Body size is not critical for critical P_O2 in scarabaeid and tenebrionid beetles

Oxygen delivery is important for most animals, especially insects, which are highly aerobic. Insects transport oxygen via an air-filled tracheal respiratory system, with gas exchange occurring by a mix of convection and diffusion (Harrison, 2009). The tracheal system acts as a ventilation system (with spiracles acting as air input valves, air sacs as bellows and tracheae as a tubular air duct system) to bring oxygen to the tracheoles, the blind-ending tubules that act as the diffusive exchange surfaces of the tracheal system. The tracheoles act analogously to vertebrate capillaries in that they supply oxygen to the cells of the body. The shapes and dimensions of the tracheal system are subject to plasticity and selection when oxygen limitation occurs, and respiratory system morphology [e.g. tracheal diameters (Henry and Harrison, 2004; Loudon, 1988); tracheolar branching (Jarecki et al., 1999)] shows compensation for changing oxygen availability.

Oxygen limitation can occur during low oxygen supply [e.g. in a hypoxic environment (Chown and Holter, 2000)] and/or high oxygen demand [e.g. during flight (Harrison and Roberts, 2000)]. Body size strongly affects oxygen demand, and metabolic rate generally increases with increasing body size. Many other anatomical, physiological and ecological characteristics of animals have also been shown to be directly related to body size (Brown and West, 2000; Brown et al., 2004; Calder, 1984; Lindstedt and Calder, 1981; McMahon and Bonner, 1983; Peters, 1983; Schmidt-Nielsen, 1984; Taylor et al., 1981), and the variation in an animal trait over a range of body sizes can be described by the allometric equation y=aM^b, where y is the trait, a is a normalization constant, M is body mass and b is the scaling exponent.

We might expect that traits associated with oxygen delivery would also be affected by (and affect) body size. On the one hand, oxygen diffusion becomes more difficult over longer distances, but on the other hand, tissue-level oxygen demand (i.e. mass-specific metabolic rate) is higher for smaller animals. Indeed, many anatomical and physiological aspects of respiratory systems exhibit isometric and allometric patterns with respect to body mass (M). In vertebrates, lung volume scales with body mass as M¹ (Tenney and Remmers, 1963), lung diffusing capacity scales as M¹ (Gehr et al., 1981) and breathing frequency scales as M^–0.25 (Worthington et al., 1991). Respiratory parameters of some invertebrates have also been shown to scale with animal body size and, importantly, to have functional consequences. For example, insect tracheal volume scales intraspecifically [Schistocerca americana; Orthoptera (Lease et al., 2006)] and interspecifically [Tenebrionidae (four species); Coleoptera (Kaiser et al., 2007)] with body mass as M^1.3, explaining enhanced respiratory capacity (Greenlee and Harrison, 2004a) and increased convective ventilation [M^1.3 (Greenlee et al., 2009)] of older insects (S. americana). Tracheal volume scales intra-instar (i.e. within an intermolt period) as M^–2.4 in S. americana (Lease et al., 2006) because within-instar tissue accumulation is constrained by a relatively rigid/fixed exoskeleton, as hypothesized by Greenlee and Harrison (Greenlee and Harrison, 2004b) and demonstrated recently (Kirkton et al., 2011; Callier and Nijhout, 2011). This >75% reduction in respiratory volume (Lease et al., 2006) explains the decreased aerobic capacity of late-instar insects [S. americana; Orthoptera (Kirkton et al., 2005; Kirkton et al., 2011)] and can also lead to oxygen limitation that triggers the molting process itself [Manduca sexta; Lepidoptera (Callier and Nijhout, 2011)]. Additionally, insect maximal tracheal system conductance scales interspecifically as M^0.7 [Orthoptera, 23 species from five families (Greenlee et al., 2007)]. When considered in conjunction with the hypermetric scaling of orthopteran tracheal volume and convection – M^1.3 (Lease et al., 2006; Greenlee et al., 2009) – these data support the idea that the matching of metabolic function to tissue needs requires more respiratory system volume and convection in larger insects.

