Klowden, M. J. & Palli, S. R. Physiological Systems in Insects 4th edn (Academic Press, 2022).

Nation, J. L. Sr. Insect Physiology and Biochemistry 4th edn (CRC Press, 2022).

Björkman, C., Gotthard, K. & Pettersson, M. W. in Encyclopedia of Insects 2nd edn (eds Resh, V. H. & Cardé, R. T.) Ch. 29 (Academic Press, 2009).

Graham, J. B., Dudley, R., Aguilar, N. M. & Gans, C. Implications of the late Palaeozoic oxygen pulse for physiology and evolution. Nature 375, 117–120 (1995).

Article 
ADS 
CAS 

Google Scholar
 

Raymond, J. & Segrè, D. The effect of oxygen on biochemical networks and the evolution of complex life. Science 311, 1764–1767 (2006).

Article 
ADS 
CAS 
PubMed 

Google Scholar
 

Dismukes, G. C. et al. The origin of atmospheric oxygen on Earth: the innovation of oxygenic photosynthesis. Proc. Natl Acad. Sci. USA 98, 2170–2175 (2001).

Article 
ADS 
CAS 
PubMed 
PubMed Central 

Google Scholar
 

Sperling, E. A. et al. Breathless through time: oxygen and animals across Earth’s history. Biol. Bull. 243, 184–206 (2022).

Article 
CAS 
PubMed 

Google Scholar
 

Payne, J. L. et al. The evolutionary consequences of oxygenic photosynthesis: a body size perspective. Photosynth. Res. 107, 37–57 (2011).

Article 
CAS 
PubMed 

Google Scholar
 

Butterfield, N. J. Oxygen, animals and oceanic ventilation: an alternative view. Geobiology 7, 1–7 (2009).

Article 
CAS 
PubMed 

Google Scholar
 

Carpenter, F. M. The Lower Permian insects of Kansas. Part 8. Additional Megasecoptera, Protodonata, Odonata, Homoptera, Psocoptera, Protelytroptera, Plectoptera, and Protoperlaria. Proc. Am. Acad. Arts Sci. 73, 29–70 (1939).

Article 

Google Scholar
 

Kukalová-Peck, J. Ephemeroid wing venation based upon new gigantic Carboniferous mayflies and basic morphology, phylogeny and metamorphosis of pterygote insects (Insecta, Ephemerida). Can. J. Zool. 63, 933–955 (1985).

Article 

Google Scholar
 

Dudley, R. Atmospheric oxygen, giant Paleozoic insects and the evolution of aerial locomotor performance. J. Exp. Biol. 201, 1043–1050 (1998).

Article 
CAS 
PubMed 

Google Scholar
 

Rutten, M. G. Geologic data on atmospheric history. Palaeogeogr. Palaeoclimatol. Palaeoecol. 2, 47–57 (1966).

Article 

Google Scholar
 

Wade, D. C. et al. Simulating the climate response to atmospheric oxygen variability in the Phanerozoic: a focus on the Holocene, Cretaceous and Permian. Clim. Past 15, 1463–1483 (2019).

Article 

Google Scholar
 

Berner, R. A. GEOCARBSULF: a combined model for Phanerozoic atmospheric O2 and CO2. Geochim. Cosmochim. Acta 70, 5653–5664 (2006).

Article 
ADS 
CAS 

Google Scholar
 

Berner, R. A. Phanerozoic atmospheric oxygen: new results using the GEOCARBSULF model. Am. J. Sci. 309, 603–606 (2009).

Article 
ADS 
CAS 

Google Scholar
 

Bergman, N. M., Lenton, T. M. & Watson, A. J. COPSE: a new model of biogeochemical cycling over Phanerozoic time. Am. J. Sci. 304, 397–437 (2004).

Article 
ADS 
CAS 

Google Scholar
 

Berner, R. A. & Canfield, D. E. A new model for atmospheric oxygen over Phanerozoic time. Am. J. Sci. 289, 333–361 (1989).

