Journal of Environmental Radioactivity 138 (2014) 116e121
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A new simplified allometric approach for predicting the biological half-life of radionuclides in reptiles N.A. Beresford a, b, *, M.D. Wood b a b
Centre for Ecology & Hydrology, Bailrigg, Lancaster LA1 4AP, UK School of Environment & Life Sciences, University of Salford, Manchester M4 4WT, UK
a r t i c l e i n f o
a b s t r a c t
Article history: Received 27 June 2014 Received in revised form 21 August 2014 Accepted 22 August 2014 Available online
A major source of uncertainty in the estimation of radiation dose to wildlife is the prediction of internal radionuclide activity concentrations. Allometric (mass-dependent) relationships describing biological half-life (T1/2b) of radionuclides in organisms can be used to predict organism activity concentrations. The establishment of allometric expressions requires experimental data which are often lacking. An approach to predict the T1/2b in homeothermic vertebrates has recently been proposed. In this paper we have adapted this to be applicable to reptiles. For Cs, Ra and Sr, over a mass range of 0.02e1.5 kg, resultant predictions were generally within a factor of 6 of reported values demonstrating that the approach can be used when measured T1/2b data are lacking. However, the effect of mass on reptilian radionuclide T1/2b is minimal. If sufficient measured data are available for a given radionuclide then it is likely that these would give a reasonable estimate of T1/2b in any reptile species. © 2014 Elsevier Ltd. All rights reserved.
Keywords: Reptile Biological half-life Allometry Radionuclide
1. Introduction It has been well-documented that a significant source of uncertainty in the estimation of the exposure of wildlife to ionising radiation is the estimation of organism radionuclide activity concentrations (Avila et al., 2004; Higley et al., 2003a; Beresford et al., 2008, 2010; Johansen et al., 2012; Yankovich et al., 2010a). Often organism activity concentrations are estimated using a simple concentration ratio relating the whole-organism activity concentration to the activity concentration in the appropriate environmental medium (typically soil for terrestrial ecosystems and water for aquatic ecosystems) (CRwo-media) (Howard et al., 2013). However, this ratio is largely dependent upon site characteristics and hence can be highly variable for a given radionuclide e organism combination (e.g. Wood et al., 2013). Alternative approaches to the use of CRwo-media have been considered (Beresford et al., 2004, 2013) including the use of allometric relationships to estimate radionuclide intake and biological half-life (T1/2b) and hence wholeorganism activity concentrations (Beresford and Vives I Batlle, 2013; Higley et al., 2003b). The application of allometric relationships in radiological environmental (wildlife) assessment models was originally proposed to address the lack of CRwo-media values
* Corresponding author. Centre for Ecology & Hydrology, Bailrigg, Lancaster LA1 4AP, UK. Tel.: þ44 1524 595856. E-mail address: [email protected] (N.A. Beresford). http://dx.doi.org/10.1016/j.jenvrad.2014.08.012 0265-931X/© 2014 Elsevier Ltd. All rights reserved.
(Higley et al., 2003b). The application of such kinetic-allometric models has the advantage that, if required, non-equilibrium activity concentrations in organisms can be estimated and such models are the advised approach for higher level assessments in some methodologies (USDOE, 2002). For example, non-equilibrium estimates may be needed for the assessment of fluctuating discharge rates from nuclear facilities or acute accidental releases of radionuclides to the environment, such as in the case of the Fukushima accident (Strand et al., 2014). Allometric scaling relates body mass (M) to a specific biological parameter (Y) (Peters, 1983):
Y ¼ aM b
(1)
where a and b (the allometric exponent) are constants. With respect to radionuclide biological half-life, allometric constants for 9 radionuclides (Cs, Co, H, Ra, Sb, Sr, U, Zn and Zr) have been presented where the allometric exponent (i.e. b) approximates to 0.25 (USDOE, 2002; Galeriu et al., 2003); information presented by MacDonald (1996) suggests this will also be the case for I. This is in agreement with allometric relationships for many other biological parameters, including metabolic rate (referred to as Kleiber's Law) (Kleiber, 1932), which scale to quartile values. As demonstrated by Beresford and Vives I Batlle (2013) an exponent of 0.25 for radionuclide biological half-life is explainable from Kleiber's Law. Hence T1/2b can be described as:
N.A. Beresford, M.D. Wood / Journal of Environmental Radioactivity 138 (2014) 116e121
T1=2b ¼ aB M 0:25
(2)
Where M is mass (kg) and aB is the multiplicand (d kg0.25). Sheppard (2001) suggested that if it can be assumed that bB (i.e. the exponent for the biological half-life allometric expression) will approximate to the same value for all elements then only an estimation of the multiplicand (i.e. aB) is required for any given element for which an allometric relationship has not been derived from empirical data. However, until recently, no method was available for estimating the multiplicand when data to fit an allometric relationship are lacking. Through algebraic derivation Beresford and Vives I Batlle (2013) proposed that the multiplicand for the allometric relationship describing radionuclide biological half-life (aB) could be estimated as:
aB ¼
ln 2 CRorgdiet aI f1
(3)
Where f1 is the fractional gastrointestinal absorption coefficient for a given element, CRorg-diet is the ratio between the activity concentrations in the whole-organism (fresh mass) and the diet (dry matter, DM), and aI is the multiplicand in the allometric model describing the dry matter intake rate of food (Ir, kg (DM) d1). CRorgdiet was assumed to be constant across all species (Beresford et al., 2004; IAEA, 2010). The allometric relationship for Ir in homeotherms approximates to:
Ir ¼ aI M 0:75
(4)
with values of aI being relatively well-documented for terrestrial vertebrates (e.g. Nagy, 2001). From Equations (2) and (3) Beresford & Vives i Batlle suggested T1/2b can be described as:
T1=2b ¼
ln 2 CRorgdiet M 0:25 aI f1
(5)
The derived approach was subsequently tested against available data for T1/2b values in 17 different mammal species (with masses ranging over at least three orders of magnitude) for Co, Cs, I and Sr (Beresford and Vives I Batlle, 2013). It was found that all predictions were within a factor of five of the measured data with a slope on a linear regression between measured and observed values of 1.4 and an intercept which is not significantly different from zero. Whilst currently only proposed for homeothermic vertebrates, we are aware that allometric models for T1/2b, such as USDOE (2002), have been used to make predictions of radionuclide activity concentrations in reptiles and amphibians (e.g. Wood et al., 2009; Beresford et al., 2010; Yankovich et al., 2010a; Johansen et al., 2012). In this paper we evaluate the extent to which the approach developed by Beresford & Vives i Batlle for homeothermic vertebrates can be applied to reptiles as an example poikilothermic vertebrates. To achieve this, it was necessary to establish a database of quality-controlled T1/2b values for reptiles. 2. Critical review of T1/2b values for reptiles A critical review was undertaken to identify studies reporting either T1/2b values or elimination rate constants (k, (d1)) from which T1/2b (d) values could be estimated:
