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The scaling and allometry of organ size associated with miniaturization in insects: A case study for Coleoptera and Hymenoptera

  • Scientific Reports 7, Article number: 43095 (2017)
  • doi:10.1038/srep43095
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The study of the influence of body size on structure in animals, as well as scaling of organs, is one of the key areas of functional and evolutionary morphology of organisms. Most studies in this area treated mammals or birds; comparatively few studies are available on other groups of animals. Insects, because of the huge range of their body sizes and because of their colossal diversity, should be included in the discussion of the problem of scaling and allometry in animals, but to date they remain insufficiently studied. In this study, а total of 28 complete (for all organs) and 24 partial 3D computer reconstructions of body and organs have been made for 23 insect species of 11 families and five orders. The relative volume of organs was analyzed based on these models. Most insect organs display a huge potential for scaling and for retaining their organization and constant relative volume. By contrast, the relative volume of the reproductive and nervous systems increases by a considerable factor as body size decreases. These systems can geometrically restrain miniaturization in insects and determine the limits to the smallest possible body size.


Body size is a parameter of utmost importance; it largely determines the morphology, physiology, and biology of organisms1. Changes in body size, especially extreme miniaturization, can result in considerable reorganizations of structure and changes of proportions of the body and organs2. The problem of allometry and scaling of organs is the subject of many studies, but most of them treat only mammals and birds (for review, see3). Insects are very convenient for studying the scaling of organs and tissues which is associated with extreme miniaturization: first, they have a huge range of body sizes (the largest is more than 2000 times as long as the smallest); second, the smallest insects are comparable in size to unicellular organisms but retain high morphological complexity4. However, scaling of organs in insects remains studied insufficiently; only studies on particular organs are available, above all on brain size5 and only some data on the relative volume of all organs in several species6,7. The purpose of this study was to provide the large-scale analysis of scaling in insect organs and miniaturization-related allometry of organs. The focus will be on the Coleoptera and Hymenoptera, which include a significant part of microinsects and the smallest known insects4.

Results and Discussion

A total of 28 complete (for all organs) and 24 partial 3D computer reconstructions of body and organs have been made for 23 insect species of 11 families and five orders (Thysanura, Psocoptera, Thysanoptera, Coleoptera, and Hymenoptera) including the smallest insects Megaphragma and Nanosella and large representatives of related taxa (the body length and body volume differed by a factor of up to 100 and about 100 000, respectively) (Table S1). The volume of organs was analyzed based on these models.

The volume of the skeleton

In adult insects generally changes proportionally to the body volume, i.e., isometrically (slope of regression is not significantly different from 1, Fig. 1, Table 1). Analysis of changes in this parameter in different groups shows (Fig. 2A) that the relative volume of the skeleton slightly increases in Coleoptera and Paraneoptera and slightly decreases in Hymenoptera as body size decreases. In spiders the weight of the skeleton markedly decreases with decreasing body size8. Interestingly, the slope of scaling of the skeleton in insects is much closer to 1 than in mammals (1.0909 to 1.14210) or birds (1.0719), which gives evidence that the insect skeleton is scaled more proportionally.

Figure 1: Scaling of organ size in adult insects.
Figure 1
Table 1: Scaling of organ volume as a function body volume in insects.
Figure 2: Changes in relative volume of organs in adults and larvae of insects of different taxa.
Figure 2

(A) skeleton, (B) musculature, (C) digestive system, (D) Malpighian tubules, (E) circulatory system and fat body, (F) reproductive system, (G) central nervous system, (H) brain.

The volume of the musculature

In insects generally changes isometrically (Fig. 1, Table 1). Decreasing relative volume with decreasing body size is found in Coleoptera and Paraneoptera (Fig. 2B). Since relative muscle strength is determined by cross-section area, which changes with linear body size at a lower rate than volume, relative muscle strength increases as body size decreases11, making it possible to increase the relative volume of the musculature. Hymenoptera are exceptional: the relative volume of their musculature slightly increases as body size decreases (Fig. 2B). Increased relative area of flight musculature in cross-sections has been shown for small dipterans12, but since no data on volumes are available for these insects, it is difficult to make conclusions about allometry. In mammals the musculature also changes isometrically (slope 0.99–1.00), and in birds its relative weight decreases as body size decreases (slope 1.08)3.

