Estimating transfer parameters in the absence of data

The calculation of transfer of radionuclides from the abiotic to the biotic environment is a well-established practice in radiological assessments. Concentration ratios provide simple means to estimate radionuclide activity in biota, from measured (or estimated) radionuclide concentrations in either a food source or an abiotic component such as soil or water. They are typically reported by element, and data compilations may include information such as soil type (e.g., sand, loam, clay) and species. The data may be for multiple species at a single location, single species at multiple locations, or represent compilations from multiple sources. Recently published guidance suggests that estimates are best made using data from the same ecosystem. This paper examines this recent guidance, in the context of using measured data from within a single ecosystem and comparing results to more generic values. Results suggest that generic values may be an adequate substitute for site-specific information. It illustrates how ionic potential may be used as an alternative to group chemical properties in estimating transfer factors. Lastly, limited evidence is found to support the concept of allometric scaling functions for elemental concentrations in plants.     

Evaluating scaling models in biology using hierarchical Bayesian approaches

Theoretical models for allometric relationships between organismal form and function are typically tested by comparing a single predicted relationship with empirical data. Several prominent models, however, predict more than one allometric relationship, and comparisons among alternative models have not taken this into account. Here we evaluate several different scaling models of plant morphology within a hierarchical Bayesian framework that simultaneously fits multiple scaling relationships to three large allometric datasets. The scaling models include: inflexible universal models derived from biophysical assumptions (e.g. elastic similarity or fractal networks), a flexible variation of a fractal network model, and a highly flexible model constrained only by basic algebraic relationships. We demonstrate that variation in intraspecific allometric scaling exponents is inconsistent with the universal models, and that more flexible approaches that allow for biological variability at the species level outperform universal models, even when accounting for relative increases in model complexity.     

Inter-comparison of models to estimate radionuclide activity concentrations in non-human biota

A number of models have recently been, or are currently being, developed to enable the assessment of radiation doses from ionising radiation to non-human species. A key component of these models is the ability to predict whole-organism activity concentrations in a wide range of wildlife. In this paper, we compare the whole-organism activity concentrations predicted by eight models participating within the IAEA Environmental Modelling for Radiation Safety programme for a range of radionuclides to terrestrial and freshwater organisms. In many instances, there was considerable variation, ranging over orders of magnitude, between the predictions of the different models. Reasons for this variability (including methodology, data source and data availability) are identified and discussed. The active participation of groups responsible for the development of key models within this exercise is a useful step forward in providing the transparency in methodology and data provenance required for models which are either currently being used for regulatory purposes or which may be used in the future. The work reported in this paper, and supported by other findings, demonstrates that the largest contribution to variability between model predictions is the parameterisation of their transfer components. There is a clear need to focus efforts and provide authoritative compilations of those data which are available.     

Can elemental composition data of crop leaves be used to estimate radionuclide transfer to tree leaves?

Estimation of radionuclide concentrations in trees may be required to estimate their radiation exposure. However, concentration ratios of radionuclides from soil to tree species are limited for many radionuclide-tree combinations. To fill this gap, it is investigated in the present paper whether stable element concentration data for leafy vegetables are representative of those for wild tree leaves, and consequently, if these stable element data for leafy vegetables can be used as analogues to describe radionuclides transfer from soil to trees. Data for stable elements in leafy vegetables collected in Japan were compared with those in leaves of about 20 tree species worldwide. The correlation coefficients of element concentrations between leafy vegetables and tree leaves were higher than 0.90 with p < 0.001 by Student’s t test, and geometric means of concentration data for most elements were within the range of data for leafy vegetables. Thus, transfer parameters derived from stable element data for leafy vegetables could generally be used to estimate concentrations in tree leaves if data for the latter are not available. However, some trees accumulate a few elements (e.g., Al, Co, Mn and Si) in their leaves to higher concentrations than observed for leafy vegetables.     