T1=2b ¼
ln 2 k
(6)
117
The review used Web of Knowledge and targeted searches of grey literature catalogues (e.g. the U.S. Department of Energy portal: http://www.osti.gov/scitech/). This identified eight references yielding a total of 117 whole-organism T1/2b values covering nine species and 11 elements. To enable comparison with the predictions from Equation (5) the identified studies also had to provide information on animal mass. As we were considering an approach to estimate radionuclide activity concentrations in organisms contaminated via ingestion, we rejected studies in which radionuclides had been administered by injection (Mayes et al. (1996) suggests that injected radionuclides may behave differently to those entering the organism via ingestion). Only studies meeting these two criteria were considered further. The final database contained 85 T1/2b values for seven species (Coluber constrictor, Elaphe obsoleta, Lampropeltis getulus, Masticophis flagellum, Natrix sipedon, Natrix taxispilota and Trachemys scripta scripta) and three elements (Cs, Ra and Sr) (see Supplementary Table 1, which also presents common species names). However, it was necessary to further evaluate the data prior to use. Scott et al. (1986) presented T1/2b values for Cs and Sr in T. scripta scripta placed in an open pond at the Savannah River site (USA). Hinton and Scott (1990) estimated seasonal values using data from the study initially reported by Scott et al. (1986) (Supplementary Table 1). However, each seasonal value appears to be based on only two measurements. We have therefore only used the overall T1/2b value calculated across the whole study period (c. 260 d), as initially reported by Scott et al. Hinton et al. (1992) presented Ra and Sr elimination rate data from a study of T. scripta scripta in an open pond at the Savannah River site. The animals were administered radioisotopes by oral gavage and whole-organism activity concentrations determined by live-monitoring 30 min, 2, 4, 5, 7, 11, 15, 30, 45 days after administration. Subsequently live-monitoring was conducted bi-monthly until 480 d after administration. Whilst the study included two levels of dietary calcium, the authors reported no significant effect of this on the elimination rates of Ra and Sr. Hinton et al. presented elimination rates for five time periods after administration (summer, autumn, winter, spring and summer-2) and also an annual mean. However, there are a number of anomalies in the resultant T1/2b values (see Supplementary Table 1). Seven T1/2b values, including examples for both Ra and Sr, are negative with a further being infinite (i.e. k ¼ 0); Hinton et al. acknowledge that the negative k values were not significantly different from zero. Furthermore, whilst it may be expected that Ra and Sr would behave similarly, the ‘seasonal’ patterns are inconsistent. From the information presented by Hinton et al., it would appear that the values for all but the first seasonal estimate are based on only two or three measurements. The estimate for the first season is based upon 9e10 measurements and, consequently, we have only considered data from this period. Hinton et al. also presented data for juveniles and hatchlings; we have not included these to remove any effect of age on our subsequent comparison of observed and predicted T1/2b values. The other data source within the final database is Staton et al. (1974). These authors presented radiocaesium data for six species of snake collected from the Savannah River site and offered an uncontaminated diet for a period of 63 d with live-monitoring being conducted at 7 d intervals. All of these data were used. Table 1 presents the T1/2b values used to compare with our subsequent predictions; data covered reptiles with masses ranging from 0.02 to 1.5 kg. We note that most of the estimated T1/2b values are longer than the length of the studies from which they were derived (see Table 1). For instance, the maximum radiocaesium half-life determined by Staton et al. (1974) for snakes from their
118
N.A. Beresford, M.D. Wood / Journal of Environmental Radioactivity 138 (2014) 116e121
Table 1 Measured T1/2b values used to compare to predicted values. Isotope
Latin name
Live mass (kg)
Study length (d)
Temp. ( C)
T1/2b (d)
137
Coluber constrictora,b Coluber constrictora,b Coluber constrictora,b Elaphe obsoletea,b Elaphe obsoletea,b Elaphe obsoletea,b Elaphe obsoletea,b Elaphe obsoletea,b Elaphe obsoletea,b Elaphe obsoletea,b Lampropeltis getulusa,b Lampropeltis getulusa,b Lampropeltis getulusa,b Masticophis flagelluma,b Natrix sipedona,b Natrix sipedona,b Natrix sipedona,b Natrix sipedona,b Natrix sipedona,b Natrix sipedona,b Natrix sipedona,b Natrix sipedona,b Natrix sipedona,b Natrix taxispilotaa,b Natrix taxispilotaa,b Natrix taxispilotaa,b Natrix taxispilotaa,b Trachemys scripta scriptab,c Trachemys scripta scriptab,c Trachemys scripta scriptac,d Trachemys scripta scriptac,d Trachemys scripta scriptac,d Trachemys scripta scriptac,d
3.88E-1 1.23E-1 5.99E-2 4.89E-1 5.95E-1 9.02E-1 1.03Eþ0 3.28E-1 7.32E-1 7.94E-1 7.53E-1 3.78E-1 3.19E-1 4.40E-1 3.38E-2 4.54E-2 3.01E-2 2.21E-2 2.74E-2 1.17E-1 4.18E-2 9.46E-2 3.16E-2 2.43E-1 5.50E-1 2.48E-1 6.68E-2 7.85E-1 7.85E-1 1.54Eþ0 6.10E-1 1.54Eþ0 6.10E-1
63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 260 260 c. 100 c. 100 c. 100 c. 100
24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 Overall Overall Summer Summer Summer Summer
2.15Eþ2e 1.37Eþ2e 4.56Eþ1e 2.50Eþ2e 1.43Eþ2e 4.30Eþ2e 1.00Eþ2e 8.60Eþ1e 6.40Eþ1e 2.15Eþ2e 1.77Eþ2e 8.60Eþ1e 6.54Eþ1e 1.08Eþ2e 3.86Eþ1e 3.81Eþ1e 5.88Eþ1e 4.01Eþ1e 7.92Eþ1e 1.88Eþ2e 4.86Eþ1e 1.12Eþ2e 2.37Eþ1e 1.77Eþ2e 2.74Eþ2e 1.43Eþ2e 1.25Eþ2e 6.40Eþ1f 3.65Eþ2f 1.39Eþ3g 8.66Eþ2g 8.66Eþ2g 2.67Eþ2g
90 85
Sr Sr
226
a b c d e f g
Cs
Ra
carnivorous. field contaminated. omnivorous. contaminated by oral gavage. Staton et al., 1974. Scott et al., 1986. Hinton et al., 1992.
63 d long study was 430 d. This will undoubtedly add some uncertainty to the estimated T1/2b values. Ambient temperature has a greater effect on the metabolic rate of reptiles than homeothermic animals. Litzgis and Hopkins (2003) report that a 10 C change in temperature will result in a change in the metabolic rate of reptiles by a factor ranging from 1.6 to 5.1. Staton et al. (1974) state a temperature for their study with snakes of 23e25 C. The other two studies for which we have used T1/2b data (Table 1) were conducted outdoors at the same location (Savannah River, Georgia) as the study of Staton et al. The National Oceanic and Atmospheric Administration data (http://www. weather.com/weather/wxclimatology/monthly/graph/USSC0003) for the Savannah River area suggest that typical average temperatures over the periods of the studies of Scott et al. (1986) and Hinton et al. (1992) would be in the range c. 10 Ce30 C. Therefore, we would expect the influence of temperature to have no more than a 4e10-fold effect across the measured data available.
