**Insects: Functional Morphology, Biomechanics and Biomimetics**

Editors

**Hamed Rajabi Jianing Wu Stanislav N. Gorb**

MDPI • Basel • Beijing • Wuhan • Barcelona • Belgrade • Manchester • Tokyo • Cluj • Tianjin

*Editors* Hamed Rajabi School of Engineering London South Bank University London United Kingdom

Jianing Wu School of Aeronautics and Astronautics Sun Yat-Sen University Shenzhen China

Stanislav N. Gorb Functional Morphology and Biomechanical Kiel University Kiel Germany

*Editorial Office* MDPI St. Alban-Anlage 66 4052 Basel, Switzerland

This is a reprint of articles from the Special Issue published online in the open access journal *Insects* (ISSN 2075-4450) (available at: www.mdpi.com/journal/insects/special issues/morphology biomechanics).

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### **Contents**


Reprinted from: *Insects* **2020**, *11*, 400, doi:10.3390/insects11070400 . . . . . . . . . . . . . . . . . . **139**

#### **Chao Wan, Rentian Cao and Zhixiu Hao**


### **About the Editors**

#### **Hamed Rajabi**

Dr Hamed Rajabi is a Lecturer in the School of Engineering at London South Bank University (LSBU). He received his first PhD in Mechanical Engineering followed by a second one in Biology. Collaborations with researchers from different backgrounds have enabled him to employ methods and techniques from different fields into his research and, thereby, answer questions that can be addressed only using multidisciplinary approaches.

Hamed is passionate about biological systems and their 'technological' complexities. He and his team aim to unravel these complexities, learn from them to develop nature-inspired concepts, and elaborate them into a technology readiness level that can be converted into marketable products, especially in the areas of structural reinforcement, lightweight construction, healthcare, and robotics.

Hamed has contributed over 55 articles in peer-reviewed journals (many of which are ranked among the highest scored articles in all research areas), one preprint, two editorials, six articles in languages other than English (including Persian, German and Japanese), and three patents. His research has been featured by many science news magazines, such as Phys.org, New Atlas, 3D Printing Industry, TechXplore, Advanced Science News, etc. He has won multiple national and international awards, including KiNSIS Best PhD Dissertation Award, and KLS Postdoctoral Award for excellent research quality. He has supervised over 40 postgraduate students. Hamed is currently providing service as a member of the Editorial Board of Frontiers in Mechanical Engineering and Journal of Bionic Engineering, and as a Standing Member of the Youth Committee of the International Society of Bionic Engineering.

#### **Jianing Wu**

Dr Jianing Wu is an Associate Professor in the School of Aeronautics and Astronautics at Sun Yat-Sen University, China. He received his PhD in Mechanical Engineering from Tsinghua University China, in 2015. He joined Georgia Institute of Technology, USA, as a postdoctoral research fellow from 2015 to 2018, worked on biolocomotion and bio-inspired systems. Later, he joined Sun Yat-Sen University as an associate professor.

Dr Wu's research interests include animal behavior, biomechanics and bio-inspired robotics. He has published 50 papers (40 of them as the first/corresponding author), including Acta Biomaterialia, Royal Society Interface, Journal of Experimental Biology and Bioinspiration & Biomimetics. These works have been cited more than 800 times at Google Scholar. The outcomes of his works have been highlighted in many world-known science media, such as Science, New York Times, New Scientists, Science Daily, Physics Org, etc.

#### **Stanislav N. Gorb**

Stanislav Gorb is Professor and Director at the Zoological Institute of the Kiel University, Germany. He received his PhD degree in zoology and entomology at the Schmalhausen Institute of Zoology of the Ukrainian Academy of Sciences in Kiev (Ukraine). Gorb was a postdoctoral researcher at the University of Vienna (Austria), a research assistant at University of Jena, a group leader at the Max Planck Institutes for Developmental Biology in Tubingen and for Metals Research ¨ in Stuttgart (Germany). Gorb's research focuses on morphology, structure, biomechanics, physiology, and evolution of surface-related functional systems in animals and plants, as well as the development of biologically inspired technological surfaces and systems. He received the Schlossmann Award in Biology and Materials Science in 1995, International Forum Design Gold Award in 2011 and Materialica "Best of" Award in 2011. In 1998, he was the BioFuture Competition winner for his works on biological attachment devices as possible sources for biomimetics. In 2018, he received Karl-Ritter-von-Frisch Medal of German Zoological Society. Gorb is Corresponding member of Academy of the Science and Literature Mainz, Germany (since 2010) and Member of the National Academy of Sciences Leopoldina, Germany (since 2011). Gorb has authored several books, more than 500 papers in peer-reviewed journals, and five patents.

### *Editorial* **Insects: Functional Morphology, Biomechanics and Biomimetics**

**Hamed Rajabi 1,\* , Jianing Wu 2,\* and Stanislav Gorb 3,\***


#### **1. Introduction to the Special Issue**

Insects are the most diverse animal taxon, both in terms of the number of species and the number of individuals. There are roughly one million described insect species, and their real number is estimated to be five to ten times this figure [1]. The total number of individual insects, on the other hand, is estimated to be as high as one million trillion [2]. This is why insects are regarded as the most successful groups of animals on Earth.

It is not the first time, nor will it be the last, that insects have become the core theme for a collection of experimental studies. However, what makes the current collection unique is the focus on understanding the complexities of insect structures, functions and potential applications that they offer. Although the functional morphology of insects remains a basic science, insect structures offer a variety of existing and potential applications in biomedical, structural, mechanical and aerospace engineering. In this Special Issue "Insects: Functional Morphology, Biomechanics and Biomimetics", we aimed to include studies that cover fundamental research and discuss practical applications, as much as possible.

In this Special Issue, our readers will read about insect structures, including wings, legs, feeding apparatus, sensory organs and ovipositors. The reader will find answers to questions such as: How do insects fly? What are the design strategies that enable insect wings to reach automatic shape control? How does the specific segmented design determine the oscillatory response of insect antennae? What are the adaptations of insect mouthparts to their feeding habits? How does a thin film of adhesive secretion contribute to attachment of insect eggs? What are the physiological and environmental factors that determine the jump performance of locusts? How can these inspire engineering innovations, such as wings for micro air vehicles, enhanced sensory systems or multifunctional microfluidic transporters?

A number of well-known scholars in the field kindly accepted our invitation and contributed to this collection. We would like to thank the authors for their invaluable contributions to this Special Issue. We appreciate their dedication, support and commitment. We would also like to thank the support of *Insects*, MDPI and its staff, who made this Special Issue possible. We very much thank the reviewers who assessed the submitted manuscripts and played a key role in improving the quality of this Special Issue. We hope that you enjoy reading this Special Issue.

#### **2. Dedication**

This Special Issue is dedicated to Professor Leonid I. Fransevich, a corresponding member of the Ukrainian National Academy of Sciences and Professor Emeritus at Schmalhausen Institute of Zoology, Kiev, Ukraine, for his work in insect functional morphology, physiology and biomechanics, and on the occasion of his 85th birthday.

Leonid Frantsevich was born in 1935 in Kiev, Ukraine. He graduated from the Faculty of Biology of the Shevchenko Kiev State University with a diploma in Biology–Zoology.

**Citation:** Rajabi, H.; Wu, J.; Gorb, S. Insects: Functional Morphology, Biomechanics and Biomimetics. *Insects* **2021**, *12*, 1108. https:// doi.org/10.3390/insects12121108

Received: 19 November 2021 Accepted: 9 December 2021 Published: 12 December 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

He defended his PhD thesis "Fauna of Lepidoptera of the Middle Dnieper Valley" (1963) and his doctoral (habilitation) dissertation "Visual analysis of space in insects" (1981), both in entomology. For over 40 years, he has been working at the Schmalhausen Institute of Zoology of the Ukrainian National Academy of Sciences, where he currently holds the position of leading researcher.

Professor Fransevich made a number of important discoveries in the studies of insects. In particular, he discovered the ability of animals to recognize random two-dimensional images by their texture. He showed astro-orientation in Coleoptera during homing and identified structural elements of the olfactory center in the insect brain (glomeruli of the deutocerebrum) by morphological characteristics. He discovered, described and experimentally studied a type of proprioceptor (arcular organ) in Coleoptera. He demonstrated the spatial stability of visual orientation behind local and astro-landmarks in insects during homing on inclined surfaces. He proposed an orientation model using polarized sky light based on a standard polarization sensitivity direction map embedded in the retinal structure and demonstrated the spatial stability of topological signs of visual key stimuli in insects.

