Fish
Fish
Fish
Fish
Fish
Fish
Fish
Fish
Fish
Fish
Fish
Fish
Mammals
Mammals
Mammals
Mammals
Mammals
Mammals
Mammals
1974
1981
1999
1999
1993
1981
1981
1973
1999
1998
1998
1981
1999
1998
1981
1993
1997
1999
1999
1998
1999
1999
1998
Steel Creek
Steel Creek
Gluboke Lake
Cooling Pond
Cooling Pond
Steel Creek
Steel Creek
Pond B
Par Pond
Pond B
L-Lake
Steel Creek
Pond B
Par Pond
Steel Creek
Kyiv Reservoir
Tovsty Forest
Emerald Camp
Novoshepelichy Forestry
Tovsty Forest
Novoshepelichy Forestry
Emerald Camp
Gluboke Lake
Aphredoderus sayanus
Aphredoderus sayanus
Carassius auratus
Ictalurus punctatus
Ictarulus punctatus
Lepomis auritus
Lepomis punctatus
Micropterus salmoides
Micropterus salmoides
Micropterus salmoides
Micropterus salmoides
Micropterus salmoides
Micropterus salmoides
Micropterus salmoides
Notropis cummingsae
Tinca tinca
Apodemus flavicollis
Apodemus flavicollis
Apodemus flavicollis
Clethrionomys glareolus
Clethrionomys glareolus
Clethrionomys glareolus
Clethrionomys glareolus
146
47
32
150
35
45
49
588
120
99
64
53
37
33
57
54
65
33
33
65
61
47
40
1.04
0.09
0.42
1.50
0.91
0.21
0.34
0.15
0.02
0.80
0.22
0.15
0.14
?0.07
0.84
0.35
2.82
4.83
0.91
2.63
1.63
3.31
1.069
1.76
0.20
?0.43
9.91
0.67
0.12
?0.14
0.18
1.14
1.18
0.01
?0.24
1.31
0.24
1.08
?0.64
11.36
25.00
?0.20
7.01
1.30
11.60
0.04
1.813
0.148b
0.375b
1.871
0.840
0.191b
0.218b
0.637b
0.345b
0.731b
0.607b
0.258b
0.725b
0.224b
0.562b
0.445b
4.638
7.726
1.438
8.481
7.563
8.529
2.095
0.956
1.791
0.251b
2.605
0.437b
0.917
0.533b
1.541
1.163
0.204b
1.243
1.005
0.925
0.330b
0.797
0.377b
0.416b
0.795b
0.654b
0.686b
0.395b
2.130
0.414b
21.782
7.815
9.011
44.020
10.178
8.426
8.680
174.218
37.209
30.382
12.877
10.053
11.135
10.274
4.866
12.798
1.613
4.150
0.489b
2.490
3.961
12.295
1.261b
1.072
0.274b
0.448b
5.477
1.162
0.218b
0.161b
3.060
0.819b
1.916
0.618b
0.259b
0.978
0.323b
0.190b
0.460b
1.171
2.276
0.533b
2.359
1.176
2.445
0.517b
aMean G1and G2for fish and mammals were 0.4470.11 and 1.0270.61, and 8.0173.41 and 5.7871.15, respectively.
bValues that do not reject the particular model at po0:05: Test values that indicate the best fit are given in italics.
T.K. Oleksyk et al. / J. Environ. Radioactivity 61 (2002) 55–74
62

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study, M. salmoides (N ¼ 588), is best fit by the normal model (Table 2). The
distribution of data from the largest sample of fish obtained from the Chornobyl
Exclusion Zone, I. punctatus (N ¼ 150), did not fit any of the distributional models
(Table 2). However, when one outlier was removed from the I. punctatus data set, the
distribution was best fit by the normal model. This illustrates that one extreme point
can influence the outcome of the model fitting calculations. Results of the A–D test
(D) for four different distributions (normal, lognormal, exponential, and Weibull)
are given in Table 2. The smallest value of D indicates the best fit for the sample
distribution. Overall, for fish there were 10 samples best fit by the normal
distribution, five by the lognormal distribution, and one by the Weibull distribution
(Table 2). We calculated D values for 16 samples of fish with sample size more than
30 individuals. Either the normal or the lognormal model fit most of the sample data.
The only exception was Lepomis punctatus from Steel Creek that was best fit by the
Weibull model.