One way to test the respiratory capacity of an organism is to determine the animal's critical oxygen partial pressure (critical P_O2, or P_crit). This is the lowest P_O2 that an animal can tolerate without compromising its metabolic capacity (Greenlee and Harrison, 2004a; Greenlee et al., 2007; Harrison et al., 2006; Kam and Lillywhite, 1994; Yeager and Ultsch, 1989). Insects are quite tolerant of hypoxic and anoxic conditions compared with vertebrates (Schmitz and Harrison, 2004), and generally have low P_crit values [1–5 kPa (Greenlee and Harrison, 2004a; Klok et al., 2010)]. Insect P_crit can be affected by respiratory system type (Schmitz and Harrison, 2004), temperature (Woods and Hill, 2004), ontogeny (Greenlee and Harrison, 2004b) and activity (reviewed by Harrison et al., 2006; Schmitz and Harrison, 2004). The pattern for how the P_crit for CO₂ release rate is related to body size seems to vary among insects. P_crit decreased with increasing body mass across developmental stages of the grasshopper S. americana (Greenlee and Harrison, 2004a), and appears to decrease with advanced life stage across developmental stages of the blowfly Phormia regina (Diptera) (Keister and Buck, 1964); however, it was constant across instars during the development of the caterpillar M. sexta (Greenlee and Harrison, 2005). In the only prior interspecific comparison, P_crit was found to be independent of body mass for grasshoppers (Greenlee et al., 2007). We are aware of no data to date that show how P_crit varies with size among adults of a single species of insects, although in amphibians P_crit was found to increase with increasing body size in Siren lacertina (Ultsch, 1974) and to not be significantly correlated with body size in the frog Rana muscosa (Bradford, 1983).

Here we investigate P_crit and maximal overall conductance from air to mitochondria (G_O2,max) in the only group of insects for which there are currently interspecific data on tracheal scaling – Coleoptera (Kaiser et al., 2007). We test the general hypothesis that the respiratory capacities of larger beetles will match their increased needs for oxygen delivery. More specifically, we predict that like many vertebrates and invertebrates, larger coleopterans will have increased absolute metabolic rates, and that metabolic rate will scale hypometrically with body mass (scaling with a slope of less than 1 on a log–log plot). Second, we predict that G_O2,max will scale with a slope similar to that of metabolic rate, and that P_crit will be similar for large and small animals. Alternatively, if oxygen delivery becomes more difficult as animals increase in size, G_O2,max will increase less strongly with size than metabolic rates, and P_crit will be higher for larger animals.

Finally, we predict that evolutionary history and life history traits may alter these relationships. In this study, the scarabaeid species were all flying species whereas the tenebrionid species were mostly non-flying species. We therefore expect these two families to exhibit different resting metabolic rates (Reinhold, 1999; Chown et al., 2007; Riveros and Enquist, 2011), and potentially different gas exchange requirements. Specifically, we predict that the higher metabolic capacities of Scarabaeidae associated with flight (Niven and Scharlemann, 2005) and the possession of air sacs (Harrison, 2009; Kaiser et al., 2007) might enable lower P_crit values and higher G_O2,max. To test these predictions, we investigate the effect of body size on normoxic and hypoxic CO₂ release rates, P_crit and G_O2,max for 14 species of the order Coleoptera from two families, Tenebrionidae and Scarabaeidae.

Adult beetles were obtained by collection in the field (Mojave Desert, CA; Sonoran Desert, AZ; Chihuahuan Desert, AZ; Magdelena and San Mateo Mountains, NM; Chiricahua and Superstition Mountains, AZ) and by purchase from biological supply companies (Hatari Invertebrates, AZ, USA; Carolina Biological Supply, Burlington, NC, USA). This sample included 96 individuals (14 species) from two families of Coleoptera: Tenebrionidae and Scarabaeidae (Table 1).

The tenebrionid species were analyzed in June 2006, and the scarabaeid species in September 2006. Tenebrionidae were collected and housed under laboratory conditions up to several months prior to experimental analyses. Because of shorter adult lifespans compared with the Tenebrionidae, the Scarabaeidae were collected or purchased within 1–2 weeks of experimental analysis. Food (apple, cereal or dung) was removed from animals >1 h before experimental analyses to minimize specific dynamic action. However, it should be recognized that neither metabolic rate nor the fuel utilized are likely in steady-state conditions within our experiments. Water was given ad libitum to animals until experimental analysis, but was not present during the experiment itself; thus animals were slowly, but only slightly, dehydrating.