Testing metabolic scaling theory using intraspecific allometries in Antarctic microarthropods

Quantitative scaling relationships among body mass, temperature and metabolic rate of organisms are still controversial, while resolution may be further complicated through the use of different and possibly inappropriate approaches to statistical analysis. We propose the application of a modelling strategy based on the theoretical approach of Akaike's information criteria and non‐linear model fitting (nlm). Accordingly, we collated and modelled available data at intraspecific level on the individual standard metabolic rate of Antarctic microarthropods as a function of body mass (M), temperature (T), species identity (S) and high rank taxa to which species belong (G) and tested predictions from metabolic scaling theory (mass‐metabolism allometric exponent b = 0.75, activation energy range 0.2–1.2 eV). We also performed allometric analysis based on logarithmic transformations (lm). Conclusions from lm and nlm approaches were different. Best‐supported models from lm incorporated T, M and S. The estimates of the allometric scaling exponent linking body mass and metabolic rate resulted in a value of 0.696 ± 0.105 (mean ± 95% CI). In contrast, the four best‐supported nlm models suggested that both the scaling exponent and activation energy significantly vary across the high rank taxa (Collembola, Cryptostigmata, Mesostigmata and Prostigmata) to which species belong, with mean values of b ranging from about 0.6 to 0.8. We therefore reached two conclusions: 1, published analyses of arthropod metabolism based on logarithmic data may be biased by data transformation; 2, non‐linear models applied to Antarctic microarthropod metabolic rate suggest that intraspecific scaling of standard metabolic rate in Antarctic microarthropods is highly variable and can be characterised by scaling exponents that greatly vary within taxa, which may have biased previous interspecific comparisons that neglected intraspecific variability.     

Using the Past to Predict the Present: Confidence Intervals for Regression Equations in Phylogenetic Comparative Methods

Two phylogenetic comparative methods, independent contrasts and generalized least squares models, can be used to determine the statistical relationship between two or more traits. We show that the two approaches are functionally identical and that either can be used to make statistical inferences about values at internal nodes of a phylogenetic tree (hypothetical ancestors), to estimate relationships between characters, and to predict values for unmeasured species. Regression equations derived from independent contrasts can be placed back onto the original data space, including computation of both confidence intervals and prediction intervals for new observations. Predictions for unmeasured species (including extinct forms) can be made increasingly accurate and precise as the specificity of their placement on a phylogenetic tree increases, which can greatly increase statistical power to detect, for example, deviation of a single species from an allometric prediction. We reexamine published data for basal metabolic rates (BMR) of birds and show that conventional and phylogenetic allometric equations differ significantly. In new results, we show that, as compared with nonpasserines, passerines exhibit a lower rate of evolution in both body mass and mass-corrected BMR; passerines also have significantly smaller body masses than their sister clade. These differences may justify separate, clade-specific allometric equations for prediction of avian basal metabolic rates.     

Stable Isotope Turnover and Half-Life in Animal Tissues: A Literature Synthesis

Stable isotopes of carbon, nitrogen, and sulfur are used as ecological tracers for a variety of applications, such as studies of animal migrations, energy sources, and food web pathways. Yet uncertainty relating to the time period integrated by isotopic measurement of animal tissues can confound the interpretation of isotopic data. There have been a large number of experimental isotopic diet shift studies aimed at quantifying animal tissue isotopic turnover rate λ (%·day^-1, often expressed as isotopic half-life, ln(2)/λ, days). Yet no studies have evaluated or summarized the many individual half-life estimates in an effort to both seek broad-scale patterns and characterize the degree of variability. Here, we collect previously published half-life estimates, examine how half-life is related to body size, and test for tissue- and taxa-varying allometric relationships. Half-life generally increases with animal body mass, and is longer in muscle and blood compared to plasma and internal organs. Half-life was longest in ecotherms, followed by mammals, and finally birds. For ectotherms, different taxa-tissue combinations had similar allometric slopes that generally matched predictions of metabolic theory. Half-life for ectotherms can be approximated as: ln (half-life) = 0.22*ln (body mass) + group-specific intercept; n = 261, p<0.0001, r² = 0.63. For endothermic groups, relationships with body mass were weak and model slopes and intercepts were heterogeneous. While isotopic half-life can be approximated using simple allometric relationships for some taxa and tissue types, there is also a high degree of unexplained variation in our models. Our study highlights several strong and general patterns, though accurate prediction of isotopic half-life from readily available variables such as animal body mass remains elusive.     

