Scaling of resting and maximum hopping metabolic rate throughout the life cycle of the locust Locusta migratoria

Interactive effects of intrinsic and extrinsic factors on metabolic rate

Metabolism energizes all biological processes, and its tempo may importantly influence the ecological success and evolutionary fitness of organisms. Therefore, understanding the broad variation in metabolic rate that exists across the living world is a fundamental challenge in biology. To further the development of a more reliable and holistic picture of the causes of this variation, we review several examples of how various intrinsic (biological) and extrinsic (environmental) factors (including body size, cell size, activity level, temperature, predation and other diverse genetic, cellular, morphological, physiological, behavioural and ecological influences) can interactively affect metabolic rate in synergistic or antagonistic ways. Most of the interactive effects that have been documented involve body size, temperature or both, but future research may reveal additional 'hub factors'. Our review highlights the complex, intimate inter-relationships between physiology and ecology, knowledge of which can shed light on various problems in both disciplines, including variation in physiological adaptations, life histories, ecological niches and various organism-environment interactions in ecosystems. We also discuss theoretical and practical implications of interactive effects on metabolic rate and provide suggestions for future research, including holistic system analyses at various hierarchical levels of organization that focus on interactive proximate (functional) and ultimate (evolutionary) causal networks. This article is part of the theme issue 'The evolutionary significance of variation in metabolic rates'.

Evolutionary genomics of camouflage innovation in the orchid mantis

The orchid mantises achieve camouflage with morphological modifications in body color and pattern, providing an interesting model for understanding phenotypic innovation. However, a reference genome is lacking for the order Mantodea. To unveil the mechanisms of plant-mimicking body coloration and patterns, we performed de novo assembly of two chromosome-level genomes of the orchid mantis and its close relative, the dead leaf mantis. Comparative genomic analysis revealed that the Scarlet gene plays an important role in the synthesis of xanthommatin, an important pigment for mantis camouflage coloration. Combining developmental transcriptomic analysis and genetic engineering experiments, we found that the cuticle was an essential component of the 'petal-like' enlargement, and specific expression in the ventral femur was controlled by Wnt signaling. The prolonged expression of Ultrabithorax (Ubx) accompanied by femoral expansion suggested that Ubx determines leg remodeling in the early developmental stage. We also found evidence of evolution of the Trypsin gene family for insectivory adaptation and ecdysone-dependent sexual dimorphism in body size. Overall, our study presents new genome catalogs and reveals the genetic and evolutionary mechanisms underlying the unique camouflage of the praying mantis, providing evolutionary developmental insights into phenotypic innovation and adaptation.

Metabolic scaling: individual versus intraspecific scaling of Nile tilapia (Oreochromis niloticus)

We examined intraspecific scaling of the resting metabolic rate (RMR) of Nile tilapia (Oreochromis niloticus) under different culture conditions and further explored the allometric relationships between organ mass (heart, liver, brain, gills, viscera, and red muscles) and blood parameters (erythrocyte size and red blood cell counts) and body mass. Oreochromis niloticus were bred in individual and group cultures. The scaling exponent of the RMR in the individual cultures was b = 0.620-0.821 (n = 30) and that in the group culture was b = 0.770 [natural logarithm (ln) RMR = 0.770 ln M - 1.107 (n = 76)]. The results of the two experimental methods were similar and were not significantly different from 0.75 (3/4), as predicted by the metabolic theory of ecology. The active and inactive organs were scaled with body mass by an exponent of 0.940 and 1.012, respectively. There was no significant relationship between the blood parameters and body mass. These results suggest that the differences in the culture methods may not have affected the allometric scaling of O. niloticus metabolism. The proportion of active and inactive organs contributed to allometric changes in the metabolic rate with body mass. Red blood cells in fish are not generally representative, and cell size can only partially explain the allometric scaling of metabolism.