Animals were weighed on a Mettler MX5 micro-balance (±0.001 mg; Mettler Toledo, Columbus, OH, USA). Mass was determined for each animal before and after hypoxic exposure to account for water loss during the experiment, and the mean of these two masses is reported. Fresh body mass of all animals ranged from 1.32 to 5444.85 mg (species means from 1.7 to 4444 mg; Table 1).

Animals were placed in a 60, 10 or 1 ml syringe modified into a flow-through respirometry chamber using CO₂-impermeable plastic tubing. We adjusted syringe size to animal body size (Table 2) to minimize variation of chamber time constants. The tips of the syringes were packed with glass wool to prevent animal escape. Syringes were enclosed to reduce stimulation of phototactic movement, and were maintained at 25±1°C using a water bath or temperature cabinet (PTC-1 Peltier cabinet, Sable Systems, Las Vegas, NV, USA). Locomotor activity and loco-static behavior were not recorded during the experiment.

We equilibrated each beetle in its chamber to experimental conditions for more than 10 min, with tubings open to room air, followed by ventilation with normoxic air for 15 to 20 min, which flushed CO₂ buildup from the animal chamber. After equilibration, chambers were connected to the analyzers and perfused with sample gas continually while the oxygen content of sample gas was changed. Each beetle was exposed to nine or 10 different partial pressures of atmospheric oxygen (21, 10, 5, 4, 3, 2, 1, 0.5 and 0 kPa O₂ plus 7.5 kPa O₂ for Scarabaeidae). Animals were exposed to each P_O2 in descending order for 15 min. This prevented metabolic rate increases caused by prior hypoxic exposure (Greenlee and Harrison, 1998). After exposure to anoxia, sample gas was restored to normoxia to determine whether animals survived and whether normoxic metabolic rates were recovered. Each experimental run lasted for 5 to 8 h.

Gas mixtures were created by diluting dry, CO₂-free air with N₂. The ratio of air to N₂ flow was controlled with a Tylan RO-28 mass flow controller and two Tylan FC-280 mass flow meters (Tylan General, San Diego, CA, USA). Air and N₂ were mixed in a 1 liter glass container with a 10 cm electrical fan, and pumped from the mixing container using a standard aquarium pump (up to 1.5 l min^–1). The air–N₂ mixture was split into three lines, each consisting of an Ascarite-packed 60 ml syringe, to scrub the air of residual CO₂, an animal respirometry chamber (syringe) and a CO₂ analyzer (two LiCor Li-6252s and one Li-6262; LiCor, Lincoln, NE, USA). Flow rates (25–100 ml min^–1) for the three lines were controlled by Brooks mass flow controllers and mass flow meters (Brooks Instruments, Hatfield, PA, USA); resolution of these flow meters is approximately 1% of the flow rate. The flow rates were adjusted to animal and chamber size (Table 2). One of the lines was equipped with an Oxzilla (tenebrionids) or a FoxBox (scarabaeids) O₂ analyzer (both Sable Systems) upstream of the animal chamber to measure/survey the set P_O2. Baseline CO₂ was measured before and after each experiment for each line with animal chambers excluded from the air flow, and baseline O₂ was measured continuously throughout each experiment.

During the scarabaeid experiments, 0.1 ml of water was injected approximately once per hour into the Ascarite scrubbing columns to minimize desiccation of animals during data collection. Increased humidity in desiccation-prone species (such as non-desert-adapted scarabaeids) reduces stress and therefore reduces the risk of stress-induced activity or metabolic rate artifacts (Hadley and Quinlan, 1993; Williams et al., 1998). This water addition elevated the humidity marginally (7% relative humidity at 25°C; to offset the desiccation potential of dry air), but the quantity of water added to the air was small enough to be considered negligible in terms of oxygen dilution. Oxygen was measured downstream of the humidifying columns.

Expedata software (Sable Systems) was used to record CO₂ (±0.2 p.p.m.), temperature and O₂ (±0.1%) throughout experimental runs at a 1 s sampling rate (Fig. 1). At the completion of each experiment, a drift correction was performed (using Expedata software and baseline air) to adjust for any (linear) CO₂ drift that may have occurred over the course of the multi-hour experiment.

