Isometric spiracular scaling in scarab beetles—implications for diffusive and advective oxygen transport

  1. Julian M Wagner
  2. C Jaco Klok
  3. Meghan E Duell
  4. John J Socha
  5. Guohua Cao
  6. Hao Gong
  7. Jon F Harrison  Is a corresponding author
  1. School of Life Sciences, Arizona State University, United States
  2. Department of Biomedical Engineering and Mechanics, Virginia Tech, United States
  3. School of Biomedical Engineering, ShanghaiTech University, China
  4. Department of Radiology, Mayo Clinic, United States

Abstract

The scaling of respiratory structures has been hypothesized to be a major driving factor in the evolution of many aspects of animal physiology. Here, we provide the first assessment of the scaling of the spiracles in insects using 10 scarab beetle species differing 180× in mass, including some of the most massive extant insect species. Using X-ray microtomography, we measured the cross-sectional area and depth of all eight spiracles, enabling the calculation of their diffusive and advective capacities. Each of these metrics scaled with geometric isometry. Because diffusive capacities scale with lower slopes than metabolic rates, the largest beetles measured require 10-fold higher PO2 gradients across the spiracles to sustain metabolism by diffusion compared to the smallest species. Large beetles can exchange sufficient oxygen for resting metabolism by diffusion across the spiracles, but not during flight. In contrast, spiracular advective capacities scale similarly or more steeply than metabolic rates, so spiracular advective capacities should match or exceed respiratory demands in the largest beetles. These data illustrate a general principle of gas exchange: scaling of respiratory transport structures with geometric isometry diminishes the potential for diffusive gas exchange but enhances advective capacities; combining such structural scaling with muscle-driven ventilation allows larger animals to achieve high metabolic rates when active.

Editor's evaluation

This paper is of interest to biologists looking to understand the scaling and geometric constraints of respiratory systems. The work shows that as beetles evolve bigger bodies, their spiracles scale with geometric isometry. As such, advective conductance increases more rapidly with body mass than does their metabolic rate, unlike their diffusive conductance, indicating that bulk air flow is required to sustain respiration in larger insects.

https://doi.org/10.7554/eLife.82129.sa0

Introduction

As animal species evolve different sizes, many aspects of their physiology and morphology scale disproportionately with one another (allometrically) with consequences for animal behavior, life history, evolution, and diversity (Bonner, 2006; West, 2017; Sibly et al., 2012). A driver of this disproportionality lies in the nonlinear scaling of geometry: doubling the radius of a sphere gives quadruple the surface area and octuple the volume; in a similar way, scaling up a small body plan gives drastically altered ratios of surface area, volume, and body length. Since the challenges associated with changes in body size have a geometric origin, they are ubiquitous. As a result, understanding the mechanisms animals use to overcome the effects of changes in geometric proportions remains a pervasive, important, and challenging biological problem. Three related aspects of animal function modulated by allometry are scaling of animal metabolic rates, often scaling with mass0.75 (West et al., 1997; Gillooly et al., 2016), limits on the maximal body sizes of specific taxa (Kaiser et al., 2007; Lane et al., 2017), and gas exchange strategies (Perry et al., 2019). For gas exchange, volume of tissue and hence potential gas exchange needs of animals scale with the cube of length (like the sphere), while surface areas tend to scale with the square of length. This leads to a decline in the ratio of surface area to volume with size. As a consequence, when animals evolve larger sizes, they may need to adapt the proportions of their respiratory structures or increase the use of advection (bulk flow) to avoid facing limitations based on processes that depend more on surface area such as diffusion.

Limitations on the capacity of larger animals to support oxygen delivery to tissues have been proposed to drive the hypometric scaling of metabolic rates with size, as well as the hypometric scaling of many physiological (e.g., heart and ventilation rates) and behavioral/ecological traits (e.g., territory size, dispersal distance) (Bonner, 2006; West, 2017; Sibly et al., 2012; West et al., 1997; Banavar et al., 2010). However, competing theories suggest that other factors, such as heat dissipation constraints, nutrient uptake constraints, or performance-safety trade-offs, drive the hypometric scaling of metabolic rates and correlated variables, and that evolutionary adaptations of respiratory systems to size allow animals to match oxygen supply to need regardless of body size (Glazier, 2014; Harrison, 2017; Harrison, 2018; White and Kearney, 2014). One important step in resolving this controversy is determining how respiratory structures and mechanisms scale. The vast majority of prior studies of the scaling of gas exchange structures have focused on vertebrates, especially mammals. In contrast, there is relatively limited information on the scaling of gas exchange structures in invertebrates, despite the fact that most animal species are invertebrates (Gillooly et al., 2016; Peters, 1983). The scaling of the insect respiratory system is of particular interest, as aspects of tracheal system structure have been reported to scale hypermetrically, in contrast to the isometric or hypometric scaling of respiratory structures in vertebrates, supporting the hypothesis that possession of a tracheal respiratory system limits insect body size (Kaiser et al., 2007; Harrison et al., 2010; Vogt and Dillon, 2013; Harrison et al., 2005; Greenlee and Henry, 2009). Here, we report the first study of the scaling of insect spiracles, the gateway of air into the body and the first step in oxygen delivery from air to tissues, presenting new insight into a key morphological pathway in this most biodiverse clade of terrestrial animals.

Gas exchange usually occurs in a series of steps, often a sequence of alternating diffusive and advective processes. The capacity for a respiratory surface to conduct oxygen (diffusive conductance, Gdiff) can be described using Fick’s law, that is

(1) Gdiff= areathicknessK,

where K is Krogh’s diffusion constant for oxygen in the barrier. The diffusive oxygen exchange across the surface (Jdiff, mol s–1) is given by

(2) Jdiff=GdiffΔPO2,

where ΔPO2 is the partial pressure gradient for oxygen across the exchanger. When gas exchange relies on diffusion across a barrier, either Gdiff or ΔPO2 must increase to match the increased oxygen demand inherent in a larger body size (a larger relative tissue volume), or oxygen supply will limit metabolic rate. Increases in Gdiff may be accomplished by either a decrease in diffuser thickness or increase in area. The ΔPO2 from air to mitochondria can be no greater than atmospheric PO2 (approximately 21 kPa at sea level); this biophysical constraint sets an upper limit on the ability of large animals to utilize increases in ΔPO2 to overcome a Gdiff that does not increase in proportion to oxygen consumption rate.

The scaling of surface area, barrier thickness, and ΔPO2 for gas exchangers across species of animals varies with clade and developmental stage. In adult vertebrates, the scaling of the passive diffusing capacity of the lung across species scales hypometrically, but matches the scaling of metabolic rates (Gillooly et al., 2016). However, the scaling of respiratory morphology differs in endotherms and ectotherms (Gillooly et al., 2016), as barrier thickness is constant with size in ectotherms, but increases with size in endotherms. As a consequence, endotherms must scale surface area of the lung more steeply than ectotherms to account for their increased barrier thickness and match the scaling of Gdiff to the scaling of metabolic rate. Bird eggs, which rely on diffusion through pores for oxygen, employ a different strategy. Eggs of larger species have relatively thicker shells (scaling with mass0.45), increasing barrier thickness with size, likely to mitigate a higher likelihood of mechanical damage (Ar and Rahn, 1985). Pore area increases proportionally with shell thickness, so Gdiff per pore is relatively constant across egg size, and larger eggs have a higher density of pores (Tøien et al., 1988). The scaling of the Gdiff of the shell overall matches the scaling of metabolic rate across species, with both scaling hypometrically (Ar and Rahn, 1985; Tøien et al., 1988). Pycnogonids (sea spiders) show yet another pattern for the diffusing capacity of their respiratory structures (their legs). Unlike either bird eggs or vertebrate lung membranes, pycnogonid barrier thickness scales isometrically (Lane et al., 2017). As in bird eggs, there is an increase in the area-specific diffusing capacity of the leg cuticle of larger pycnogonids, although the morphological basis remains unclear (Lane et al., 2017). However, the increases in diffusive conductance of the respiratory exchanger are not sufficient to match increases in metabolic rates with size, so the ΔPO2 across the leg cuticle increases in larger pycnogonid species, which may limit maximal species size in this taxa (Lane et al., 2017).

Advective steps in gas exchange can occur using either air or aqueous media and represent a second broad strategy for delivering gases to tissues. The morphological capacity for a structure to transport a fluid by advection, Gadv, m4 s kg–1, can be described from Poiseulle’s law,

(3) Gadv=area28 dynamic viscosity  length.

Given this relationship, the advective transport of oxygen through the structure (Jadv, mol s–1) is given by

(4) Jadv=Gadv[O2]ΔHP

where [O2] is the concentration of O2 in the fluid (mol m–3), and ΔHP is the hydrostatic pressure gradient across the structure (kg m–1 s–2). Some examples in mammals illustrate how morphology scales for structures relying on advection. In mammals, the radius of the aorta scales with mass0.375, and the length of the aorta scales with mass0.25, suggesting that Gadv of the aorta scales with mass1.25 (4 * 0.375 − 0.25) (Holt et al., 1981). The tracheal–bronchial system is the advective structure for air transport in vertebrates; radius scales with mass0.39 while lengths scale with mass0.27, suggesting that Gadv for mammalian aorta and bronchial systems scale with mass1.29 (Stahl, 1967). Gdiff for these same structures, on the other hand, scale as mass0.5. Thus, the morphological structures of mammalian respiratory systems seem to scale such that advective capacities increase more than metabolic rates in larger species, while diffusive capacities decline. Of course, mammalian oxygen transport through the bronchial tree and circulatory system is thought to rely on advection regardless of size.