Article 
ADS 
CAS 
PubMed 

Google Scholar
 

Wigglesworth, V. B. Growth and regeneration in the tracheal system of an insect, Rhodnius prolixus (Hemiptera). Q. J. Microsc. Sci. 95, 115–137 (1954).


Google Scholar
 

Snelling, E. P., Duncker, R., Jones, K. K., Fagan-Jeffries, E. P. & Seymour, R. S. Flight metabolic rate of Locusta migratoria in relation to oxygen partial pressure in atmospheres of varying diffusivity and density. J. Exp. Biol. 220, 4432–4439 (2017).

Article 
PubMed 

Google Scholar
 

Harrison, J. F. et al. Air sacs are a key adaptive trait of the insect respiratory system. J. Exp. Biol. 226, jeb245712 (2023).

Article 
PubMed 

Google Scholar
 

Socha, J. J., Förster, T. D. & Greenlee, K. J. Issues of convection in insect respiration: insights from synchrotron X-ray imaging and beyond. Respir. Physiol. Neurobiol. 173, S65–S73 (2010).

Article 
PubMed 

Google Scholar
 

Schmitz, A. & Perry, S. F. Stereological determination of tracheal volume and diffusing capacity of the tracheal walls in the stick insect Carausius morosus (Phasmatodea, Lonchodidae). Physiol. Biochem. Zool. 72, 205–218 (1999).

Article 
CAS 
PubMed 

Google Scholar
 

Hartung, D. K., Kirkton, S. D. & Harrison, J. F. Ontogeny of tracheal system structure: a light and electron-microscopy study of the metathoracic femur of the American locust, Schistocerca americana. J. Morphol. 262, 800–812 (2004).

Article 
PubMed 

Google Scholar
 

Snelling, E. P., Seymour, R. S., Runciman, S., Matthews, P. G. D. & White, C. R. Symmorphosis and the insect respiratory system: a comparison between flight and hopping muscle. J. Exp. Biol. 215, 3324–3333 (2012).

PubMed 

Google Scholar
 

Dejours, P. Principles of Comparative Respiratory Physiology 2nd revised edn (Elsevier/North-Holland Biomedical Press, 1981).

Weis-Fogh, T. Diffusion in insect wing muscle, the most active tissue known. J. Exp. Biol. 41, 229–256 (1964).

Article 
CAS 
PubMed 

Google Scholar
 

Centanin, L., Gorr, T. A. & Wappner, P. Tracheal remodelling in response to hypoxia. J. Insect Physiol. 56, 447–454 (2010).

Article 
CAS 
PubMed 

Google Scholar
 

Jarecki, J., Johnson, E. & Krasnow, M. A. Oxygen regulation of airway branching in Drosophila is mediated by branchless FGF. Cell 99, 211–220 (1999).

Article 
CAS 
PubMed 

Google Scholar
 

VandenBrooks, J. M. et al. Supply and demand: how does variation in atmospheric oxygen during development affect insect tracheal and mitochondrial networks? J. Insect Physiol. 106, 217–223 (2018).

Article 
CAS 
PubMed 

Google Scholar
 

Harrison, J. F. et al. Developmental plasticity and stability in the tracheal networks supplying Drosophila flight muscle in response to rearing oxygen level. J. Insect Physiol. 106, 189–198 (2018).

Article 
CAS 
PubMed 

Google Scholar
 

Gjoni, V., Tan, H., Hirst, A., Kratina, P. & Atkinson, D. Locomotion reveals contrasting responses in body mass-scaling of metabolic rates between winged and wingless arthropods. Ecol. Lett. 28, e70277 (2025).

Article 
PubMed 

Google Scholar
 

Duell, M. E., Klok, C. J., Roubik, D. W. & Harrison, J. F. Size-dependent scaling of stingless bee flight metabolism reveals an energetic benefit to small body size. Integr. Comp. Biol. 62, 1429–1438 (2022).

