The measurement of 86Rb turnover recently has been suggested as a useful method for measuring field metabolic rate in small animals. We investigated a proposed mechanism of 86Rb turnover, its analogy to K+, by comparing the turnover of 86Rb in a model insect, the rhinoceros beetle Xylotrupes gideon, fed a diet of plum jam or plum jam enriched with K+ or Rb+. The turnover of 86Rb in the beetles on the K+ and the Rb+ diets was higher than that for beetles on the jam diet (F2,311=32.4; P=1.58×10−13). We also exposed the beetles to different ambient temperatures to induce differences in metabolic rate () while feeding them the jam and K+ diets. was higher at higher ambient temperature (Ta) for both jam (F1,11=14.56; P=0.003) and K+ (F1,8=15.39; P=0.004) dietary groups, and the turnover of 86Rb was higher at higher Ta for both jam (F1,11=10.80; P=0.007) and K+ (F1,8=12.34; P=0.008) dietary groups. There was a significant relationship between 86Rb turnover and for both the jam (F1,11=35.00; P=1.0×10−3) and the K+ (F1,8=64.33; P=4.3×10−5) diets, but the relationship differed between the diets (F1,19=14.07; P=0.001), with a higher 86Rb turnover in beetles on the K+-enriched than on the jam diet at all Ta. We conclude that 86Rb turnover is related to K+ metabolism, and that this is the mechanism of the relationship between 86Rb turnover and . Studies relating 86Rb turnover to should maintain dietary [K] as close as possible to that of natural diets for the most accurate calibrations for free-ranging animals.
The metabolic rate of an animal is a measure of that animal's energy expenditure and reflects the cost of living (Hulbert and Else, 2004). The basal metabolic rate (BMR) is generally used to compare the metabolic rate of endotherms to each other, being the metabolic rate measured under defined conditions when an animal is inactive, post-absorptive and non-reproductive within the thermoneutral zone (Ricklefs et al., 1996; McNab, 1997). The standard metabolic rate (SMR) is measured under less stringent conditions when an animal is at rest, and is broadly considered to represent the minimal cost of living (Hulbert and Else, 2004). In insects there is no definition for BMR, and the SMR is usually used for comparative purposes (Quinlan and Gibbs, 2006). Metabolic rate can be readily measured in the laboratory by direct calorimetry, which involves measuring the heat produced by an animal (Kleiber, 1961; McLean and Tobin, 1987). More commonly used is indirect calorimetry, including flow-through respirometry, which measures the gas metabolism of an animal (either oxygen consumption, , or carbon dioxide production, , or both) and is recognised as one of the easiest and most accurate approaches to the measurement of metabolism (Frappell, 2006). These are often used as proxies for true calorimetric representations of energy expenditure by virtue of relatively straightforward conversions to calorimetry, providing the respiratory exchange ratio (RER) or respiratory quotient (RQ) is known.
While laboratory measures of metabolic rate are informative in a comparative context (Brody and Procter, 1932; Kleiber, 1932; Elgar and Harvey, 1987; McNab, 1997), it is often difficult to extrapolate these measurements under controlled conditions to the cost of living in dynamic ecological scenarios. The utility of extrapolating metabolic rate data from captive animals to free-living animals has been questioned, especially when the latter experience different conditions such as food supply, quality of life and weather compared with laboratory conditions (Nagy, 1987). In contrast, the field metabolic rate (FMR) is measured in animals that are free-ranging in their natural environment (Ricklefs et al., 1996) and reflects the summary cost of living for that animal in its natural environment. The FMR includes the costs of BMR, SMR, thermoregulation, locomotion, feeding, predation avoidance, alertness, posture and digestion (Nagy, 1987). As FMR is measured over several days, the average daily rate of metabolism is often referred to as daily energy expenditure (DEE) or average daily metabolic rate (ADMR). DEE and ADMR are considered to be the most relevant measure of metabolism for ecological studies as they come nearest to the real measure of metabolic rate under natural conditions when an animal pursues all its natural functions in that environment.