The design of the insect tracheal system is fundamentally different from either the vertebrate respiratory system or that of skin-breathing aquatic invertebrates; and it remains unclear how the components of the system scales. In insects, spiracles provide a (usually) gated opening to an air-filled conduit system that branches through the insect, with oxygen transported in the gas phase to the most distal surface of the tracheoles, with transport then occurring in the liquid phase from tracheole to mitochondria (Harrison et al., 2013). Since Krogh’s demonstration that diffusion should suffice for oxygen transport in a relatively large Lepidopteran larvae, diffusion has been considered to be an important mechanism of gas exchange in insects (Krogh, 1920; Hetz and Bradley, 2005). However, many insects, including small ones, supplement diffusion with advection, especially when active (Harrison et al., 2013; Socha et al., 2010; Wasserthal et al., 2018). The spiracles are potentially an important step in insect gas exchange, since they are relatively small (difficult to see by eye in most insects) and yet must sustain all gas flux. It appears that spiracle morphology just matches gas exchange needs at peak metabolic performance with little additional capacity; for example, sealing of just one thoracic spiracle reduces flight metabolic rate in Drosophila (Heymann and Lehmann, 2006). At present it is not clear whether the size of spiracles should best match Gdiff, Gadv, or some other physiological capacity. To shed light on this question, we used micro-computed tomography (micro-CT) (Iwan et al., 2015) to provide the first interspecific examination of the scaling of spiracles, using 10 species of scarab beetles spanning two orders of magnitude in mass, including some of the most massive extant species (Figure 1).

Scarab beetles include large bodied individuals and have eight spiracles.

(A) Phylogenetic tree for the scarab beetles used in this study showing size distribution among clades (branch lengths are meaningless). (B) Location of the eight spiracles in the scarab body. (C) 3D reconstruction of the tracheal trunks in the thorax, legs, and abdomen of Dicronorrhina derbyana; spiracles are shown in white. The larger images of spiracles show the size of the opening (dark in color) compared to the mushroom-shaped (white) atrium behind and the differences in spiracle shape. (D) Transverse X-ray slice through the third abdominal spiracle with diameter, α, and depth, β, measures illustrated.

Results

All spiracles scaled with geometric isometry for area, depth, area/depth (which corresponds to diffusive capacity), and area2/depth (which corresponds to advective capacity) Figure 1 (Figure 2, Figure 2—figure supplements 3 and 4, Supplementary files 1 and 2). Some example regressions with confidence intervals for the slopes are shown in Figure 2, illustrating scaling isometry, the larger size of the mesothoracic spiracle, and the tight size distribution of the more anterior spiracles as compared to the posterior; regressions and confidence intervals for each spiracle are in Supplementary file 4. The mesothoracic spiracle was much larger than any of the other spiracles, consistent with the general trend of increasing spiracular area closer to the anterior of the animal (Figure 2—figure supplement 3, Supplementary file 2). The area of the mesothoracic spiracles was approximately four times larger than both the metathoracic spiracles, and abdominal spiracles 1–3, and abdominal spiracles 4–6 were approximately half the size of the more anterior abdominal spiracles (Figure 2—figure supplement 3). Not only were anterior spiracles larger than posterior, but they also had much lower variability around the trend line within the species assayed in this study (Figure 2, Figure 2—figure supplement 3). In comparison, the depth of the spiracles showed much less variability in tightness of the distribution around the scaling trend lines (Figure 2, Figure 2—figure supplement 3).

Figure 2 with 4 supplements see all
Isometric scaling of scarab beetle spiracles.

Spiracle area scales with geometric isometry (A, B), with much tighter distribution about the isometric model for the large anterior spiracles compared to the smaller posterior spiracles. In A, B, D, and E, the light gray lines show isometric scaling (slopes of 0.67 for area and 0.33 for depth). (C) shows estimates for the variability for regression models for the various spiracles (S mesothoracic, T metathoracic, 1–6 abdominal), calculated as the standard deviation divided by 10regression intercept, which represents the spiracle area for a 1 g beetle. Black diamond and line show the median and 2.5th–97th residual standard deviation divided by 10regression intercept calculated on nonparametric bootstrap samples. The white diamond and gray interval represent the median and 3rd–97th highest posterior density interval for the standard deviation divided by 10regression intercept calculated from parameter samples from the Bayesian regression. We see a trend toward much higher variability in posterior spiracle area as compared to anterior. In contrast to spiracle area, spiracle depth shows similar variability in all spiracles (D–F) regardless of position.

The diffusive capacity of a spiracle (Gdiff, nmol s–1 kPa–1) at 25°C was calculated using Equation 1, with K calculated as D * β, with D (the diffusivity constant for O2 in air) = 0.178 cm2 s–1 (Lide, 1991) and β (the capacitance coefficient for oxygen in air) = 404 nmol cm–3 kPa–1 (Piiper et al., 1971). To calculate total diffusive or advective capacity per beetle, the diffusive/advective capacity for all eight spiracles was summed and doubled (to obtain the total for both sides of the animal). As with individual spiracles, the combined diffusing capacity of all the spiracles scaled isometrically, with a slope not significantly different from 0.33 (Figure 3A, Supplementary files 3–5). The upper 95% confidence limit for this slope was 0.505, well less than any reported interspecific scaling exponent for metabolic rate.

Scaling of the spiracles is insufficient for diffusive capacities across the spiracles to match expected increases in metabolic rate, so for pure diffusive gas exchange, the required partial pressure for oxygen must increase with size.

In contrast, advective capacities through the spiracles likely match or exceed the scaling of flight metabolic rate. (A) The log10 of total spiracular diffusive capacity per beetle (nmol s–1 kPa–1) increases with beetle size, with a slope estimated as 0.39. This slope was not significantly different from the 0.33 predicted from isometric scaling. The upper 95% confidence limit for the slope was 0.505, lower than any reported metabolic scaling slopes for insects. A metabolic rate slope of 0.75, commonly found for resting insects and animals more generally, is shown in light gray. (B) The log10 PO2 gradient (kPa) across the spiracles required to diffusively supply the oxygen demand of beetles increases with beetle size. The lower, purple line shows the estimated PO2 gradient across the spiracles to support diffusive gas exchange at rest; this increases from approximately 0.05–0.49 kPa as beetles increase in body size across this range. The less steeply upward sloping greenish and steeper yellow lines shows the estimated PO2 gradient across the spiracles during flight, assuming a 90× aerobic scope if flight metabolic rates scale with an exponent of 0.67 or 1.19, as found for large insects and small insects, respectively (Duell et al., 2022). The upper gray band indicates where the partial pressure of oxygen needed for calculated beetle metabolic demand exceeds the 21 kPa atmospheric oxygen level. (C) Hypermetric scaling of log10 summed advective capacity (m3 s–1 kPa–1) versus log10(body mass). There are uncertainties in the scaling of metabolic rate in flying insects: depending on size and study, slopes have ranged from 0.67 to 1.19. Confidence limits for advecting capacity include 1.19 but not 0.67. Equations of regression lines and confidence intervals for the slopes are shown for each plot.

The ∆PO2 across the spiracles if gas exchange occurs completely by diffusion was calculated for various oxygen consumption rates using Equation 2. To calculate the ∆PO2 across the spiracles needed to supply the beetle’s total resting metabolic demand by diffusion, the metabolic rate for a quiescent beetle at a body temperature of 25°C of a given mass was estimated from Chown et al., 2007 with the following equation: log10(metabolic rate (μW)) = 3.2 + 0.75 log10(mass (g)). This metabolic rate was converted to an oxygen consumption rate assuming an RQ of 0.85 (20.7 μj nl–1). For resting metabolic rate (slope of 0.75, shown as the repeated light gray background lines), the required pO2 gradient across spiracles necessary to supply oxygen by diffusion was small but increased by an order of magnitude, from about 0.05 kPa in the smallest beetles to nearly 0.5 kPa in the largest scarabs (Figure 3B).

Estimating the scaling of gas exchange during flight of flying beetles has uncertainties. Niven and Scharlemann calculated a scaling coefficient for insect flight of 1.07 (Niven and Scharlemann, 2005). Duell and Harrison recently reassessed the scaling of flight metabolism in insects, and found that the scaling coefficients for flight metabolic rates depended on insect size, with a scaling coefficient of 1.19 for insects weighing less than 58 mg and of 0.67 for insects weighing more than 58 mg (Duell et al., 2022). As all of the beetles used in this study were larger than 58 mg, it seems likely that their flight metabolic rates scale hypometrically, with a slope less than 1. Scaling patterns can vary across clades (Ehnes et al., 2011; Capellini et al., 2010), so ideally, we would employ measures of the flight metabolic rates of the scarab beetles in this study. Unfortunately, most beetles cannot sustain flight in the small containers required for respiromety. Flight metabolic rates have as yet only been reported for four species (Duell et al., 2022), and the slope of the scaling relationship for these four species has great uncertainty. Thus, based on the current literature, the scaling exponent flight metabolic rates in insect likely ranges between 0.67 and 1.19, depending on size.