Interspecific relationships between egg size and the level of parental investment per offspring in echinoderms

The relationship between the size of an egg and its energy content was analyzed using published data for 47 species of echinoderms. Scaling relationships were evaluated for all species, as well as for subsets of the species, based on mode of development. Regressions were calculated using linear, power function, full allometric, and second-order polynomial models. The full allometric model is preferred because it is relatively simple and the most general. Among these species of echinoderms, larger eggs contain more energy. Egg energy content scales isometrically across a wide range of egg sizes both among and within different modes of development. The only exception is among species with feeding larval development, where there does not seem to be a clear scaling relationship. In most cases, the regressions were statistically significant and explained a very large proportion of the variance in energy content. However, there were wide confidence intervals around the estimated regression parameters. In all cases, the predictive power of the regression was poor, requiring large differences in egg size to yield significantly different predictions of energy content. Consequently, egg size is of limited value for the quantitative prediction of egg energy content and should be used with caution in life-history studies.     

Static allometry of unicellular green algae: scaling of cellular surface area and volume in the genus Micrasterias (Desmidiales)

The surface area‐to‐volume ratio of cells is one of the key factors affecting fundamental biological processes and, thus, fitness of unicellular organisms. One of the general models for allometric increase in surface‐to‐volume scaling involves fractal‐like elaboration of cellular surfaces. However, specific data illustrating this pattern in natural populations of the unicellular organisms have not previously been available. This study shows that unicellular green algae of the genus Micrasterias (Desmidiales) have positive allometric surface‐to‐volume scaling caused by changes in morphology of individual species, especially in the degree of cell lobulation. This allometric pattern was also detected within most of the cultured and natural populations analysed. Values of the allometric S:V scaling within individual populations were closely correlated to the phylogenetic structure of the clade. In addition, they were related to species‐specific cellular morphology. Individual populations differed in their allometric patterns, and their position in the allometric space was strongly correlated with the degree of allometric S:V scaling. This result illustrates that allometric shape patterns are an important correlate of the capacity of individual populations to compensate for increases in their cell volumes by increasing the surface area. However, variation in allometric patterns was not associated with phylogenetic structure. This indicates that the position of the populations in the allometric space was not evolutionarily conserved and might be influenced by environmental factors.     

Self-similarity and the relationship between abundance and range size

Patterns in the relationships among the range, abundance, and distribution of species within a biome are of fundamental interest in ecology. A self-similarity condition, imposed at the community level and previously demonstrated to lead to the power-law form of the species-area relationship, is extended to the species level and shown to predict testable power-law relationships between range size and both species abundance and area of census cell across scales of spatial resolution. The predicted slopes of plots of log(range size) versus log(abundance) are shown to be in good agreement with data from British breeding bird and mammal censuses and with data on the distribution of fern species in old-growth forest. The predicted slopes of plots of log(range size) versus log (area of census cell) are consistent with the limited available data for British plant species. Self-similarity provides a testable theoretical framework for a unified understanding of patterns among the range, abundance, and distribution of species.     