mammals, as given in Beresford and Vives I Batlle (2013), to make predictions of the biological half-life of radionuclides in reptiles. Input values for Ra (not considered by Beresford & Vives i Batlle) were sourced from IAEA (2010) and Yankovich et al. (2010b) following the approach of Beresford & Vives i Batlle. With the exception of one value, all predictions were underestimates; in the case of Cs the underestimates were by 1e2 orders of magnitude (Fig. 1). There was comparatively less variation in predicted values for a given radionuclide than in the measured values. However, it is possible to source values for the constants in Equation (5) (i.e. f1, CRorg-diet and aI) which are more appropriate for reptiles. Nagy (2001) presented allometric equations for the dry matter intake (DMI) of reptiles (Table 2) from which values of aI for carnivorous reptiles (i.e. appropriate for snakes in Table 1) of 0.0067 can be estimated. There were no values directly appropriate for the turtle species (i.e. for omnivorous feeders or testudinata) presented by Nagy, although a generic reptile value of 0.0064 could be estimated. Values of f1 for reptiles of 0.25, 0.2 and 0.5 for Cs, Ra and Sr respectively have been published (Peters and Brisbin, 1996; Hinton et al., 1992; Hinton and Scott, 1990). Whilst it would be preferable to have CRmeat-diet or CRorg-diet values measured in reptiles these were not available. However, elemental concentrations in reptiles appear to be broadly similar to those in mammals (Yoshinaga et al., 1992) so we assumed that the mammal CRmeat-diet sourced from IAEA (2010) would be applicable to reptiles. To convert this to a CRorg-diet appropriate for reptiles we assumed that for Cs the wholeorganism activity concentration is the same as that in meat (Yankovich et al., 2010b). For radium we have assumed that the whole-organism activity concentration in turtles will be 12 times higher than that in meat (Wood et al., 2010). We note that the conversion from meat to whole-organism for Sr given in Wood et al. is questionable as it is derived from a short term study of Ca (Jeffree, 1991). Therefore, we have estimated a ratio of turtle wholeorganism to meat for Sr of 1070 from data presented by Yoshinaga et al. (1992) and Kienzle et al. (2006). The CRorg-diet values used were 0.39 for Cs for all reptiles and 2.12 and 23.6 for Ra and Sr respectively, the latter two being derived specifically for turtles. Predictions using these reptile specific parameters within Equation (5) are presented in Fig. 2. Predicted values are improved over those presented in Fig. 1. Values for Ra and Sr are now overestimated by a factor of 1.5e13. Predictions for radiocaesium are, with the exception of one prediction, within an order of magnitude of the measured data. As seen in Fig. 1, there is less variation in the predicted than measured values.
3. Predicting biological half-life using the Beresford & Vives i Batlle equation Given that the published allometric relationships for homeothermic vertebrates are being used to make predictions for reptiles (see above) initially we have used Equation (5) with parameters for
Fig. 1. A comparison of measured radionuclide biological half-life in reptiles with predictions using Equation (5) and parameters as presented in Beresford and Vives I Batlle (2013) for mammals.
N.A. Beresford, M.D. Wood / Journal of Environmental Radioactivity 138 (2014) 116e121 Table 2 Allometric constants describing daily dry matter intake for different groupings of reptiles adapted from Nagy (2001). Note that Nagy presents allometric relationships to predict DMI in g d1 from animal mass in g. Values of aI presented here predict daily intake in kg from animal mass in kg. To convert from the values of aI as presented by Nagy to those used here the following equation was used: ðaI 1000bI Þ=1000. Grouping
n
aI ðd kgbI Þ
bI
All reptiles All lizards Desert lizards Iguanian lizards Iguanidae Lacertidae Phrynosomatidae Scleroglossan Varanidae Carnivorous reptiles Herbivorous reptiles Insectivorous lizards
55 48 16 17 4 10 9 31 11 18 9 27
6.39E-03 7.40E-03 1.14E-02 6.33E-03 6.45E-03 2.45E-02 1.07E-03 7.56E-03 7.50E-03 6.70E-03 4.73E-03 6.02E-03
0.92 0.944 1.047 0.884 0.782 1.166 0.542 0.961 0.915 0.963 0.717 0.914
119
constants in Equation (5)) though there was less variation in the predicted values for Cs. Only one of the 33 predictions deviated by more than a factor of 6 from the measured value; a prediction of the Sr T1/2b in T. scripta scripta was predicted to be 14 times higher than the measured value. 5. Discussion
However, a number of authors have shown that the exponent on the allometric model for Br for poikilothermic reptiles is higher than that for homeothermic mammals (and birds). For reptiles exponents for field metabolic rate in the range c. 0.80e0.92 have been proposed (Nagy, 2005; Isaac and Carbone, 2010). Therefore, following the logic of Beresford & Vives i Batlle that the exponent for Equation (5) is (1 e the exponent describing Br), the exponent describing T1/2b for reptiles should be in the range 0.08e0.20. The exponents of allometric models for dry matter intake presented for reptiles (Table 2) should approximate to those for Br (Nagy, 2001). For snakes we used the value of aI for carnivorous reptiles and assumed an exponent for Equation (5) of 0.037 (i.e. 1e0.963). For turtles we used the values presented for all reptiles by Nagy (i.e. an exponent of 0.08 is assumed for Equation (5)). Fig. 3 presents predictions using reptile specific exponents and other inputs to Equation (5). Predictions were similar to those in Fig. 2 (where an exponent of 0.25 was used with reptile specific
We obtained relatively poor reptile T1/2b predictions using the equation to predict T1/2b as presented by Beresford and Vives I Batlle (2013) with constants derived from mammal data (Fig. 1). This demonstrates that existing models for homeothermic vertebrates (e.g. as presented in the RESRAD BIOTA model (USDOE, 2004)) should not be applied to reptiles and also likely amphibians. Reptile-specific parameters for the equation of Beresford & Vives i Batlle were relatively easy to derive, and using these, all predictions were within an order of magnitude of the measured values though there was a tendency for over-prediction. The only exception was the prediction for Sr in T. scripta scripta for which the predicted value was just over an order of magnitude higher than the measured value. Such a level of prediction would typically be thought to be acceptable using allometric models which are proposed to represent qualitative trends over orders of magnitude of body mass (Higley and Bytwerk, 2007). However, we acknowledge that there were few data available to compare with our predictions. Similarly, data available to parameterise the model were often limited. For instance, all of the f1 values used were for T. scripta scripta and no reptile-specific data were available for CRorg-diet. Within the wider literature discussing allometry, there is considerable discussion of the numeric value of the exponent (West et al., 1997; Hoppeler and Weibel, 2005; Isaac and Carbone, 2010; Agutter and Tuszynski, 2011). To compare the effect of the exponent used in Equation (5), Fig. 4 presents a comparison of the influence of different exponents over the mass range of living reptiles (from Wood et al., 2011). For this purpose, we have assumed that ln2/aIf1CRorg-diet equated to unity. The exponents compared are those of 0.037 (carnivorous reptiles) and 0.08 (‘all reptiles’), we have also included that used for homeotherms by Beresford & Vives i Batlle (i.e. 0.25). Over the seven-orders of magnitude mass range, the predicted biological half-lives for reptiles vary by less than a factor of 4 using an exponent of 0.08 and less that a factor of 2 using an exponent of 0.037. Therefore, there is little variation in predicted T1/2b with mass for reptiles. This is not the case for homeotherms, M0.25 predicting values varying approximately 60 fold over the mass range in Fig. 4.
Fig. 2. A comparison of measured radionuclide biological half-life in reptiles with predictions using Equation (5) and reptile specific values of f1 and CRorg-diet.
Fig. 3. A comparison of measured radionuclide biological half-life in reptiles with predictions using Equation (5) and reptile specific values for f1, CRorg-diet and bB.
4. Adapting the Beresford & Vives i Batlle equation for reptilian metabolic rate The exponent used in Equation (5) is derived for mammals based upon the allometric model presented by Kleiber (1947) where metabolic rate (Br) is described by:
Br ¼ aM 0:75
(7)
120
N.A. Beresford, M.D. Wood / Journal of Environmental Radioactivity 138 (2014) 116e121
Biological half-life data for Sr and Ra were all from T. scripta scripta and Nagy (2001) does not provide a DMI relationship for Testudinata species. It is perhaps questionable whether the DMI relationships derived from species without a shell are applicable to Testudinates, adding some uncertainty to the predictions for T. scripta scripta. 6. Conclusions
Fig. 4. A demonstration of the effect of the exponent (bB) used within Equation (5) assuming that ln2/aIf1CRorg-diet ¼ 1.