Leonid Frantsevich was the first to use the skeletal model of the kinematic system of walking insects for the purpose of describing and analyzing movements, solving the inverse kinematics problem for reconstructing the joint angles, which are not directly observed. Using inverse kinematics methods, he studied the kinematics of locomotor maneuvers in walking insects: turns on a plane, overturns, walking on thin rods, turning at the end of a thin rod, as well as the kinematics of opening–closing elytra in Coleoptera. He contributed to the research on the kinematics and mechanism of deployment of the arolium (a sticky pad at the insect pretarsus) and the role of pre-stressed structures in this process. Having studied the mechanics of the composed middle coxa in dipterans, Leonid Frantsevich showed that this structure is a marker of the body segment to which the leg is attached and discovered manifestations of homeosis (the appearance of a structure in another body segment) in certain dipteran taxa.

From autumn 1986 to 1988, Leonid Frantsevich headed the work of Kiev zoologists in the Chornobyl NPP site and the Exclusion Zone. At that time, his research developed in two directions: radioecology and general ecology. He calculated the volume of the removal of the radionuclides from the Exclusion Zone by migratory birds and then proposed an integral estimate of the offset as a product of three quantities. The resulting estimate turned out to be insignificant in comparison with the total removal of radionuclides outside the zone and did not require specific countermeasures.

In 1989–1994, Leonid Frantsevich and his colleagues carried out a wide bioindication of 90Sr pollution of water bodies and land on the basis of the beta radioactivity of mollusk shells. Maps of 90Sr pollution of the Kiev region and rivers of the Dnieper basin were compiled. The experience of data generalization for multi-species collections was used to reconstruct the radioactive pollution of various species of wild animals based on the study of a few representative species, which are accepted as comparison standards. This standardization made it possible to depict the radionuclide contamination of wild animals on a map (2000). Based on the methods of processing multicomponent collections, Leonid Frantsevich created the first model for optimizing the permissible levels of radionuclides in food (1997).

Leonid Frantsevich was the first to draw attention to the fact that, in most of the exclusion and resettlement zones (over 98% of the total area—about 3000 km<sup>2</sup> ), the course of events in biocenoses was determined not by the harmful effect of radiation, but rather by the removal of anthropogenic pressure on wildlife after the evacuation of the population, eliminating large-scale engineering interventions. Research and accounting of general ecological patterns were needed for the management of the alienated territories. He proposed the concept of a mosaic reserve of the Exclusion Zone with the allocation of scientifically or nature-protected lands. The principle of the mosaic reserve was approved by the Scientific and Technical Council under the Administration of the Exclusion Zone.

Leonid Frantsevich has been very successful and productive (over 150 original publications and related books, the most significant of which are "Visual analysis of space in insects" (1980), "Spatial orientation of animals" (1986) and "Animals in the radioactive zone" (1991). During his career, he has received several awards for his many contributions to science, including the State Prize of the USSR (1987), the State Prize of the Ukraine (2004) and being elected as a corresponding member of the Ukrainian National Academy of Sciences (1990), to name a few.

We organized this Special Issue in honor of Professor Frantsevich's distinguished scientific career over the past 60 years. This Special Issue consists of original research articles and review articles related to the functional morphology and biomechanics of insects, his favorite topic.

**Funding:** This research received no external funding.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


### *Article* **The Geometry and Mechanics of Insect Wing Deformations in Flight: A Modelling Approach**

#### **Robin Wootton**

Department of Biosciences, University of Exeter, Address for correspondence 61 Thornton Hill, Exeter EX4 4NR, UK; r.j.wootton@exeter.ac.uk

Received: 16 June 2020; Accepted: 13 July 2020; Published: 17 July 2020

**Abstract:** The nature, occurrence, morphological basis and functions of insect wing deformation in flight are reviewed. The importance of relief in supporting the wing is stressed, and three types are recognized, namely corrugation, an M-shaped section and camber, all of which need to be overcome if wings are to bend usefully in the morphological upstroke. How this is achieved, and how bending, torsion and change in profile are mechanically interrelated, are explored by means of simple physical models which reflect situations that are visible in high speed photographs and films. The shapes of lines of transverse flexion are shown to reflect the timing and roles of bending, and their orientation is shown to determine the extent of the torsional component of the deformation process. Some configurations prove to allow two stable conditions, others to be monostable. The possibility of active remote control of wing rigidity by the thoracic musculature is considered, but the extent of this remains uncertain.

**Keywords:** insects; wings; deformation; flight; bending; torsion; camber; control; physical models

#### **1. Introduction**

This paper has a dual function: to review the occurrence of flight-related deformations in the morphological upstroke of insect wings and to investigate the geometric principles underlying the interaction of bending, torsion and camber change, by means of simple physical models.

Orthodox, flight-adapted insect wings are smart structures: they are flexible aerofoils whose three-dimensional shape from instant to instant in flight is largely determined by their elastic response to the aerodynamic and inertial forces they are receiving. While the profile of the wing base can normally be altered and controlled by the direct flight muscles of the thorax, the absence of muscles within the wing requires that three-dimensional shape control beyond the base is to a great extent automatic — encoded in the wing's detailed structure. Four decades ago, I discussed the nature and function of the deformations they undergo, and identified a range of morphological adaptations to facilitate and to limit them [1]. The extensive research carried out since then has expanded and broadly confirmed these early conclusions and predictions [2–26] (in particular, see [19,21] for summaries of the extensive Russian literature), and major advances in insect aerodynamics have greatly helped to interpret their significance, e.g., [27–35].

Our knowledge of wing kinematics and deformations has come from high speed still and cine photography and video-recording. These sources show, unsurprisingly, that in the insects studied, the wings' cyclic deformations are not rigidly determined: they vary in extent, even within a given flight sequence. To take just one example, high speed photographs of *Panorpa communis* (Mecoptera) in the upstroke published by Brackenbury [16] show virtually no bending in the wings, and Brodsky and Ivanov [4], filming tethered individuals, found little wing flexion, but a short high speed movie sequence of *Panorpa germanica* shortly after take-off shows extensive upstroke bending of the forewings and particularly the hindwings increasing from stroke to stroke [14] (Figure 1). These are different

species, but their wings are structurally identical, and one would expect similar behaviour in both. These variations between strokes may be passive: wing shape must certainly be influenced by variations in angular velocity in the translation part of the stroke and in angular acceleration around stroke reversal. However, there is a possibility that, in some insects at least, a degree of control of bending, passive torsion and section may be exerted remotely by muscles at the wing base, and it is interesting to explore how such control might be achieved. Furthermore, wings, as resonant structures, need to deform appropriately at their actual flapping frequencies, and it is entirely possible that they may be tunable by active control of wing rigidity.

**Figure 1.** (**a**) Tracings of three frames from the same upstroke of *Panorpa germanica* from a high-speed film by A.R. Ennos. Note the very different bending modes of forewings and hindwings, reflecting the different lengths of the subcosta, SCP, and that flexion and torsion persist throughout the half-stroke. (**b**) Fore and hind wings of *Panorpa germanica.* Here, and in subsequent wing illustrations, the median flexion line is shown in blue, transverse flexion lines in red and the claval flexion line in green.

In the last two decades, particularly stimulated by the biomimetic possibilities in the development of micro air vehicles, there has been a great increase in interest in the structure, properties and functioning of the wings of certain groups: hawkmoths [25,26,29,36], locusts [23,37–39], hoverflies [40–42] and, above all, Odonata [43–50]; see [46–48] for reviews of the extensive literature, in which modelling has played an increasingly important role. Models have long been valuable in understanding wing functioning, and Wootton et al. [24] identified a logical sequence from conceptual though physical and analytical models to increasingly sophisticated computational simulations of individual species.

Each stage in this sequence has both advantages and limitations. Computational models now rightly dominate the literature, but they are vulnerable to incorrect initial assumptions, and, historically, some of the most useful information has come from simple physical models, based on direct observation of insects in flight and simple manipulation of wings. These are easy and quick to construct and have allowed the swift investigation and testing of a range of observed phenomena in a broad range of insects, in some cases giving direction to analytical and computational modelling of complete wings or wing components [3,12,23,24,38,47,49–55].

In 1999, I further discussed wing design, deformation and control in the wider context of invertebrate paraxial locomotory appendages, and illustrated how the principles underlying the in-flight deformation of many wings can be learned as a first approximation by modelling them as simple shells; see [55] for a wider range of references to research since 1981. The present paper uses physical models of this kind to extend the discussion by exploring how aspects of the geometry of the wings may affect their deformations in flight and to suggest how these may in theory be actively influenced and controlled remotely from the axilla. It will focus primarily on species that have either been specifically investigated or for which good photographic information is available. A selection of highspeed photographs by Stephen Dalton and John Brackenbury, some but not all previously published, are included with the authors' generous permission.