ALLOMETRIC CONSTRAINTS AND THE EVOLUTION OF ALLOMETRY

Morphological traits often covary within and among species according to simple power laws referred to as allometry. Such allometric relationships may result from common growth regulation, and this has given rise to the hypothesis that allometric exponents may have low evolvability and constrain trait evolution. We formalize hypotheses for how allometry may constrain morphological trait evolution across taxa, and test these using more than 300 empirical estimates of static (within‐species) allometric relations of animal morphological traits. Although we find evidence for evolutionary changes in allometric parameters on million‐year, cross‐species time scales, there is limited evidence for microevolutionary changes in allometric slopes. Accordingly, we find that static allometries often predict evolutionary allometries on the subspecies level, but less so across species. Although there is a large body of work on allometry in a broad sense that includes all kinds of morphological trait–size relationships, we found relatively little information about the evolution of allometry in the narrow sense of a power relationship. Despite the many claims of microevolutionary changes of static allometries in the literature, hardly any of these apply to narrow‐sense allometry, and we argue that the hypothesis of strongly constrained static allometric slopes remains viable.     

Reproductive allometry in Malaysian rain forest trees: Biomechanics versus optimal allocation

Summary Quantitative predictions of reproductive allometry in iteroparous plants may be derived from two bodies of theory: biomechanics and optimal allocation theory. Biomechanical theory predicts allometric scaling exponents between reproductive (R) and vegetative (V) biomass in the range of 0.44–1.33, while very general models of life history evolution predictR–V exponents > 1 in all cases. These predictions are examined in light of allometric patterns of flower and fruit production in 32 species of Malaysian rain forest trees. Among these species the mean estimatedR–V exponents are in the range 1.8–2.0 for staminate flower, pistillate flower and fruit production. This range of exponent values provides unambiguous support for some of the general predictions of optimal allocation models, but not for biomechanical theory. Optimal allocation models also predict a positive relationship between species size andR–V slope and a positive relationship between species size andR–V intercept parameters. The latter, but not the former prediction is supported by the data.R–V allometries in sexes of dioecious species were also found to differ in intercept, though not slope, reflecting smaller sizes at reproductive onset in staminate trees. Further critical examinations of reproductive allometry are encouraged as a relatively unexplored avenue for increasing the contact of theory and data in studies of life history evolution in long-lived organisms such as tropical trees.     

The use of dietary calcium intake of dairy ruminants to predict the transfer coefficient of radiostrontium to milk

Transfer coefficients (the equilibrium ratio be-tween radionuclide activity concentration in milk or meat and the daily intake of radionuclide) are widely used to predict the contamination of animal products following the release of radionuclides into the environment. For a transfer coefficient to be generally applicable, its value must be constant for a range of circumstances. However, this is not the case for radiostrontium, the behaviour of which is strongly influenced by that of the homeostatically controlled nutrient, calcium. In this study, a relationship is derived between radiostrontium transfer coefficients and dietary calcium intake which takes into account the observed ratio for strontium:calcium transfer to milk. This relationship is tested against a range of observed data collated from the literature (n = 30) and found to account for 93% of the variability in transfer coefficient values. Model calculations show that a reduction in F _m of at least 40%–60% would be expected if dairy cattle, fed rations typical for well-managed herds, were supplemented with 100–200 g per day. Larger reductions would be predicted when dietary calcium intake is low. Received: 14 October 1996 / Accepted in revised form: 26 November 1996     

The Allometry of Coarse Root Biomass: Log-Transformed Linear Regression or Nonlinear Regression?

Precise estimation of root biomass is important for understanding carbon stocks and dynamics in forests. Traditionally, biomass estimates are based on allometric scaling relationships between stem diameter and coarse root biomass calculated using linear regression (LR) on log-transformed data. Recently, it has been suggested that nonlinear regression (NLR) is a preferable fitting method for scaling relationships. But while this claim has been contested on both theoretical and empirical grounds, and statistical methods have been developed to aid in choosing between the two methods in particular cases, few studies have examined the ramifications of erroneously applying NLR. Here, we use direct measurements of 159 trees belonging to three locally dominant species in east China to compare the LR and NLR models of diameter-root biomass allometry. We then contrast model predictions by estimating stand coarse root biomass based on census data from the nearby 24-ha Gutianshan forest plot and by testing the ability of the models to predict known root biomass values measured on multiple tropical species at the Pasoh Forest Reserve in Malaysia. Based on likelihood estimates for model error distributions, as well as the accuracy of extrapolative predictions, we find that LR on log-transformed data is superior to NLR for fitting diameter-root biomass scaling models. More importantly, inappropriately using NLR leads to grossly inaccurate stand biomass estimates, especially for stands dominated by smaller trees.     