For calculations of the partial pressure gradient across the spiracles during flight, a critical factor is the magnitude of the aerobic scope. Three studies to date measured resting and flight metabolic rates for beetles ranging in body mass from 0.3 to 1.3 g; two used tethered flight and one free flight (Chappell, 1997; Rogowitz and Chappell, 2000; Auerswald et al., 1998). Because it is challenging to induce maximal flight performance and measure aerobic metabolic rate, and we are interested in what the oxygen partial pressure gradient might be across the spiracles during maximal flight performance, we used the highest aerobic scopes reported for individual beetles in these studies, which were 80, 90, and 110× higher than resting metabolic rates. We used the median of these values (90×) to estimate maximal aerobic metabolic rate during flight relative to quiescent one gram beetles. Because there is uncertainty in the scaling of metabolic rates during flight, the required PO2 gradient across the spiracles to support gas exchange by diffusion at rest and during flight was calculated by rearranging Equation 2 and performing unit conversions as follows:

(5) ΔPO2 (kPa)=((10log10(AS) + 3.20+EXPlog10(mass (g))μW)(1 μJs1 μW)(nL20.7 μJ)(1 nmol24.5 nL)(areadepth (cm) )(0.178 cm2sec)(404 nmolcm3kPa)),

where conversion factors of 20.7 kJ/l and 24.5 mol/l were assumed for O2 at 25°C, AS is the aerobic scope (1 for resting [log10(1) = 0 in the equation] and 90 for a flying 1 g insect [log10(90) = 1.954 in the equation]), and EXP is the scaling exponent for metabolic rate.

For small beetles, the estimated PO22 gradient across spiracles during flight was 2–5 kPa. Thus, plausibly, beetles in the smallest size range may be able to deliver sufficient oxygen to the tissues by diffusion, though further studies of conductance of the tracheal system between the spiracles and flight muscles will be required to answer this question. For the largest beetles, the required PO2 gradient across spiracles during flight substantially exceeded 21 kPa, indicating that during maximal aerobic flight performance, diffusion cannot supply oxygen across the spiracles, and certainly not to the flight muscles (Figure 3B, Supplementary file 5). Regardless of whether flight metabolic rate scales with exponents of 0.67–1.19, because metabolic rates increase more with size than spiracular diffusing capacity, the required PO2 gradient across spiracles increases with body size for diffusive gas exchange (Figure 3B).

Advective capacity was calculated using Equation 3, assuming a dynamic viscosity of air of 1.86 × 10–8 kPa s (Lide, 1991). The calculated advective capacity for all spiracles increased with an estimated slope of 1.1, that was greater (95% confidence limits 0.84–1.34) than the minimum scaling exponent for flight metabolic rate (0.67), also greater than the estimated slope of metabolic rate for resting insects (slope of 0.75, light gray lines), but included maximum scaling exponent reported for flight metabolic rates in insects (1.19, Figure 3C).

Discussion

Spiracles scaled with geometric isometry. Isometric scaling of diffusive capacities means that diffusion becomes increasingly less able to meet oxygen demands in larger beetles, with the required gradient for oxygen transport by diffusion through the spiracles increasing by an order of magnitude over two orders of magnitude in body mass. Conversely, our data demonstrate that the advective capacities of the spiracles scale more positively than resting metabolic rates. For flight metabolic rates, uncertainties in the scaling exponent for flight metabolic rates of beetles means that we can only conclude that the scaling exponents for advective capacities of the spiracles may match or possibly exceed those of metabolic rates. These results demonstrate that large insects must rely on advection through the spiracles in order to achieve their maximal aerobic flight metabolic rates. Our results also imply that there is no physical constraint associated with spiracular gas exchange that limits insect size and metabolic rates.

It is important to note that our analysis only assessed required PO2 gradient across spiracles, not within the entire tracheal system. Within the body of insects, gases must be transported through the large tracheal trunks, and then down the branching smaller tracheae and tracheoles in the gas phase, and then finally through liquid phases in the ends of the tracheoles and from the tracheoles to the mitochondria. As yet, we have little information on the relative resistances of these various steps. Based on the PCO2 gradient between the spiracles and tracheal trunks, and between the tracheal trunks and the hemolymph (perhaps similar to cellular PCO2), the resistance of the internal tracheal system to CO2 transport to active muscles likely substantially exceeds that of the spiracles in active, locomoting animals, whereas spiracular and tracheal resistances may be similar in resting animals (Harrison, 1997). This raises the interesting question of whether large insects can supply their resting metabolic rate by diffusion alone. The fact that the calculated required PO2 gradient across the spiracles required to sustain resting metabolic rate for the largest beetles in this study is only 0.5 kPa would suggest that the answer is yes. This conclusion is supported by our experience (unpublished observations) that even very large larval and adult scarab beetles (>30 g) can recover from anoxia, which strongly suggests that diffusion can sustain at least the minimal aerobic metabolic rate necessary to restart ventilation.

While the spiracles scale isometrically in beetles, this pattern does not occur universally for tracheal structures, or consistently across clades. Comparing tenebrionid beetles interspecifically, the leg tracheae scale hypermetrically, but the head tracheae scale isometrically (Kaiser et al., 2007). Within a bumblebee species, one spiracle scales isometrically (Vogt and Dillon, 2013). In the leg of growing locust (Schistocerca americana), the diffusing capacity of the large longitudinal tracheae of the leg scales hypometrically (Harrison et al., 2005), whereas in a growing caterpillar (Manduca sexta), diameters of most tracheae scale isometrically (Lundquist et al., 2018). Why different scaling patterns are observed in these different cases is unclear; more in-depth analysis of the required gas transport and the mechanism of transport are needed to evaluate the scaling of individual tracheal system structures. Plausibly the various steps in gas exchange scale similarly (a hypothesis of symmorphosis) as has been suggested for mammalian respiratory systems (Weibel et al., 1991), but resolution of this question in insects will require further study.

Diffusive capacities of the spiracles scaled with mass0.39, well below the scaling slope for resting oxygen consumption rate (approximately 0.75); thus, diffusion across the spiracles becomes more challenging for larger insects. The required O2 gradient across the spiracles to supply the metabolic demand by diffusion increases by approximately an order of magnitude from our smallest to largest beetles, but the size effect on the required PO2 gradient is less important than the effect of activity. For quiescent beetles, the PO2 gradients across the spiracles necessary for diffusion are low (0.05–0.5 kPa depending on size). However, during endothermic flight, the required PO2 gradient across the spiracles increases from 5 to 35 kPa for a scaling exponent of 0.67 or from 2 to 174 kPa for a scaling exponent of 1.19, which is impossible to achieve because the maximum partial pressure of oxygen in air is only 21 kPa. With metabolic rates scaling with mass0.75 and spiracular depth with mass0.33, spiracular area would need to scale with mass1.08 (0.75 + 0.33) to conserve the required PO2 gradient to support diffusion across all insect sizes.

By contrast, advective capacity scales with mass1.1, exceeding or matching the scaling of flight metabolic rate, depending on insect size (Duell et al., 2022). Interpretation of these results is challenging as we do not know how ventilatory flow varies with size in insects. Ventilatory airflow is difficult to measure in insects, because there are so many spiracles, because these spiracles can be variably gated, and because flow can be tidal or unidirectional. If insects can match ventilation to flight metabolic rate across body size, then no changes in oxygen extraction efficiency will be necessary. If ventilatory airflow is matched to flight metabolic rate, then the scaling of advective capacities of the spiracles with an exponent of 1.1 implies that the pressures required to drive convection either remain the same with size (if flight metabolic rate scales with an exponent near 1.1) or falls with size (if flight metabolic rate scales with an exponent of 0.67 or 0.75), for example. Any conclusions on this topic must be very cautious because in the beetles that have been best studied, ventilation during flight includes both tidal flow through some of the thoracic spiracles and unidirectional flow out the abdominal spiracles (Miller, 1966). The much larger size of the thoracic than abdominal spiracles suggests that ventilation of the flight muscles may be primarily tidal through the thoracic spiracles, with unidirectional flow out the abdominal spiracles supplying other parts of the body.

We also observe much tighter distributions in the scaling pattern for the area of the large anterior spiracles as compared to the smaller posterior ones. This result may suggest that the large anterior spiracles are more constrained in their morphology, since they presumably provide the gas exchange needed for metabolically demanding tissues like the flight muscle.

There are some important caveats when interpreting our data. Insect spiracles are morphologically complex structures. We made 3D measurements using tomographic imaging, but analyzed air transport capacities by modeling the spiracle as a cylinder, which could over or underestimate capacity depending on factors like valve position and the complex shape of the spiracular atrium. Furthermore, our CT scans were conducted on sacrificed specimens; the assessment of spiracles of living insects could offer insights not possible with static morphology. For example, living insects might control the shape of the bellows-like atrium and valves in a concerted way to promote air flow. As yet, we know little about how the tracheal system structure and function might scale differently in different species. As an example of a fairly dramatic difference in tracheal system function across beetle clades, some Cerambycid beetles use draft inward ventilation through the mesothoracic spiracle during flight, whereas most scarab beetles autoventilate the thorax using wing movements (Miller, 1966; Amos and Miller, 1965). Dung beetle species vary between exhaling nearly all to none of their air out the mesothoracic spiracles, with species from more arid environments exhibiting more expiration via the mesothoracic spiracle (Duncan and Byrne, 2005). Multiple beetle species collapse parts of their tracheal system to produce advective airflow, both in adults and as pupae (Pendar et al., 2015; Socha et al., 2008; Waters et al., 2013). Though it is unclear how respiration via tracheal collapse differs with size and in different species, the prevalence of active breathing further highlights the need for advective airflow for insect function. The phylogenetic, life history, and environmental influences on tracheal system structure, function, and scaling seem likely to be a ripe area for future research.