I am not concerned here with the shape changes in the expanded anal fans of the hindwings of Orthoptera, Dictyoptera and some other orders (23, 37, 38, 39, 52), or with the flight deformations in Coleoptera hindwings, which are strongly influenced by the flexible lines by which these fold up at rest [17]. The emphasis is on mechanisms involving some transverse bending, particularly, but not exclusively, in forewings. Hindwings also deform in many groups, depending on their relative length and on the presence or absence of wing coupling. The latter also influences the nature of forewing deformation—compare the Trichoptera in Figure 2.

**Figure 2.** Tracings of successive frames from films of two Trichoptera in tethered flight, comparing a species with uncoupled wings (**a**–**c**) with a species in which the wings are coupled (**d**–**f**). From [56], redrawn after [6]. (**a**–**c**) *Rhyacophila nubile* (Rhyacophilidae). (**d**–**f**) *Ceraclia senilis* (Leptoceridae).

#### *1.1. Rigidity, Flexibility and Active Control*

In typical flight-adapted wings, certain areas are clearly adapted for rigid support, with thick veins, high relief and sometimes thickened membrane. These are generally in the proximal part of the wing and along the more anterior veins. Posterior support, necessary to prevent the wing from pitching into the airflow, is in the forewings and many hindwings of Neoptera generally provided by a rigid clavus, or in many Diptera by automatic mechanisms that lower the trailing edge in response to aerodynamic loading, a situation which is also characteristic of Odonata [12,15,50]. The forewings of Ephemeroptera have no clear clavus, but the anal area provides similar posterior stiffening.

In most insects, the profile of the wing base can alter by hinge-wise bending along specific longitudinal flexion lines [1,2,4,5], of which the most important and widespread are the claval flexion line and the median flexion line—the "remigial furrow" of Martynov [57] and Grodnitsky and Morozov [8]. Basal profile change is a frequent component of the active torsion of the whole wing during the stroke cycle and is the only way in which thoracic muscles can directly deform the wing.

All other deformations are passive responses to aerodynamic, inertial and occasional impact forces, and they tend to be concentrated in more distal areas of the wing, where the relief is flatter, the longitudinal veins are more slender, even sometimes absent, and cross-veins are relatively thin and flexible. These areas are sometimes clearly delineated by a visible transverse flexion line, marked by local areas of thinning of membrane and veins—"thyridia"—or by points or lines of soft cuticle that interrupt the veins themselves.

#### *1.2. The Functions of Bending*

Typical wings are thin, springy plates, stiffened by tubular veins, whose mass and thickness diminish along the span. Bending is often a simple response to the inertial forces as the wings decelerate at stroke reversal. Importantly, they only significantly flex ventrally; sometimes around the bottom of the stroke, followed by a sharp straightening, and sometimes throughout most of the upstroke. Dorsal bending is normally slight or absent, though long wings can sometimes flex alarmingly in response to gusts of wind or in extreme accelerations. Otherwise, the principal function of deformation is aerodynamic optimisation: to create necessary force asymmetry between the downstroke and the upstroke, or to generate bursts of unsteady lift.

The shape of the downstroke is fairly consistent: the wing is extended and pronated, usually slightly cambered, with a degree of spanwise twist—"washout", the ideal situation for generating steady lift. Upstroke deformations can be far greater. In some cases, they merely serve to "feather" the wing by reducing its effective area or its angle of attack, so minimising adverse aerodynamic force, but many insects need to develop usefully directed lift throughout the stroke cycle. For this, passive torsion within the span is usually crucial. In Odonata, in many Diptera and in some other insects with uncoupled wings, most of the remigium can swing across like a sail around the supporting anterior veins, but in many other insects—particularly those with coupled wings, like Hemiptera, Hymenoptera, many Lepidoptera and some Trichoptera (Figure 2), or those with a long clavus—torsion is concentrated more distally and is facilitated by a degree of ventral bending, often accompanied by a reversal of camber from dorsally convex to dorsally concave. This brings the distal part of the wing into a favourable angle of attack and suitable profile for generating usefully directed force in the translational part of the stroke, and the dynamic process of changing shape can probably create valuable unsteady lift around stroke reversal.

This paper will use models to investigate the relationships between bending, torsion and camber in wings of this kind, including some Ephemeroptera, Hemiptera, Plecoptera, Megaloptera, Mecoptera and Hymenoptera. These three aspects of deformation are intimately connected. Flexural and torsional rigidity are affected by relief, which in wings can take the form of camber, corrugation or a combination of the two. Whereas a flat plate, or a relatively flat corrugated plate, is equally flexible to dorsal and ventral bending, camber in a thin plate imposes bending asymmetry, as a force applied to the concave side tends to increase the height of the section and hence its rigidity, while a force on the convex side causes the sides to buckle outwards and the section to flatten—an effect familiar to anyone who has used an extending steel ruler [1]. The supporting areas of wings commonly have a degree of built-in camber, ensuring that wing flexion is always ventral. Where the aerodynamic and inertial forces are centred behind the torsional axis, a cambered wing is also asymmetric in twisting, far more resistant to pronation than to supination [51,53] Both these properties are appropriate to the upstroke and are often crucial in determining the shape and attitude of the distal, most aerodynamically effective part of the wing. Under aerodynamic loading, the deformable area of the wing often assumes a cambered section, dorsally convex in the downstroke but concave in the upstroke, and this reversal of camber is also related to aspects of the wing's geometry, as we shall see.

#### *1.3. Modelling Insect Wing Deformation*

For the purpose of modelling, I am distinguishing three types of support.

#### 1.3.1. Corrugation

Ephemeroptera and Odonata have fully corrugated wings, with all main vein stems diverging from close to the wing base and alternately occupying the crests and troughs of a fluted structure. Odonate wings do not bend significantly, but in several families of Ephemeroptera, Edmunds and Traver [58] found "bullae"—patches of soft, flexible cuticle—aligned across the wing in three or four of the main concave veins of the forewings, and they correctly identified these as adaptations to ventral bending. Mayfly bullae and their alignment have recently been described in more detail [59].

*Ephemera* species (Figure 3) have bullae on four major longitudinal concave veins: the subcosta SCP, two branches of the posterior radius RP and the posterior media MP, in a nearly straight line across the wing. Brodsky [19] observed bending in the subimago of *Ephemera vulgata* in flight, though he did not see it in the imago. Four other mayfly families, with quite different flight behaviours, have no bullae. Images found online of the much photographed *Palingenia longicauda*, which does not have bullae, show that ventral flexion can occur in their absence; the bullae appear to be adaptations for sharp, small-radius bending, without damage to the veins.

**Figure 3.** Forewing of *Ephemera vulgata* (Ephemeroptera). The positions of the bullae are shown by red spots.

#### 1.3.2. An M Section

The remigial supporting areas of Plecoptera, Megaloptera, Mecoptera, Trichoptera and many Lepidoptera and Diptera typically have two longitudinal concave troughs. The leading edge spar formed by the costa C, the subcosta SCP and the anterior radius RA is the first; it provides support as far as the point where the SCP ends as a separate vein. The second trough follows the median flexion line, close to the media M in most Plecoptera, *Sialis* (Megaloptera), *Panorpa* (Mecoptera), and most Trichoptera and Diptera. Lepidoptera vary greatly [5]. In Noctuidae, like the *Phlogophora* figured here, the median flexion line lies well anteriorly in the wing. Transverse bending occurs in some members of all these orders, often (except for Diptera) in both fore and hind wings. Wing deformation in Diptera

also varies depending on proportions and on the presence or absence of one or more costal breaks and flexion lines [13].

The pattern of bending is strongly influenced by the length of SCP, which often terminates very short of the wing tip, so that the anterior concavity is flattened beyond. Here, and beyond the clavus which provides posterior support, the section is like a shallow letter M or an inverted W.

Figure 4 shows a selection of wings in these groups, together with some photographs and drawings demonstrating the deformations they undergo. The drawings indicate the main flexion lines.

**Figure 4.** (**a**) *Isogenus nubecola* forewing. (**b**) Tracing of a frame of *I. nubecola* at the start of the upstroke in tethered flight. (**c**) *Sialis lutaria* forewing. (**d**) *S. lutaria* in late upstroke. (**e**) *Phlogophora meticulosa* forewing. (**f**) *P. meticulosa* in late upstroke. (**a**) and (**b**) are redrawn after Brodsky [60]. (**d**) and (**f**) are copyright Stephen Dalton. (**d**) has previously been published in [61], (**f**) in [62]. Red: transverse flexion line. Blue: median flexion line. Green: claval flexion line.