Using µCT in live larvae of a large wood-boring beetle to study tracheal oxygen supply during development

How respiratory structures vary with, or are constrained by, an animal's environment is of central importance to diverse evolutionary and comparative physiology hypotheses. To date, quantifying insect respiratory structures and their variation has remained challenging due to their microscopic size, hence only a handful of species have been examined. Several methods for imaging insect respiratory systems are available, in many cases however, the analytical process is lethal, destructive, time consuming and labour intensive. Here, we explore and test a different approach to measuring tracheal volume using X-ray micro-tomography (µCT) scanning (at 15 µm resolution) on living, sedated larvae of the cerambycid beetle Cacosceles newmannii across a range of body sizes at two points in development. We provide novel data on resistance of the larvae to the radiation dose absorbed during µCT scanning, repeatability of imaging analyses both within and between time-points and, structural tracheal trait differences provided by different image segmentation methods. By comparing how tracheal dimension (reflecting metabolic supply) and basal metabolic rate (reflecting metabolic demand) increase with mass, we show that tracheal oxygen supply capacity increases during development at a comparable, or even higher rate than metabolic demand. Given that abundant gas delivery capacity in the insect respiratory system may be costly (due to e.g. oxygen toxicity or space restrictions), there are probably balancing factors requiring such a capacity that are not linked to direct tissue oxygen demand and that have not been thoroughly elucidated to date, including CO₂ efflux. Our study provides methodological insights and novel biological data on key issues in rapidly quantifying insect respiratory anatomy on live insects.

JumpDetector: An automated monitoring equipment for the locomotion of jumping insects

Continuous jumping behavior, a kind of endurance locomotion, plays important roles in insect ecological adaption and survival. However, the methods used for the efficient evaluation of insect jumping behavior remain largely lacking. Here, we developed a locomotion detection system named JumpDetector with automatic trajectory tracking and data analysis to evaluate the jumping of insects. This automated system exhibits more accurate, efficient, and adjustable performance than manual methods. By using this automatic system, we characterized a gradually declining pattern of continuous jumping behavior in 4th-instar nymphs of the migratory locust. We found that locusts in their gregarious phase outperformed locusts in their solitary phase in the endurance jumping locomotion. Therefore, the JumpDetector could be widely used in jumping behavior and endurance locomotion measurement.

Impact of Different Developmental Instars on Locusta migratoria Jumping Performance

Ontogenetic locomotion research focuses on the evolution of locomotion behavior in different developmental stages of a species. Unlike vertebrates, ontogenetic locomotion in invertebrates is poorly investigated. Locusts represent an outstanding biological model to study this issue. They are hemimetabolous insects and have similar aspects and behaviors in different instars. This research is aimed at studying the jumping performance of Locusta migratoria over different developmental instars. Jumps of third instar, fourth instar, and adult L. migratoria were recorded through a high-speed camera. Data were analyzed to develop a simplified biomechanical model of the insect: the elastic joint of locust hind legs was simplified as a torsional spring located at the femur-tibiae joint as a semilunar process and based on an energetic approach involving both locomotion and geometrical data. A simplified mathematical model evaluated the performances of each tested jump. Results showed that longer hind leg length, higher elastic parameter, and longer takeoff time synergistically contribute to a greater velocity and energy storing/releasing in adult locusts, if compared to young instars; at the same time, they compensate possible decreases of the acceleration due to the mass increase. This finding also gives insights for advanced bioinspired jumping robot design.

The Effect of Oxygen Limitation on a Xylophagous Insect's Heat Tolerance Is Influenced by Life-Stage Through Variation in Aerobic Scope and Respiratory Anatomy