Our finding of isometric scaling of insect spiracles would appear to differ from reports for tracheae of mammals, in which radius scales with mass0.39 and lengths with mass0.27 (Tenney and Bartlett, 1967). However, confidence limits from our study included these scaling slopes, suggesting that respiratory scaling of tracheal morphology may be congruent across these disparate groups. Tenney and Bartlett’s study (Tenney and Bartlett, 1967) had greater power, as it examined 43 species ranging over 5 orders of magnitude in body mass. However, it worth noting that they did not consider error in their slope estimates, test for statistical differences in slopes between the radii and lengths, or consider phylogeny, so the conclusion that mammalian tracheae scale nonisometrically (and differently from insect spiracles) could benefit from rigorous comparative analysis.

Conclusions: Insect spiracles scale with geometric isometry in beetles, which means that diffusive capacities increase much less than metabolic rates as body size increases, while advective capacities increase similarly or more rapidly than do metabolic rates. These are general principles of gas exchange that should apply to respiratory structures of any animal clade exhibiting isometric scaling. For resting insects, the required PO2 gradient across the spiracles necessary to supply resting oxygen consumption increases strongly with size, but remains small in even the largest insects, suggesting that resting gas exchange can be accomplished by diffusion even in very large insects. In contrast, our data clearly demonstrate that maximal aerobic flight cannot be accomplished by diffusion in large beetles.

Methods

Acquisition of raw micro-CT images

Seventeen individuals of 10 species (1–2 individuals per species) of scarab beetles (Figure 1a) with a size range from 0.097 to 18 g were obtained via breeders from online sources. We examined the following species: Goliathus goliathus, Coelorrhina hornimani, Dicronorrhina derbyana, Mecynorrhina torquata, Eudicella euthalia, Protaetia orientalis, Popilia japonica, Trypoxylus dichotomus, Dynastes hercules, and Cyclocephalis borealis. Most species had both male and females represented. Most specimens were scanned using a micro-CT scanner (Skyscan 1172, Bruker, Bilerica, MA, USA) equipped with a Hammamatsu 1.3 MP camera and Hammamatsu SkyScan Control software at Virginia Tech. To maintain tracheal structure in their natural configuration, we used a minimal preparation of fresh samples (Socha and DeCarlo, 2008). All beetles were killed using ethyl acetate fumes, stored at 4°C, and scanned within 3 days. They were warmed back to room temperature to avoid motion artifacts from fluid flow, placed in X-ray translucent polyimide tubing (Kapton, Dupont), and centered on a brass stage with putty. Power was set at 10 W, voltage was adjusted for optimum brightness and contrast (70–96 kV), with currents between 104 and 141 μA. Beetles were scanned with 0.4° rotation steps for 180° with frame averaging. A flat-field correction was applied to all scans to account for subtract aberrations. All raw projection images were collected a size of 1024 × 1280 pixels, yielding a scaling of 12–98 μm/pixel that was independent of beetle size. Average measured spiracle dimensions for width/height/depth for the smallest beetles were around 10 pixels and hence resolvable with minimally 10% resolution. Small beetles could be captured in a single scan, but larger beetles were scanned sequentially in segments along their longitudinal axis by varying their position relative to the beam.

Dynastes hercules were too large to be scanned with the same instrument, so these beetles were imaged using an in-house-built bench-top micro-focus X-ray computed tomography (micro-CT) platform (see Sen Sharma et al., 2014; Gong et al., 2015 for details) at Virginia Tech. The X-ray tube (Oxford Instrument, Inc) was operated at 70 kV and tube power was fixed at 20 W. Images were collected with an X-ray flat-panel detector (model C7921, Hamamatsu, Inc) operated at 1 × 1 binning mode, with a detector element size of 50 × 50 µm. The axial scanning field-of-view was 37.2 mm in diameter. In each scan, images were collected at 0.5° intervals as the beetle was rotated through 360°, resulting in a total of 720 X-ray projections per scan. Because the specimen was larger than the field of view, multiple scans were conducted sequentially along the animal’s anterior–posterior axis to image the entire body. The axial slice images were reconstructed using the standard filtered back-projection reconstruction algorithm, with an image matrix of 1008 × 1012 px and an isotropic pixel size of 36.8 × 36.8 µm.

Image reconstruction and measurements

Raw micro-CT images were imported into NRecon reconstruction software from SkyScan (Bruker, Bilerica, MA, USA). Ring artifact and beam hardening corrections were applied where necessary, and contrast was optimized using the software’s interactive histogram feature. For large beetles that required multiple scans, reconstructions were set to align and fuse automatically. Slices generated in NRecon were imported into Avizo 9 software (Thermo Fisher Scientific, Waltham, MA, USA) for 3D reconstructions.

Spiracles were identified by the characteristic slit-like shape of the opening, and the bellows-shaped air sac behind it (Figure 1B–D). Spiracle locations were confirmed by dissection on representative specimens. Measurements were taken for one of the paired six abdominal and two thoracic spiracles for each beetle (Figure 1B, C). A few scans had small aberrant regions (e.g., blurriness) due to challenges in scanning, so which spiracle was measured varied between the symmetric right and left side of an animal based on which region of the scan was best resolved. Diameters of the spiracular opening were measured at the widest point of opening to the outside air in the transverse and sagittal planes. Area of the opening was then calculated assuming an elliptical shape, with the lengths of the semi-major/minor axes being the diameters measured in the transverse and sagittal planes (Figure 1D). The depth of the spiracle was measured from the outer opening to the interior valve connecting the spiracle to the tracheal trunk (Figure 1D). The sex, mass and dimensions of all measured spiracles are provided in Supplementary files 1 and 2.

Calculations and statistical analyses

We measured the scaling relationships for each spiracle separately, using log–log plots. As dependent variables in these regressions, we tested log10 transformed spiracular depth, area, area/depth (as an index of the diffusive capacity of the spiracle, see Equation 1), and area2/depth (as an index of the resistance of the spiracle to advective flow, see Equation 3).

We used two statistical approaches to assess the role of the phylogenetic relatedness of the animals in scaling patterns: a phylogenetic generalized linear model (pGLS) and a generative Bayesian model. We ran and plotted pGLS results in R (Garnier, 2016; Orme, 2018; Pinheiro et al., 2021; Harmon et al., 2008; Revell, 2012; Paradis et al., 2004; R Development Core Team, 2016). The goal of pGLS is to account for nonindependence of data points due to phylogenetic relatedness in construction of the linear model, which requires a phylogeny of the study species (Freckleton et al., 2002). We spliced together such a phylogeny from multiple published scarab phylogenies. The branch positions for beetle subfamilies (Dynastinae, Rutelinae, and Cetoniinae) were determined using Hunt et al., 2007. The branches within Dynastinae were placed in the tree using work from Rowland and Miller, 2012, and the branches of Cetoniinae determined with two trees, one from Holm, 1993; Micó et al., 1993 and the other Holm (Holm, 1993; Micó et al., 1993). Four of the genera in this study were present in the tree for Coleoptera constructed by Bocak et al., 1993, which indicated the same branch places as our spliced tree, providing some positive confirmation for this tree structure. Branch lengths were set to a value of one because actual branch lengths are not known. Similar to pGLS, we built a Bayesian model assuming that the data were generated by a multivariate normal distribution with the covariance matrix given by the amount of shared ancestry between species (amount of shared branch length). See supplemental methods for the details of the model, selection of priors, and python code. Detailed information on the analysis is available at the website for the paper here: https://julianmwagner.github.io/spiracle_scaling/ and at the corresponding repository (https://github.com/julianmwagner/spiracle_scaling, copy archived at swh:1:rev:0ad9383b23d156430adcaae2d53861b595205e72; Wagner, 2022). Analyses indicated that the parameter characterizing the degree of phylogenetic signal in our data (λ) was nonidentifiable (Figure 2—figure supplements 1 and 2); this result means that our data do not inform this parameter and it could take on any value from zero (no phylogenetic signal) to one (strong phylogenetic signal) with similar probability. Hence, we opted to omit the use of phylogenetic covariance from our models since (1) the total nonidentifiability made selecting a single λ via maximum likelihood for the frequentist pGLS dubious, and (2) including it added no explanatory value to our Bayesian regression (parameter samples for λ were essentially straight from the prior). We instead used nonparametric bootstrapping (10,000 bootstrap replicates with ordinary least squares regression slopes/intercepts/residual standard deviation as the summary statistics) to obtain confidence intervals for our slope and intercept values. Additionally, we performed a Bayesian linear regression. Our model was a normal likelihood with mean given by a line with slope and intercept parameters. To obtain parameter estimates, we sampled using the Stan implementation of Hamiltonian Monte Carlo (cmdstanpy) in Python. See supplemental methods for the details of the model, selection of priors, and Python code and at the paper website/repository listed above. No data were excluded.

We defined isometric scaling as scaling as follows: mass0.67 for areas mass0.33 for area/depth mass1 for area2/depth, according to basic principles of geometric similarity (assuming mass is proportional to volume). We observed whether the 95% confidence interval given by bootstrapping/parameter samples for the slope of our measures of spiracle morphology overlapped with the isometric prediction. To produce any p values, we calculated the number of bootstrap replicates with test statistic at least as extreme as a particular value of interest, for example slope compared to isometry.

Data availability

All data are provided in the supplementary files.

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Decision letter

  1. George H Perry
    Senior and Reviewing Editor; Pennsylvania State University, United States
  2. Philip GD Matthews
    Reviewer; University of British Columbia, Canada

In the interests of transparency, eLife publishes the most substantive revision requests and the accompanying author responses.

Decision letter after peer review:

[Editors’ note: the authors submitted for reconsideration following the decision after peer review. What follows is the decision letter after the first round of review.]