Trophic position and metabolic rate predict the long-term decay process of radioactive cesium in fish: a meta-analysis

Understanding the long-term behavior of radionuclides in organisms is important for estimating possible associated risks to human beings and ecosystems. As radioactive cesium (¹³⁷Cs) can be accumulated in organisms and has a long physical half-life, it is very important to understand its long-term decay in organisms; however, the underlying mechanisms determining the decay process are little known. We performed a meta-analysis to collect published data on the long-term ¹³⁷Cs decay process in fish species to estimate biological (metabolic rate) and ecological (trophic position, habitat, and diet type) influences on this process. From the linear mixed models, we found that 1) trophic position could predict the day of maximum ¹³⁷Cs activity concentration in fish; and 2) the metabolic rate of the fish species and environmental water temperature could predict ecological half-lives and decay rates for fish species. These findings revealed that ecological and biological traits are important to predict the long-term decay process of ¹³⁷Cs activity concentration in fish.     

Pollinator size and its consequences: Robust estimates of body size in pollinating insects

Body size is an integral functional trait that underlies pollination‐related ecological processes, yet it is often impractical to measure directly. Allometric scaling laws have been used to overcome this problem. However, most existing models rely upon small sample sizes, geographically restricted sampling and have limited applicability for non‐bee taxa. Allometric models that consider biogeography, phylogenetic relatedness, and intraspecific variation are urgently required to ensure greater accuracy. We measured body size as dry weight and intertegular distance (ITD) of 391 bee species (4,035 specimens) and 103 hoverfly species (399 specimens) across four biogeographic regions: Australia, Europe, North America, and South America. We updated existing models within a Bayesian mixed‐model framework to test the power of ITD to predict interspecific variation in pollinator dry weight in interaction with different co‐variates: phylogeny or taxonomy, sexual dimorphism, and biogeographic region. In addition, we used ordinary least squares regression to assess intraspecific dry weight ~ ITD relationships for ten bees and five hoverfly species. Including co‐variates led to more robust interspecific body size predictions for both bees and hoverflies relative to models with the ITD alone. In contrast, at the intraspecific level, our results demonstrate that the ITD is an inconsistent predictor of body size for bees and hoverflies. The use of allometric scaling laws to estimate body size is more suitable for interspecific comparative analyses than assessing intraspecific variation. Collectively, these models form the basis of the dynamic R package, “pollimetry,” which provides a comprehensive resource for allometric pollination research worldwide.     

A comparison of methods for fitting allometric equations to field metabolic rates of animals

We re-examined data for field metabolic rates of varanid lizards and marsupial mammals to illustrate how different procedures for fitting the allometric equation can lead to very different estimates for the allometric coefficient and exponent. A two-parameter power function was obtained in each case by the traditional method of back-transformation from a straight line fitted to logarithms of the data. Another two-parameter power function was then generated for each data-set by non-linear regression on values in the original arithmetic scale. Allometric equations obtained by non-linear regression described the metabolic rates of all animals in the samples. Equations estimated by back-transformation from logarithms, on the other hand, described the metabolic rates of small species but not large ones. Thus, allometric equations estimated in the traditional way for field metabolic rates of varanids and marsupials do not have general importance because they do not characterize rates for species spanning the full range in body size. Logarithmic transformation of predictor and response variables creates new distributions that may enable investigators to perform statistical analyses in compliance with assumptions underlying the tests. However, statistical models fitted to transformations should not be used to estimate parameters of equations in the arithmetic domain because such equations may be seriously biased and misleading. Allometric analyses should be performed on values expressed in the original scale, if possible, because this is the scale of interest.     