The volume of the digestive system

In insects generally changes allometrically (slope of regression is significantly different from 1, Fig. 1, Table 1). The relative volume decreases in Coleoptera, almost unchanged in Hymenoptera, and increases in Paraneoptera as body size decreases (Fig. 2C). Isometry and decrease can be explained by the gut efficiency, determined by surface area, which changes with body size at a lower rate than volume, so that efficiency increases as body size decreases13. The slope of the digestive system, including the gut content, is similar in insects to that of mammals (1.062) and much smaller than in birds (1.204) or other reptiles (1.389)14. Malpighian tubules generally show similar trends as the digestive system, except in Hymenoptera, in which their relative volume increases as body size decreases (Figs 1 and 2D).

The volume of the circulatory system and fat body

In insects generally changes isometrically (Fig. 1, Table 1). Analysis of separate taxa shows that the relative volume of this system somewhat increases in Hymenoptera and Paraneoptera, and decreases in Coleoptera as body size decreases (Fig. 2E). The decrease found in Coleoptera probably reflects the almost complete absence of the circulatory system of Ptiliidae4. Since the volume of the circulatory system in insects depends on many factors (amount of reserve substances, degree of reproductive products development, age, etc.15), data on the types of changes within orders can change as new, more extensive material becomes available.

Because of the extremely small diameter of the tracheae, the volume of the respiratory system could not be calculated, but considering the strong reduction of this system in microinsects4, it can be assumed that its relative volume decreases as body size decreases, which is compensated by the higher passive respiration efficiency in smaller insects.

The volume of the central nervous system

Strongly changes allometrically as body size decreases (Fig. 1, Table 1); in insects generally and all studied taxa, the relative volume of this system strongly increases as body size decreases (Fig. 2G). The greatest relative volume of this system among adult insects is found in Hymenoptera (about 12%). First-instar larvae of Coleoptera and first-instar nymphs of Paraneoptera have considerably greater relative volumes of this system compared to adults. The relative volume of this system in the first-instar nymph of the thrips Heliothrips haemorrhoidalis is about 17%, which is almost 5 times as great as in the adult. Increasing relative size of this system has also been shown in other small arthropods5,12,16,17,18,19.

The relative volume of the brain (cerebral index), widely used in discussions of the evolution of neural activity in animals1, should be considered separately. The relative weight of the human brain is 2.5%; it was long believed that cerebral index among animals was the highest in hummingbirds, 8.33%, but it reaches 8.36% in the miniature hymenopteran Trichogramma, 11.95% in first-instar nymphs of the psocopteran Liposcelis, and 15% in Brachymyrmex, some of the smallest ants20. The rule of brain size changing allometrically with body size, known as Haller’s rule or brain–body allometry, has been confirmed for many vertebrates21,22,23,24,25,26, insects5,12,20,27,28,29,30, spiders19, or other invertebrates5; it is fully realized in the smallest insects; moreover, our results considerably broaden the scope of this rule. The slope of the brain in insects is comparable to that of mammals, in which it varies, according to different data, from 0.664 to 0.763. The only exceptions to Haller’s rule are several laboratory lines of Trichogramma30. Megaphragma also has markedly smaller relative brain volume than larger representatives of related taxa, because of the anucleate neurons, a unique feature of this genus31; therefore, data on the volume of the cerebrum and of the central nervous system of Megaphragma were excluded from the main analysis. Data on the link between the complexity of behavior and brain size in vertebrates are extremely interesting, but among insects such data are available only for social species5,32,33. The behavior of microinsects never became subject of special studies, but all principal behaviors typical of large representatives of related groups are found also in microinsects. It has also been shown that in microscopic spiders body size diminution does not result in simplification of behavior34,35.