Thank you for submitting the paper "Isometric Spiracular Scaling in Scarab Beetles: Implications for Diffusive and Advective Oxygen Transport" for consideration by eLife. Your article has been reviewed by 2 peer reviewers, and the evaluation has been overseen by a Reviewing Editor and a Senior Editor. The following individual involved in review of your submission has agreed to reveal their identity: Philip GD Matthews (Reviewer #1).

Comments to the Authors:

We are sorry to say that, after consultation with the reviewers, we have decided that this work will not be considered further for publication by eLife.

That said, because there are otherwise many positives in your work, I would sincerely welcome a new submission if the major concerns noted by the reviewers – related to stronger justification/support for the scaling assumptions on which the results are dependent – could be addressed adequately, along with your best effort to address other points also raised in the reviews below.

Reviewer #1 (Recommendations for the authors):

The authors were examining how the morphology of insect spiracles change as insects increase in body mass, specifically to determine how their diffusive and advective conductances scale with body mass, and how these exponents compare with the exponent describing the scaling of metabolic rate with body mass.

The scaling analysis uses spiracle morphology extracted from 3D micro-CT scans of beetles taken across a 180-fold range of body mass. This approach clearly reveals that spiracles scale with exponents that are not significantly different from those predicted from geometric isometry, with linear dimensions increasing with body mass (M) as M^0.33, area M^0.67, and volume M^1. From these geometric relationships the diffusive and advective conductance of the spiracles were estimated using reasonable simplifying assumptions. Clearly, diffusion cannot deliver sufficient oxygen to sustain the metabolic requirements of large or active beetles, and the bulk flow of air must be required. Given that the advective conductance scales with M^1.1, this mechanism scales with a sufficiently high exponent meet the oxygen delivery needs of active insects of all masses.

Comparing the scaling exponents for spiracle conductance against an exponent of 0.75 for insect metabolic rate is potentially an issue, since the capacity of the respiratory system and its spiracles should be matched to the insect's maximum aerobic O2 uptake requirements (i.e., during flight or activity) not their metabolic rate at rest when oxygen demand is low. The metabolic rate of flying insects scale with body mass with an exponent that is substantially higher than M^0.75, with interspecific analysis suggesting M^1.10 (Niven and Scharlemann 2005) or intraspecifically M^1.02 in hopping locusts (Snelling et al. 2011). Interestingly, the flight exponent is also the same exponent calculated in this study for the scaling of spiracle advective conductance (M^1.1). As such, estimating the metabolic rate of flying endothermic beetles to be 90× resting MR, while also assuming resting metabolic rate scales with mass^0.75, doesn't capture the iso/hyperallometric relationship between body mass and metabolic rate during flight or vigorous locomotory activity, but the scaling exponent for advective conductance is comparable to the hyperallometric value for flight metabolic rate.

An implicit assumption in this analysis is that how the spiracles scale with body mass reflects the oxygen delivery capacity of the insect's entire respiratory system. This would be true if either every part of the insect's respiratory system has a conductance that is matched with every other part (symmorphic), such that every part of the gas exchange pathway shared the same scaling exponent and equal capacity for oxygen delivery. If not, then the spiracles must possess the lowest (i.e., rate-limiting) conductance for oxygen uptake – the rest of the tracheal system could have an overall higher capacity or a higher scaling exponent, but this capacity would be unrealized due to the restricted transport of oxygen through the spiracles. In either of these cases, the scaling relationship of the spiracles conductance with body mass would be the same as the oxygen delivery capacity of the insect's tracheal system. However, it is also possible that spiracular conductance scales with a higher exponent than the conductance of other parts of the respiratory system, in which case the spiracles might not be the rate-limiting part of the oxygen transport pathway, and would possess an unrealized capacity. In this case, the scaling exponent for the spiracles would not reflect the tracheal system's oxygen delivery capacity. The validity of the authors' choice in assuming that the insect respiratory system is symmorphic (or that the spiracles are rate-limiting) is partly addressed with the observation that the metabolic rate of Drosophila is reduced when a single thoracic spiracle is blocked (L124). But is there any other evidence to support symmorphosis or rate-limiting spiracles? Given that this relationship must be true to accept the overall argument being presented, it would be good to see additional arguments put forward to support this position.

How the conductance of the spiracles is related to the insect's total oxygen uptake is even more complicated when considering advection, since oxygen delivery through the tracheal system isn't limited by atmospheric oxygen partial pressure as diffusion rate is, and can be increased dramatically, essentially only being limited by the capacity of the tracheal air-sacs' ability to pump air. However, how the tracheal pump's power (Power = Pressure x Flow or 'Q') scales with insect body mass may not yet be known. Without knowing this, there is some uncertainty in predicting what the oxygen delivery associated with the hyper-allometric scaling of spiracular advective conductance would be.

While diffusion can operate through all spiracles simultaneously, the total advective capacity can vary depending on which spiracles act as influx and efflux points (assuming continuous advective flow), as well as how these elements are interconnected, or whether all spiracles function together simultaneously during a period in inhalation followed by exhalation. Thus, the total advective capacity and the resulting oxygen delivery rate is determined by how the spiracles operate together. In this paper the total advective capacity is assumed to be the capacity of all spiracles functioning simultaneously (i.e., the summed capacity of all sixteen spiracles) which would only be possible for half the time (assuming inhalation and exhalation are of equal duration).

Overall, this paper does achieve its aim of generating a valuable data set and using this to determine how spiracle morphology scales with beetle body mass. The analysis presented convincingly shows that while diffusion could support the metabolic oxygen demands of a small or resting beetle, advection is required to deliver the oxygen needed for any energetic activity. This also suggests that an insect's size is not constrained by spiracular gas exchange even if the spiracles grow proportionally with body mass and insect size. From an evolutionary point of view this is interesting as it suggests prehistoric giant insects would likely have conformed to this pattern, indicating their size was not limited by oxygen delivery capacity.

While the morphometrics and scaling exponents that are derived from them are all very nicely done and very clear, I think that there needs to be some discussion to explain the rationale behind your use of the M^0.75 relationship for MR as the exponent you are comparing the spiracular conductance exponents against, rather than using scaling exponents derived for flying or active MR, where the exponent is >1. Likewise, I'd be keen to see some mention of the assumptions underlying why examining the diffusive and advective conductances of the spiracles is revealing, when the capacity of this comparatively small part of the gas exchange pathway may exceed the internal conductance. Ideally more compelling evidence should be provided showing either symmorphosis of gas transport across the tracheal system or that the spiracles are likely to be the rate-limiting conductance within the tracheal system.

Likewise, it'd be great to see some rationale behind how you might expect the tracheal pump's capacity to scale with body mass, since this will determine if the oxygen delivery capacity associated with the spiracle's advective conductance also scales with M^1.1. For example, if it is assumed that tracheal pump power scales isometrically (M^1), then as advective conductance scales with M^1.1, would this increase flow, and therefore oxygen delivery, with the same exponent? Would pressure decrease in larger insects? Presenting some background to the assumptions around how the insect generates an advective flow through its spiracles, and how this might scale with insect body mass, is important to be able to appreciate how increasing spiracle conductance would change the volumetric flow of air and, therefore, oxygen delivery.

It is interesting that the mesothoracic spiracles show the tightest relationship with bodymass, given that these spiracles lie closest to the most metabolically demanding tissue: the thoracic flight musculature. Given the possibility/likelihood of unidirectional advective flow during activity (in through the thoracic and out through the abdominal spiracles), how does the summed advective conductance of the thoracic spiracles compare to that of the summed abdominal spiracular conductance? Is there an excess advective capacity in the abdominal spiracles, assuming they are functioning as "exhaust spiracles" relative to the thoracic "intake spiracles"? Would assuming continuous unidirectional flow (in through some spiracles and out through others) alter the scaling exponent or only the elevation of the advective conductance relationship? Could this be considered in the analysis?

Specific comments:

L33: I'd consider changing the exponent you consider from the resting metabolic rate (M^0.75) to that for flight MR (M^1.1)

L114: "… remains unclear how the components of the system scales". Change to "scale"

L266: "The mesothoracic spiracle was" change to "were"? I know you only measured one, but there are two of them

L294: "one spiracle scales isometrically" change to "one spiracle pair scales isometrically"

Reviewer #2 (Recommendations for the authors):

The study aimed to determine gas transport capacity of tracheal spiracles in different sized scarab beetles using micro-CT scans. The authors assumed that metabolic rate scales with a scaling exponent of 0.75. They found that spiracle size does not sufficiently increase with increasing body size to allow diffusive oxygen supply but increases more than required to satisfy metabolic demands during advective gas exchange. The data are of interest for Biologists working on the respiratory system of animals but need experimental proof of the scaling exponent used as a reference.

The entire conclusion of the study is based upon the assumption that metabolic rate exactly scales with a 0.75 exponent. Many previous studies, however, showed that this scaling exponent is only valid among a large range of body sizes and (to some extent) including also vertebrates. In single clades, scaling exponents may significantly be different from 0.75. This means that the finding that diffusion is not sufficient in larger beetles depends on the correct scaling coefficient for metabolic rate in these animals. The authors do not provide separate measurements of metabolic rate to more reliably estimate the 0.75 coefficient in scarab beetles. This is, however, critical for the outcome of the study. In equations 1 and 2, the authors nicely explain that diffusion should linearly depend on spiracle geometry. This assumption matches the data in figure 2, showing slopes close to 0.75. In figure 3A, by contrast, total diffusive capacity increases much less than spiracle geometry, which runs apparently counter to the data in Figure 2. This needs an explanation.