Inmammals,frequencydistributions
categories were best fit by a lognormal and one by an exponential model
(Table 2). Data from two of the largest mammalian sample sets, A. flavicollis
(N ¼ 65) and C. glareolus (N ¼ 65) from Tovsty Forest, fit the lognormal
model (Fig. 1c and d) but not the normal model. The lognormal model
failed to fit only two mammalian populations, A. flavicollis and C. glareolus from
Emerald Camp (Table 2). D values were calculated for seven mammalian
populations with N > 30: The data for almost all the samples were well fit by the
lognormal distribution. However, both the exponential and Weibull models fit the A.
flavicollis data from Novoshepelichy Forestry better than the lognormal model.
However, two of our samples did not fit any of our models at the 95% significance
level (Table 2).
of
137Csforsixspecies-location
3.2. Regressions of mean on S
All three groups of samples (fish from SRS, fish from the Chornobyl
Exclusion Zone and mammals from the Chornobyl Exclusion Zone) demonstrate
a statistically significant positive linear relationship between the S and mean
(Fig. 2). Such a relationship indicates that the data for the samples from
our study were not normally distributed, because mean and variance are independent
for a normal distribution (Hahn & Shapiro, 1967). The regressions for each
of the three groups were highly significant. Visual examination of the plots of the
residuals revealed that there were no apparent trends in the residuals that would
indicate curvilinearity or that their distributions were non-normal. Additional
samples would need to be obtained to make an exact test for the normality of the
residuals.
The relationship between S and mean for137Cs distribution in samples of fish from
Chornobyl was linear with a slope=0.2170.02 (N ¼ 9; r2¼ 0:85; and po0:001;
Fig. 2a). Samples of the populations from the SRS fit a similar linear model with
slope=0.2170.02 (N ¼ 13; r2¼ 0:91; and po0:001; Fig. 2b). Since the slopes were
not significantly different from each other (F1; 22¼ 0:02; p ¼ 0:89), data were pooled
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Page 10

for the SRS and Chornobyl samples, and a regression for the pooled data calculated.
The resulting regression had a slope=0.2170.01 (r2¼ 0:88; po0:001; Fig. 2c). The
slope of the relationship between S and mean for137Cs in mammals had a value of
1.0370.05 (N ¼ 14; r2¼ 0:89; and po0:001; Fig. 2d). Slopes for mammals and fish
were significantly different from each other (F1; 36¼ 94:08; po0:0001). If a point
representing C. glareolus from Tovsty Forest was omitted from the regression due to
its unusually high S to mean ratio, the slope for mammals decreased to 0.8370.05
(r2¼ 0:91; po0:001). When the data were log-transformed, the relationships
between S and mean were not significant for either group of fish or for mammals
(p > 0:05). There was also a significant relationship between the third (G1: skewness)
and fourth (G2: kurtosis) moments of the distributions in fish and a highly
significant relationship in mammals: slopes of G1 vs. G2 were 1.570.05 in both
cases, but their intercepts were different. G1was larger for mammals than for fish
(one tailed test, pp0:05), and G2 was larger in mammals as well (one tailed test
po0:001).
Fig. 2. Regressions were forced through the origin for the linear relationships between the standard
deviations and means for137Cs muscle concentrations in the following: (a) Eight sample sets of fish from
the Chornobyl Exclusion Zone. Slope is given 72 standard errors in parentheses, ** po0:001 for test of
slope equal to zero. (b) Twelve sample sets of fish from the Savannah River Site. (c) Combined sample sets
from Chornobyl and SRS, whose slopes did not differ significantly (p > 0:05). (d) Regression was forced
through the origin for the relationship between the standard deviation and mean for137Cs for 14 sample
sets of mammals. Slope is given 72 standard errors in parentheses. **po0:001 for test of slope equal to
zero.
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3.3. Spatial distribution of radiation
Data from TLDs dispersed at the study locations are presented in Table 3. The
slope of the relationship between S and mean of radiation dose rates measured by
TLDs left in the field was 0.7170.04 (N ¼ 7; r2¼ 0:97; and po0:001). The mean
dose rates in the field (mrad/h) varied between 13.2 and 414.6mrad/h (Table 3).