The reproductive system

In insects generally changes allometrically and increases in relative volume as body size decreases (Fig. 1, Table 1). The same trend is found in Coleoptera and Paraneoptera (Fig. 2F). Increasing relative volume of the reproductive system in free-living insects is associated with the relative egg size strongly increasing as body size decreases4. The relative volume of the reproductive system varies considerably among coleopterans, apparently because of the dependence of this parameter on the reproductive stage. Negative allometry has also been shown in linear measurements of the genital apparatus of many insects and spiders36. The gonads have a much greater slope in insects than in birds, in which it is 0.76–0.923. Among hymenopterans, this parameter markedly decreases as body size decreases, because in egg parasitoids the relative size of the egg shows no distinct increase: their larvae, which develop in the host egg, are strongly de-embryonized and consume little or no yolk37.

Thus, most insect organs show huge scaling potentials, retaining their organization4 and even relative volume as body size decreases to small fractions of its initial values. The skeleton, musculature, and circulatory systems change isometrically over the entire studied series of insects. The relative volume of those organs the efficiency of which is determined by area (the digestive system and Malpighian tubules) or diffusion rate (the tracheal system), parameters that increase as body size decreases, is smaller in smaller insects, but the relative volumes of the reproductive and nervous systems strongly increases as body size decreases. These systems can geometrically restrain miniaturization in insects and determine the limits of the smallest possible body size. The greatest rate of relative volume increase at decreasing body size is found in the nervous system; in the smallest insects this parameter reaches nearly one-fifth, making the cerebral index (relative brain weight) considerably greater than in any animals for which it is known, including humans. Although the range of body sizes in the studied insects is comparable to that of vertebrates, most organ systems in insects demonstrate much smaller allometry, suggesting that the organization of insects has a greater scaling capacity.


Experimental procedures

The material was fixed in FAE (formaldehyde, acetic acid, ethanol) and embedded in Araldite by the standard method. The resulting blocks were used to make complete series of cross-sections and longitudinal sections 1 μm for specimens less than 2 mm long and 2–4 μm for specimens more than 2 mm long. For 3D computer modeling, the series of sections were photographed under a Motic BA410 microscope. After alignment of sections and calibration of the resulting stack, the body and organs were modeled in the program Bitplane Imaris. All structures were outlined manually and automatically recalculated as three-dimensional. Most of the 3D reconstructions used in this study have been published in earlier studies on the morphology of various microinsects (review4, animated 3D-pdf38 and etc.). The volume of organs and body (without legs, wings, antennae, and other appendages) was calculated using 3D reconstructions in Bitplane Imaris statistical module. The volume of the skeleton (legs, wings, antennae, and other appendages) was calculated based on the area of the integument and average thickness of the cuticle calculated from 80 measurements (eight in each of ten equidistant sections evenly distributed over the body). The volume of the fat body and hemolymph was determined as the difference between the body volume and total volumes of all organs. The obtained volumes were analyzed in R with a SMATR 3 package using the Standardized Major Axis (SMA) and Ordinary Least Squares (OLS) estimation (which are usually used for analyzing morphological allometry39). Non-independence of the data was controlled in the ape package40 using Phylogenetic Generalized Least Squares (PGLS) for samples of one specimen per species and in the MCMCglmm package41 using Markov chain Monte Carlo generalized linear mixed models (MCMCglmm) for samples of more than one specimen per species. The phylogenetic data were obtained from the Open Tree of Life online database42.

List of taxa examined

Thysanura Latreille, 1796

Lepismatidae Latreille, 1802

Lepisma saccharina Linnaeus, 1758

Psocoptera Shipley, 1904

Liposcelididae Enderlein, 1911

Liposcelis bostrychophila Badonnel 1931

Psocidae Shipley, 1904

Copostigma sp.

Thysanoptera Haliday, 1836

Thripidae Stevens, 1829

Heliothrips haemorrhoidalis (Bouché, 1833)

Coleoptera Linnaeus, 1758

Ptiliidae Erichson, 1845

Nanosella russica Polilov, 2008

Nanosella sp.

Primorskiella anodonta Polilov, 2008

Porophila mystacea Polilov, 2008

Mikado sp.

Acrotrichis grandicollis (Mannerheim, 1844).