The LiCor analyzers were calibrated by flowing CO₂ standard gases (measured ±0.1 p.p.m.) through the entire system as set up for the animal measurements, at the identical flow rates (and therefore chamber pressures) as when the animal measurements were performed. Ambient temperatures were also constant (±1°C) throughout the experiments. We used multiple calibration gases to confirm that the recorded output was linearly related to CO₂ concentration. Overall resolution of the CO₂ release rates was better than ±3% of the measured rates (LiCor resolution of 1%, adjusted for flow rates and CO₂ concentrations of the smallest beetles), and equilibration times of combined animal chambers and tubing (∼2.82 ml; <40 cm of Bev-A-Line tubing, 3 mm inner diameter) are presented in Table 2.

Mean CO₂ release rate was determined for each animal, at each P_O2, averaged over a ∼10 min period. If CO₂ release appeared cyclic or discontinuous, care was taken to ensure that the sample selection encompassed one or more complete cycles of CO₂ burst release. Individual P_crit values for CO₂ release rate were then determined by statistically identifying the P_O2 at which CO₂ release rate dropped. Because of a high variability in CO₂ release, we slightly modified Greenlee and Harrison's method of calculating P_crit(Greenlee and Harrison, 2004a), which utilizes the confidence intervals (CI) of CO₂ release. P_crit values presented in this paper represent the P_O2 where: (1) mean CO₂ release rate at P_crit drops below the lower 95% CI of CO₂ release rate at the previous, higher P_O2 and (2) mean CO₂ release rate at any subsequent, more hypoxic P_O2 did not rise above the mean CO₂ release rate at the P_crit.

For approximately 10 individuals, we could not identify a P_crit with these criteria; in these cases, visual inspection of the original CO₂ release trace was used to identify the P_crit. Mean P_crit for each species was calculated by averaging the P_crit values for individuals. To calculate O₂ consumption from CO₂ release, a respiratory quotient (RQ) of 0.8 was used (Lighton, 1988). By dividing O₂ consumption at the P_crit by the P_crit, we were able to estimate maximum conductance (μmol O₂ h^–1 kPa^–1) for oxygen from the atmosphere to the oxygen-consuming tissues of the beetles (G_O2,max) [first defined for an insect model by Kestler (Kestler, 1985)], based on the assumptions that spiracles are completely open, tracheolar fluid is removed and ventilation is maximized at P_crit (Greenlee and Harrison, 2004a). Under these conditions, it is plausible that the major resistance to gas exchange is in the liquid phase (from tracheoles to mitochondria), given the much higher capacitance and diffusion rates of oxygen in air compared with water (Kestler, 1985).

Statistical analyses were conducted to determine whether there was a body size and/or phylogenetic effect on CO₂ release rate at normoxia, P_crit for CO₂ release rate, CO₂ release rate at anoxia and G_O2,max. For this, we performed ordinary least squares (OLS) and standardized/reduced major axis (SMA) regression analyses of mean species values across all species examined, with family as a categorical value. We additionally conducted an independent contrast analysis in Mesquite (Maddison and Maddison, 2006) using the PDAP module (MESQUITE V1.12) and in R using the ‘ape’ package (Paradis et al., 2004) to make phylogenetic corrections. The topology of the phylogenetic tree was constructed using previously published work (Doyen and Tschinkel, 1982; Kaiser et al., 2007; Mestrovic et al., 2006; Smith et al., 2006) and consultation with Dr Kelly Miller (Museum of Southwestern Biology, University of New Mexico, Albuquerque, NM, USA) and Dr Clarke Scholtz (Department of Zoology and Entomology, University of Pretoria, Gauteng, South Africa). To test for the influence of phylogenetic effects, we performed OLS and SMA line-fits on independent contrasts using normalized branch lengths. To control the influence of phylogenetic relationships, we repeated the analysis with branch lengths set equal to one and haphazardly altered positions of individual species within the phylogenetic tree. We additionally tested for potential within-species size effects by analyzing the regression functions of P_crit on size within the species for which we had sufficient specimens.