A series of comparative investigations in Russia in the 1980s and 1990s have supplied valuable information on wing deformations in flight [2,5–8,19,21,60]. In all cases, the insects were tethered, so the kinematics may not necessarily reflect free flight, but they illustrate the deformations that the wings allowed. Brodsky [60] filmed *Isogenus nubecula* (Plecoptera) and took a series of high-speed photographs of *Sialis morio* (Megaloptera) [19]. Ivanov filmed *Rhyacophila nubile*, *Ceraclia senilis*, *Brachycentrus subnubilis* and *Arctopsyche ladogensis* (Trichoptera) [6], and Grodnitsky with colleagues filmed a range of Lepidoptera [5,8,21]. All showed a degree of ventral bending at the end of the downstroke. Figure 4b, of *Isogenus* immediately after the extreme point of transverse bending, shows a deep groove in the remigium proximal to the flexion, and the distal area is strongly supinated. Later frames from the same sequence show rapid straightening and completion of torsion early in the upstroke, and Brodsky's images of *Sialis* and Ivanov's of Trichoptera show relatively fast recovery, but a high-resolution photograph of *Sialis lutaria* in free flight by Dalton [62] (Figure 4d) shows flexion and reversed camber at an advanced upstroke stage. The same seems to be the case in his photograph of *Phlogophora meticulosa* (Figure 4f)*,* indicating that flexion is maintained throughout the half-stroke, as it appears in Ennos' film of *Panorpa* (Figure 1) and in some of Grodnitsky's moth images [21].

#### 1.3.3. Camber

The basal sections of the forewing remigium of most auchenorrhychous Homoptera have a cambered section. The membrane between the veins is often thickened, a condition that is more strongly developed in the hemielytra of Heteroptera. The camber sometimes continues into the more deformable, distal area; otherwise, this is flat. The clavus, which varies considerably in length, is typically strongly three-dimensional and rigid, and any bending happens at or beyond its apex. A median flexion line is probably frequently present, though not always obvious in Homoptera and detectable only by manipulation [20].

Cicadas (Figure 5a–c) have a particularly obvious transverse flexion line in the forewing, as do Tettigarctidae, Hylicidae and some Cixiidae and Psyllidae [20]. In each case, the line follows a curved path from a break in the costal margin to the end of the clavus, with the apex of the curve towards the wing base—significantly, as we shall see. A variety of other Homoptera show the parallel development of a transverse, straight alignment of cross-veins, presumably localising bending. Cicadas have no median flexion line. Photographs by John Brackenbury (Figure 5b,c) show different degrees of transverse bending and camber reversal in *Tibicina haematodes*.

The hemielytra of Heteroptera (Figure 6) show the clearest differentiation between supporting and deformable areas in any insect. Posterior support continues beyond the clavus as a sclerotised bar at the trailing edge of the remigium. Betts [9,10] found that ventral flexion in flight does not follow the line of the corium margin but takes place within the deformable membrane, along a straight line between the anterior end of the corium and the tip of the posterior sclerotised bar, and this is evident in Brackenbury's photograph of *Palomena prasina* (Pentatomidae) (Figure 6b, from [16]). Several families of Heteroptera have an additional transverse flexion line within the corium: the cuneal fracture. In Miridae, at least, bending can occur at this point as well as at the tip of the corium, increasing the degree of distal supination (Figure 6c, from [16]).

**Figure 5.** Upstroke deformation in *Tibicina haematodes* (Cicadidae). (**a**) The forewing. (**b**), (**c**) Two images of the upstroke. (**b**) Mid-upstroke, (**c**) early upstroke. (**b**) and (**c**) copyright John Brackenbury. (**b**) has previously been published in [16]. Red: transverse flexion line. Green: claval flexion line.

A cambered wing base is also typical of Hymenoptera, where fusion of the stems of M and the anterior cubitus CUA has eliminated the usual difference in relief between the two veins. Brackenbury [18] has reviewed wing deformation in a range of Hymenoptera. Figure 7b,c, from [16], clearly show flexion, torsion and camber reversal in a wood wasp and an ichneumon, and a photograph of a vespid in [61] and various high speed video sequences which are available online indicate that these are widespread in the order. In coupled wings like these, flexion in the small hindwings is virtually absent, and in-span bending and torsion are restricted to the distal part of the forewing, beyond the coupling.

Examples of forewing M sections and cambered sections are shown in Figure 8. Note that both categories show an overall dorsally convex curvature, ensuring preferential resistance to dorsal bending. The M section wings are distinguished by the presence of a concave branch of the median vein (arrowed), with the median flexion line adjacent.

**Figure 6.** Wing proportions and upstroke deformation in Heteroptera. (**a**) Pentatomidae. (**b**) Alydidae. (**c**) Miridae. (**d**) *Palomena prasina* (Pentatomidae) early in the upstroke. (**e**) *Leptoterna dolabrata* (Miridae) in mid upstroke, showing flexion at the cuneal fracture, aiding supination. (**a**–**c**) From [61], (**d**) and (**e**) copyright John Brackenbury, previously published in [16]. Red: transverse flexion lines. Blue: median flexion line. Green: claval flexion line.

**Figure 7.** Upstroke deformation in Hymenoptera, showing flexion, torsion and camber reversal. (**a**) Forewing of *Urocerus gigas* (Siricidae). (**b**) *Urocerus gigas* male in mid upstroke. (**c**) *Ophion luteus* (Ichneumonidae) in early upstroke. (**b**) and (**c**) copyright John Brackenbury, previously published in [16]. Red: transverse flexion line. Blue: median flexion line. Green: claval flexion line.

**Figure 8.** Forewing sections. (**a**) and (**b**) are M sections: (**a**) *Phrygania* (Trichoptera), (**b**) *Sialis*(Megaloptera). (**c**) and (**d**) are cambered sections: (**c**) *Urocerus* (Hymenoptera), (**d**) *Cercopis* (Homoptera). The lines indicate where the sections were cut.

#### **2. Materials and Methods**

All models were made of card and paper. The variations in the rigidity and resilience of the different areas of the wing can be crudely replicated by varying the thickness of the materials. The models are simple to construct, and readers are encouraged to make and play with their own versions.

#### *2.1. Corrugation*

Model 1 (Figure 9a) was made from an A4 sheet of paper, with a density of 80 g/m<sup>2</sup> , and follows Edmunds and Traver [58] in representing the Ephemeroptera condition as a pleated paper fan with a transverse line of notches, simulating the bullae, cut in the concave pleats. With the base held, gentle downward force was applied beyond the bullae until yielding occurred.

#### *2.2. The M Section*

Models 2 and 3 (Figure 9b–d) were made from thin card, with a density of 175 g/m<sup>2</sup> , though density was not critical. Both measured 29.5 mm × 12 mm. Model 2 represented the M section alone, without anterior support from the leading edge spar or posterior support from the clavus. The sheet was longitudinally folded into three equal panels, and the centre panel was folded in half to form an M section. One end was held firmly by insertion into an expanded polystyrene block, representing the wing base, and downward force was applied to the distal end.

Model 3 had the same dimensions as Model 2, but a long triangular concave fold was added to each of the outer panels, corresponding to the leading edge spar and the clavus, to stiffen the proximal part of the model.

**Figure 9.** (**a**–**d**) Models 1–3 deforming. (**a**) Model 1. (**b**), (**c**) Model 2. In (**b**), the position is stable. In (**c**), under greater load, the sides are buckling outward, allowing unstable flexion that returns to position (**b**) when the load is removed. Flexion is directly transverse. (**d**) Model 3. The extra anterior and posterior folds delay unstable bending under load, and the flexion line is curved. The arrows indicate the approximate points and directions of the applied bending force.

#### *2.3. Camber*

The wings were modelled as rectangles, measuring 29.5 mm × 11.5 mm, with a supporting base made of stiff card and a distal deformable area of standard printing paper, with a density of 80 g/m<sup>2</sup> (Figure 10).

One flexion line AO, parallel to the long sides of the rectangle and corresponding to a median flexion line, was made by cutting partway through the depth of the card. Camber was adjusted experimentally by bending along this line. Its height was represented by the angle ε about the axis AO. The other flexion line, which could be transverse or oblique, was provided by the distal edge of the supporting card. In actual wings, this line is usually curved, but to simplify the geometry in the models, it was made of two straight lines, BO and OD, meeting the median flexion line at point O. This is an acceptable simplification: models with a curved flexion line behaved in exactly the same way.