Values for the controls left in the US and Chornobyl Laboratory did not differ
significantly from each other (adjusted t-test, N ¼ 40; t ¼ ?0:65; and p ¼ 0:5). The
mean dose rates at ground level along the transects in Steel Creek varied from 2.3
and 20.6mrad/h (Smith et al., 1981). The individual determinations showed an even
greater variation equivalent to that seen at Chornobyl. The slope of the relationship
between S and the means of the dose rates at ground level in Steel Creek was
1.0970.06 (r2¼ 0:82).
4. Discussion
4.1. Shapes of137Cs frequency distributions in fish and mammals
The frequency distributions of137Cs in both fish and mammal populations from
Chornobyl and SRS tend to be skewed and leptokurtotic. In addition, the most
skewed distributions are also the most leptokurtotic distributions. Almost all of the
values for the third and fourth moments in our study have positive skewness and
kurtosis. We do not have high confidence in any one estimate, since the sample sizes
required to reliably estimate skewness and kurtosis need to be at least 150 and 1000,
respectively (Snedecor & Cochran, 1981). However, we are confident that the trend
Table 3
Locations, sample sizes per group (N), means (mrad/hour), standard deviations (S), variances (S2), and the
extreme values (maximum and minimum) of the dosimeter readings
Location NMeana
Sa
S2
Maximum valueMinimum value
Control SREL
Control Chornobyl
Emerald Camp
Gluboke Lake Woods
Gluboke Lake Shore
Novoshepelichy Forestry
Prypiat city
Tovsty Forest
Zymovishce village
16
34
28
22
30
20
9
20
10
10.41
10.78
29.67
414.58
44.69
169.88
16.24
13.22
14.26
1.96
1.70
19.06
312.62
25.24
81.98
2.01
2.19
1.59
3.84
2.88
14.73
14.06
80.68
1461.25
109.30
404.50
20.46
18.09
17.53
7.76
7.43
8.94
24.56
8.59
86.86
14.53
9.87
12.46
363.10
97733.17
636.88
6720.64
4.05
4.78
2.53
Total189
aThe relationship between SðYÞ and mean values (X) for is Y ¼ 0:71X: N ¼ 7; r2¼ 0:97; and po0:001
(we included only TLDs in the field locations). Confidence intervals for the slope are 70.04.
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Page 12

for both moments is positive. The trend for high positive kurtosis and some of the
larger values for kurtosis, especially in mammals, suggests that we should detect
significant kurtosis values for most of the mammalian populations with larger
sample sizes. Moreover, data from many mammalian populations appear to fit
distribution models that have a high degree of skewness and kurtosis: i.e., lognormal
and exponential. Even in the data from samples of fish that fit the normal model
best, there are positive values for skewness and kurtosis. It seems likely that the
normal distribution would seldom be the best model to fit the distribution of137Cs in
mammal and fish populations if adequately large numbers of samples were
obtained.
When our data were log-transformed, the relationship between S and the
mean of the
the data handled the transformation of the data well, since no relationship
between the first two moments of the distribution would be expected for a normal
distribution (Hahn & Shapiro, 1967). Log-transformations are a recommended
approach for the analyses of this type of data when using parametric statistical
techniques for analyses, especially when there is no need to seek a more definitive
model.
Most frequency distributions in fish appear to be nearly normal but with a
tendency for a few large values on the right side of the distribution. These types of
distributions were best fit by the lognormal, exponential or Weibull distributions
(Table 2). Other studies have also indicated a lognormal or Weibull shape for fish
distributions. In Ugedal et al. (1995), the distribution for two species of fish fit the
lognormal distribution best. In Pinder and Smith (1975), 54% of all types of samples
(soils, plants and animals) were best fit with a lognormal model, but 36% of samples
were best fit with the Weibull.
We demonstrated a situation when, on the one hand, in the separate by-
population analysis normal model was not rejected for most of the fish populations.
On the other hand, a generalized coefficient of variation (CV) was around 20% as
estimated from the slope of the relationship between the mean and standard
deviation, indicating that, in general, fish population tends to be not normal and
skewed. This result is very similar to that calculated by H( a akanson (1999) for the
European lake fish (CV=22%) and Whicker et al. (1990) for the largemouth bass
(CV=16%). As the slope approaches zero, the data for the samples that fit on the
regression line tend to approach the normal distribution. Thus, most fish
distributions although slightly skewed and leptokurtotic can still be fit with a
normal model.