CO₂ release during normoxia (21 kPa O₂) was independent of phylogenetic relationship (t=–0.39, P>0.5), but was significantly correlated with body mass (t=6.36, P<0.005). OLS regression analysis revealed that absolute metabolic rate (MR) scaled with body mass (M) for Tenebrionidae (MR=0.06M^0.73±0.14; r²=0.84, P=0.004), Scarabaeidae (MR=0.09M^0.78±0.13; r²=0.88, P=0.002) and all Coleoptera (MR=0.08M^0.75±0.10; r²=0.83, P<0.00; Fig. 3, Tables 1, 3). None of these slopes were statistically distinguishable from M^0.75. Because the scaling relationship was not significantly different between tenebrionid and scarabaeid beetles, we analyzed the influence of phylogenetic relationships for all species using a phylogenetic tree that included both families (Fig. 2). SMA regression analysis on phylogenetically independent contrasts (PICs) (MR=0.12M^1.04; 95% CI=0.73–1.48) was not significantly different from OLS regression analysis (MR=0.08M^0.75; Fig. 3, Table 3). Mass dependence of normoxic CO₂ release was higher (i.e. CO₂ release scaled steeper with body mass) in scarabaeid beetles (MR=M^1.05±0.22; r²=0.82) than tenebrionid beetles (MR=M^0.89±0.20; r²=0.80) when phylogenetically corrected at the level of family (OLS on PIC, forced through zero), though this difference was not statistically significant. Please note that animal activity was not measured during this experiment and our data for normoxic CO₂ release are therefore not standard resting measurements of metabolic rate.

The general tendency across individuals (not shown), species (Fig. 4, Table 1) and families (Fig. 5) of Coleoptera was for mean CO₂ release to decrease as P_O2 decreased. However, the pattern of decreased CO₂ release rates varied considerably between individuals, species and families. In some species, moderate hypoxia stimulated elevated CO₂ release rates, perhaps because of stimulation of escape behavior (e.g. Cryptoglossa muricata and Eleodes armatus; Fig. 4A). For individuals, the reaction to hypoxia was even more variable (Fig. 1), with frequent cases of increases and decreases in CO₂ release rate within the same animal at sequentially decreasing P_O2. This individual variation was more pronounced in some species than others, as illustrated by the size of the standard error bars in Fig. 4 (e.g. Tribolium castaneum versus Dynastes granti).

There were also some differences between Coleopteran families with respect to CO₂ release patterns. Scarabaeid species had significantly higher CO₂ release rates than tenebrionid species at every P_O2 (ANCOVA with CO₂ release rate as a dependent variable, mass as a covariate, and family and P_O2 as categorical predictors, P=0.01; Fig. 5). Tenebrionid species tended to decrease mean CO₂ release rates upon hypoxic exposure (Fig. 5), though the P_O2 triggering the drop varied between species (e.g. Eleodes obscurus dropped at ∼5 kPa O₂, while T. castaneum had a slight drop at 5 kPa O₂, but then a more prominent drop at ∼2 kPa O₂; Fig. 4A). Scarabaeid species, in contrast (Fig. 5), showed a tendency to increase average CO₂ release rates upon initial exposure to hypoxic conditions (e.g. D. granti at ∼5 kPa O₂, Aphodius sp. 1 at ∼10 kPa O₂; Fig. 4B), followed by a decrease in average CO₂ release rate upon exposure to a lower P_O2 (∼2 kPa O₂ for both species; Fig. 4B). The effect of P_O2 on CO₂ release rates was significant for both families (P=0.03), although the difference in release patterns between the families was not significant (ANCOVA with CO₂ release rate as a dependent variable, mass as a covariate, and family and P_O2 as categorical predictors, P>0.5 for family × P_O2).

The effect of body mass on CO₂ release rates during normoxia (21 kPa O₂) and anoxia (0 kPa O₂) was compared using OLS on species means (i.e. phylogenetically uncorrected), OLS on PIC, and SMA on PIC (Table 3). During both normoxia and anoxia, CO₂ release rate scaled with body size, but to different degrees depending on the oxygen exposure and the type of statistical analysis. Scaling coefficients again tended to be slightly higher when phylogenetically corrected than when uncorrected (e.g. b=0.94 versus 0.85 for anoxic conditions; Table 3), although these differences were not statistically significant. Scaling coefficients for CO₂ release were higher in normoxic conditions compared with anoxic conditions when phylogenetically corrected, although in contrast slopes were higher in anoxic conditions compared with normoxic conditions when analyzed without phylogenetic correction (Table 3). However, regardless of analysis type, the scaling intercept for CO₂ release was lower for anoxic than normoxic conditions, and this pattern was consistent across all Coleoptera (Table 3) and within each family (data not shown). The effect of P_O2 on CO₂ release rate was significant (ANCOVA with CO₂ release rate as a dependent variable, mass as a covariate and P_O2 as a predictor, F_11,127=2.39, P=0.01).