These models therefore had three variables: the obliqueness of the transverse flexion line, measured by the angle ζ between the longitudinal axis and a straight line joining B and D; the angle BOD, as measured in the flat model; and ε. The first two were part of the model's design, while the third could be manipulated.

In Model 4 (Figure 10a), BOD was straight, so angle BOD = 180◦ and ζ = 90◦ . In Model 5 (Figure 10b), BOD = 120◦ and ζ = 90◦ . In Model 6 (Figure 10c), BOD = 90◦ and ζ = 60◦ . In Model 7 (Figure 10d), the anterior supporting card extended to the end of the model. BOD was 90◦ and ζ 40◦ .

One more model, Model 8 (Figure 10e), was produced in order to investigate the specific wing conformation of some families of Heteroptera which have an extra transverse flexion line, the cuneal fracture, and a longitudinal flexion line well anterior to the mid line. The model was made using thinner card than in Models 4-8, as the supporting base needed some flexibility if the model was to function. This is of course closer to the situation in actual insects than the thick card used in the other models; the latter was chosen so that the camber could conveniently be measured as the angle ε.

**Figure 10.** Models 4–8. (**a**) Model 4. (**b**) Model 5. (**c**) Model 6. (**d**) Model 7. (**e**) Model 8. The broken line is the outline in the unflexed state. Model 4 is stable only when unflexed; Models 5, 6 and 7 are bistable. Model 5 shows flexion only; Models 6 and 7 show torsion as well as bending. Model 8: explanation in the text. Red lines correspond to transverse flexion lines, blue lines to median flexion lines in wings.

#### **3. Results**

#### *3.1. Corrugation: Model 1*

ζ

ε Pressing on the dorsal surface caused the cut pleats to move dorsally and the fan to flatten and bend ventrally, creating an effective one-way hinge. When the fan was allowed to expand laterally, the model was stable only in the unflexed state. In the actual wing, the veins on the ridges and the stiffness of the convex pleats would bring about an elastic return to the unbent state. If expansion was prevented, the fan buckled irreversibly.

#### *3.2. The M Shaped Section, Models 2 and 3*

Model 2. Moderate pressure applied to the dorsal side caused the concave ridge to click abruptly upward into the plane of the convex ridges, forming a sharp hinge in the concave ridge, with only minimal curvature in the convex ridges and momentary slight lateral elastic overall expansion, which recovered as the new position was reached; the model was bistable. Further pressure reached a threshold at which the sides of the model buckled outwards and the section underwent catastrophic, unstable bending, returning elastically to the intermediate position when pressure was released.

Model 3. Moderate pressure applied to the dorsal side caused the concave ridge to click upwards, as in Model 2. The extra anterior and posterior folds extended beyond the resulting hinge. A shallow v-shaped flexion line developed between the apices of the extra folds and the hinge. When the dorsal side was pressed harder, the extra folds prevented lateral buckling, and the model was able to undergo appreciably greater stable flexion (Figure 9d). In supplementary models in which the extra folds were shorter, overall bending did occur beyond their apices.

#### *3.3. Cambered Sections, Models 4–9*

When flat, and ε = 180◦ , all models responded equally to forces applied to the upper and lower surfaces, but as soon as slight camber was introduced, they bent only ventrally. Figure 10 illustrates what happened to each model when camber was applied to the card component, slightly reducing ε, and a downward bending force was applied by finger to the flexible paper component distally to the transverse flexion line. The same deformations could be induced by drag forces if the models were flapped.

When camber was applied to the base, Model 4 (Figure 10a), where angle BOD = 180◦ and ζ = 90◦ , was stable in only one position, with a positive camber in the paper component. A downward force on the flexible area bent it ventrally, but it returned elastically as soon as the force was released. Other models, not illustrated, in which BOD was 180◦ and ζ was acute, were also monostable.

All the other models, Models 5–7 (Figure 10b–d), where angle BOD < 180◦ , had two stable positions: straight, with a positive camber in the paper component, and deflected, with a negative camber. They could be snapped from one position to the other by downward and upward finger pressure. Model 5 simply bent, but in Models 6 and 7, the paper component twisted as well as bent. Other models, not illustrated, showed that the ratio of torsion to bending increases as ζ decreases, and this reached an extreme in Model 8, where the anterior support extended to the end of the model and there was no overall bending.

Models, again not illustrated, where ζ was constant but angle BOD varied, showed that the magnitude of bending and torsion at a given value of ε increased as BOD increased. The geometry here is essentially the same as that described by Haas and Wootton [54] in a practical and theoretical analysis of the mechanisms involved in the folding of the hind wings of beetles and some blaberid cockroaches, and the analytical model which they derived can be applied to the present problem. For this reason, I have used the same letters for points and angles as appear in their paper.

In their model (Figure 11a,b), four fold lines, three of one sense (concave or convex) and one of the other, meet at a single point, the "origin" O. If the model is planar and is capable of being folded completely flat along these lines, opposite pairs of angles around the origin must each total 180◦ .

In Figure 10, Models 5, 6 and 7 can be seen to correspond to those in Figure 11. In these, when camber was applied by reducing ε, and the paper membrane depressed into the concave position the latter assumed a curved section, whose apex automatically assumed the position of the convex fold line OC in Figure 11a. We can redraw Figure 10c, Model 6, as Figure 11d, with the line of the apex of the curve represented by a line, OC. Figures 10c and 11d are effectively Figure 11c upside down, with angle ε below the model, AO, BO and DO convex instead of concave, and BC concave.

ζ

ε

ε

**Figure 11.** (**a**) A four-fold system, found extensively in Coleoptera hindwings. (**b**) The same, schematized for analysis by Haas and Wootton [54]. (**c**) The system partly folded. (**d**) Figure 9c modified, with a line representing the lowest axis of the curved membrane. Greek letters in (**b**) represent the planar angles around the origin, O.

ε Haas and Wootton [54] applied vector analysis to calculate the coordinates of point C: c (x), c(y), c(z), for any given value of ε, assuming the fold lines to be of equal length, equal to 1. Using the dot product, they derived three simultaneous equations:

$$\begin{aligned} \text{Cost } \alpha &= \mathbf{c}(\mathbf{x})^\ast \cos \delta + \mathbf{c}(\mathbf{y})^\ast \sin \delta \cos \varepsilon + \mathbf{c}(\mathbf{z})^\ast \sin \delta^\ast \sin \varepsilon \\\\ \text{Cost } \beta &= \mathbf{c}(\mathbf{x})^\ast \cos \gamma + \mathbf{c}(\mathbf{y})^\ast \sin \gamma \\\\ 1 &= \mathbf{c}(\mathbf{x})^2 + \mathbf{c}(\mathbf{y})^2 + \mathbf{c}(\mathbf{z})^2 \end{aligned}$$

Comparing Models 4–7: experimenting by manipulation shows that for a given value of ε, the magnitude and speed of deflection increase and leverage decline with greater values of angle BOD. When BOD is large, a tiny increase in ε causes significant bending, as well as torsion if ζ is acute. In Model 4 (Figure 10a), with BOD = 180◦ , deflection is theoretically maximal, as the paper could fold back flat over the cardboard—but, in fact, increasing ε merely increases distal camber; there is no leverage to drive deflection.

Manipulating Model 8 showed that increasing the camber about the longitudinal flexion line stiffened anterodistal support, opposing bending at the cuneal fracture.

#### **4. Discussion**

The limitations of the models discussed here are self-evident. Insect wings are not rectangles, flexion lines are often not straight or angular, and paper and card do not replicate the gradations in stiffness and resilience of insect cuticle. Their justification lies in the fact that they mimic deformations that are *known* to happen in flight. They are developed by experimenting with materials until their behaviour when manipulated matches that observed in actual wings. They then provide an appropriate first method for examining the geometry and mechanics underlying wing deformations, and they serve to give some direction to future investigations.

Corrugation in wings provides rigidity to transverse bending, but allows compliance to deformation that is parallel to the ridges and channels, and also to torsion provided that any cross-veins are flexible or have flexible joints with the longitudinal veins, like those discovered in Odonata by Newman [3] and comprehensively mapped by Appel and Gorb [63]. Odonata wings show torsion and camber change between half-strokes but have no bending adaptations; any bending being large-radius elastic responses to extreme loads, with immediate recovery.

This is not so with Ephemeroptera. Flight in mayflies, though brief, is crucial to reproductive success, and there is every reason to suppose their wings to be highly adapted for aerodynamic efficiency in the competitive circumstances of mating and oviposition. Bullae are characteristic of the families that use vertical nuptial flights. Vertical flight with a horizontal stroke plane allows aerodynamic force symmetry between the half-strokes, but bending may be needed for force asymmetry in directional flight by the subimagines and females; more kinematic information is needed. Bending requires the wing to flatten, compressing the veins in the concave pleats, and the bullae, like the notches in Model 1, allow these to buckle into the plane of the ridge veins without damage, with the stiffness of the ridge veins driving the elastic return. The bullae are almost in a straight line across the wing, so that flexion will be unstable, and the wing will return elastically, driven by the stiffness of the ridge veins.