Article 
PubMed 
PubMed Central 

Google Scholar
 

Wagner, J. M. et al. Isometric spiracular scaling in scarab beetles — implications for diffusive and advective oxygen transport. eLife 11, e82129 (2022).

Article 
CAS 
PubMed 
PubMed Central 

Google Scholar
 

Kaiser, A. et al. Increase in tracheal investment with beetle size supports hypothesis of oxygen limitation on insect gigantism. Proc. Natl Acad. Sci. USA 104, 13198–13203 (2007).

Article 
ADS 
CAS 
PubMed 
PubMed Central 

Google Scholar
 

Greenlee, K. J., Nebeker, C. & Harrison, J. F. Body size-independent safety margins for gas exchange across grasshopper species. J. Exp. Biol. 210, 1288–1296 (2007).

Article 
CAS 
PubMed 

Google Scholar
 

Henry, J. R. & Harrison, J. F. Effects of body size on the oxygen sensitivity of dragonfly flight. J. Exp. Biol. 217, 3447–3456 (2014).

PubMed 

Google Scholar
 

Lease, H. M., Klok, C. J., Kaiser, A. & Harrison, J. F. Body size is not critical for critical PO2 in scarabaeid and tenebrionid beetles. J. Exp. Biol. 215, 2524–2533 (2012).

Article 
PubMed 

Google Scholar
 

Harrison, J. F., Klok, C. J. & Waters, J. S. Critical PO2 is size-independent in insects: implications for the metabolic theory of ecology. Curr. Opin. Insect Sci. 4, 54–59 (2014).

Article 
PubMed 

Google Scholar
 

Cannell, A. E. R. The engineering of the giant dragonflies of the Permian: revised body mass, power, air supply, thermoregulation and the role of air density. J. Exp. Biol. 221, jeb185405 (2018).

Article 
PubMed 

Google Scholar
 

Hoppeler, H. & Kayar, S. R. Capillarity and oxidative capacity of muscles. Physiology 3, 113–116 (1988).

Article 

Google Scholar
 

Mathieu-Costello, O., Suarez, R. K. & Hochachka, P. W. Capillary-to-fiber geometry and mitochondrial density in hummingbird flight muscle. Respir. Physiol. 89, 113–132 (1992).

Article 
CAS 
PubMed 

Google Scholar
 

Mathieu-Costello, O., Szewczak, J. M., Logemann, R. B. & Agey, P. J. Geometry of blood-tissue exchange in bat flight muscle compared with bat hindlimb and rat soleus muscle. Am. J. Physiol. Regul. Integr. Comp. Physiol. 262, R955–R965 (1992).

Article 
CAS 

Google Scholar
 

Snelling, E. P. et al. A structure-function analysis of the left ventricle. J. Appl. Physiol. 121, 900–909 (2016).

Article 
PubMed 
PubMed Central 

Google Scholar
 

Snelling, E. P., Seymour, R. S., Matthews, P. G. D. & White, C. R. Maximum metabolic rate, relative lift, wingbeat frequency and stroke amplitude during tethered flight in the adult locust Locusta migratoria. J. Exp. Biol. 215, 3317–3323 (2012).

PubMed 

Google Scholar
 

Mizisin, A. P. & Josephson, R. K. Mechanical power output of locust flight muscle. J. Comp. Physiol. A 160, 413–419 (1987).

Article 

Google Scholar
 

Weis-Fogh, T. Respiration and tracheal ventilation in locusts and other flying insects. J. Exp. Biol. 47, 561–587 (1967).

Article 
CAS 
PubMed 

Google Scholar
 

Harrison, J. F. & Wasserthal, L. T. in The Insects: Structure and Function 5th edn (eds Simpson, S. J. & Douglas, A. E.) 501–545 (Cambridge Univ. Press, 2013).