Temperature has a profound impact on insect fitness and performance via metabolic, enzymatic or chemical reaction rate effects. However, oxygen availability can interact with these thermal responses in complex and often poorly understood ways, especially in hypoxia-adapted species. Here we test the hypothesis that thermal limits are reduced under low oxygen availability - such as might happen when key life-stages reside within plants - but also extend this test to attempt to explain that the magnitude of the effect of hypoxia depends on variation in key respiration-related parameters such as aerobic scope and respiratory morphology. Using two life-stages of a xylophagous cerambycid beetle, Cacosceles (Zelogenes) newmannii we assessed oxygen-limitation effects on metabolic performance and thermal limits. We complement these physiological assessments with high-resolution 3D (micro-computed tomography scan) morphometry in both life-stages. Results showed that although larvae and adults have similar critical thermal maxima (CTmax) under normoxia, hypoxia reduces metabolic rate in adults to a greater extent than it does in larvae, thus reducing aerobic scope in the former far more markedly. In separate experiments, we also show that adults defend a tracheal oxygen (critical) setpoint more consistently than do larvae, indicated by switching between discontinuous gas exchange cycles (DGC) and continuous respiratory patterns under experimentally manipulated oxygen levels. These effects can be explained by the fact that the volume of respiratory anatomy is positively correlated with body mass in adults but is apparently size-invariant in larvae. Thus, the two life-stages of C. newmannii display key differences in respiratory structure and function that can explain the magnitude of the effect of hypoxia on upper thermal limits.

Misconceptions and issues regarding allometric scaling during the drug development process

INTRODUCTION

Allometry is the study of size and its consequences. The simple hypothesis of allometric scaling is that all physiological parameters are proportional to body size or body mass. This review examines the development of theory-based allometry or fixed exponents (0.75 and 1.0 for basal metabolic rate and volume, respectively) and the evidence for or against the theory. The main focus of this report is to show the readers that there is enough evidence from experimental data that negate the concept of theory-based allometry in biology, physiology, and pharmacokinetics. Areas covered: In this review, the history of the development of theoretical allometry and the strong evidence against theory-based allometry demonstrated by experimental data is provided. During drug development, allometry is applied to both inter-species (from animals to humans) and intra-species (adults to children) scaling. These two forms of allometric scaling in the context of theory-based allometry are discussed and provide insight on scientific progress that refute theory-based allometry. Expert opinion: Theory-based allometry is a mere theory and experimental data and real-life observations strongly negate the existence of such a theory. Pharmacostatistical and physiological models based on theory-based allometry can be misleading and incorrect because the theory-based allometric exponent 0.75 is not universal. The exponents of allometry are data dependent and are not fixed in the universe.

Flight metabolic rate of Locusta migratoria in relation to oxygen partial pressure in atmospheres of varying diffusivity and density

Flying insects have the highest mass-specific metabolic rate of all animals. Oxygen is supplied to the flight muscles by a combination of diffusion and convection along the internal air-filled tubes of the tracheal system. This study measured maximum flight metabolic rate (FMR) during tethered flight in the migratory locust Locusta migratoria under varying oxygen partial pressure (P_O2 ) in background gas mixtures of nitrogen (N₂), sulfur hexafluoride (SF₆) and helium (He), to vary O₂ diffusivity and gas mixture density independently. With N₂ as the sole background gas (normodiffusive-normodense), mass-independent FMR averaged 132±19 mW g^-0.75 at normoxia (P_O2 =21 kPa), and was not limited by tracheal system conductance, because FMR did not increase in hyperoxia. However, FMR declined immediately with hypoxia, oxy-conforming nearly completely. Thus, the locust respiratory system is matched to maximum functional requirements, with little reserve capacity. With SF₆ as the sole background gas (hypodiffusive-hyperdense), the shape of the relationship between FMR and P_O2  was similar to that in N₂, except that FMR was generally lower (e.g. 24% lower at normoxia). This appeared to be due to increased density of the gas mixture rather than decreased O₂ diffusivity, because hyperoxia did not reverse it. Normoxic FMR was not significantly different in He-SF₆ (hyperdiffusive-normodense) compared with the N₂ background gas, and likewise there was no significant difference between FMR in SF₆-He (normodiffusive-hyperdense) compared with the SF₆ background gas. The results indicate that convection, not diffusion, is the main mechanism of O₂ delivery to the flight muscle of the locust when demand is high.