Transfer of radionuclides to ants, mosses and lichens in semi-natural ecosystems

There is a scarcity of data on transfer of both natural and anthropogenic radionuclides to detritivorous invertebrates for use in the assessment of radiation exposure. Although mosses and lichens have been extensively used in biomonitoring programs, the data on transfer of radionuclides to these species are limited, particularly for natural radionuclides. To enhance the available data, activity concentrations of ¹³⁷Cs, ²²⁶Ra and ²²⁸Ra were measured in ants, mosses and lichens and corresponding undisturbed soil collected from semi-natural ecosystems in Serbia and Montenegro and biota/soil concentration ratios (CR) calculated. Since the majority of internal dose to biota is expected to come from ⁴⁰K, the activity concentrations of this radionuclide were also determined. The mean CR values for ¹³⁷Cs, ²²⁶Ra and ²²⁸Ra in ants analyzed in this study were found to be 0.02, 0.06 and 0.02, respectively. The mean CR values of radionuclides in mosses were found to be 2.84 for ¹³⁷Cs, 0.19 for ²²⁶Ra and 0.16 for ²²⁸Ra, while those in lichens were found to be 1.08 for ¹³⁷Cs, 0.15 for ²²⁶Ra and 0.13 for ²²⁸Ra. The CR values obtained in this study were compared with default CR values used in the ERICA Tool database and also with those reported in other studies.     

Asymptotic height as a predictor of growth and allometric characteristics in malaysian rain forest trees

The growth and physiological characteristics of canopy trees are expected to differ systematically from those of understory trees on the basis of size-dependent aspects of biomechanics, resource availability, and life history. Although such differences have previously been noted, there has been relatively little effort to quantify these in terms of interspecific allometric relationships. Asymptotic maximal height (H_max) is advocated as a measure of the size of dicotyledonous woody plants for this purpose. Height diameter (H–D) relationships in 38 species within six genera of Malaysian rain forest trees are well described by an asymptotic model, and thus provide a basis for estimating H_max using static observational data. Three important aspects of tree growth strategies are shown to be predictable on the basis of these values: average tree growth rates are positively related to H_max, while wood density and the initial allometric slope of (species-specific) H–D relationships are negatively related to H_max. These patterns may be explained by an association of low light levels with slow growth and high density wood in understory species; the latter property may in turn allow for relatively high allometric slopes of H–D relationships in saplings of small-statured species. Analyses that control for phylogenetic differences provide evidence that such interspecific allometric patterns are the product of convergent evolution. These results are consistent with the idea that much ecological variation within species-rich taxa of southeast Asian rain forest trees is related to differentiation along a vertical axis of tree size.     

Radionuclide transfer to marine biota species: review of Russian language studies

An extensive programme of experiments on transfer of radionuclides to aquatic species was conducted in the former USSR starting from the early 1950s. Only a few of these studies were made available in the English language literature or taken into account in international reviews of radionuclide behaviour in marine ecosystems. Therefore, an overview of original information on radionuclide transfer to marine biota species available from Russian language literature sources is presented here. The concentration ratio (CR) values for many radionuclides and for marine species such as: ²³⁹Pu, ¹⁰⁶Ru and ⁹⁵Zr (crustacean), ⁵⁴Mn, ⁹⁰Sr, ⁹⁵Nb, ¹⁰⁶Ru, ¹³⁷Cs ²³⁹Pu, ²⁴¹Am and natural U (molluscs), and ⁵⁴Mn, ⁹⁰Sr, ¹³⁷Cs and ¹⁴⁴Ce (fish) are in good agreement with those previously published, whilst for some of them, in particular, for ³²P and ¹¹⁰Ag (crustaceans), ³⁵S (molluscs), ³²P, ³⁵S, ⁹⁵Nb, and ¹⁰⁶Ru (macroalgae) and ⁶⁰Co and ^239,240Pu (fish) the data presented here suggest that changes in the default CR reference values presented in recent marine reviews may be required. The data presented here are intended to supplement substantially the CR values being collated within the handbook on Wildlife Transfer Coefficients, coordinated under the IAEA EMRAS II programme.