The mean P_crit for CO₂ release rate for each beetle species examined in this study was ≤3 kPa O₂ (Fig. 4, Table 2), and across all species was 1.76 kPa O₂. Some species had a relatively higher P_crit than others (e.g. Eleodes obsoletus porcatus versus Tomarus gibbosus; Fig. 4A,B). The mean P_crit for scarabaeid beetles (1.36 kPa) was lower than that for tenebrionid beetles (2.16 kPa), but this difference was not statistically significant (ANOVA with P_crit as dependent variable and family as predictor, F_1,12=3.601, P=0.082). This lack of significance may be attributable to low statistical power because of the small sample size (N=7 for each family). However, the variance in P_crit values did differ significantly between the two coleopteran families examined. Specifically, tenebrionid beetles showed a wider range of P_crit values than did scarabaeid beetles (two-sample F-test for variance, P=0.01; also see Fig. 6, top graphs versus bottom).

P_crit was independent of body size both across and within beetle families (Fig. 7). There was no significant effect of beetle body size on P_crit regardless of whether data were phylogenetically corrected and analyzed at the level of coleopteran order (SMA on PIC; P>0.5) or family (SMA on PIC; tenebrionid P>0.5, scarabaeid P>0.5), or whether they were analyzed across coleopteran order prior to phylogenetic correction (OLS; P>0.5). In addition, when P_crit was examined intraspecifically, it again appears to be independent of body size. No scaling relationship between body size and P_crit occurred within any one taxon (Fig. 6).

G_O2,max was independent of phylogenetic relationship (t=–1.62, P>0.5), but was significantly correlated with body mass (t=12.82, P<0.005). As beetle body size increased, G_O2,max increased hypometrically, with specific exponents and intercepts again dependent on the method used to fit the line (e.g. OLS, G_O2,max =0.05M^0.78versus SMA on PIC, G_O2,max=0.01M^0.94; 95% CI=0.73–1.21; Table 3).

The mass dependence of G_O2,max was similar for scarabaeid and tenebrionid beetles regardless of whether analyzed as species averages (OLS: tenebrionid, G_O2,max=0.03M^0.79, r²=0.95; scarabaeid, G_O2,max=0.08M^0.81, r²=0.98) or phylogenetically corrected at the level of family (OLS on PIC, forced through zero: tenebrionid, G_O2,max=M^0.88, r²=0.90; scarabaeid, G_O2,max=M^0.90, r =0.92). The slopes of both of these relationships overlapped M^0.75 (for tenebrionid G_O2,max, 95% CI=0.34–1.59; for scarabaeid G_O2,max, 95% CI=0.63–1.25).

In this study we examined P_crit in conjunction with insect body size, and thus simultaneously assessed the net outcome of several supply and demand trade-offs that might affect insect oxygen limitation: increased oxygen demand (due to increased body size), decreased mass specific oxygen demand (due to increased body size), potentially increased oxygen supply (due to increased convective capacity from larger tracheal volumes) and potentially decreased oxygen supply (due to decreased diffusive capacity over longer tracheal lengths). Our data show that the capacity of the insect respiratory system matches oxygen needs across a large range of masses. Metabolic rates and tracheal conductances scaled similarly with size, and P_crit was size-independent, whether examined within species, across species within families or across the two tested beetle families.

Normoxic metabolic rates of beetles increased hypometrically (M^0.75 OLS, but M^1.04 SMA on PIC) with respect to beetle body size in our study, and did so with interspecific exponents similar to those in the published literature for insects [M^0.82 OLS, but M^0.75 phylogenetic generalized least squares (Chown et al., 2007)] and for beetles [M^0.66 OLS, but M^0.73 SMA (Riveros and Enquist, 2011)] despite the hypermetric scaling of the dimensions of the insect respiratory system (Lease et al., 2006; Kaiser et al., 2007; Greenlee et al., 2009). The scarabaeid scaling of metabolic rate in our study (M^0.78) was higher than that reported in the scientific literature [M^0.54 (Riveros and Enquist, 2011)], and our tenebrionid scaling exponent (M^0.73) fell between previously reported values of M^0.68 (Riveros and Enquist, 2011), M^0.94 (Lighton and Fielden, 1995) and M^1.06 (Duncan et al., 2002) (all OLS). These slope similarities occurred despite the fact that the intention of the present study was to achieve a baseline CO₂ release rate against which to index metabolic decline during oxygen limitation respirometry, so our normoxic CO₂ release rate measurements were for a truncated period of time compared with those of studies focused on measurement of resting metabolic rates.