Effects of fat and exoskeletal mass on the mass scaling of metabolism in Carabidae beetles

The rate at which organisms metabolize resources and consume oxygen is tightly linked to body mass. Typically, there is a sub-linear allometric relationship between metabolic rates and body mass (mass-scaling exponent b < 1). The origin of this pattern remains one of the most intriguing and hotly debated topics in evolutionary physiology. A decrease in mass-specific metabolic rates in larger organisms might reflect disproportionate increases in body components with low metabolic activity, such as storage and skeletal tissues. Addressing this hypothesis, we studied standard metabolic rates, body mass, and fat and exoskeletal mass in males and females from 15 species of Carabidae beetles. There was a sub-linear allometric relationship of metabolic rate with body mass: b = 0.72 (phylogeny not considered), b = 0.54 (phylogeny considered). The latter exponent was significantly lower than 0.75, which is sometimes regarded as a universal exponent value in the mass scaling of metabolic rates. Contrary to our hypothesis, the relative contribution of fat and the exoskeleton to body mass decreased, rather than increased with body mass, as indicated by the sub-linear allometric mass scaling of both components (b < 1). Supporting the role of metabolically inert body components in shaping metabolic scaling, the exponents (b) for metabolism became slightly smaller (b = 0.70, phylogeny not considered; 0.52, phylogeny considered) when we removed lipids and the exoskeleton from body mass calculations and considered only the lean mass of soft tissue in the mass scaling. Overall, our results indicate that, in beetles, the relative content of metabolically inert components changes across species according to species-specific body mass. Nevertheless, we did not find evidence that this changing contribution plays a central role in the origin of interspecific metabolic scaling in carabids. Our findings stress the need for finding alternative explanations, at least in carabids, for the origin of the mass scaling of metabolic rates.

Mass scaling of metabolic rates in carabid beetles (Carabidae) – the importance of phylogeny, regression models and gas exchange patterns

The origin of the allometric relationship between standard metabolic rate (MR) and body mass (M), often described as MR=aMb, remains puzzling and interpretation of the mass-scaling exponent, b may depend on the methodological approach, shapes of residuals, coefficient of determination (r2) and sample size. We investigated the mass scaling of MRs within and between species of Carabidae beetles. We used ordinary least squares (OLS) regression, phylogenetically generalized least squares (PGLS) regression and standardized major axis (SMA) regression to explore the effects of different model-fitting methods and data clustering caused by phylogenetic clades (grade shift) and gas exchange patterns (discontinuous, cyclic and continuous). At the interspecific level, the relationship between MR and M was either negatively allometric (b&lt;1) or isometric (b=1), depending on the fitting method. At the intraspecific level, the relationship either did not exist or was isometric or positively allometric (b&gt;1), and the fit was significantly improved after the analysed dataset was split according to gas exchange patterns. The studied species originated from two distinct phylogenetic clades that had different intercepts but a common scaling exponent (OLS, 0.61) that was much shallower than the scaling exponent for the combined dataset for all species (OLS, 0.71). The best scaling exponent estimates were obtained by applying OLS while accounting for grade shifts or by applying PGLS. Overall, we show that allometry of MR in insects can depend heavily on the model fitting method, the structure of phylogenetic non-independence and ecological factors that elicit different modes of gas exchange.

Why does offspring size affect performance? Integrating metabolic scaling with life-history theory

Within species, larger offspring typically outperform smaller offspring. While the relationship between offspring size and performance is ubiquitous, the cause of this relationship remains elusive. By linking metabolic and life-history theory, we provide a general explanation for why larger offspring perform better than smaller offspring. Using high-throughput respirometry arrays, we link metabolic rate to offspring size in two species of marine bryozoan. We found that metabolism scales allometrically with offspring size in both species: while larger offspring use absolutely more energy than smaller offspring, larger offspring use proportionally less of their maternally derived energy throughout the dependent, non-feeding phase. The increased metabolic efficiency of larger offspring while dependent on maternal investment may explain offspring size effects-larger offspring reach nutritional independence (feed for themselves) with a higher proportion of energy relative to structure than smaller offspring. These findings offer a potentially universal explanation for why larger offspring tend to perform better than smaller offspring but studies on other taxa are needed.