On the other hand, the relationship between S and mean in mammals had a much
higher slope and thus a higher coefficient of variation, indicating a stronger
departure from the normal distribution than seen for fish. Frequency distributions of
137Cs for small mammals from Chornobyl were generally highly skewed and
leptokurtotic. Unfortunately, there were no samples of mammals with more than 65
individuals. For mammals, there were large numbers of lower values for
followed by a long tail of large values (e.g., A. flavicollis and C. glareolus; Fig. 1c and
d, respectively). This pattern was so distinctly different from the nearly bell-shaped
137Cs distributions no longer existed. Calculating the log of
137Cs
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Page 13

distribution of fish that it was possible to visually separate distributions for fish and
mammals.
There are a large number of distributions that could be used for statistical
applications (Hahn & Shapiro, 1967). We limited our investigation to only four of
the most common distributions that have been used to describe137Cs distributions
before (Pinder & Smith, 1975). In the future, it would be interesting to include other
models to describe similar data as suggested in Parker et al. (1999). The lognormal,
exponential, and Weibull models describe distributions with long, skewed tails on the
right side. The normal model fits a symmetrical and mesokurtic bell-shaped
distribution (Zar, 1984). The exponential model indicates an extremely skewed
distribution. Lognormal and especially Weibull distributions can take a variety of
different shapes with different values of skewness and kurtosis. By testing all of these
distributions at the same time, we were able to find at least one model that fits the
data from each of our samples with one exception of a fish sample and two mammals
that did not fit any of the models (Table 2). In many cases, more than one model fit
the sample data. Using distribution models with three or more parameters would
undoubtedly result in finding one that would fit all of the sample data in this paper,
but it becomes more difficult to understand the factors that shape such distributions.
4.2. Factors that influence shapes of frequency distributions in vertebrates
Multiple factors are probably involved in shaping frequency distributions in fish
and mammals. These factors may have multiplicative effects if the frequency
distributions are lognormal (Parker et al., 1999), but the way the factors interact is
not known. However, these factors probably always include the spatial heterogeneity
of the distribution of the contaminant in the environment, although the importance
of this factor may differ among different habitat types (e.g., aquatic vs. terrestrial). If
highly contaminated spots are scarce, the resulting distribution of randomly taken
samples will tend to be skewed. The more homogeneous the spatial distribution of
the contaminant, the more we would expect the frequency distribution to be fit by
the normal model. Since the distributions in the mammals and fish were skewed, we
would predict that the distributions for the soils and sediments are at least as skewed
and possibly even more skewed than they are for the fish and mammals (Pinder &
Smith, 1975).
There is a striking similarity between the value of the slope of the relationship
between S and mean in mammals and in nine groups of TLDs distributed across the
terrestrial environment in different terrestrial locations of the Chornobyl Exclusion
zone. In fact, similarity increased when a point representing C. glareolus from Tovsty
Forest was deleted from the data, and the value of the slope for the mammals
decreased. While it might be more appropriate to use137Cs concentrations in the
soils to calculate the relationship for the terrestrial environment, the similarity of the
slopes suggests that the same factor(s) shapes both sets of distributions. We would
predict that the slope of the relationship for the S and mean for soil concentrations
would be similar to that for mammal concentrations and TLD doses. It is likely that
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Page 14

the distribution in mammals is simply a reflection of the spatial distribution of the
contaminant in the environment (Table 4).
Unfortunately, we do not have matching data for fish and their aquatic
environment. If the distribution of the contaminant is more heterogeneous in the
terrestrial environment than in the aquatic environment, frequency distributions for
small mammals should be more skewed than those for fish. Distributions of137Cs
were most skewed in mammals. Variance of the frequency distribution among
individual mammals may be an indicator of how homogeneously the contaminant is
dispersed in the environment: the higher the variation among the contaminant
concentrations in the individual samples from the location, the more heterogeneous
is the spatial pattern of contamination. Sampling a location with only few high
values yields a skewed distribution and a number of locations with this type of
distribution would yield a relatively high slope, because of the higher S values in the
relation to the mean.
The relationship between S and the mean for radiation dose rate from our
terrestrial locations at Chornobyl gave a relatively high slope of 0.74 (Table 3). The
same relationship for the dose rates on the flood plain of Steel Creek gave a similarly
high slope (1.09). In addition, 20 and 12 of the 32 transects showed significant
skewness and kurtosis, respectively (Smith et al., 1981). The spatial dispersion of
137Cs is very heterogeneous for both the Steel Creek and Chornobyl locations. On a
local scale, both areas could be characterized as having a few highly contaminated
spots dispersed in a matrix of relatively low contamination. These findings are
concordant with findings for the aquatic environment at Chornobyl. Sampling of
sediments indicate that the distribution of radiocesium in ponds in the Chornobyl
area was very patchy and could vary over 100% in samples collected only a few
meters apart (Jagoe et al., 1997). Thus, the sediments in aquatic habitats and
floodplains of creeks probably have similarly high heterogeneity.