All beetles investigated in this study showed a general decrease in mean CO₂ release rate as P_O2 decreased, though the patterns of CO₂ release rates varied across species (Fig. 4). Most tenebrionid species showed a simple and steady decrease in mean CO₂ release rate as P_O2 decreased, whereas most scarabaeid species showed an increase in mean CO₂ release rate at mild hypoxia, followed by a decrease in mean CO₂ release rate at extreme hypoxia. This suggests a temporary increase in scarabaeid tracheal conductance (ventilation frequency and/or tidal volume) at mild hypoxia, which may ameliorate/delay the effects of hypoxia at the tissue level. Alternatively, this increase in CO₂ release rate could be an indication of hypoxia-induced activation of escape behavior, as seen in some larvae (Wingrove and O'Farrell, 1999). Dissimilar CO₂ release rate patterns for the families may also be due to an inherent lack of discontinuous gas exchange cycles in most North American Tenebrionidae (Lighton, 1998).

P_crit in this study is the critical transition point between aerobic metabolic function of inactive animals and oxygen-compromised metabolic function. The P_crit for CO₂ release rate of all coleopteran species examined in this study was ≤3 kPa, a value that supports other evidence that insects tolerate much lower partial pressures of oxygen than vertebrates (reviewed in Greenlee and Harrison 2004a; Schmitz and Harrison, 2004). The mean P_crit of scarabaeid and tenebrionid species did not significantly differ, suggesting that gas exchange capacities are matched to metabolic rates similarly in these two families. However, the P_crit values of scarabaeid species were more constrained (i.e. occurred over a narrower range of values; P<0.05) than those of tenebrionids, suggesting that Scarabaeidae may have greater selective pressure on oxygen delivery capabilities than Tenebrionidae. This may be based on their life history, because some scarabaeid species live in burrows and/or decaying organic material, which often makes for hypoxic micro-environments (Holter, 1991; Holter, 1994), and other scarabaeid species may have high metabolic capacities associated with flight (Niven and Scharlemann, 2005).

Coleopteran P_crit did not vary with body size for inactive animals treated identically, suggesting that gas exchange capacities are well-matched to tissue needs across this wide range of beetle body sizes. The largest and smallest scarab species, D. granti (mean mass of 4.44 g) and Aphodius sp. 1 (mean mass of 5.01 mg), both had P_crit values of 0.9 kPa; the largest and smallest tenebrionid species (E. obscura, mean mass of 1.41 g, and T. castaneum, mean mass of 1.70 mg) both had P_crit values of 2.3 kPa (Table 2). Thus, our data support previous conclusions (Greenlee et al., 2007) that larger insect species are not more easily limited by oxygen delivery than smaller insects. However, the relationship between insect body size and oxygen delivery is a complex one. Proportional investment in the tracheal system is higher in larger insects (Lease et al., 2006; Kaiser et al., 2007), and insect developmental P_O2 has been shown to affect both adult body size (smaller at lower P_O2) (e.g. Klok et al., 2009) and tracheal system investment (lower at higher P_O2) (e.g. Henry and Harrison, 2004), which together offer clear evidence that insect body size is linked to insect oxygen delivery capacity (reviewed by Harrison et al., 2010). An additional consideration is that the animals in our study were measured mostly at rest or during low-level activity. Critical values may very well show different patterns with respect to body size when measured on animals completely at rest, or alternatively, during highly aerobic activities such as flight or running. Hypoxic limitations to activity may in fact be of greater ecological importance than hypoxic limitations at rest; for example, if P_crit during maximal activity were to positively scale with body size, gas exchange capacities may limit maximum body size in highly active insects.