Differences in scaling and morphology between lumbricid earthworm ecotypes

Many soft-bodied invertebrates use a flexible, fluid-filled hydrostatic skeleton for burrowing. The aim of our study was to compare the scaling and morphology between surface-dwelling and burrowing earthworm ecotypes to explore the specializations of non-rigid musculoskeletal systems for burrowing locomotion. We compared the scaling of adult lumbricid earthworms across species and ecotypes to determine if linear dimensions were significantly associated with ecotype. We also compared the ontogenetic scaling of a burrowing species, Lumbricus terrestris, and a surface-dwelling species, Eisenia fetida, using glycol methacrylate histology. We found that burrowing species were longer, thinner, and had higher length-to-diameter ratios than non-burrowers, and that L. terrestris was thinner for any given body mass compared to E. fetida. We also found differences in the size of the musculature between the two species that may correlate with surface crawling or burrowing. Our results suggest that adaptations to burrowing for soft-bodied animals include a disproportionately thin body and strong longitudinal muscles.

Metabolic scaling in animals: methods, empirical results, and theoretical explanations

Life on earth spans a size range of around 21 orders of magnitude across species and can span a range of more than 6 orders of magnitude within species of animal. The effect of size on physiology is, therefore, enormous and is typically expressed by how physiological phenomena scale with mass(b). When b ≠ 1 a trait does not vary in direct proportion to mass and is said to scale allometrically. The study of allometric scaling goes back to at least the time of Galileo Galilei, and published scaling relationships are now available for hundreds of traits. Here, the methods of scaling analysis are reviewed, using examples for a range of traits with an emphasis on those related to metabolism in animals. Where necessary, new relationships have been generated from published data using modern phylogenetically informed techniques. During recent decades one of the most controversial scaling relationships has been that between metabolic rate and body mass and a number of explanations have been proposed for the scaling of this trait. Examples of these mechanistic explanations for metabolic scaling are reviewed, and suggestions made for comparing between them. Finally, the conceptual links between metabolic scaling and ecological patterns are examined, emphasizing the distinction between (1) the hypothesis that size- and temperature-dependent variation among species and individuals in metabolic rate influences ecological processes at levels of organization from individuals to the biosphere and (2) mechanistic explanations for metabolic rate that may explain the size- and temperature-dependence of this trait.

Intraspecific scaling of the resting and maximum metabolic rates of the crucian carp (Carassius auratus)

The question of how the scaling of metabolic rate with body mass (M) is achieved in animals is unresolved. Here, we tested the cell metabolism hypothesis and the organ size hypothesis by assessing the mass scaling of the resting metabolic rate (RMR), maximum metabolic rate (MMR), erythrocyte size, and the masses of metabolically active organs in the crucian carp (Carassius auratus). The M of the crucian carp ranged from 4.5 to 323.9 g, representing an approximately 72-fold difference. The RMR and MMR increased with M according to the allometric equations RMR = 0.212M (0.776) and MMR = 0.753M (0.785). The scaling exponents for RMR (b r) and MMR (b m) obtained in crucian carp were close to each other. Thus, the factorial aerobic scope remained almost constant with increasing M. Although erythrocyte size was negatively correlated with both mass-specific RMR and absolute RMR adjusted to M, it and all other hematological parameters showed no significant relationship with M. These data demonstrate that the cell metabolism hypothesis does not describe metabolic scaling in the crucian carp, suggesting that erythrocyte size may not represent the general size of other cell types in this fish and the metabolic activity of cells may decrease as fish grows. The mass scaling exponents of active organs was lower than 1 while that of inactive organs was greater than 1, which suggests that the mass scaling of the RMR can be partly due to variance in the proportion of active/inactive organs in crucian carp. Furthermore, our results provide additional evidence supporting the correlation between locomotor capacity and metabolic scaling.