An assumption in this paper, and Beresford and Vives I Batlle (2013) for homeothermic species, is that T1/2b has an allometric relationship scaling to (1 e the exponent describing Br). However, USDOE (2002) present allometric relationships for some elements (Pu, Am, Ce, Eu and Th) which scale to circa 0.8. The reasons for this are unclear although Beresford & Vives i Batlle noted that none of these elements are essential. We are unable to confirm the relationships given in USDOE (2002) as the underlying data are not presented. We acknowledge that Nagy (2001) presented a wider range of allometeric parameters describing dry matter food intake for reptiles than we have used here. These were grouped by, for instance, feeding type or taxonomic family. The number of data used to derive some of these allometeric expressions was relatively small, some being based upon only 10 or less observations. The exponent for the allometric relationship presented by Nagy for some of the smaller datasets deviates from those used here, for instance the exponent for Phrynosomatidae is 0.542 (n ¼ 9) based upon a relatively small range in mass (3.2e52.5 g). Nagy advised against extrapolation outside the mass range of data used to derive the relationships he presents. Using the Phrynosomatidae relationship, within the mass range of data available to Nagy, the difference in predicted T1/2b to that using the ‘all reptile’ expression was approximately a factor of two only. If the group-specific expressions presented by Nagy were used to derive parameters for Equation (5), we recommend that the user does not apply them outside the mass range presented by Nagy (2001) and also takes into account the amount of data used to derive the parameters presented by Nagy. Nagy (2001) presented dry matter intake relationships for two groups for which the exponents (bI) are in excess of 1: Lacertidae (bI ¼ 1.166; n ¼ 10) and desert lizards (bI ¼ 1.047; n ¼ 16). Using the logic presented above this would result in negative exponents for biological half-life (0.166 and 0.047 respectively) and hence a predicted decrease in biological half-life with increasing mass. Though predicted biological half-lives would be within a factor of two of those estimated using the ‘all reptile’ expression over the mass ranges that are applicable for the Lacertidae (1.1e47.3 g) and desert lizard (2.6e167 g), this is does not appear to be logical. We suggest that in these instances the exponent for T1/2b is unlikely to be significantly different to 0 (implying no change in T1/2b with mass). Furthermore, we note that the compilations of allometric relationships for metabolic rate by Isaac and Carbone (2010) and Nagy (2005) do not give an exponent in excess of 1 for any reptile grouping.
Given the small influence of mass on T1/2b predictions for reptiles, if sufficient reported T1/2b values are available for a given element then it is likely that these would be applicable to any reptile. This is demonstrated by the data presented here for Cs. All of the 28 reported values of Cs T1/2b for reptiles, covering a 50-fold mass range (Table 1), are within a factor of 5 of the mean. However, the relatively good agreement between predicted and measured T1/2b in Fig. 3 demonstrates that if no reptile data are available for a given radionuclide then Equation (5) populated with reptile-specific parameter values will give reasonable estimates. Furthermore, the elements considered within this paper cover a range of biological behaviours. This suggests that the application of our model to other elements should be possible, accepting that there are currently some elements (i.e. Pu, Am, Ce, Eu and Th from USDOE (2002)) that do not appear to scale as expected. It should be possible to populate the equation to predict biological half-life as proposed by Beresford and Vives I Batlle (2013) (i.e. Equation (5) above) for other types of organism assuming that appropriate dry matter intake relationships, aI, f1 and CRorg-diet values are available. However, it is likely that such information may be sparse for some organisms. The approach derived here may also be relevant to the modelling of non-radioactive contaminants. Some approaches to assessing exposure of wildlife to non-radioactive contaminants use allometric expressions within their parameterisation (e.g. Sample and Suter, 1994). Acknowledgements The input of N.A. Beresford to this paper was funded by the EURATOM STAR Network of Excellence (Fission-2010-3.5.1269672) (www.star-radioecology.org) and that of M.D. Wood by a University of Salford Vice Chancellor's Research Scholarship. The reptile T1/2b database used here is being developed as part of the IAEA MODARIA programme's Working Group 8 activities (www-ns. iaea.org/projects/modaria) and will subsequently be made freely available. Appendix A. Supplementary data Supplementary data related to this article can be found at http:// dx.doi.org/10.1016/j.jenvrad.2014.08.012. References Agutter, P.S., Tuszynski, J.A., 2011. Analytic theories of allometric scaling. J. Exp. Biol. 214, 1055e1062. Avila, R., Beresford, N.A., Agüero, A., Broed, R., Brown, J., Iospje, M., Robles, B., ~ ez, A., 2004. Study of the uncertainty in estimation of the exposure of nonSuan human biota to ionizing radiation. J. Radiol. Prot. 24, A105eA122. Beresford, N.A., Broadley, M.R., Howard, B.J., Barnett, C.L., White, P.J., 2004. Estimating radionuclide transfer to wild species e data requirements and availability for terrestrial ecosystems. J. Radiol. Prot. 24, A89eA103. Beresford, N.A., Barnett, C.L., Brown, J., Cheng, J.-J., Copplestone, D., Filistovic, V., Hosseini, A., Howard, B.J., Jones, S.R., Kamboj, S., Kryshev, A., Nedveckaite, T., n, R., Sazykina, T., Vives i Batlle, J., Vives-Lynch, S., Olyslaegers, G., Saxe Yankovich, T., Yu, C., 2008. Inter-comparison of models to estimate radionuclide activity concentrations in non-human biota. Radiat. Environ. Biophys. 47, 491e514.