Acrotrichis montandoni (Allibert, 1844)

Hydraenidae Mulsant, 1844

Ochthebius sp.

Staphylinidae Lameere, 1900

Atheta sp.

Aleochara sp.

Staphylinus caesareus Cederhjelm, 1798.

Corylophidae LeConte, 1852

Sericoderus lateralis (Gyllenhal, 1827)

Orthoperus atomus (Gyllenhal, 1808)

Hymenoptera Linnaeus, 1758

Mymaridae Haliday, 1833

Anaphes flavipes (Förster, 1841)

Anagrus sp.

Trichogrammatidae Haliday et Walker, 1851

Trichogramma evanescens Westwood, 1833

Trichogramma sp.

Megaphragma mymaripenne Timberlake, 1924

Eulophidae Westwood, 1829

Hemiptarsenus sp.

Additional Information

How to cite this article: Polilov, A. A. and Makarova, A. A. The scaling and allometry of organ size associated with miniaturization in insects: A case study for Coleoptera and Hymenoptera. Sci. Rep. 7, 43095; doi: 10.1038/srep43095 (2017).

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  1. 1.

    Scaling: Why Is Animal Size So Important? Cambridge Univ. Press (1984).

  2. 2.

    & Miniaturization of body size: organismal consequences and evolutionary significance. Annu. Rev. Ecol. Syst. 24, 501–519 (1993).

  3. 3.

    Size, function, and life history. Dover publication, INC (1996).

  4. 4.

    Small is beautiful: features of the smallest insects and limits to miniaturization. Ann. Rev. Entomol. 60, 103–121 (2015).

  5. 5.

    & Grade changes in brain–body allometry: morphological and behavioural correlates of brain size in miniature spiders, insects and other invertebrates. Adv. Insect. Physiol. 40, 155–214 (2011).

  6. 6.

    & Miniaturization effects in larvae and adults of Mikado sp. (Coleoptera: Ptiliidae), one of the smallest free-living insects. Arthropod. Struct. Dev. 38, 247–270 (2009).

  7. 7.

    & Developmental stages of the hooded beetle Sericoderus lateralis (Coleoptera: Corylophidae) with comments on the phylogenetic position and effects of miniaturization. Arthropod. Struct. Dev. 39, 52–69 (2010).

  8. 8.

    , & Scaling of Supportive Tissue Mass. Q. Rev. Biol. 54, 139–148 (1979).

  9. 9.

    , & Scaling of Skeletal Mass to Body Mass in Birds and Mammals. Am. Nat. 113, 103–122 (1979).

  10. 10.

    & Etude comparative du métabolisme énergétique dans la série animale. J. Physiol. 56, 489–524 (1964).

  11. 11.

    Strength and Weight of Insects. Ann. Entomol. Soc. Am. 21, 601–606 (1928)

  12. 12.

    Histological changes correlated with evolutionary changes in body size. Evolution 2, 218–230 (1948).

  13. 13.

    Problems of relative growth. Methuen (1932).

  14. 14.

    et al. Allometry of visceral organs in living amniotes and its implications for sauropod dinosaurs. Proc. R. Soc. B 276, 1731–1736 (2009).

  15. 15.

    & Beeinflussung der Ultrastruktur von Fettkorper und Mitteldarm des Staphyliniden Atheta fungi (Grav.) durch Umwelteinflusse. Zool. Jahrb. Abt. Anat. Ontog. Tiere. 103, 73–84 (1980).

  16. 16.

    Untersuchungen an gehirnen verschieden grosser, jeweils verwandter Coleopteren- und Hymenopteren. Arten Zool. Jb. Abt. Allg. Zool. 62, 1–64 (1949).

  17. 17.

    & Larval head morphology of Hydroscapha natans LeConte 1874 (Coleoptera, Myxophaga, Hydroscaphidae) with special reference to miniaturization. Zoomorphology 118, 103–116 (1998).

  18. 18.

    , & Strepsipteran brain and effect of miniaturization (Insecta). Arthropod Struct. Dev. 34, 301–313 (2005).