The effects of temperature and body mass on jump performance of the locust Locusta migratoria

Locusts jump by rapidly releasing energy from cuticular springs built into the hind femur that deform when the femur muscle contracts. This study is the first to examine the effect of temperature on jump energy at each life stage of any orthopteran. Ballistics and high-speed cinematography were used to quantify the energy, distance, and take-off angle of the jump at 15, 25, and 35°C in the locust Locusta migratoria. Allometric analysis across the five juvenile stages at 35°C reveals that jump distance (D; m) scales with body mass (M; g) according to the power equation D = 0.35M^{0.17±0.08 (95% CI)}, jump take-off angle (A; degrees) scales as A = 52.5M^0.00±0.06, and jump energy (E; mJ per jump) scales as E = 1.91M^1.14±0.09. Temperature has no significant effect on the exponent of these relationships, and only a modest effect on the elevation, with an overall Q₁₀ of 1.08 for jump distance and 1.09 for jump energy. On average, adults jump 87% farther and with 74% more energy than predicted based on juvenile scaling data. The positive allometric scaling of jump distance and jump energy across the juvenile life stages is likely facilitated by the concomitant relative increase in the total length (L_f+t; mm) of the femur and tibia of the hind leg, L_f+t = 34.9M^0.37±0.02. The weak temperature-dependence of jump performance can be traced to the maximum tension of the hind femur muscle and the energy storage capacity of the femur's cuticular springs. The disproportionately greater jump energy and jump distance of adults is associated with relatively longer (12%) legs and a relatively larger (11%) femur muscle cross-sectional area, which could allow more strain loading into the femur's cuticular springs. Augmented jump performance in volant adult locusts achieves the take-off velocity required to initiate flight.

Maximum metabolic rate, relative lift, wingbeat frequency and stroke amplitude during tethered flight in the adult locust Locusta migratoria

Flying insects achieve the highest mass-specific aerobic metabolic rates of all animals. However, few studies attempt to maximise the metabolic cost of flight and so many estimates could be sub-maximal, especially where insects have been tethered. To address this issue, oxygen consumption was measured during tethered flight in adult locusts Locusta migratoria, some of which had a weight attached to each wing (totalling 30-45% of body mass). Mass-specific metabolic rate increased from 28±2 μmol O(2) g(-1) h(-1) at rest to 896±101 μmol O(2)g(-1) h(-1) during flight in weighted locusts, and to 1032±69 μmol O(2) g(-1) h(-1) in unweighted locusts. Maximum metabolic rate of locusts during tethered flight (m(O(2)); μmol O(2) h(-1)) increased with body mass (M(b); g) according to the allometric equation m(O(2))=994M(b)(0.75±0.19), whereas published metabolic rates of moths and orchid bees during hovering free flight (h(O(2))) are approximately 2.8-fold higher, h(O(2))=2767M(b)(0.72±0.08). The modest flight metabolic rate of locusts is unlikely to be an artefact of individuals failing to exert themselves, because mean maximum lift was not significantly different from that required to support body mass (95±8%), mean wingbeat frequency was 23.7±0.6 Hz, and mean stroke amplitude was 105±5 deg in the forewing and 96±5 deg in the hindwing - all of which are close to free-flight values. Instead, the low cost of flight could reflect the relatively small size and relatively modest anatomical power density of the locust flight motor, which is a likely evolutionary trade-off between flight muscle maintenance costs and aerial performance.

Symmorphosis and the insect respiratory system: a comparison between flight and hopping muscle