There are several ways that DEE can be measured. Heart rate has been measured in free-living animals and, using correlations of heart rate with metabolism, converted to DEE (Bevan and Butler, 1992; Bevan et al., 1994; Bevan et al., 1995a). More often, stable isotope turnovers have been used, in what is known as the doubly labelled water method (DLW) (Lifson et al., 1955; Schoeller, 1988; Westerterp and Plasqui, 2004). The DLW method calculates CO2 production by measuring the fractional turnover of isotopes of hydrogen (i.e. 2H or 3H) and oxygen (i.e. 18O). The accuracy and precision of the DLW method make it ideal for studies in some free-living animals (Schoeller and Webb, 1984; Williams and Nagy, 1984; Williams, 1985; Nagy et al., 1990; Tiebout and Nagy, 1991; Bevan et al., 1995b; Speakman, 1998; Jones et al., 2009). A key aspect to the DLW method, however, is the requirement to sample body fluids from the subject animal, which has made its application to invertebrate systems difficult and limited (Buscarlet et al., 1978; King and Hadley, 1979; Yokota, 1979; Cooper, 1983; Wolf et al., 1996), and also to recapture the animals within the biological half-life of the isotopes, which is often prohibitively short in small animals (Speakman, 1997; Bradshaw and Bradshaw, 2007).
As an alternative to the measurement of stable isotope turnover, radio-isotopic turnovers have been used to measure FMR (Relman, 1956; Odum and Golley, 1963; Argoud et al., 1987). It has now been fairly well established that the turnover of rubidium-86 (86Rb), a gamma and beta radio-emitter, correlates well with metabolic rate in vertebrates (Mishima and Odum, 1963; Fairbanks and Burch, 1968; Baker and Dunaway, 1975; Williamson, 1975; Peters et al., 1995; Peters, 1996; Bradshaw and Bradshaw, 2007; Tomlinson et al., 2013), and that there are some general patterns to this relationship that span all of the taxa studied so far (Tomlinson et al., 2013). Radio-isotope enrichment, particularly of gamma emitters, can be measured by whole-body counting, obviating the need for sub-sampling of the body pool (Bradshaw and Bradshaw, 2007). Furthermore, radio-isotope enrichment provides a simpler avenue for measuring FMR, and one that extends the recapture period far beyond that of DLW in small animals because the biological half-life of the isotopes is longer (Bradshaw and Bradshaw, 2007; Tomlinson et al., 2013). The method may be particularly applicable to measuring FMR in insects (Tomlinson et al., 2013).
Our lack of a quantified mechanism that links 86Rb biological turnover (86Rb kb, where kb is the biological elimination constant) to FMR is, however, a limitation of the technique (Tomlinson et al., 2013). It is hypothesised that the body handles Rb+ similarly to the way it handles K+ because Rb+ is an alkali metal with a single electron in its outer orbital (group I), and appears in the periodic table below K+ (Bradshaw and Bradshaw, 2007; Tomlinson et al., 2013). The measure of 86Rb kb is probably an indirect measure of K+ turnover, and because [K+] is tightly regulated in the body, the turnover may simply be a measure of K+ intake. Peters et al. (Peters et al., 1995), however, presented evidence that 86Rb kb was not simply a measure of K+ intake in lizards, because the relationship between 86Rb kb and metabolic rate remained even after accounting for food intake. The other possibility is that 86Rb kb is measuring metabolic rate via some mechanism that is related to K+, such as ATP utilisation by the ubiquitous Na+/K+-ATPase in cell membranes that maintains high intracellular [K+] and low intracellular [Na+]. An increase in the activity of the Na+/K+-ATPase should be proportional to oxidative metabolism, and if Rb+ turnover captures the change in activity of the pump, then the measure will be related to metabolic rate but may also be influenced by K+ intake.
The purpose of the present study was twofold; firstly, to validate the use of 86Rb kb to measure the DEE of an insect (in this case, Xylotrupes gideon Guérin-Méneville 1830) to provide a proof of concept that the technique could be used to measure FMR in insect taxa; secondly, to test the effects of increased dietary potassium intake upon the association of 86Rb kb with .
RESULTS AND DISCUSSION
There was no significant change in X. gideon body mass during the experiments (F2,24=0.196; P=0.824; Njam=11, NK=9, NRb=4). The mean (±s.e.) body mass was 3.84±0.43 g for the jam diet, 4.15±0.43 g for the K+ diet and 4.47±0.4 3g for the Rb+ diet.