The authors leave open the question of how important spiracle opening area is for oxygen flux compared to the rest of the tracheal system. Even assuming that spiracle area satisfies oxygen supply via diffusion, an animal might rely on advective flow because of other tracheal constraints. The above concern also holds for the slope assuming advective oxygen supply. For very small beetles, moreover, equations 3 and 4 might be too simplistic because they do not consider the fluid mechanic effects associated to flows at low Reynolds number. While Reynolds number-dependent phenomena do not change much at large Reynolds number, the thick boundary layer might hinder advective flow at low Reynolds numbers.

The study determined gas transport capacity of tracheal spiracles in different sized beetles using micro-CT scans. The authors found that spiracle area does not sufficiently increase with increasing body size for diffusive oxygen supply. Assuming advection, by contrast, spiracle area increases more than required to satisfy metabolic demands. The manuscript is written clearly and the topic is of interest for Biologists working on the respiratory system of animals. Although I much sympathize with the approach and the data, my impression is that findings and conclusion are too controversial and thus recommend publication in a more specialized journal.

The authors only compare their findings to the 0.75 slope at resting metabolic rate. On page 7, however, they mention that spiracle morphology should match gas exchange needs at peak metabolic performance. I assume that all tested species are capable of flight (?). As flight costs increase with decreasing body size due to viscous drag on wings and body, we would not expect isometric scaling of spiracle openings for diffusive gas exchange. This aspect should be considered in a revised version of the manuscript.

Length. The manuscript consists of 5 pages Introduction, 7 pages Methods, 1 page Results and 4 pages Discussion sections and thus needs a major revision towards balanced section length. The data set is comparatively small and I suggest to add measurements of metabolic rates for each beetle (see comment above).

Statistics. The data in figures 2 and 3 are barely normally distributed and my impression is that the slopes thus strongly depend on the two data points of the smallest beetles (-1 body mass). As the slope only depends on 10 data points in total, I recommend further statistics that evaluates the unequal(?) data distribution.

https://doi.org/10.7554/eLife.82129.sa1

Author response

[Editors’ note: the authors resubmitted a revised version of the paper for consideration. What follows is the authors’ response to the first round of review.]

Reviewer #1 (Recommendations for the authors):

The authors were examining how the morphology of insect spiracles change as insects increase in body mass, specifically to determine how their diffusive and advective conductances scale with body mass, and how these exponents compare with the exponent describing the scaling of metabolic rate with body mass.

The scaling analysis uses spiracle morphology extracted from 3D micro-CT scans of beetles taken across a 180-fold range of body mass. This approach clearly reveals that spiracles scale with exponents that are not significantly different from those predicted from geometric isometry, with linear dimensions increasing with body mass (M) as M^0.33, area M^0.67, and volume M^1. From these geometric relationships the diffusive and advective conductance of the spiracles were estimated using reasonable simplifying assumptions. Clearly, diffusion cannot deliver sufficient oxygen to sustain the metabolic requirements of large or active beetles, and the bulk flow of air must be required. Given that the advective conductance scales with M^1.1, this mechanism scales with a sufficiently high exponent meet the oxygen delivery needs of active insects of all masses.

Comparing the scaling exponents for spiracle conductance against an exponent of 0.75 for insect metabolic rate is potentially an issue, since the capacity of the respiratory system and its spiracles should be matched to the insect's maximum aerobic O2 uptake requirements (i.e., during flight or activity) not their metabolic rate at rest when oxygen demand is low. The metabolic rate of flying insects scale with body mass with an exponent that is substantially higher than M^0.75, with interspecific analysis suggesting M^1.10 (Niven and Scharlemann 2005) or intraspecifically M^1.02 in hopping locusts (Snelling et al. 2011). Interestingly, the flight exponent is also the same exponent calculated in this study for the scaling of spiracle advective conductance (M^1.1). As such, estimating the metabolic rate of flying endothermic beetles to be 90× resting MR, while also assuming resting metabolic rate scales with mass^0.75, doesn't capture the iso/hyperallometric relationship between body mass and metabolic rate during flight or vigorous locomotory activity, but the scaling exponent for advective conductance is comparable to the hyperallometric value for flight metabolic rate.

We agree that there is some evidence that flight metabolic rate scales with a higher exponent than 0.75 in insects, and we have added this point to the text. We have also included a reference to a new, recently accepted manuscript from our lab (Duell and Harrison, manuscript included as a supplementary file in this submission) which found that flight metabolic rate scales hypermetrically (slope = 1.19) for insects below 58 mg, and hypometrically (slope = 0.67) above 58 mg. This recent paper utilized all of the data in the Niven and Scharlemann’s analysis (n = 54) combined with newer data for 38 additional species collected in our lab and others. In the Duell and Harrison study, the regression line for insects larger than 58 mg (which would include all of the beetles used in this manuscript) had a slope significantly lower than 1, supporting our conclusion that advective capacities scale with a steeper slope than flight metabolic rates, at least over this range of body masses. In any case, our primary conclusion that diffusion though the spiracles becomes increasingly challenging with larger insects remains unchanged. Spiracular advective capacities (which scale 1.1 with mass) match the scaling of flight metabolic rate if Niven and Scharlemann’s analysis is used, or exceed the scaling of flight metabolic rates if the Duell and Harrison analysis is used.

An ideal resolution of this issue would require measurement of the flight metabolic rates of a large number of scarab beetles, as suggested by reviewer 2, as it is plausible that the scaling of flight metabolic rate is order-specific. Unfortunately, most scarab beetles cannot hover or even sustain flight in containers small enough allow detectable changes in carbon dioxide levels, and so it is currently impossible to measure their free-flight flight metabolic rates by gas exchange. We developed a brain stimulation method that induced strong flight in tethered flying Mecynorrhina savagei, one of the large beetles used in this study, and were able to measure flight metabolic rate for this species; the data from which is included in the Duell and Harrison study. Because of these technical challenges, measuring the scaling of flight metabolic rates for the beetles used in this study is beyond the scope of this manuscript. We examined the scaling relationship for the four beetle species for which there are published records, plus our data for M. savagei, and, not surprisingly, the confidence limits for the calculated regression line included 0.67 and 1.2, so this approach was not able to resolve this issue. We have added information to the text to describe the uncertainties of how flight metabolic rate scales in insects, and beetles in particular, and have redone Figure 3c to show how the required PO2 gradients across the spiracles will vary if flight metabolic rates scale with exponents of 0.67 or 1.19. We now conclude that spiracular advective capacities may match or exceed flight gas exchange needs.

An implicit assumption in this analysis is that how the spiracles scale with body mass reflects the oxygen delivery capacity of the insect's entire respiratory system. This would be true if either every part of the insect's respiratory system has a conductance that is matched with every other part (symmorphic), such that every part of the gas exchange pathway shared the same scaling exponent and equal capacity for oxygen delivery. If not, then the spiracles must possess the lowest (i.e., rate-limiting) conductance for oxygen uptake – the rest of the tracheal system could have an overall higher capacity or a higher scaling exponent, but this capacity would be unrealized due to the restricted transport of oxygen through the spiracles. In either of these cases, the scaling relationship of the spiracles conductance with body mass would be the same as the oxygen delivery capacity of the insect's tracheal system. However, it is also possible that spiracular conductance scales with a higher exponent than the conductance of other parts of the respiratory system, in which case the spiracles might not be the rate-limiting part of the oxygen transport pathway, and would possess an unrealized capacity. In this case, the scaling exponent for the spiracles would not reflect the tracheal system's oxygen delivery capacity. The validity of the authors' choice in assuming that the insect respiratory system is symmorphic (or that the spiracles are rate-limiting) is partly addressed with the observation that the metabolic rate of Drosophila is reduced when a single thoracic spiracle is blocked (L124). But is there any other evidence to support symmorphosis or rate-limiting spiracles? Given that this relationship must be true to accept the overall argument being presented, it would be good to see additional arguments put forward to support this position.

This comment from the reviewer made us realize that we needed to work to clarify our manuscript to indicate that all of our calculations and discussions refer only to transport through the spiracles, not the entire tracheal system. We had already used the adjective “spiracular” to indicate that diffusive and advective capacities only indicate transport through the spiracles, not the entire tracheal system. But we have now added sentences at several points in the manuscript to emphasize this point. It is certainly plausible that the entire tracheal system scales similarly as we have found for spiracles, but our data do not address that.

We have added information to the discussion in an attempt to make it clear that this study does not resolve the question of which steps in gas exchange likely have the greatest relative resistance, or how the overall tracheal system scales in insects.

How the conductance of the spiracles is related to the insect's total oxygen uptake is even more complicated when considering advection, since oxygen delivery through the tracheal system isn't limited by atmospheric oxygen partial pressure as diffusion rate is, and can be increased dramatically, essentially only being limited by the capacity of the tracheal air-sacs' ability to pump air. However, how the tracheal pump's power (Power = Pressure x Flow or 'Q') scales with insect body mass may not yet be known. Without knowing this, there is some uncertainty in predicting what the oxygen delivery associated with the hyper-allometric scaling of spiracular advective conductance would be.

Absolutely. We agree, and have incorporated some of the reviewer’s text into the discussion. Our data can be used to estimate diffusion gradients that will occur across spiracles if diffusion is the sole mechanism for gas exchange (which is likely in some cases, for example during recovery from drowning). Our data also allows us to calculate spiracular resistance to flow, but we completely agree that scaling of advection in insects will require direct measurements of advective flow. As the reviewer knows, this is considerably more challenging than in vertebrates due to the multiple entry and exit points for the respiratory system, and advective flow only been measured for a few insects, especially during flight, so this remains a future goal for the field.