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Mayes, R.W., Beresford, N.A., Howard, B.J., Vandecasteele, C.M., Stakelum, G., 1996. The use of the true absorption coefficient as a measure of the bioavailability of radiocaesium in ruminants. Radiat. Environ. Biophys. 35, 101e109. Nagy, K.A., 2001. Food requirements of wild animals: predictive equations for freeliving mammals, reptiles and birds. Nutr. Abstr. Rev. 71, 21Re31R. Nagy, K.A., 2005. Field metabolic rate and body size. J. Exp. Biol. 208, 1627e1634. Peters, R.H., 1983. The Ecological Implications of Body Size. Cambridge University Press, Cambridge. Peters, E.L., Brisbin, I.L., 1996. Environmental influences on the 137Cs kinetics of the yellow-bellied turtle (Trachemys scripta). Ecol. Monogr. 66 (1), 115e136. Sample, B.E., Suter, G.W., 1994. Estimating Exposure of Terrestrial Wildlife to Contaminants. ES/ER/TM-125. Oak Ridge National Laboratory, Oak Ridge, Tennessee. Scott, D.E., Whicker, F.W., Gibbons, J.W., 1986. Effect of season on the retention of 137 Cs and 90Sr by the yellow-bellied slider turtle (Pseudemys scripta). Can. J. Zool. 64 (12), 2850e2853. Sheppard, S.C., 2001. Toxicants in the environment: bringing radioecology and chignac, F., Howard, B.J. (Eds.), Radioactive Polecotoxicology together. In: Bre lutants Impact on the Environment. EDP Sciences, France, pp. 63e74. Staton, M.A., Brisbin, I.L., Geiger, R.A., 1974. Some aspects of radiocesium retention in naturally contaminated captive snakes. Herpetologica 30, 204e211. Strand, P., Aono, T., Brown, J.E., Garnier-Laplace, J., Hosseini, A., Sazykina, T., Steenhuisen, F., Vives i Batlle, J., 2014. Assessment of Fukushima-derived radiation doses and effects on wildlife in Japan. Environ. Sci. Technol. Lett. 1, 198e203. United States Department of Energy (USDOE), 2002. A Graded Approach for Evaluating Radiation Doses to Aquatic and Terrestrial Biota. Technical Standard DOE-STD-1153e2002, Module 1e3. USDOE, Washington, DC. United States Department of Energy (USDOE), 2004. RESRAD-biota: a Tool for Implementing a Graded Approach to Biota Dose Evaluation. User's Guide, Version 1. United States Department of Energy Standard. DOE/EH-0676. ISCORS Technical Report 2004-02. USDOE, Washington, DC. West, G.B., Brown, J.H., Enquist, B.J., 1997. A general model for the origin of allometric scaling laws in biology. Science 276, 122e126. Wood, M.D., Beresford, N.A., Barnett, C.L., Copplestone, D., Leah, R.T., 2009. Assessing radiation impact at a protected coastal sand dune site: an intercomparison of models for estimating the radiological exposure of non-human biota. J. Environ. Radioact. 100, 1034e1052. Wood, M.D., Beresford, N.A., Howard, B.J., Copplestone, D., 2013. Evaluating summarised radionuclide concentration ratio datasets for wildlife. J. Environ. Radioact. 126, 314e325. Wood, M.D., Beresford, N.A., Semenov, D.V., Yankovich, T.L., Copplestone, D., 2010. Radionuclide transfer to reptiles. Radiat. Environ. Biophys. 49, 509e530. Wood, M.D., Beresford, N.A., Yankovich, T.L., Semenov, D.V., Copplestone, D., 2011. Addressing current knowledge gaps on radionuclide transfer to reptiles. Radioprotection 46 (6), S521eS527. Yankovich, T.L., Vives i Batlle, J., Vives-Lynch, S., Beresford, N.A., Barnett, C.L., Beaugelin-Seiller, K., Brown, J.E., Cheng, J.-J., Copplestone, D., Heling, R., Hosseini, A., Howard, B.J., Kamboj, S., Kryshev, A.I., Nedveckaite, T., Smith, J.T., Wood, M.D., 2010a. An International model validation exercise on radionuclide transfer and doses to freshwater biota. J. Radiol. Prot. 30, 299e340. Yankovich, T.L., Beresford, N.A., Wood, M., Aono, T., Andersson, P., Barnett, C.L., Bennett, P., Brown, J., Fesenko, S., Hosseini, A., Howard, B.J., Johansen, M., Phaneuf, M., Tagami, K., Takata, H., Twining, J., Uchida, S., 2010b. Whole-body to tissue concentration ratios for use in biota dose assessments for animals. Radiat. Environ. Biophys. 49, 549e565. Yoshinaga, J., Suzuki, T., Hongo, T., Minagawa, M., Ohtsuka, R., Kawabe, T., Inaoka, T., Akimichi, T., 1992. Mercury concentration correlates with the nitrogen stable isotope ratio in the animal food of Papuans. Ecotoxicol. Environ. Saf. 24, 37e45.
Contents lists available at ScienceDirect
Journal of Environmental Radioactivity journal homepage: www.elsevier.com/locate/jenvrad
A new simplified allometric approach for predicting the biological half-life of radionuclides in reptiles N.A. Beresford a, b, *, M.D. Wood b a b
Centre for Ecology & Hydrology, Bailrigg, Lancaster LA1 4AP, UK School of Environment & Life Sciences, University of Salford, Manchester M4 4WT, UK
a r t i c l e i n f o
a b s t r a c t
Article history: Received 27 June 2014 Received in revised form 21 August 2014 Accepted 22 August 2014 Available online
A major source of uncertainty in the estimation of radiation dose to wildlife is the prediction of internal radionuclide activity concentrations. Allometric (mass-dependent) relationships describing biological half-life (T1/2b) of radionuclides in organisms can be used to predict organism activity concentrations. The establishment of allometric expressions requires experimental data which are often lacking. An approach to predict the T1/2b in homeothermic vertebrates has recently been proposed. In this paper we have adapted this to be applicable to reptiles. For Cs, Ra and Sr, over a mass range of 0.02e1.5 kg, resultant predictions were generally within a factor of 6 of reported values demonstrating that the approach can be used when measured T1/2b data are lacking. However, the effect of mass on reptilian radionuclide T1/2b is minimal. If sufficient measured data are available for a given radionuclide then it is likely that these would give a reasonable estimate of T1/2b in any reptile species. © 2014 Elsevier Ltd. All rights reserved.
Keywords: Reptile Biological half-life Allometry Radionuclide
1. Introduction It has been well-documented that a significant source of uncertainty in the estimation of the exposure of wildlife to ionising radiation is the estimation of organism radionuclide activity concentrations (Avila et al., 2004; Higley et al., 2003a; Beresford et al., 2008, 2010; Johansen et al., 2012; Yankovich et al., 2010a). Often organism activity concentrations are estimated using a simple concentration ratio relating the whole-organism activity concentration to the activity concentration in the appropriate environmental medium (typically soil for terrestrial ecosystems and water for aquatic ecosystems) (CRwo-media) (Howard et al., 2013). However, this ratio is largely dependent upon site characteristics and hence can be highly variable for a given radionuclide e organism combination (e.g. Wood et al., 2013). Alternative approaches to the use of CRwo-media have been considered (Beresford et al., 2004, 2013) including the use of allometric relationships to estimate radionuclide intake and biological half-life (T1/2b) and hence wholeorganism activity concentrations (Beresford and Vives I Batlle, 2013; Higley et al., 2003b). The application of allometric relationships in radiological environmental (wildlife) assessment models was originally proposed to address the lack of CRwo-media values
* Corresponding author. Centre for Ecology & Hydrology, Bailrigg, Lancaster LA1 4AP, UK. Tel.: þ44 1524 595856. E-mail address: [email protected] (N.A. Beresford). http://dx.doi.org/10.1016/j.jenvrad.2014.08.012 0265-931X/© 2014 Elsevier Ltd. All rights reserved.