The effect of dietary K+ and Rb+ on 86Rb washout
The rapid biological decay of 86Rb in X. gideon on all three diets indicates that 86Rb was being excreted, possibly through the same excretory processes as K+. The elimination of K+ is a well-described aspect of insect iono-regulation (Schweikl et al., 1989; Wieczorek et al., 1989; Klein et al., 1991; Wieczorek et al., 1991; Maddrell and O'Donnell, 1992; Wieczorek, 1992; Zeiske, 1992; O'Donnell, 2008), and K+ and Rb+ are excreted through the same homeostatic processes (Ringer, 1884; Shoemaker et al., 1972; Lehninger, 1975; Metzler, 1977). The increased 86Rb kb in beetles on both the K+ and Rb+ experimental diets compared with the jam diet suggests that increases in K+ intake increase the 86Rb kb. Furthermore, the turnover rates of both the K+ and Rb+ diet groups were the same, consistent with data reported by Fairbanks and Burch (Fairbanks and Burch, 1968), implying that, although 86Rb is obviously analogous to Rb+, it is also an analogue of K+.
There was some variability around the general exponential decline (Fig. 1), where from day to day some measures tended to occasionally plateau, or sometimes increase at low levels of enrichment. This was probably a result of measurement variability, as small shifts in the posture of the beetles have higher proportional impacts on activity counts at low levels of enrichment. It is, however, also possible that the beetles managed to re-ingest some excreted 86Rb isotope, and that their enrichment genuinely rose. Although this is a difficulty of using radioisotopes in contained and contaminated environments, it is unlikely to be a problem in the field, where excreted isotope should dissipate rapidly.
86Rb kb, temperature and metabolic rate
The rate of CO2 production increased significantly with increasing ambient temperature (Ta) (F1,19=30.1, P=2.71×10−5; Njam=5, NK=4), and there was no effect of diet (F1,19=0.031; P=0.862; Fig. 2A). At Ta=20°C the was 0.11±0.01 l day−1, which increased to 0.15±0.01 l day−1 at 25°C and 0.18±0.01 l day−1 at 30°C on the jam diet. At Ta=20°C the was 0.11±5.0×10−4 l day−1, which increased to 0.16±0.005 l day−1 at 25°C and 0.18±0.02 l day−1 at 30°C on the K+ diet.
The 86Rb kb increased significantly with increasing Ta (F1,19=19.4, P=3.03×10−4; Njam=5, NK=4), and was significantly higher on the K+-supplemented diet than on the jam diet at each Ta (F1,19=73.2; P=6.10×10−8; Fig. 2B). At Ta=20°C the 86Rb kb was 0.536±0.098 kb g, which increased to 0.656±0.119 kb g at 25°C and 0.964±0.078 kb g at 30°C on the jam diet. At Ta=20°C the 86Rb kb was 1.22±0.108 kb g, which increased to 2.14±0.129 kb g at 25°C and 2.24±0.276 kb g at 30°C on the K+ diet.
Although the washout trials established a link between K+ excretion and 86Rb kb, this is not informative of DEE, nor of any association between DEE and 86Rb kb. Consistent with our expectations for an ectotherm (Lighton, 1996; Komai, 1998; Zhou et al., 2000; Acar et al., 2001; Woodman et al., 2007; Gibbs and Hoshizaki, 2008), DEE increased with increasing Ta. Furthermore, consistent with the expectation that 86Rb kb should increase similarly to (Peters et al., 1995; Peters, 1996; Bradshaw and Bradshaw, 2007; Tomlinson et al., 2013), 86Rb kb also increased with increasing Ta.
As there was no difference in the of the beetles on the control diet and the K+ experimental diet, it is apparent that additional K+ intake had no effect on DEE. However, consistent with the washout trials, the relationship of 86Rb kb to Ta had a higher slope in the beetles receiving the K+ diet to that in those receiving the jam diet. A more intuitive way of interpreting these data is that at the same Ta there was a higher 86Rb kb in the K+ experimental diet group than in the jam diet group. As was not different between the two groups, presumably the effect was related to K+ elimination, independent of the role of K+ in what we measured as the metabolic rate ().
The effect of metabolic rate on 86Rb washout
There was a significant linear relationship between and 86Rb kb for both the jam (F1,11=35.00; P=1.0×10−3) and the K+ diets (F1,8=64.33; P=4.3×10−5). The relationship had a significantly higher slope, resulting in higher 86Rb kb for a given , on the K+-enriched diet compared with the jam diet (F1,19=215.8; P=7.95×10−12; Fig. 2C).