The same problem faces other groups that use high relief for rigidity but need to bend. Hemiptera and Hymenoptera tend to meet this by relatively sharp differentiation between the rigid supporting base of the remigium and a flatter distal area, using the properties of camber to limit bending to ventral only. Many other insects, particularly among Plecoptera and Holometabola, show more gradual diminution of relief along the span and allow bending across moderate relief by upward buckling. Here, this is true of only one vein and an adjacent flexion line but is similar in principle to the situation in Ephemeroptera and paralleled in Models 2 and 3. In these cases, thyridia often serve the same function as the bullae of mayflies, allowing local buckling without damage.

With both solutions, there seems to be a distinction between some situations, as shown in Brodsky's film of *Isogenia*, where bending—sometimes extreme—takes place around stroke reversal, followed by rapid straightening and torsion in the early part of the upstroke, and others, where some flexion continues throughout the upstroke, usually combined with some torsion and camber reversal. Both are likely to have aerodynamic consequences. The sharp, angular acceleration in the former situation may create useful transient unsteady lift; the latter condition would give steady favourable lift throughout the translational part of the upstroke.

In the former case, monostable bending, as in Models 3 and 4, is acceptable, but in the second, bistability is useful, and a curved flexion line is common, as simulated in Models 5, 6 and 7 and visible in those of *Sialis*, *Phlogophora*, *Panorpa*, *Tibicina*, *Urocerus* and *Ophion* (Figures 5–7). In these cases, bending can contribute to torsion, and an oblique flexion line becomes valuable—expressed as ζ in Models 6 and 7, where flexion and torsion are interdependent. The inclination ζ depends greatly on the relative lengths of the anterior and posterior supports—of SCP and the clavus (in Heteroptera, the secondary rigid extension). This is illustrated in the Heteroptera in Figure 6a, and in the difference between the fore and hind wings of *Panorpa* (Figure 1) [14]. The ratio of bending to torsion depends on the value of ζ. The extreme condition, with torsion only, occurs where the anterior support extends to the wing tip, as in Model 7, e.g., in Odonata, sphingid moths and many Diptera and Hymenoptera, although many flies and Hymenoptera have a costal break—two in some Diptera—which allow a degree of flexion [18]. This can also enhance torsion, and the same is true of the cuneal fracture in mirid bugs (Figure 6c). Costal breaks in many Diptera are unusually proximally situated, and ventral flexion and consequent torsion are sometimes extreme—for example, in the supremely kinematically versatile *Calliphora*, whose wing can flex at two points, namely at the end of the SCP and close to the base [1,64,65]. Ennos [65] has discussed the possible aerodynamic implications of this, suggesting that the option of ventral flexion may give extra control of the force vector in all planes and contribute to their remarkable manoeuvrability.

Very little change in the basal camber of Model 7 was needed to alter distal wing torsion significantly, and the same was true of both bending and torsion in Model 6. Model 8 is also significant. As Betts [9] showed, the cuneal fracture may offer the options of flexion there, or across the membrane, or both, and this could well be controllable by altering the basal section about the median flexion line.

The physical models described demonstrate some mechanisms by which insects could potentially remotely control the instantaneous rigidity and shape of their wings in flight—but do they? The basal section in many insects certainly alters during the stroke by hinge-wise bending along the claval flexion line, but it is not yet clear how often and to what extent flexion along the median flexion line is actively employed to influence distal shape and attitude in flight. Basal camber could in theory be modified by altering the timing and/or amplitude of shortening of the basalar and subalar muscles. These typically act antagonistically to pronate and supinate the wing respectively over the fulcrum of the pleural wing process; a reduction, phasic or tonic, in the shortening amplitude of one or both could potentially induce camber in part of the stroke, but it may not be as simple as this. In the well-documented case of locust forewings, which control the distal angle of attack by assuming a basal z-shaped profile in the upstroke by flexion about both the median and claval flexion lines [66,67], the basalar and subalar muscles apparently act together to pronate the wing in the downstroke, while the principal supinator is the flexor muscle [68]. Heteroptera, many of which have a clear median flexion line in the corium that would seem to make them excellent candidates for active section control, have no basalar muscles; the wing is pronated phasically by the indirect dorsal longitudinal muscle acting through the first and second axillary sclerites [9,69]. The subalar muscle could perhaps induce basal camber by shortening tonically over several stroke cycles, but this is pure conjecture.

Too little is still known about the precise operation of the basal direct muscles and axillary sclerites of most insects, and electrophysiological as well as morphological research will be necessary to determine whether in any particular case of stroke-by-stroke variation in wing shape is actively controlled and wing rigidity actively tuned.

Whether or not the insects exert active profile control, the mechanisms do have possible technical applications. Much recent work has gone into designing wings for micro air vehicles, but these have for the most part been relatively unsophisticated, utilising the wings' flexibility but not attempting section control. I have suggested elsewhere how the principles explored in this paper could be used in an insect-based MAV, with minimal additional actuation [70].

#### **5. Conclusions**

Interest in the intricate, fascinating structure of insect wings has grown enormously in recent years, with the expansion of biomimetic engineering and the development of new micromorphological techniques and computational modelling. Understandably, the emphasis has been on a few species, predominantly Odonata and Diptera, with outstanding flight capabilities. The broader picture provided by comparative studies, and hence of interest to entomologists as well as engineers, has in general been lacking. This paper has attempted to show how simple, quickly built, physical models can continue to be useful in investigating aspects of wing design, in explaining parallel adaptations across the range of insect groups and by indicating directions for more sophisticated modelling.

#### **Funding:** This research received no external funding.

**Acknowledgments:** I acknowledge with thanks the permission of the following societies for permission to reproduce the following figures: the Royal Entomological Society for Figure 1b, the Norwegian Academy of Science and Letters for Figure 2 and the Entomological Society of America for Figure 6a–c. I am particularly grateful to Stephen Dalton and John Brackenbury for allowing me to crop and reproduce their superb high-speed photographs, in Figure 4 (S.D.) and Figures 5–7 (J.B.).

**Conflicts of Interest:** The author declares no conflict of interest.

#### **References**


© 2020 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

### *Review* **Wing Design in Flies: Properties and Aerodynamic Function**

#### **Swathi Krishna , Moonsung Cho, Henja-Niniane Wehmann, Thomas Engels and Fritz-Olaf Lehmann \***

Department of Animal Physiology, Institute of Biosciences, University of Rostock, 18059 Rostock, Germany; swathi.krishna@uni-rostock.de (S.K.); moonsung.cho@uni-rostock.de (M.C.); henja-niniane.wehmann@uni-rostock.de (H.-N.W.); thomas.engels@uni-rostock.de (T.E.)

**\*** Correspondence: fritz.lehmann@uni-rostock.de; Tel.: +49-381-498-6301

Received: 21 June 2020; Accepted: 19 July 2020; Published: 23 July 2020

**Abstract:** The shape and function of insect wings tremendously vary between insect species. This review is engaged in how wing design determines the aerodynamic mechanisms with which wings produce an air momentum for body weight support and flight control. We work out the tradeoffs associated with aerodynamic key parameters such as vortex development and lift production, and link the various components of wing structure to flight power requirements and propulsion efficiency. A comparison between rectangular, ideal-shaped and natural-shaped wings shows the benefits and detriments of various wing shapes for gliding and flapping flight. The review expands on the function of three-dimensional wing structure, on the specific role of wing corrugation for vortex trapping and lift enhancement, and on the aerodynamic significance of wing flexibility for flight and body posture control. The presented comparison is mainly concerned with wings of flies because these animals serve as model systems for both sensorimotor integration and aerial propulsion in several areas of biology and engineering.