(Higley et al., 2003b). The application of such kinetic-allometric models has the advantage that, if required, non-equilibrium activity concentrations in organisms can be estimated and such models are the advised approach for higher level assessments in some methodologies (USDOE, 2002). For example, non-equilibrium estimates may be needed for the assessment of fluctuating discharge rates from nuclear facilities or acute accidental releases of radionuclides to the environment, such as in the case of the Fukushima accident (Strand et al., 2014). Allometric scaling relates body mass (M) to a specific biological parameter (Y) (Peters, 1983):
Y ¼ aM b
(1)
where a and b (the allometric exponent) are constants. With respect to radionuclide biological half-life, allometric constants for 9 radionuclides (Cs, Co, H, Ra, Sb, Sr, U, Zn and Zr) have been presented where the allometric exponent (i.e. b) approximates to 0.25 (USDOE, 2002; Galeriu et al., 2003); information presented by MacDonald (1996) suggests this will also be the case for I. This is in agreement with allometric relationships for many other biological parameters, including metabolic rate (referred to as Kleiber's Law) (Kleiber, 1932), which scale to quartile values. As demonstrated by Beresford and Vives I Batlle (2013) an exponent of 0.25 for radionuclide biological half-life is explainable from Kleiber's Law. Hence T1/2b can be described as:
N.A. Beresford, M.D. Wood / Journal of Environmental Radioactivity 138 (2014) 116e121
T1=2b ¼ aB M 0:25
(2)
Where M is mass (kg) and aB is the multiplicand (d kg0.25). Sheppard (2001) suggested that if it can be assumed that bB (i.e. the exponent for the biological half-life allometric expression) will approximate to the same value for all elements then only an estimation of the multiplicand (i.e. aB) is required for any given element for which an allometric relationship has not been derived from empirical data. However, until recently, no method was available for estimating the multiplicand when data to fit an allometric relationship are lacking. Through algebraic derivation Beresford and Vives I Batlle (2013) proposed that the multiplicand for the allometric relationship describing radionuclide biological half-life (aB) could be estimated as:
aB ¼
ln 2 CRorgdiet aI f1
(3)
Where f1 is the fractional gastrointestinal absorption coefficient for a given element, CRorg-diet is the ratio between the activity concentrations in the whole-organism (fresh mass) and the diet (dry matter, DM), and aI is the multiplicand in the allometric model describing the dry matter intake rate of food (Ir, kg (DM) d1). CRorgdiet was assumed to be constant across all species (Beresford et al., 2004; IAEA, 2010). The allometric relationship for Ir in homeotherms approximates to:
Ir ¼ aI M 0:75
(4)
with values of aI being relatively well-documented for terrestrial vertebrates (e.g. Nagy, 2001). From Equations (2) and (3) Beresford & Vives i Batlle suggested T1/2b can be described as:
T1=2b ¼
ln 2 CRorgdiet M 0:25 aI f1
(5)
The derived approach was subsequently tested against available data for T1/2b values in 17 different mammal species (with masses ranging over at least three orders of magnitude) for Co, Cs, I and Sr (Beresford and Vives I Batlle, 2013). It was found that all predictions were within a factor of five of the measured data with a slope on a linear regression between measured and observed values of 1.4 and an intercept which is not significantly different from zero. Whilst currently only proposed for homeothermic vertebrates, we are aware that allometric models for T1/2b, such as USDOE (2002), have been used to make predictions of radionuclide activity concentrations in reptiles and amphibians (e.g. Wood et al., 2009; Beresford et al., 2010; Yankovich et al., 2010a; Johansen et al., 2012). In this paper we evaluate the extent to which the approach developed by Beresford & Vives i Batlle for homeothermic vertebrates can be applied to reptiles as an example poikilothermic vertebrates. To achieve this, it was necessary to establish a database of quality-controlled T1/2b values for reptiles. 2. Critical review of T1/2b values for reptiles A critical review was undertaken to identify studies reporting either T1/2b values or elimination rate constants (k, (d1)) from which T1/2b (d) values could be estimated:
T1=2b ¼
ln 2 k
(6)
117
The review used Web of Knowledge and targeted searches of grey literature catalogues (e.g. the U.S. Department of Energy portal: http://www.osti.gov/scitech/). This identified eight references yielding a total of 117 whole-organism T1/2b values covering nine species and 11 elements. To enable comparison with the predictions from Equation (5) the identified studies also had to provide information on animal mass. As we were considering an approach to estimate radionuclide activity concentrations in organisms contaminated via ingestion, we rejected studies in which radionuclides had been administered by injection (Mayes et al. (1996) suggests that injected radionuclides may behave differently to those entering the organism via ingestion). Only studies meeting these two criteria were considered further. The final database contained 85 T1/2b values for seven species (Coluber constrictor, Elaphe obsoleta, Lampropeltis getulus, Masticophis flagellum, Natrix sipedon, Natrix taxispilota and Trachemys scripta scripta) and three elements (Cs, Ra and Sr) (see Supplementary Table 1, which also presents common species names). However, it was necessary to further evaluate the data prior to use. Scott et al. (1986) presented T1/2b values for Cs and Sr in T. scripta scripta placed in an open pond at the Savannah River site (USA). Hinton and Scott (1990) estimated seasonal values using data from the study initially reported by Scott et al. (1986) (Supplementary Table 1). However, each seasonal value appears to be based on only two measurements. We have therefore only used the overall T1/2b value calculated across the whole study period (c. 260 d), as initially reported by Scott et al. Hinton et al. (1992) presented Ra and Sr elimination rate data from a study of T. scripta scripta in an open pond at the Savannah River site. The animals were administered radioisotopes by oral gavage and whole-organism activity concentrations determined by live-monitoring 30 min, 2, 4, 5, 7, 11, 15, 30, 45 days after administration. Subsequently live-monitoring was conducted bi-monthly until 480 d after administration. Whilst the study included two levels of dietary calcium, the authors reported no significant effect of this on the elimination rates of Ra and Sr. Hinton et al. presented elimination rates for five time periods after administration (summer, autumn, winter, spring and summer-2) and also an annual mean. However, there are a number of anomalies in the resultant T1/2b values (see Supplementary Table 1). Seven T1/2b values, including examples for both Ra and Sr, are negative with a further being infinite (i.e. k ¼ 0); Hinton et al. acknowledge that the negative k values were not significantly different from zero. Furthermore, whilst it may be expected that Ra and Sr would behave similarly, the ‘seasonal’ patterns are inconsistent. From the information presented by Hinton et al., it would appear that the values for all but the first seasonal estimate are based on only two or three measurements. The estimate for the first season is based upon 9e10 measurements and, consequently, we have only considered data from this period. Hinton et al. also presented data for juveniles and hatchlings; we have not included these to remove any effect of age on our subsequent comparison of observed and predicted T1/2b values. The other data source within the final database is Staton et al. (1974). These authors presented radiocaesium data for six species of snake collected from the Savannah River site and offered an uncontaminated diet for a period of 63 d with live-monitoring being conducted at 7 d intervals. All of these data were used. Table 1 presents the T1/2b values used to compare with our subsequent predictions; data covered reptiles with masses ranging from 0.02 to 1.5 kg. We note that most of the estimated T1/2b values are longer than the length of the studies from which they were derived (see Table 1). For instance, the maximum radiocaesium half-life determined by Staton et al. (1974) for snakes from their
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N.A. Beresford, M.D. Wood / Journal of Environmental Radioactivity 138 (2014) 116e121
Table 1 Measured T1/2b values used to compare to predicted values. Isotope
Latin name
Live mass (kg)
Study length (d)
Temp. ( C)
T1/2b (d)
137
Coluber constrictora,b Coluber constrictora,b Coluber constrictora,b Elaphe obsoletea,b Elaphe obsoletea,b Elaphe obsoletea,b Elaphe obsoletea,b Elaphe obsoletea,b Elaphe obsoletea,b Elaphe obsoletea,b Lampropeltis getulusa,b Lampropeltis getulusa,b Lampropeltis getulusa,b Masticophis flagelluma,b Natrix sipedona,b Natrix sipedona,b Natrix sipedona,b Natrix sipedona,b Natrix sipedona,b Natrix sipedona,b Natrix sipedona,b Natrix sipedona,b Natrix sipedona,b Natrix taxispilotaa,b Natrix taxispilotaa,b Natrix taxispilotaa,b Natrix taxispilotaa,b Trachemys scripta scriptab,c Trachemys scripta scriptab,c Trachemys scripta scriptac,d Trachemys scripta scriptac,d Trachemys scripta scriptac,d Trachemys scripta scriptac,d
3.88E-1 1.23E-1 5.99E-2 4.89E-1 5.95E-1 9.02E-1 1.03Eþ0 3.28E-1 7.32E-1 7.94E-1 7.53E-1 3.78E-1 3.19E-1 4.40E-1 3.38E-2 4.54E-2 3.01E-2 2.21E-2 2.74E-2 1.17E-1 4.18E-2 9.46E-2 3.16E-2 2.43E-1 5.50E-1 2.48E-1 6.68E-2 7.85E-1 7.85E-1 1.54Eþ0 6.10E-1 1.54Eþ0 6.10E-1
63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 260 260 c. 100 c. 100 c. 100 c. 100
24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 Overall Overall Summer Summer Summer Summer
2.15Eþ2e 1.37Eþ2e 4.56Eþ1e 2.50Eþ2e 1.43Eþ2e 4.30Eþ2e 1.00Eþ2e 8.60Eþ1e 6.40Eþ1e 2.15Eþ2e 1.77Eþ2e 8.60Eþ1e 6.54Eþ1e 1.08Eþ2e 3.86Eþ1e 3.81Eþ1e 5.88Eþ1e 4.01Eþ1e 7.92Eþ1e 1.88Eþ2e 4.86Eþ1e 1.12Eþ2e 2.37Eþ1e 1.77Eþ2e 2.74Eþ2e 1.43Eþ2e 1.25Eþ2e 6.40Eþ1f 3.65Eþ2f 1.39Eþ3g 8.66Eþ2g 8.66Eþ2g 2.67Eþ2g
90 85
Sr Sr
226
a b c d e f g
Cs
Ra
carnivorous. field contaminated. omnivorous. contaminated by oral gavage. Staton et al., 1974. Scott et al., 1986. Hinton et al., 1992.