We have shown that 86Rb kb is related to metabolic rate in an insect, and that the measure is changed when dietary [K+] intake is altered. Buscarlet et al. (Buscarlet et al., 1974) stated that the biological half-life of radioisotopes in insects obeys the same laws as those regulating metabolism, and good correlations between metabolic rate and 86Rb kb have been reported in vertebrates (Peters et al., 1995; Peters, 1996; Bradshaw and Bradshaw, 2007; Tomlinson et al., 2013). The results for the control jam diet were not congruent with a previous meta-analysis of 86Rb kb for ectotherms (Tomlinson et al., 2013) (Fig. 3), registering at a lower elevation, with lower 86Rb kb at a given . The data for X. gideon on the K+ experimental diet, however, were congruent with those previous findings (Fig. 3). Deviations from the established pattern could be an artefact of elevated K+ elimination to maintain ionic balance on the higher [K+] diet, but this interpretation was not supported by the meta-analysis, where the K+-enriched diet group conformed to expectations. This raises two possibilities: either our jam diet had a lower [K+] than is normal in the natural diet of X.gideon, or the previous published literature was based on animals receiving K+-enriched diets. While the [K+] of our K+ experimental diet was similar to the 1.81±0.14 mg g−1 reported by the USDA (USDA, 2004) for naturally occurring levels of K+ in fruit, the [K+] of jam was substantially lower (0.75 mg g−1). This suggests that our jam diet provided less than the normal dietary K+ for the beetles, while our K+ experimental diet in fact represents a more accurate control. Under such a scenario our data would be consistent with previous findings (Fig. 3). The dietary K+ has not previously been controlled or reported in other studies. Such a confounding of comparative interpretation strengthens our recommendation that, although 86Rb kb can be used to infer FMR in a broad range of taxa, dietary K+ should be carefully controlled in any laboratory validations of the technique to mimic the [K+] that a species will be consuming in the wild.
The mechanism of association between 86Rb kb and DEE has been speculated to be the substitution of 86Rb+ for K+ by the Na+/K+-ATPase that transports K+ into, and Na+ out of, cells in an active process that consumes ATP (Peters et al., 1995; Peters, 1996; Bradshaw and Bradshaw, 2007; Tomlinson et al., 2013). Peters et al. (Peters et al., 1995) extensively explored the possibilities that 86Rb kb and 22Na kb were co-correlated with both the metabolic rate and the dietary intake of the ions, and managed to separate the effectors for each isotope using statistical methods. While 22Na kb was mostly influenced by food intake, 86Rb kb was most strongly associated with DEE (Peters et al., 1995). Following the conclusions of Peters et al. (Peters et al., 1995), with some inferences from our data presented here, we speculate that, after the bolus of initial enrichment, the Na+/K+-ATPase transports most of the injected 86Rb+ into cells, thus entering an intracellular pool. The movement of K+ (and 86Rb+) out of the cell should be directly proportional to the activity of the Na+/K+-ATPase, as intracellular K+ is regulated. As the activity of the Na+/K+-ATPase comprises a large component of DEE (Withers, 1992), the rate of this exchange should increase or decrease proportionally with metabolic rate. An increase in dietary K+ will result in an increase in the excretion of K+ (and 86Rb+), and it is the extracellular fluid that is filtered by the Malpighian tubule system to produce excreta. The mechanism suggested is that 86Rb+ is released from the cell at a rate that is proportional to metabolic rate, and the rate of excretion of K+ (and 86Rb+) from the extracellular fluid is proportional to K+ intake. When 86Rb+ leaves the cell, some of it will be excreted, while some will return to the intracellular fluid via the Na+/K+-ATPase. If the rate of excretion of K+ (and 86Rb+) from the extracellular fluid increases when K+ intake increases, then the balance of 86Rb+ exchange between the intracellular and extracellular pools is altered. While the transfer of 86Rb+ from the intracellular to the extracellular pool remains constant, more of that 86Rb+ will be excreted from the extracellular pool, reducing the probability of a given molecule of 86Rb+ being transported back to the intracellular pool via Na+/K+-ATPase, and increasing its probability of being excreted. While there is a constant movement of 86Rb from the intracellular to the extracellular fluid in proportion to metabolic rate, the excretion of 86Rb from the extracellular fluid increases when K+ intake increases. The association of 22Na with food intake probably results from 22Na being maintained mostly in the extracellular body pool that is regulated in response to ionic intake with food, and is only tangentially influenced by the Na+/K+-ATPase and metabolic rate.