**Keywords:** locomotion; animal flight; wing structure; aerodynamics; flight force

#### **1. Introduction**

Insect wings are complex, three-dimensional structures that are under selective pressures towards functional optima. These optima result from multiple requirements, and also from evolutionary influences relevant to the animal's fitness. Wings have mainly evolved for locomotion and produce aerodynamic forces during gliding and flapping flight at high wing beat frequencies of up to 1000 Hz [1]. The air flows generated for flight mainly depend on wing kinematics, the wing's overall planform, and the dynamics of elastic deformation owing to inertial and aerodynamic loading. Pinpointing the factors that shape the evolution of wings and flapping kinematics is key to any in-depth understanding of flight. Within the past decades, numerous comprehensive reviews and book chapters have been published on insect flight, focusing on components such as aerodynamic mechanisms for lift enhancement [2–11], power requirements for wing flapping [12–15], wing kinematics and control [16–21], and the efficiency with which muscle mechanical power is turned into weight supporting lift [22,23]. This review is engaged in the link between three-dimensional wing structure and aerodynamics, focusing on recently published studies on the aerodynamic performance of wings in differently-sized insects. The review highlights the behavior of wings in flies because these animals often serve as model systems for aerial propulsion in both biology and engineering.

Insect wings receive their mechanical strength and endurance from two main components: on the microscopic level, the three-dimensional composition of proteins and chitin-based cuticle layers [24–27], and on the macroscopic level, the distribution and three-dimensional morphology of veins and elastic

interconnecting membranes [28–33]. This light-weight design helps insect wings to widely resist external forces using chitin as the main chemical component [34]. Veins greatly vary in density, size, and shape between animal species and determine the wing's structure and mechanical behaviors under load, such as bending and twisting [29,35–39]. Veins provide structural support to a wing, preventing the wing from tear [40,41] and host sensory receptors such as campaniform sensilla and innervated bristles, including their afferent nerves [42–47]. By contrast, wing membranes are aerodynamic active surfaces and composed of multiple layers of cuticle [25,27,48] with a thickness ranging from ~0.5 µm in small insects to ~1.0 mm in forewings (elytra) of large beetles [28,49]. Veins and membranes form fine geometrical structures that are typically of much smaller scale than the primary flow structures at wings, such as wing tip and leading edge vortices, and referenced as wing corrugation [50]. Coarse-scale structures, by contrast, typically refer to the wing's overall curvature and termed chordwise and spanwise wing camber [51]. Throughout the past decades, several technical developments, such as high-resolution micro-computed tomography (µCT), have helped to better understand the various aspects of wing morphology for structural integrity [27,52], while robotic and numerical studies on insect flight have highlighted the aerodynamic significance of three-dimensional wing design [53–57].

Numerous studies have been published on the aerodynamic performance of translating [58–66] and root-flapping rigid wings [8,67–74]. The aerodynamics of dynamically deforming insect wings, by contrast, is less clear. Wing bending and twisting change the wing's local angle of attack during flapping motion. Wing bending and twist is thus similar to changes in wing kinematics and change flow and force production. Wings may have an anisotropy in mean stiffness for ventral versus dorsal loading that unbalances force production during upstroke and downstroke, even in cases in which wing hinge articulation is the same in both halfstrokes [27,37,75]. Moreover, as spanwise stiffness in insect wings is approximately one to two orders of magnitude larger than chordwise stiffness, wings often deform in a characteristic fashion [37,76]. There is a continuing debate on the potential benefits of dynamic shape changes in flapping flight because some authors reported aerodynamic advantages of wing deformation for lift production [77–80], while other authors found disadvantages [80–82].

In this review, we work out the significance and tradeoffs of wing design for aerodynamic key parameters such as vortex development and lift production. This is achieved by disassembling the wing's various properties and linking the components in wing structure to aerodynamics, power consumption and flight efficiency. The sections start with flow phenomena in a simple, flat, rectangular wing. In the second section, we focus on the benefits of elliptical and tapered wing shapes as found in many species, including flies. This section also highlights that even simple genetic modifications of fly wing planforms lead to measurable changes in aerodynamic performance. In the third section, we consider the wing's three-dimensional morphology. A recent numerical study, for example, showed that the three-dimensional shape of rigid fly wings attenuates both lift production and aerodynamic efficiency rather than enhancing these measures compared to a flat wing [83]. In the last section, we focus on the aerodynamic consequences of elastic deformation in morphological complex wings. Although elastic wings share similar fluid dynamic properties with rigid wing, an animal must cope with the dynamically changing conditions because these changes may attenuate the ability and precision of flight and body posture control.

#### **2. Aerodynamic Properties of Root-Flapping Rectangular Wings**

Rigid, flat, rectangular wings are often used to understand fundamental aerodynamic principles and represent the most simple approach towards insect flight [84] (Figure 1). They are investigated at different kinematic patterns such as revolving [85–87] and pitching motions [88–91]. Most studies though focused on the dynamics of the leading edge vortex that develops on the upper wing side at high angle of attack [8,72,92–100]. In contrast to a translating wing at high Reynolds number, the leading edge vortex in root-flapping and revolving insect wings is stably attached to the dorsal wing surface and enhances lift throughout the stroke cycle [72,92,101]. It obtains its stability from the viscosity of air and axial flow between wing hinge and wing tip [102,103]. Although a rectangular root-flapping plate

produces all characteristic types of vortices and flows typical for insect wings, it suffers from low span efficiency compared to an elliptically shaped insect wing. Span efficiency is similar to Rankine–Froude efficiency, which typically refers to mean efficiency of propulsion in a complete wing flapping cycle of an animal during hovering conditions [104,105]. By contrast, instantaneous span efficiency varies during wing flapping and is the ratio between ideal power requirements for lift production and the actual requirements [106]. Span efficiency is maximum when the distribution of vertical velocities is uniform in the wing's downwash [107,108]. Under this condition, the kinetic energy of the downwash is minimal owing to the non-linear, velocity-squared relationship between kinetic energy and wake velocity. If velocities vary within the wake, the velocity-squared relationship produces costs at elevated velocities that are not saved by the regions with low fluid velocities (Figure 2).

A pair of translating, flat wings has maximum span efficiency if it produces an elliptical lift distribution from tip to tip (Figure 2b) [109]. Span efficiency depends on the geometry of a wing, i.e., planform and camber, and its kinematics, but not on the wing's aspect ratio and wing loading [107]. In general, the left and right wing of a two-winged insect can either be considered a single aerodynamic system or both wings may function as two aerodynamically independent systems. In the first case, each wing should have a semi-elliptical shape that results in an ellipse if both wings are connected via the insect body, where as in the second case each wing should have an elliptical shape for maximum span efficiency. Both geometrical cases yield higher span efficiency than a translating rectangular wing with same aspect ratio, and are thus beneficial for gliding flight of an insect. However, this conclusion only holds if the wings are flat and not twisted because an appropriate twist of a rectangular wing may equalize the downwash distribution via changes in local angle of attack.

**Figure 1.** Characteristics of fly wings. (**a**) Detached wing of the blowfly *Calliphora vomitoria*, mounted to a steel holder. (**b**) Deformation of a blowfly wing (green) during loading by a ~64 µN point force (white dot) applied normal to the ventral wing side (arrow) [75]. Grey, surface profile without load. (**c**–**e**) Spanwise and chordwise wing profiles along the axes of rotation in three differently-sized fly species (*Drosophila melanogaster*, *Musca domestica*, *Calliphora vomitoria*). The wing profiles are superimposed on natural wing models (grey). The profiles separately show wing camber (Cam) and wing corrugation (Cor). Both wing components were numerically extracted from the natural wing shape (Nat) according to a procedure outlined in Engels et al. [83]. The out-of-plane component (z) is exaggerated by a factor of 2 for better clarity.

**Figure 2.** Ideal distribution of spanwise lift in translating and revolving wings. Distribution of vertical downwash velocity during translation in an (**a**) rectangular and (**b**) elliptical insect wing. At constant forward flight velocity, the inflow towards the wing is uniform. The ideal elliptical wing shape spreads spanwise vorticity that produces maximum span and Rankine–Froude efficiencies. (**c**) In a revolving wing, the non-uniform inflow requires adjustments in wing shape for maximum efficiency. (**d**) Distribution of spanwise circulation in an elliptical wing according to Prandtl [109], Betz [110] and Goldstein [111]. (**e**) Ideal wing shape for maximum span efficiency in a revolving wing according to Prandtl–Betz and Goldstein (see Supplementary Materials).