63 d long study was 430 d. This will undoubtedly add some uncertainty to the estimated T1/2b values. Ambient temperature has a greater effect on the metabolic rate of reptiles than homeothermic animals. Litzgis and Hopkins (2003) report that a 10 C change in temperature will result in a change in the metabolic rate of reptiles by a factor ranging from 1.6 to 5.1. Staton et al. (1974) state a temperature for their study with snakes of 23e25 C. The other two studies for which we have used T1/2b data (Table 1) were conducted outdoors at the same location (Savannah River, Georgia) as the study of Staton et al. The National Oceanic and Atmospheric Administration data (http://www. weather.com/weather/wxclimatology/monthly/graph/USSC0003) for the Savannah River area suggest that typical average temperatures over the periods of the studies of Scott et al. (1986) and Hinton et al. (1992) would be in the range c. 10 Ce30 C. Therefore, we would expect the influence of temperature to have no more than a 4e10-fold effect across the measured data available.
mammals, as given in Beresford and Vives I Batlle (2013), to make predictions of the biological half-life of radionuclides in reptiles. Input values for Ra (not considered by Beresford & Vives i Batlle) were sourced from IAEA (2010) and Yankovich et al. (2010b) following the approach of Beresford & Vives i Batlle. With the exception of one value, all predictions were underestimates; in the case of Cs the underestimates were by 1e2 orders of magnitude (Fig. 1). There was comparatively less variation in predicted values for a given radionuclide than in the measured values. However, it is possible to source values for the constants in Equation (5) (i.e. f1, CRorg-diet and aI) which are more appropriate for reptiles. Nagy (2001) presented allometric equations for the dry matter intake (DMI) of reptiles (Table 2) from which values of aI for carnivorous reptiles (i.e. appropriate for snakes in Table 1) of 0.0067 can be estimated. There were no values directly appropriate for the turtle species (i.e. for omnivorous feeders or testudinata) presented by Nagy, although a generic reptile value of 0.0064 could be estimated. Values of f1 for reptiles of 0.25, 0.2 and 0.5 for Cs, Ra and Sr respectively have been published (Peters and Brisbin, 1996; Hinton et al., 1992; Hinton and Scott, 1990). Whilst it would be preferable to have CRmeat-diet or CRorg-diet values measured in reptiles these were not available. However, elemental concentrations in reptiles appear to be broadly similar to those in mammals (Yoshinaga et al., 1992) so we assumed that the mammal CRmeat-diet sourced from IAEA (2010) would be applicable to reptiles. To convert this to a CRorg-diet appropriate for reptiles we assumed that for Cs the wholeorganism activity concentration is the same as that in meat (Yankovich et al., 2010b). For radium we have assumed that the whole-organism activity concentration in turtles will be 12 times higher than that in meat (Wood et al., 2010). We note that the conversion from meat to whole-organism for Sr given in Wood et al. is questionable as it is derived from a short term study of Ca (Jeffree, 1991). Therefore, we have estimated a ratio of turtle wholeorganism to meat for Sr of 1070 from data presented by Yoshinaga et al. (1992) and Kienzle et al. (2006). The CRorg-diet values used were 0.39 for Cs for all reptiles and 2.12 and 23.6 for Ra and Sr respectively, the latter two being derived specifically for turtles. Predictions using these reptile specific parameters within Equation (5) are presented in Fig. 2. Predicted values are improved over those presented in Fig. 1. Values for Ra and Sr are now overestimated by a factor of 1.5e13. Predictions for radiocaesium are, with the exception of one prediction, within an order of magnitude of the measured data. As seen in Fig. 1, there is less variation in the predicted than measured values.
3. Predicting biological half-life using the Beresford & Vives i Batlle equation Given that the published allometric relationships for homeothermic vertebrates are being used to make predictions for reptiles (see above) initially we have used Equation (5) with parameters for
Fig. 1. A comparison of measured radionuclide biological half-life in reptiles with predictions using Equation (5) and parameters as presented in Beresford and Vives I Batlle (2013) for mammals.
N.A. Beresford, M.D. Wood / Journal of Environmental Radioactivity 138 (2014) 116e121 Table 2 Allometric constants describing daily dry matter intake for different groupings of reptiles adapted from Nagy (2001). Note that Nagy presents allometric relationships to predict DMI in g d1 from animal mass in g. Values of aI presented here predict daily intake in kg from animal mass in kg. To convert from the values of aI as presented by Nagy to those used here the following equation was used: ðaI 1000bI Þ=1000. Grouping
n
aI ðd kgbI Þ
bI
All reptiles All lizards Desert lizards Iguanian lizards Iguanidae Lacertidae Phrynosomatidae Scleroglossan Varanidae Carnivorous reptiles Herbivorous reptiles Insectivorous lizards
55 48 16 17 4 10 9 31 11 18 9 27
6.39E-03 7.40E-03 1.14E-02 6.33E-03 6.45E-03 2.45E-02 1.07E-03 7.56E-03 7.50E-03 6.70E-03 4.73E-03 6.02E-03
0.92 0.944 1.047 0.884 0.782 1.166 0.542 0.961 0.915 0.963 0.717 0.914
119
constants in Equation (5)) though there was less variation in the predicted values for Cs. Only one of the 33 predictions deviated by more than a factor of 6 from the measured value; a prediction of the Sr T1/2b in T. scripta scripta was predicted to be 14 times higher than the measured value. 5. Discussion
However, a number of authors have shown that the exponent on the allometric model for Br for poikilothermic reptiles is higher than that for homeothermic mammals (and birds). For reptiles exponents for field metabolic rate in the range c. 0.80e0.92 have been proposed (Nagy, 2005; Isaac and Carbone, 2010). Therefore, following the logic of Beresford & Vives i Batlle that the exponent for Equation (5) is (1 e the exponent describing Br), the exponent describing T1/2b for reptiles should be in the range 0.08e0.20. The exponents of allometric models for dry matter intake presented for reptiles (Table 2) should approximate to those for Br (Nagy, 2001). For snakes we used the value of aI for carnivorous reptiles and assumed an exponent for Equation (5) of 0.037 (i.e. 1e0.963). For turtles we used the values presented for all reptiles by Nagy (i.e. an exponent of 0.08 is assumed for Equation (5)). Fig. 3 presents predictions using reptile specific exponents and other inputs to Equation (5). Predictions were similar to those in Fig. 2 (where an exponent of 0.25 was used with reptile specific
We obtained relatively poor reptile T1/2b predictions using the equation to predict T1/2b as presented by Beresford and Vives I Batlle (2013) with constants derived from mammal data (Fig. 1). This demonstrates that existing models for homeothermic vertebrates (e.g. as presented in the RESRAD BIOTA model (USDOE, 2004)) should not be applied to reptiles and also likely amphibians. Reptile-specific parameters for the equation of Beresford & Vives i Batlle were relatively easy to derive, and using these, all predictions were within an order of magnitude of the measured values though there was a tendency for over-prediction. The only exception was the prediction for Sr in T. scripta scripta for which the predicted value was just over an order of magnitude higher than the measured value. Such a level of prediction would typically be thought to be acceptable using allometric models which are proposed to represent qualitative trends over orders of magnitude of body mass (Higley and Bytwerk, 2007). However, we acknowledge that there were few data available to compare with our predictions. Similarly, data available to parameterise the model were often limited. For instance, all of the f1 values used were for T. scripta scripta and no reptile-specific data were available for CRorg-diet. Within the wider literature discussing allometry, there is considerable discussion of the numeric value of the exponent (West et al., 1997; Hoppeler and Weibel, 2005; Isaac and Carbone, 2010; Agutter and Tuszynski, 2011). To compare the effect of the exponent used in Equation (5), Fig. 4 presents a comparison of the influence of different exponents over the mass range of living reptiles (from Wood et al., 2011). For this purpose, we have assumed that ln2/aIf1CRorg-diet equated to unity. The exponents compared are those of 0.037 (carnivorous reptiles) and 0.08 (‘all reptiles’), we have also included that used for homeotherms by Beresford & Vives i Batlle (i.e. 0.25). Over the seven-orders of magnitude mass range, the predicted biological half-lives for reptiles vary by less than a factor of 4 using an exponent of 0.08 and less that a factor of 2 using an exponent of 0.037. Therefore, there is little variation in predicted T1/2b with mass for reptiles. This is not the case for homeotherms, M0.25 predicting values varying approximately 60 fold over the mass range in Fig. 4.