Weibel and Taylor's theory of symmorphosis predicts that the structural components of the respiratory system are quantitatively adjusted to satisfy, but not exceed, an animal's maximum requirement for oxygen. We test this in the respiratory system of the adult migratory locust Locusta migratoria by comparing the aerobic capacity of hopping and flight muscle with the morphology of the oxygen cascade. Maximum oxygen uptake by flight muscle during tethered-flight is 967 ± 76 μmol h-1 g-1 (body mass-specific, ± 95% CI), whereas the hopping muscles consume a maximum of 158 ± 8 during jumping. The 6.1-fold difference in aerobic capacity between the two muscles is matched by a 6.4-fold difference in tracheole lumen volume, which is 3.5×108 ± 1.2×108 μm3 g-1 in flight muscle and 5.5×107 ± 1.8×107 in the hopping muscles, a 6.4-fold difference in tracheole inner cuticle surface area, which is 3.2×109 ± 1.1×109 μm2 g-1 in flight muscle and 5.0×108 ± 1.7×108 in the hopping muscles, and a 6.8-fold difference in tracheole radial diffusing capacity, which is 113 ± 47 μmol kPa-1 h-1 g-1 in flight muscle and 16.7 ± 6.5 in the hopping muscles. However, there is little congruence between the 6.1-fold difference in aerobic capacity and the 19.8-fold difference in mitochondrial volume, which is 3.2×1010 ± 3.9×109 μm3 g-1 in flight muscle and only 1.6×109 ± 1.4×108 in the hopping muscles. Therefore, symmorphosis is upheld in the design of the tracheal system, but not in relation to the amount of mitochondria, which might be due to other factors operating on the molecular level.

Allometric scaling of discontinuous gas exchange patterns in the locust Locusta migratoria throughout ontogeny

The discontinuous gas exchange cycle (DGC) is a three-phase breathing pattern displayed by many insects at rest. The pattern consists of an extended breath-hold period (closed phase), followed by a sequence of rapid gas exchange pulses (flutter phase), and then by a period in which respiratory gases move freely between insect and environment (open phase). This study measured CO2 emission in resting locusts Locusta migratoria throughout ontogeny, in normoxia (21 kPa PO2), hypoxia (7 kPa PO2) and hyperoxia (40 kPa PO2), to determine whether body mass and ambient O2 affects DGC phase duration. In normoxia, mean CO2 production rate (MCO2; μmol h-1) scales with body mass (Mb; g) according to the allometric power equation, MCO2 = 9.9Mb0.95±0.09, closed phase duration (C; min) scales with body mass according to the equation, C = 18.0Mb0.38±0.29, closed+flutter period (C+F; min) scales with body mass according to the equation, C+F = 26.6Mb0.20±0.25, and open phase duration (O; min) scales with body mass according to the equation, O = 13.3Mb0.23±0.18. Hypoxia results in a shorter closed phase and longer open phase across all life stages, whereas hyperoxia elicits a shorter closed, closed+flutter, and open phase across all life stages. The tendency for larger locusts to exhibit both a longer closed, and closed+flutter period, might arise if the positive allometric scaling of locust tracheal volume prolongs the time taken to reach the minimum O2 and maximum CO2 set-points that determine the duration of these respective periods, whereas an increasingly protracted open phase could reflect the additional time required for larger locusts to expel CO2 through a relatively longer tracheal pathway. Observed changes in phase duration under hypoxia possibly serve to maximise O2 uptake from the environment, while the response of the DGC to hyperoxia is difficult to explain, but could be affected by elevated levels of reactive oxygen species.

Symmorphosis and the insect respiratory system: allometric variation

Taylor and Weibel's theory of symmorphosis predicts that structures of the respiratory system are matched to maximum functional requirements with minimal excess capacity. We tested this hypothesis in the respiratory system of the migratory locust, Locusta migratoria, by comparing the aerobic capacity of the jumping muscles with the morphology of the oxygen cascade in the hopping legs using an intraspecific allometric analysis of different body mass (Mb) at selected juvenile life stages. The maximum oxygen consumption rate of the hopping muscle during jumping exercise scales as Mb1.02±0.02, which parallels the scaling of mitochondrial volume in the hopping muscle, Mb1.02±0.08, and the total surface area of inner mitochondrial membrane, Mb0.99±0.10. Likewise, at the oxygen supply end of the insect respiratory system, there is congruence between the aerobic capacity of the hopping muscle and the total volume of tracheoles in the hopping muscle, Mb0.99±0.16, the total inner surface area of the tracheoles, Mb0.99±0.16, and the anatomical radial diffusing capacity of the tracheoles, Mb0.99±0.18. Therefore, the principles of symmorphosis are upheld at each step of the oxygen cascade in the respiratory system of the migratory locust.