The way in which an animal uses its environmental space is an important factor
that influences the shape of the frequency distribution. Animals with high mobility
should perceive the contaminant to be more homogeneous in their environments.
Large home range size and long movement distances will reduce the skewness of the
distribution and result in a distribution of137Cs approaching the normal one (Pinder
Table 4
Locations, means (mrad/h) and standard deviations (S) of the dosimeter readings and the coresponding
standard deviations of137Cs distributions of the sampled populations of small mammals from the sampled
locations
LocationMean TLDS Apodemus
flavicollis
Chletrionomys
glareolus
Muscardinus
avellanarius
Sorex
araneus
Emerald Camp
Gluboke Lake
Novoshepelichy Forestry
Tovsty Forest
29.67
414.58
169.88
13.22
19.06
312.62
81.98
2.19
68.05
833.18
292.98
38.30
253.95
894.72
2122.73
73.77
26.35
F
275.33
F
11.18
338.57
201.93
F
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Page 15

& Smith, 1975), almost as if the animals were integrating over the spatial distribution
of the contaminant. Species that do not move much in search of food would tend to
have more skewed frequency distributions like the small mammals in this study. We
predict that larger and more mobile vertebrates should have more normal frequency
distributions than those of small, less mobile vertebrates.
The degree of movement may help explain the lower S in fish, since fish may move
around their habitat more easily than mammals. Interspecific differences in
movement might also explain some of the variations among frequency distributions
of mammals or fish. However, we sampled across a number of fish populations
including populations of predators (largemouth bass), herbivores (carp) and species
feeding in the benthic foodchain (catfish). Our mammalian samples were confined to
small rodents and insectivores. It is therefore possible that if we included larger
mammals like rabbits, foxes or wild boar in the analysis, the relationship between the
S and the mean would change dramatically, since larger mammals have larger home
ranges and should tend to have a less skewed, more normal-like distribution of137Cs
(e.g., like white-tailed deer on the SRS (Wentworth, 1998)). Differences in the
elimination rates of a contaminant can also generate lognormal distributions for
137Cs (Koch, 1966). Larger animals are able to maintain a constant body function
thus counteracting the environmental variation because of their slower metabolism.
The larger body would also require a greater amount of food. This leads to the
increased home ranges as well as to the integration across a gradient of
contamination. This must result in a more normal, less skewed distribution for a
population as a whole. On the other hand, shrews should have distributions
closely resembling the heterogeneity of the environment, because they have
high metabolism, resulting in shorter biological half-lives of the elements in their
bodies.
Large animals with a large contaminant-accumulation storage (higher body mass,
specific tissues with higher affinity to certain contaminants, etc.) may accumulate the
contaminant over longer periods of time. There is strong evidence for the
relationship between body size and137Cs content in some species of fish (Koulikov
& Ryabov, 1992; Ugedal et al., 1995) but not for others (Peles et al., 2000b). Often
bioacummulation is associated with age (McCreedy, Jagoe, Glickman, & Brisbin,
1997). The way in which these various factors interact to produce a frequency
distribution is not well understood. It might be worthwhile to compare
concentrations in closely related species that live in the water and in the terrestrial
environment (e.g., amphibians), as well as different life stages of the same organism
that change their environment from aquatic to terrestrial.
Wentworth (1988) studied radiocesium in nearly 30,000 white-tailed deer collected
over 31 years, but did not calculate S for any of the samples in his study, only for the
total sample. It is still apparent from the illustrated data in his work that the
distribution is skewed but it does not appear to be as skewed as the distributions for
the small mammals in this study. James Novak (pers. comm.) calculated the mean
and S for concentrations of137Cs in four sub-samples of white-tailed deer collected
on or near the SRS. The sub-samples consisted of 20–144 whitetails (total N ¼ 218)
and their Ss ranged from 26.1% to 58.8% of their mean. The mean S was 50.6% of
137Cs
T.K. Oleksyk et al. / J. Environ. Radioactivity 61 (2002) 55–7469