Fig. 2. A comparison of measured radionuclide biological half-life in reptiles with predictions using Equation (5) and reptile specific values of f1 and CRorg-diet.
Fig. 3. A comparison of measured radionuclide biological half-life in reptiles with predictions using Equation (5) and reptile specific values for f1, CRorg-diet and bB.
4. Adapting the Beresford & Vives i Batlle equation for reptilian metabolic rate The exponent used in Equation (5) is derived for mammals based upon the allometric model presented by Kleiber (1947) where metabolic rate (Br) is described by:
Br ¼ aM 0:75
(7)
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Biological half-life data for Sr and Ra were all from T. scripta scripta and Nagy (2001) does not provide a DMI relationship for Testudinata species. It is perhaps questionable whether the DMI relationships derived from species without a shell are applicable to Testudinates, adding some uncertainty to the predictions for T. scripta scripta. 6. Conclusions
Fig. 4. A demonstration of the effect of the exponent (bB) used within Equation (5) assuming that ln2/aIf1CRorg-diet ¼ 1.
An assumption in this paper, and Beresford and Vives I Batlle (2013) for homeothermic species, is that T1/2b has an allometric relationship scaling to (1 e the exponent describing Br). However, USDOE (2002) present allometric relationships for some elements (Pu, Am, Ce, Eu and Th) which scale to circa 0.8. The reasons for this are unclear although Beresford & Vives i Batlle noted that none of these elements are essential. We are unable to confirm the relationships given in USDOE (2002) as the underlying data are not presented. We acknowledge that Nagy (2001) presented a wider range of allometeric parameters describing dry matter food intake for reptiles than we have used here. These were grouped by, for instance, feeding type or taxonomic family. The number of data used to derive some of these allometeric expressions was relatively small, some being based upon only 10 or less observations. The exponent for the allometric relationship presented by Nagy for some of the smaller datasets deviates from those used here, for instance the exponent for Phrynosomatidae is 0.542 (n ¼ 9) based upon a relatively small range in mass (3.2e52.5 g). Nagy advised against extrapolation outside the mass range of data used to derive the relationships he presents. Using the Phrynosomatidae relationship, within the mass range of data available to Nagy, the difference in predicted T1/2b to that using the ‘all reptile’ expression was approximately a factor of two only. If the group-specific expressions presented by Nagy were used to derive parameters for Equation (5), we recommend that the user does not apply them outside the mass range presented by Nagy (2001) and also takes into account the amount of data used to derive the parameters presented by Nagy. Nagy (2001) presented dry matter intake relationships for two groups for which the exponents (bI) are in excess of 1: Lacertidae (bI ¼ 1.166; n ¼ 10) and desert lizards (bI ¼ 1.047; n ¼ 16). Using the logic presented above this would result in negative exponents for biological half-life (0.166 and 0.047 respectively) and hence a predicted decrease in biological half-life with increasing mass. Though predicted biological half-lives would be within a factor of two of those estimated using the ‘all reptile’ expression over the mass ranges that are applicable for the Lacertidae (1.1e47.3 g) and desert lizard (2.6e167 g), this is does not appear to be logical. We suggest that in these instances the exponent for T1/2b is unlikely to be significantly different to 0 (implying no change in T1/2b with mass). Furthermore, we note that the compilations of allometric relationships for metabolic rate by Isaac and Carbone (2010) and Nagy (2005) do not give an exponent in excess of 1 for any reptile grouping.
Given the small influence of mass on T1/2b predictions for reptiles, if sufficient reported T1/2b values are available for a given element then it is likely that these would be applicable to any reptile. This is demonstrated by the data presented here for Cs. All of the 28 reported values of Cs T1/2b for reptiles, covering a 50-fold mass range (Table 1), are within a factor of 5 of the mean. However, the relatively good agreement between predicted and measured T1/2b in Fig. 3 demonstrates that if no reptile data are available for a given radionuclide then Equation (5) populated with reptile-specific parameter values will give reasonable estimates. Furthermore, the elements considered within this paper cover a range of biological behaviours. This suggests that the application of our model to other elements should be possible, accepting that there are currently some elements (i.e. Pu, Am, Ce, Eu and Th from USDOE (2002)) that do not appear to scale as expected. It should be possible to populate the equation to predict biological half-life as proposed by Beresford and Vives I Batlle (2013) (i.e. Equation (5) above) for other types of organism assuming that appropriate dry matter intake relationships, aI, f1 and CRorg-diet values are available. However, it is likely that such information may be sparse for some organisms. The approach derived here may also be relevant to the modelling of non-radioactive contaminants. Some approaches to assessing exposure of wildlife to non-radioactive contaminants use allometric expressions within their parameterisation (e.g. Sample and Suter, 1994). Acknowledgements The input of N.A. Beresford to this paper was funded by the EURATOM STAR Network of Excellence (Fission-2010-3.5.1269672) (www.star-radioecology.org) and that of M.D. Wood by a University of Salford Vice Chancellor's Research Scholarship. The reptile T1/2b database used here is being developed as part of the IAEA MODARIA programme's Working Group 8 activities (www-ns. iaea.org/projects/modaria) and will subsequently be made freely available. Appendix A. Supplementary data Supplementary data related to this article can be found at http:// dx.doi.org/10.1016/j.jenvrad.2014.08.012. References Agutter, P.S., Tuszynski, J.A., 2011. Analytic theories of allometric scaling. J. Exp. Biol. 214, 1055e1062. Avila, R., Beresford, N.A., Agüero, A., Broed, R., Brown, J., Iospje, M., Robles, B., ~ ez, A., 2004. Study of the uncertainty in estimation of the exposure of nonSuan human biota to ionizing radiation. J. Radiol. Prot. 24, A105eA122. Beresford, N.A., Broadley, M.R., Howard, B.J., Barnett, C.L., White, P.J., 2004. Estimating radionuclide transfer to wild species e data requirements and availability for terrestrial ecosystems. J. Radiol. Prot. 24, A89eA103. Beresford, N.A., Barnett, C.L., Brown, J., Cheng, J.-J., Copplestone, D., Filistovic, V., Hosseini, A., Howard, B.J., Jones, S.R., Kamboj, S., Kryshev, A., Nedveckaite, T., n, R., Sazykina, T., Vives i Batlle, J., Vives-Lynch, S., Olyslaegers, G., Saxe Yankovich, T., Yu, C., 2008. Inter-comparison of models to estimate radionuclide activity concentrations in non-human biota. Radiat. Environ. Biophys. 47, 491e514.
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