Huang, S.-P., Talal, S., Ayali, A. & Gefen, E. The effect of discontinuous gas exchange on respiratory water loss in grasshoppers (Orthoptera: Acrididae) varies across an aridity gradient. J. Exp. Biol. 218, 2510–2517 (2015).

Article 
PubMed 

Google Scholar
 

Clapham, M. E. & Karr, J. A. Environmental and biotic controls on the evolutionary history of insect body size. Proc. Natl Acad. Sci. USA 109, 10927–10930 (2012).

Article 
ADS 
CAS 
PubMed 
PubMed Central 

Google Scholar
 

Ellers, O. et al. Induced power scaling alone cannot explain griffenfly gigantism. Integr. Comp. Biol. 64, 598–610 (2024).

Article 
CAS 
PubMed 

Google Scholar
 

Price, P. W. Insect Ecology 3rd edn (John Wiley & Sons, 1997).

Gee, H. A (Very) Short History of Life on Earth (Pan Macmillan, 2021).

Vermeij, G. J. Gigantism and its implications for the history of life. PLoS ONE 11, e0146092 (2016).

Article 
PubMed 
PubMed Central 

Google Scholar
 

Snelling, E. P. et al. Scaling of morphology and ultrastructure of hearts among wild African antelope. J. Exp. Biol. 221, jeb184713 (2018).

Article 
PubMed 

Google Scholar
 

Kreuzer, F. Oxygen supply to tissues: the Krogh model and its assumptions. Experientia 38, 1415–1426 (1982).

Article 
CAS 
PubMed 

Google Scholar
 

Howard, C. V. & Reed, M. G. Unbiased Stereology: Three Dimensional Measurement in Microscopy (BIOS Scientific, 1998).

Schneider, C. A., Rasband, W. S. & Eliceiri, K. W. NIH Image to ImageJ: 25 years of image analysis. Nat. Methods 9, 671–675 (2012).

Article 
CAS 
PubMed 
PubMed Central 

Google Scholar
 

Snelling, E. P., Seymour, R. S. & Runciman, S. Moulting of insect tracheae captured by light and electron-microscopy in the metathoracic femur of a third instar locust Locusta migratoria. J. Insect Physiol. 57, 1312–1316 (2011).

Article 
CAS 
PubMed 

Google Scholar
 

Snelling, E. P. Data for insect flight muscle tracheole scaling [data set]. Zenodo https://doi.org/10.5281/zenodo.18523523 (2026).

Snelling, E. P. R coding for insect flight muscle tracheole scaling. Zenodo https://doi.org/10.5281/zenodo.18523485 (2026).

Orme, D. The caper package: comparative analysis of phylogenetics and evolution in R, version 1.0.1. CRAN https://CRAN.R-project.org/package=caper (2018).

R Core Team. R: A Language and Environment for Statistical Computing. https://www.R-project.org (R Foundation for Statistical Computing, 2025).

Chesters, D. The phylogeny of insects in the data-driven era. Syst. Entomol. 45, 540–551 (2020).

Article 

Google Scholar
 

Pagel, M. Inferring the historical patterns of biological evolution. Nature 401, 877–884 (1999).

Article 
ADS 
CAS 
PubMed 

Google Scholar
 

Hartigan, J. A. & Hartigan, P. M. The dip test of unimodality. Ann. Statist. 13, 70–84 (1985).

Article 
MathSciNet 

Google Scholar
 

Maechler, M. diptest: Hartigan’s dip test statistic for unimodality — corrected, version 0.76-0. CRAN https://CRAN.R-project.org/package=diptest (2022).

Tercel, M. P. T. G., Veronesi, F. & Pope, T. W. Phylogenetic clustering of wingbeat frequency and flight-associated morphometrics across insect orders. Physiol. Entomol. 43, 149–157 (2018).

Article 

Google Scholar
 

Burnham, K. P. & Anderson, D. R. Multimodel inference: understanding AIC and BIC in model selection. Sociol. Methods Res. 33, 261–304 (2004).

Article 
MathSciNet 

Google Scholar