FMR is a useful ecological measurement because it quantifies the energetic link between a species and its environment. It can be used to understand the impacts of temperature and climate (Anderson and Jetz, 2005), reproduction (Fyhn et al., 2001; Bevan et al., 2002; Jodice et al., 2003), ecosystem productivity (Bradshaw and Bradshaw, 1999; Bradshaw and Bradshaw, 2007; Bradshaw et al., 2007), dispersal (Clusella Trullas et al., 2006) and anthropogenic disturbance upon a species of interest. Although the DLW method has broad support and application for measuring FMR, the technique has theoretical and practical limits, where some species and habitats are not suitable for the technique (for review, see Tomlinson et al., 2013). The biological turnover of radioactive 86Rb has been proposed as an alternative that avoids some of the limitations of DLW, and may be applicable to taxa that are unsuitable for DLW (Peters et al., 1995; Peters, 1996; Bradshaw and Bradshaw, 2007; Tomlinson et al., 2013). A problem with using 86Rb kb as a measure of an animal's metabolism is a lack of understanding of the mechanistic link between metabolism and the turnover of 86Rb (Bradshaw and Bradshaw, 2007; Tomlinson et al., 2013). One suggested mechanistic pathway is that Rb+ turnover is related to K+ turnover, and we here provide some evidence to support that contention.
Measurement of 86Rb kb is a cheap, non-invasive and practical technique to measure DEE and FMR in small vertebrates and insects. We found that the 86Rb kb was influenced by dietary levels of K+ and Rb+, but that changes in the intake of these ions did not affect . Although there were significant relationships between and 86Rb kb, the relationship was different in beetles on the different diets, presumably as a result of the influence of K+ elimination upon 86Rb kb. These data support the likelihood that 86Rb kb is related to DEE and FMR via the action of the ubiquitous Na+/K+-ATPase. Future calibrations of 86Rb kb with will need to control [K+] intake to natural levels in order to maximise the accuracy of the relationship between 86Rb kb and DEE to make it ecologically relevant as a measure of FMR.
MATERIALS AND METHODS
Animal source and maintenance
We tested the association between 86Rb kb and the dietary intake of K+ using rhinoceros beetles (X. gideon, Coleoptera; Scarabidae; Dynastinae), native to India, south-east Asia, Papua New Guinea, Australia, the British Solomon Islands and the New Hebrides (Bedford, 1975). They are regarded as pests of coconut palm plantations in the southern regions of Asia and several regions of the Pacific (Zelazny and Alfiler, 1987). These insects are approximately 4 g mass, and thus large enough to enrich with radioisotope by injection, and also available through a pet trade in Australia. Mature beetles (15 male and 16 female) were purchased in two separate shipments from the Australian Insect Farm (Innisfail, QLD, Australia), shipped overnight to the U.W.A. Crawley campus in Western Australia, and maintained for 15 days prior to the beginning of experiments. The beetles were maintained in Perspex tanks (25 cm height×15 cm width×30 cm length) kept in a laboratory room near windows. The laboratory was maintained at 23.5±0.1°C constantly. The beetles were kept on a bed of organic mulch (Richgro Ezi-Wet Organic Mulch, Australia) and fed an ad libitum control diet of mashed peaches (Ardmona, Australia) and commercially available plum jam (IXL, Australia).
The beetles were assigned randomly to three treatment groups. The beetles on the jam diet received fresh mashed peaches and plum jam daily. The other groups received the same diet, except that the plum jam was enriched with 0.53 g of either KCl (Merck) or RbCl (BDH Chemicals Ltd) added to 375 ml of plum jam. The final [K+] of the jam diet was 0.35 mg g−1, while the K+ and Rb+ diets were enriched to 1.42 mg g−1, as measured by flame photometry. All other elements of the diet were unchanged, and water and food were provided ad libitum. Throughout the experiments, the beetles were weighed daily to monitor their condition using a balance (Sartorius) with a precision of 0.1 mg. In cases where body mass declined by more than 10%, the food quantity offered was increased.
Isotope enrichment and counting protocols
This research was conducted under UWA Radiation Safety Approval 09/07/01.
At the beginning of each experiment, each beetle was injected with 0.1 ml of a 0.05 MBq 86RbCl solution (Perkin Elmer) in sterile saline (0.09% NaCl, Intravenous Infusion BP, Baxter). Dilutions were made in a sterile, disposable 1 ml syringe (Livingstone, Australia), and administered via a 27G needle (Terumo, Japan). The beetles were injected through the ventral integument between abdominal segments one and two. It is presumed that the injectate entered directly into the haemocoel. Following the injections, the beetles were returned to their respective tanks where they remained for a 24 h equilibration period until the experimental measurements began.