G_O2,max scaled with mass in a manner similar to that of metabolic rate (Table 3); a similar result was found in an interspecific comparison of grasshoppers (Greenlee et al., 2007). This may have been achieved by the hypermetric scaling coefficients that exist for tracheal volume and air sac volume (reviewed earlier), and may enable the similar P_crit values seen in large and small beetles. Although G_O2,max may vary because of nutritional influences on RQ, G_O2,max was higher for the scarabaeid family than the tenebrionid family, consistent with the fact that scarabaeid species fly and have extensive air sacs, and thus likely have greater maximal oxygen needs and delivery capacities than tenebrionid species. The mass dependence of G_O2,max, however, was similar for scarabaeid and for tenebrionid beetles. Assessment of maximal conductance during maximal tissue needs could further elucidate whether gas exchange capacity limits maximum body size of insects. G_O2,max is likely higher during activity because of increased convection (and perhaps other changes), and conceivably the scope for overall conductance varies with size. Ideally, all of these tests would be conducted during maximal aerobic performance. However, this is technically challenging, and no scaling study has ever done this for any group of animals.

It should be noted that systematic variation in RQ, particularly interactions between body mass and P_O2, might have affected our assessment of mass effects on P_crit and G_O2,max, as well as on the standard errors of these values. Oxygen consumption rates were calculated assuming a constant RQ of 0.8. However, if, for example, larger animals were more sensitive to hypoxia, then we might expect larger animals to increase RQ more significantly during hypoxia (i.e. to have a higher CO₂ emission rate relative to oxygen consumption). This could cause the P_crit value for CO₂ emission to be higher than the P_crit for oxygen consumption for larger species; such an effect could also bias the scaling exponent for G_O2,max towards higher values. Oxygen consumption is much more technically challenging to measure over short time periods in small insects than CO₂ emission rates; thus, as yet, there are no data to suggest that RQ does vary systematically with mass and hypoxia in insects. However, eventually, it will be important to test this possibility to affirm the lack of a relationship between body mass and P_crit for aerobic metabolic rate in insects.

The interspecific scaling of P_crit has not previously been investigated for any group of insects for which we know how tracheal investment scales, and the intraspecific scaling of P_crit has not previously been reported for adults of any insect species. Here we investigated the effect of body size on normoxic and hypoxic CO₂ release rates and on P_crit for two families of beetles. As predicted, both tenebrionid and scarabaeid beetles exhibit mass-related metabolic scaling similar to hypometric equations reported in the literature. Coleopteran P_crit, in contrast, was not size-dependent. Although variance in P_crit was smaller for scarabaeid beetles than tenebrionid beetles, reflecting potential differences between these coleopteran families with respect to oxygen delivery constraints, P_crit was similar for large and small animals, regardless of family. The P_crit thus appears to be unaffected by body size for both tenebrionid and scarabaeid beetles.

However, morphological constraints on oxygen delivery capacity could limit maximum body size in insects (Kaiser et al., 2007) and other animals (Payne et al., 2010). Investment in structural support may also contribute to an upper size limit for vertebrates, because endoskeleton scales hypermetrically with body mass (Prange et al., 1979), although it probably does not generally do so for insects, because exoskeletal chitin increases isometrically with body mass (M¹) (Lease and Wolf, 2010). Two exceptions, interestingly, are Coleoptera and Orthoptera, where exoskeletal chitin scaling is hypermetric (M^1.1; statistically distinguishable from M¹ for Coleoptera) (Lease and Wolf, 2010). Regardless of the exoskeleton's potential role in limiting beetle maximal body size, there is a large and growing body of evidence that insect body size is constrained by tracheal oxygen delivery (Harrison et al., 2010). Our results, however, suggest that atmospheric oxygen level is not likely to limit maximal insect body size because of limitations on metabolic rate. Instead, it appears that the limit on insect body size may be trade-offs associated with the need for increased tracheal investment as insect size increases (Harrison et al., 2010; Kaiser et al., 2007; Lease et al., 2006) and/or that in some regions of the body (e.g. the legs) an increasing need for investment in the tracheal system may lead to space limitations (Harrison et al., 2010; Kaiser et al., 2007).

We thank Michael Quinlan and Ian Murray for assistance with arthropod acquisition; Blair Wolf and Jim Brown for input at preliminary stages of this project; Melanie Frazier for instruction on phylogenetic correction of data using R; and two anonymous reviewers for comments that improved the quality of the manuscript.