While diffusion can operate through all spiracles simultaneously, the total advective capacity can vary depending on which spiracles act as influx and efflux points (assuming continuous advective flow), as well as how these elements are interconnected, or whether all spiracles function together simultaneously during a period in inhalation followed by exhalation. Thus, the total advective capacity and the resulting oxygen delivery rate is determined by how the spiracles operate together. In this paper the total advective capacity is assumed to be the capacity of all spiracles functioning simultaneously (i.e., the summed capacity of all sixteen spiracles) which would only be possible for half the time (assuming inhalation and exhalation are of equal duration).

We also agree with this important point, and have added sentences to the discussion as suggested.

Overall, this paper does achieve its aim of generating a valuable data set and using this to determine how spiracle morphology scales with beetle body mass. The analysis presented convincingly shows that while diffusion could support the metabolic oxygen demands of a small or resting beetle, advection is required to deliver the oxygen needed for any energetic activity. This also suggests that an insect's size is not constrained by spiracular gas exchange even if the spiracles grow proportionally with body mass and insect size. From an evolutionary point of view this is interesting as it suggests prehistoric giant insects would likely have conformed to this pattern, indicating their size was not limited by oxygen delivery capacity.

We agree that our data on the scaling of spiracular advective capacities provides some support that prehistoric giant insects would likely not have been limited by spiracular oxygen transport, though as noted by the reviewer above, this analysis does not include the oxygen transport capacity of the entire system. We have added a few sentences to the discussion on this point.

While the morphometrics and scaling exponents that are derived from them are all very nicely done and very clear, I think that there needs to be some discussion to explain the rationale behind your use of the M^0.75 relationship for MR as the exponent you are comparing the spiracular conductance exponents against, rather than using scaling exponents derived for flying or active MR, where the exponent is >1.

As noted above, we have added new information, based on a recently accepted manuscript, on the scaling of flight metabolic rates in insects, and redone Figure 3b to predict the PO2 gradient across the spiracles depending on two “extreme” estimates of the scaling of flight metabolic rate. We have also added material discussing the uncertainties in the scaling of flight metabolic rate in insects, and beetles in particular.

Likewise, I'd be keen to see some mention of the assumptions underlying why examining the diffusive and advective conductances of the spiracles is revealing, when the capacity of this comparatively small part of the gas exchange pathway may exceed the internal conductance. Ideally more compelling evidence should be provided showing either symmorphosis of gas transport across the tracheal system or that the spiracles are likely to be the rate-limiting conductance within the tracheal system.

Our data do not address whether symmorphosis occurs in the tracheal system, or the relative importance of spiracular resistance to gas exchange. Doing so would require measures of the other aspects of the tracheal system, a nontrivial endeavor, and ideally assessment of the relative roles of diffusion and advection in the various steps (for which we currently lack published methods). Nonetheless, we would argue that the measurements we have provided of the spiracles are novel and do provide important fresh insights into the evolution of the insect tracheal system. We show, for the first time, that spiracles scale isometrically, and that this means that diffusion across the spiracles becomes increasingly more challenging as insects increase in size. We also make the important and, to our knowledge, new point that this relationship between isometric scaling of respiratory structure and diffusive capacities should be general for animals. We have worked to revise the discussion and abstract to ensure that this point is clear.

Likewise, it'd be great to see some rationale behind how you might expect the tracheal pump's capacity to scale with body mass, since this will determine if the oxygen delivery capacity associated with the spiracle's advective conductance also scales with M^1.1. For example, if it is assumed that tracheal pump power scales isometrically (M^1), then as advective conductance scales with M^1.1, would this increase flow, and therefore oxygen delivery, with the same exponent? Would pressure decrease in larger insects? Presenting some background to the assumptions around how the insect generates an advective flow through its spiracles, and how this might scale with insect body mass, is important to be able to appreciate how increasing spiracle conductance would change the volumetric flow of air and, therefore, oxygen delivery.

Unfortunately, there are no literature data on how advection scales in insects, and, as noted above, measuring advective flow, especially during flight, is nontrivial. We have added some material to the discussion on this topic to clarify this point.

It is interesting that the mesothoracic spiracles show the tightest relationship with bodymass, given that these spiracles lie closest to the most metabolically demanding tissue: the thoracic flight musculature. Given the possibility/likelihood of unidirectional advective flow during activity (in through the thoracic and out through the abdominal spiracles), how does the summed advective conductance of the thoracic spiracles compare to that of the summed abdominal spiracular conductance? Is there an excess advective capacity in the abdominal spiracles, assuming they are functioning as "exhaust spiracles" relative to the thoracic "intake spiracles"? Would assuming continuous unidirectional flow (in through some spiracles and out through others) alter the scaling exponent or only the elevation of the advective conductance relationship? Could this be considered in the analysis?

This is a very interesting point that we had not thought of. In fact, the summed conductances of the thoracic spiracles far exceed the conductances of the summed abdominal spiracles; we have added new supplementary tables that enable a reader to see this easily. The mechanisms of gas exchange in some flying beetles were addressed by Miller (1966), and we have used information from his analysis to address these interesting points in the discussion.

Specific comments:

L33: I'd consider changing the exponent you consider from the resting metabolic rate (M^0.75) to that for flight MR (M^1.1)

As noted above, we feel that the best, newest data indicates that flight metabolic rate scales hypometrically (slope = 0.67), but have added discussion of the uncertainties in how flight metabolic rate scales in insects and beetles in particular.

L114: "… remains unclear how the components of the system scales". Change to "scale"

Done.

L266: "The mesothoracic spiracle was" change to "were"? I know you only measured one, but there are two of them

Done.

L294: "one spiracle scales isometrically" change to "one spiracle pair scales isometrically"

Done.

Reviewer #2 (Recommendations for the authors):

The study aimed to determine gas transport capacity of tracheal spiracles in different sized scarab beetles using micro-CT scans. The authors assumed that metabolic rate scales with a scaling exponent of 0.75. They found that spiracle size does not sufficiently increase with increasing body size to allow diffusive oxygen supply but increases more than required to satisfy metabolic demands during advective gas exchange. The data are of interest for Biologists working on the respiratory system of animals but need experimental proof of the scaling exponent used as a reference.

The entire conclusion of the study is based upon the assumption that metabolic rate exactly scales with a 0.75 exponent.

We disagree. We demonstrate isometric scaling of the spiracles, and show 0.33 that this means that diffusing capacities of the spiracles scale with m. Our major conclusion is that diffusion across the spiracles becomes increasingly challenging as beetles become larger. That conclusion would only be invalid if metabolic rates scaled interspecifically with a scaling exponent of 0.33 or less. The scaling of metabolic rate has been documented many times for insects, and the exponents are always considerably higher than 0.33, using in the range of 0.75. Our primary conclusion is robust and not dependent on any exact scaling exponent of metabolic rate.

Many previous studies, however, showed that this scaling exponent is only valid among a large range of body sizes and (to some extent) including also vertebrates. In single clades, scaling exponents may significantly be different from 0.75. This means that the finding that diffusion is not sufficient in larger beetles depends on the correct scaling coefficient for metabolic rate in these animals. The authors do not provide separate measurements of metabolic rate to more reliably estimate the 0.75 coefficient in scarab beetles. This is, however, critical for the outcome of the study.

We addressed this issue in detail in the response to reviewer 1. Briefly, we have added data from a recently accepted manuscript that supports our prior suggestion that flight metabolic rates scale hypometrically in large insects (with a slope of 0.67), very similar to the scaling pattern that has been shown for flying birds and bats. We agree that it would be wonderful to have flight metabolic rates for a larger number of scarab beetles; unfortunately, as described above, this is a very challenging proposition and so is beyond the scope of this paper. Accordingly, we have revised one aspect of our conclusions, and now indicate that spiracular advective capacities may exceed or match the scaling of flight metabolic rates.

In equations 1 and 2, the authors nicely explain that diffusion should linearly depend on spiracle geometry. This assumption matches the data in figure 2, showing slopes close to 0.75. In figure 3A, by contrast, total diffusive capacity increases much less than spiracle geometry, which runs apparently counter to the data in Figure 2. This needs an explanation.

Figure 2 shows that spiracular area scales approximately with mass 0.67, and spiracular depth scales approximately with mass 0.33. Spiracular diffusing capacity, which is shown in Figure 3, depends on spiracular area divided by spiracular depth (equation 1). 0.67 – 0.33 = 0.34, which is approximately the scaling of total spiracular conductance as shown in Figure 3.

The authors leave open the question of how important spiracle opening area is for oxygen flux compared to the rest of the tracheal system. Even assuming that spiracle area satisfies oxygen supply via diffusion, an animal might rely on advective flow because of other tracheal constraints. The above concern also holds for the slope assuming advective oxygen supply. For very small beetles, moreover, equations 3 and 4 might be too simplistic because they do not consider the fluid mechanic effects associated to flows at low Reynolds number. While Reynolds number-dependent phenomena do not change much at large Reynolds number, the thick boundary layer might hinder advective flow at low Reynolds numbers.

As pointed out above, our data are restricted to spiracular morphology, and our analysis is based on how body size affects the diffusing and advective capacities of the spiracles; we did not measure and cannot draw conclusions about the remainder of the tracheal system. We agree that small insects can and do use advection, even at rest. The fact that this occurs is one of the major unresolved issues in insect respiratory physiology. We have added discussion of this interesting point to the discussion.