Whole-body radioactivity counts during the washout study were made using a portable gamma counter (PSR8, Nucleonics, UK) with a 50×50 mm sodium iodide crystal, while counts during the respirometry trial were made using an AmpTek GammaRad V (AmpTek, USA) gamma counter with a 76×76 mm sodium iodide crystal. During the counting procedure, the beetles were enclosed in a 50 mm diameter plastic vial and restrained from moving by a styrofoam plug the same diameter as the vial placed above the beetle. To reduce the effects of external sources of radiation, the vial was enclosed within a cylindrical lead shield. Each time the 86Rb remaining in a beetle was measured, three 60 s background counts were recorded. Following the background counts, a minimum of three 60 s counts were taken with the beetle in the chamber. Each set of counts was averaged, and only accepted when the variation between the three counts was less than 2%. The averaged background count was subtracted from the averaged radioactivity count of each beetle.
86Rb washout trials
To test whether increased dietary intake of K+ and Rb+ changed the rate of biological elimination of 86Rb, we measured and compared the rate of decay over time (henceforth referred to as the washout). After the injection of 86Rb, the beetles were measured daily for at least 26 days until the enrichment reached background levels in each beetle. Each day the percentage of the isotope remaining in each beetle was calculated with reference to its initial enrichment.
86Rb turnover, temperature and metabolic rate
Following the washout trial, where no difference was found in 86Rb washout between the K+ and Rb+ diets (see Results and Discussion), the Rb+ experimental group was removed from the next phase of experimentation. A four-channel flow-through respirometry system was constructed following Withers (Withers, 2001). Compressed air was passed through a mass flow controller (Aarlborg DFC-17, USA) at a rate of 200 ml min−1 (ambient temperature and pressure dry). The air was passed into a cylindrical glass chamber (85 mm length×70 mm diameter) bedded with organic mulch, in which the beetle was housed for the duration of the experiment. The excurrent airstream was dried with Drierite (anhydrous calcium sulphate, W. A. Hammond Company Ltd, USA), used in line with recommendations by White et al. (White et al., 2006) to minimise CO2 absorption, and passed through a Qubit S151 infrared CO2 analyser (Qubit systems Inc., USA). Each respirometry system was maintained at constant nominal temperatures (Ta) of 20, 25 or 30°C. Analog data signals from all the equipment were interfaced to a computer via a DataQ 710 data acquisition board, and collected every minute using a custom-written Visual Basic version 6.0 data acquisition program. A minimum 12 h baseline was run before and after each respirometry trial, recording the background [CO2] of a blank chamber including the mulch bedding. Using as the sole measure of metabolic rate depends on the assumption that the RER does not change from treatment to treatment, but as this usually changes in response to the proportional representation of dietary lipids and carbohydrates (Withers, 1992), this is probably a safe assumption with the controlled diets presented here.
The beetles were weighed prior to respirometry trials, and their radioactivity counted. The beetles were then exposed to each temperature in a random order for 2 days. During the respirometry trials, the beetles were weighed daily, and their radioactivity counted. While the beetles were removed from the chamber, the respirometry systems were allowed to return to baseline. While they were in the respirometry chamber, the beetles were provided with their experimental diet and water ad libitum.
Body mass was compared between diets and over time using a two-way repeated measures ANOVA. Exponential effects of time on 86Rb decay nested by diet were tested by ANOVA with Tukey post hoc tests to compare the different diets. Non-linear least squares models were used to characterise the 86Rb exponential decay relationships of each diet over time. The significance of these relationships was tested by linear regression using ln-transformed decay. Following the discussion by Warton and Hui (Warton and Hui, 2011), the percentage of corrected biological decay was not arcsin transformed prior to parametric analysis. Linear mixed effects models were used to characterise the relationships between and Ta, and between 86Rb kb and Ta, nested within dietary treatments. Reduced major axis regression was used to characterise the relationships between 86Rb kb and within dietary groups. These relationships were compared for slope and intercept between experimental groups using ANCOVA. Statistical analyses were performed in R version 2.15.2 using the packages ‘car’, ‘nlme’, ‘multcomp’ and ‘biology’ (Logan, 2010). Data are presented as means ± s.e.
Thanks go to Emeritus Professor Don Bradshaw for the use of his PSR8 gamma counter, and to Professor Phil Withers and Hai Ngo for the use of respirometry equipment and extensive technical advice. Dr Murray Logan's advice on statistical analysis using R is gratefully acknowledged.
This research was partially funded under the Australian Research Council Linkage Grant LP110200304 ‘The spatial energetics of pollination failure in habitat restoration’.
The authors declare no competing financial interests.