  19. 19.

    et al. The allometry of CNS size and consequences of miniaturization in orb-weaving and cleptoparasitic spiders. Arthropod. Struct. Dev. 40, 521–529 (2011).

  20. 20.

    , & The allometry of brain miniaturization in ants. Brain Behav. Evol. 77, 5–13 (2011).

  21. 21.

    Allometry in primates, with emphasis on scaling and evolution of brain. Contrib. to primatol. 5, 244–292 (1975).

  22. 22.

    Brain-weight and bodyweight of mammals. J. Gen. Psychol. 16, 379–389 (1937).

  23. 23.

    Analyse volumetrique compaire des principales subdividions enciphaliques chez les reptiles sauriens. J. Hirnforsch. 17, 513–537 (1976).

  24. 24.

    Relative brain size and basal metabolic rate in terrestrial vertebrates. Nature 29, 57–60 (1981).

  25. 25.

    & Relative brain size and ecology in birds. J. Zool. 207, 151–169 (1985).

  26. 26.

    The Principles of Brain Evolution. Sinaur Assoc. Inc (2005).

  27. 27.

    , & Brain allometry in bumblebee and honeybee workers. Brain Behav. Evol. 66, 50–61 (2005).

  28. 28.

    , & On being small: brain allometry in ants. Brain Behav. Evol. 69, 220–228 (2007).

  29. 29.

    & Brain allometry and neural plasticity in the bumblebee Bombus terrestris. Brain Behav. Evol. 75, 138–148 (2010).

  30. 30.

    , , & Breaking Haller’s rule: brain-body size isometry in a minute parasitic wasp. Brain Behav. Evol. 81, 86–92 (2013).

  31. 31.

    The smallest insects evolve anucleate neurons. Arthropod Struct. Dev. 41, 27–32 (2012).

  32. 32.

    & Relationships between foraging efficiency and the size of the head and component brain and sensory structures in the red wood ant. Brain Res. 16, 85–104 (1969).

  33. 33.

    Size and behavior in ants: constraints on complexity. Proc. Natl. Acad. Sci. USA 82, 8548–8551 (1986).

  34. 34.

    Miniaturized orb-weaving spiders: behavioural precision is not limited by small size. Proc. R. Soc. B 274, 2203–2209 (2007).

  35. 35.

    Are smaller animals behaviourally limited? Lack of clear constraints in miniature spiders. Anim. Behav. 81, 813–823 (2011).

  36. 36.

    Static allometry and animal genitalia. Evolution 63, 48–66 (2009).

  37. 37.

    Очерки по сравнительной эмбриологии перепончатокрылых (Essays on the Comparative Embryology of Hymenoptera). Leningrad Univ. Press (1961).

  38. 38.

    & The anatomy of the thrips Heliothrips haemorrhoidalis (Thysanoptera, Thripidae) and its specific features caused by miniaturization. Arthropod stru. Dev. 45(5), 496–507 (2016).

  39. 39.

    , , & smatr 3 - an R package for estimation and inference about allometric lines. Methods Ecol. Evol. 3, 257–259 (2012).

  40. 40.

    , & APE: analyses of phylogenetics and evolution in R language. Bioinformatics 20, 289–290 (2004).

  41. 41.

    MCMC Methods for Multi-Response Generalized Linear Mixed Models: The MCMCglmm R Package. J. Stat. Softw. 33(2), 1–22 (2010).

  42. 42.

    Open Tree of Life (2016).

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We are grateful to E. Rakhimberdiev for consulting us on data analysis. The collecting of the material and examination of the musculature were supported by the Russian Foundation for Basic Research (project nos. 14-04-00638 and 15-34-20490); the rest of this study was supported by the Russian Science Foundation (project no. 14-14-00208).

Author information


  1. Department of Entomology, Faculty of Biology, Lomonosov Moscow State University, Moscow 119234, Russia

    • Alexey A. Polilov
    •  & Anastasia A. Makarova


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A.A.P. designed the study, A.A.P. and A.A.M. collected and analyzed the data, A.A.P. wrote and edited the manuscript.

Competing interests

The authors declare no competing financial interests.

Corresponding author

Correspondence to Alexey A. Polilov.

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