The study determined gas transport capacity of tracheal spiracles in different sized beetles using micro-CT scans. The authors found that spiracle area does not sufficiently increase with increasing body size for diffusive oxygen supply. Assuming advection, by contrast, spiracle area increases more than required to satisfy metabolic demands. The manuscript is written clearly and the topic is of interest for Biologists working on the respiratory system of animals. Although I much sympathize with the approach and the data, my impression is that findings and conclusion are too controversial and thus recommend publication in a more specialized journal.

The authors only compare their findings to the 0.75 slope at resting metabolic rate. On page 7, however, they mention that spiracle morphology should match gas exchange needs at peak metabolic performance. I assume that all tested species are capable of flight (?). As flight costs increase with decreasing body size due to viscous drag on wings and body, we would not expect isometric scaling of spiracle openings for diffusive gas exchange. This aspect should be considered in a revised version of the manuscript.

This topic is discussed in detail in response to reviewer 1. Briefly here, all beetles used here are capable of flight, but do not hover, and so measurement of flight metabolic rates by gas exchange poses technical challenges in these species that are beyond the scope of this study. We now have added a paragraph to the discussion explaining the uncertainties in the scaling of flight metabolic rates for these beetles. We have added new references from a recently accepted manuscript that documents that flight metabolic rates scale differently in insects depending on body size. For small insects (below 58 mg), flight metabolic rates scale hypermetrically, plausibly because of the changes that occur in aerodynamic requirements as Reynolds number changes. For flying insects heavier than 58 mg, flight metabolic rates scale hypometrically, as observed in vertebrates. To address the concerns about uncertainty in the scaling flight metabolic rates, we have revised our conclusions to indicate that spiracular advective capacities either match or exceed gas exchange needs during flight.

Length. The manuscript consists of 5 pages Introduction, 7 pages Methods, 1 page Results and 4 pages Discussion sections and thus needs a major revision towards balanced section length. The data set is comparatively small

While the number of species is comparatively small, the morphological detail in the measurements of spiracular morphology is large.

Approximately one person-year was required to collect all of the micro-CT images, and an additional person-year to analyze all of them. No prior studies have presented similar detailed morphological analyses of spiracular diffusing capacity, even for a single insect species or spiracle. Thus, the assessment of all spiracles for ten species, including some of the largest insects alive today, is a major advance. As noted in the introduction, although invertebrates represent the majority of all species and are of tremendous ecological and evolutionary importance, we lack fundamental data on how body size affects respiratory system structure and function, and so feel that the material we present here is a major advance. Finally, we make a new point, to our knowledge, that isometric scaling of respiratory structures will be associated with reduced mass specific diffusive capacities generally in animals.

and I suggest to add measurements of metabolic rates for each beetle (see comment above).

As noted above, measurement of flight metabolic rates of flying beetles is technically very challenging because most cannot hover; so unfortunately, this suggestion is not practical. As noted above, we have added a reference to a new paper whose analysis supports the idea that flight metabolic rates in large insects scale hypometrically, as in vertebrates.

Statistics. The data in figures 2 and 3 are barely normally distributed and my impression is that the slopes thus strongly depend on the two data points of the smallest beetles (-1 body mass). As the slope only depends on 10 data points in total, I recommend further statistics that evaluates the unequal(?) data distribution.

We also had similar concerns, which is one reason we opted to perform our analysis in both a Bayesian parametric way (with clearly stated assumptions of normality) and frequentist non-parametric way (which doesn’t make assumptions of normality).

Non-parametric approach – no assumption of normality – takes into account the uneven data distribution

Our non-parametric bootstrapping approach does not rely on an assumption of normality to generate confidence intervals on the slopes. In particular, the bootstrapping operates by taking a random sample from the dataset (with replacement) of the same number of datapoints as the original dataset and calculating a summary statistic on that sample (for our inference, the summary statistic is a slope generated by numerical optimization). On average, around 11% of the bootstrap sample generated by this procedure and which we calculated slopes for do not contain either of the small beetles as datapoints. Thus, the results of the absence of these points influences the range of slopes generated and hence the bootstrap derived confidence intervals. In figure 2B, for example, the confidence interval for the range of slope estimates is non-symmetric, with a larger range of low slopes compared to the median as opposed to slopes higher than the median. Bootstrap samples with no small beetles are one reason for this larger range of smaller slopes in the posterior spiracles. Further, for fitting the regressions whose slopes we used as a summary statistic we used a minimization of the sum of squares of the residuals via numerical optimization; this approach doesn’t require or assume a normal distribution about a line for the data. It calculates the best fit via optimization as mentioned. To get an estimate on the ‘σ’ from the bootstrapping used in figure 2C to look at how variable the different spiracle sizes were, we calculate the residual standard deviation for each regression output from our bootstrap sample; calling this ‘σ’ does analogize it the σ of a normal distribution (it is the standard deviation of a normal distribution if the data are normally distributed about the fit line). Regardless of whether the data are normal, these residual standard deviations give an indication of how far away the datapoints are on average from the fit line and, we think, are worth displaying. The results of estimates for σ of an explicitly normal Bayesian model are also shown and show the same trend as the residual standard deviations from bootstrapping. The non-parametric confidence intervals for 2C are also generated by bootstrapping and so take into account what the absence of the small beetles does to the parameter estimates.

Almost all of our plots in the main text which show regressions/confidence intervals (except figure 2C,F) use the non-parametric analysis described above which takes into account both the sparse data distribution for the small animal body sizes and doesn’t assume normality.

Parametric approach

We agree that, especially given the small number of datapoints, it is difficult to have strong confidence that the datapoints are normally distributed about the linear mathematical model that we estimate parameters for. Even so, we wanted to perform our analysis in multiple ways so we could use separate statistical techniques to have more confidence in the robustness of the parameter estimates we generated. Hence, we made a Bayesian model which explicitly assumes that our data points are generated by a normal distribution with mean on a line with parameters for slope and intercept and a standard deviation. The posterior predictive distributions for the resulting models do look like the normal model does a pretty good job of encapsulating the data (supplemental figure 4, the squiggly grey intervals represent 80% and 95% percentiles for data drawn from the posterior for the model). For these posterior distributions, generally 1-2 out of 10 datapoints falls outside the 80% confidence interval, which is about right given the point numbers. However, due to concerns that the normal distribution was too strong an assumption, we ran with the above-described non-parametric approach for almost all purposes of inference.

https://doi.org/10.7554/eLife.82129.sa2

Article and author information

Author details

  1. Julian M Wagner

    School of Life Sciences, Arizona State University, Tempe, United States
    Contribution
    Investigation, Methodology, Validation, Visualization, Writing – original draft, Writing – review and editing
    Competing interests
    No competing interests declared
  2. C Jaco Klok

    School of Life Sciences, Arizona State University, Tempe, United States
    Contribution
    Writing – original draft, Methodology, Writing – review and editing, Visualization
    Competing interests
    No competing interests declared
  3. Meghan E Duell

    School of Life Sciences, Arizona State University, Tempe, United States
    Contribution
    Methodology, Writing – review and editing, Visualization
    Competing interests
    No competing interests declared
  4. John J Socha

    Department of Biomedical Engineering and Mechanics, Virginia Tech, Blacksburg, United States
    Contribution
    Resources, Funding acquisition, Investigation, Methodology, Supervision, Writing – review and editing, Visualization
    Competing interests
    No competing interests declared
    ORCID icon "This ORCID iD identifies the author of this article:" 0000-0002-4465-1097
  5. Guohua Cao

    School of Biomedical Engineering, ShanghaiTech University, Shanghai, China
    Contribution
    Resources, Supervision, Visualization
    Competing interests
    No competing interests declared
  6. Hao Gong

    Department of Radiology, Mayo Clinic, Rochester, United States
    Contribution
    Software, Supervision
    Competing interests
    No competing interests declared
  7. Jon F Harrison

    School of Life Sciences, Arizona State University, Tempe, United States
    Contribution
    Conceptualization, Resources, Data curation, Software, Writing – original draft, Funding acquisition, Methodology, Writing – review and editing, Validation, Project administration, Visualization
    For correspondence
    j.harrison@asu.edu
    Competing interests
    No competing interests declared
    ORCID icon "This ORCID iD identifies the author of this article:" 0000-0001-5223-216X

Funding

National Science Foundation (IOS 1122157)

  • Jon F Harrison

National Science Foundation (IOS 1558052.)

  • John J Socha
  • Jon F Harrison

The funders had no role in study design, data collection, and interpretation, or the decision to submit the work for publication.

Acknowledgements

This research was supported in part by funds from the School of Life Sciences Undergraduate Research (SOLUR) Program through the School of Life Sciences at Arizona State University, Tempe Campus, and by NSF IOS 1122157 and 1558052.

Senior and Reviewing Editor

  1. George H Perry, Pennsylvania State University, United States

Reviewer

  1. Philip GD Matthews, University of British Columbia, Canada

Publication history

  1. Preprint posted: April 8, 2022 (view preprint)
  2. Received: July 24, 2022
  3. Accepted: August 16, 2022
  4. Accepted Manuscript published: September 13, 2022 (version 1)
  5. Version of Record published: September 29, 2022 (version 2)
  6. Version of Record updated: September 30, 2022 (version 3)

Copyright

© 2022, Wagner et al.

This article is distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use and redistribution provided that the original author and source are credited.

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  1. Julian M Wagner
  2. C Jaco Klok
  3. Meghan E Duell
  4. John J Socha
  5. Guohua Cao
  6. Hao Gong
  7. Jon F Harrison
(2022)
Isometric spiracular scaling in scarab beetles—implications for diffusive and advective oxygen transport
eLife 11:e82129.
https://doi.org/10.7554/eLife.82129

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