In contrast to translating wings, in revolving and root-flapping wings, local blade velocity increases with increasing distance from root to tip, producing a non-uniform inflow distribution (Figure 2c). This changes the ideal, root-to-tip elliptical distribution in circulation (Figure 2d). Thus, an elliptical wing does not produce a uniform downwash distribution during revolving or root-flapping motion, requiring an eccentric planform for maximum span efficiency. Betz, Prandtl and Goldstein [110–112] estimated the optimal distribution of circulation in flat propeller wings, assuming flow leakages at the tip and root and thus zero circulation at the revolving axis (Figure 2c). Based on their results, we estimated the optimal wing shape in Figure 2e and for the calculations in Figure 3 (see Supplementary Materials). In contrast to Betz and Prandtl, Nabawy and Crowther [113–115] derived the optimal wing shape of two revolving wings assuming the elliptical circulation distribution of a pair of translating wings, with maximum circulation at the revolving axis. In this theoretical case, wing chord must continuously increase from wing tip to root in order to compensate for the drop in inflow velocity, leading to an "optimum" wing shape [114,115]. However, the latter design cannot produce a uniform downwash as in Prandtl–Betz's estimate. In sum, the expected lower span efficiency in a rectangular wing may have fueled the evolution of elliptical insect wings for gliding flight. The expected lower span efficiency of elliptical wings during wing flapping, by contrast, might have led to the development of wing shapes that taper off towards the wing tip. Besides numerous biological pressures on wing planform development, it should be noted that span efficiency is only one aerodynamic factor that determines the costs of wing flapping as other costs such as inertial power requirements may also significantly contribute to total flight power expenditures [116].

#### **3. The Aerodynamic Benefits of an Ideal Planform**

Wing shape in insects is diverse. Significant shape measures are aspect ratio and the wing's planform. High aspect ratio wings minimize induced drag and provide high lift-to-drag ratios by reducing the three-dimensional flow effects associated with tip vortices [117]. Aspect ratio also determines the stability of the leading edge vortex during wing flapping [117]. There is a wide variety of aspect ratios found in insect wings ranging from approximately 1.5 to 5.8 [118–122]. In Diptera, previous studies reported aspect ratios of 2.91–3.14 for *Drosophila* [121,122], 2.88 for *Musca* [83], and 2.62–2.93 for *Calliphora* [119,121]. The highest aerodynamic forces in hovering, root-flapping insect-like wings are produced at an aspect ratio of approximately 3.0 [123]. As already mentioned, wing planform determines both the ability of a wing to produce lift and the span efficiency. Span efficiency for a gliding wing typically varies between 0.7 and 0.85 [106] and previous studies on animal locomotion thus used a standard generic value of 0.83 [108]. The latter value is comparatively close to the maximum efficiency of an ideal wing with elliptical shape for translation and is not reached for root flapping wings at low advance ratios.

Flow measurements in differently-sized moths, for example, show that span efficiency in flapping flight is much smaller and varies between species. As the tested moth species had wings with similar aspect ratio and planform, there is no trend in span efficiency with increasing body size [108]. Lowest efficiency of 0.31 was measured in the smallest moth species *Hemaris fuciformis* with 0.2 g body mass, 0.6 in the intermediate-sized species *Deilephila elpenor* and with 0.85 g body mass and 0.46 in the largest species *Manduca sexta* with 1.44 g body mass [108]. These data imply that the generic value of 0.83 might not be a suitable approximation in flying insects. Eventually, butterfly wing planforms, in particular, produce elevated lift and thrust coefficients compared to any other planforms [124]. In these species, the coefficients of force production increase with increasing taper ratio and aspect ratio. This increasing performance, however, occurs at the cost of increasing power requirements for flight and thus at the cost of a reduction in aerodynamic efficiency [124].

For this review, we additionally calculated the aerodynamic quantities of revolving (Figure 3) and flapping (Figure 4) wings of a blowfly, as well as simple rectangular and ideal-shaped wings in order to compare their performance. The ideal wing shape was calculated according to the estimation by Prandtl–Betz in Figure 2e. The numerical simulations were performed using a previously published numerical model [83,125] combined with a wavelet-adaptive solver [126], and efficiency was calculated as Rankine–Froude efficiency [127]. Table 1 shows that revolving rectangular and fly wings perform similarly, producing approximately the same amount of lift. The fly wing, however, produces this force at slightly higher efficiency (0.23) compared to a rectangular wing (0.22). Both values are approximately half of the values calculated from quasi-steady approach on flapping insects wings [128]. Surprisingly, an ideal-shaped wing for rotation is less effective because most wing area is concentrated at the wing base where the wing's inflow velocity is low. The ideal-shaped wing produces ~52% less lift at ~29% less efficiency than rectangular and natural fly wings (Table 1).

− − **Figure 3.** Aerodynamics of revolving wings. (**a**–**c**) Upper row: aerodynamic characteristics of three flat, continuously revolving wings (rectangular wing, ideal wing for rotation, wing of a blowfly). Middle row: data show iso-surface with vorticity magnitude of 75 s−<sup>1</sup> (grey) superimposed on a vorticity iso-surface with 150 s−<sup>1</sup> (red). The flow is shown after ~0.4 revolutions after motion onset. Lower row: pressure difference (∆p \*) between dorsal and ventral wing sides, and normalized to the uniform wing loading pressure. The latter value is equal to body weight divided by the surface area of two wings. (**d**,**e**) Time evolution of vertical lift in *d* and aerodynamic power in *e*. After motion onset (grey, left), lift and power stabilize approximately after 0.3 revolutions (grey, right). Dots are mean values calculated from ~0.32–~0.5 revolutions (grey, right). Wing length and area are identical in all wings. For numerical modeling see [83]. Orange, rectangular wing; blue, wing of *Calliphora vomitoria*; and red, ideal-shaped wing.

− − **Figure 4.** Evolution of vorticity in a flapping rectangular (left) and blowfly (right) wing. (**a**–**g**) Vorticity distribution at the beginning of the 3rd flapping cycle (t = 0–1) after motion onset. Vorticity of a flapping wing of *Calliphora vomitoria* slightly differs from the flow in the rectangular wing. Data show iso-surface with vorticity magnitude of 75 s−<sup>1</sup> (semi-transparent grey) superimposed on a vorticity iso-surface with 150 s−<sup>1</sup> (red). LEV, leading edge vortex; TEV, trailing edge vortex; TIV, wing tip vortex. For performance data and wing kinematics confer to Table 1 and a previously published study [83], respectively. Wing length and area are identical in both wings.


**Table 1.** Aerodynamic characteristics of single wings with various shape during revolving and flapping motion. Wing shapes are shown in Figures 1–3.

Data are calculated by a three-dimensional numerical simulation model that was refined from a previously published code (https://arxiv.org/abs/1912.05371). All tested wings have similar area (28.0 mm<sup>2</sup> ) and length (9.76 mm), and were flat without corrugation and camber. Mean vertical force was derived from t = ~0.32 to t = 0.5 revolutions after motion onset in the revolving wing, and from the 3rd flapping cycle in flapping wings. Efficiency, Froude efficiency for wing flapping [127]; n.a., no data available. Reynolds number is calculated from mean wing tip velocity and mean wing chord. <sup>1</sup> Horizontal stroke plane, 112 Hz, 40◦ angle of attack, Reynolds number = 1320. <sup>2</sup> Inclined stroke plane (−20◦ , nose-down), 40◦ angle of attack during upstroke, 20◦ angle of attack during downstroke, 0.22 cycle for wing rotation, 150 Hz stroke frequency, Reynolds number = 1320 [83].

Adding kinematic reversals to the revolving kinematic pattern (flapping motion) has little effect on the performance of a rectangular and natural fly wing (Table 1). However, the time evolution of lift production suggests that a rectangular wing produces more lift during up- and downstroke than the fly wing, while the fly wing produces more lift during the stroke reversals.

Although aerodynamic force production changes with changing wing planform, there is little variation in the wake behind wings with different geometry [129,130] (Figure 4). This is demonstrated by the pressure distribution of differently-shaped wings in Figure 3 and by experimental investigations on different categories of elliptic wing planforms with same aspect ratio and total area at Reynolds numbers typical for wing motion in flying insects between 160 and 3200 [130]. The latter study suggests that wake structure mainly depends on shape of the wing's leading edge rather than planform. The authors argue that the leading edge shape determines the shear layer feeding the leading edge vortex, and thus the development of leading edge vortices and the associated flow topology [131]. Similar results are reported on mosquito flight using computational fluid mechanics and in vivo flow measurements [94]. The latter study shows that apart from leading edge vortices, also trailing edge vortices and rotational drag are responsible for elevated lift production. This was concluded from the low-pressure distribution on the suction side of the wing near the trailing wing edge. The wing planform of fruit flies, by contrast, does not produce similar low pressure regions although both insects fly at similar Reynolds numbers [94].

In general, researchers often assume that the specific wing shape of an insect species is close to an optimum, reflecting the result of a selection process on the animal's aerial performance. A unique approach toward the aerodynamic consequences of wing planforms in flies, however, implies that wing shape also results from aerodynamically non-adaptive factors [47]. Flight tests on fruit flies with genetically modified wing shape using targeted RNA interference demonstrate that wildtype controls, with wing aspect ratios of ~2.5, have a reduced flight capacity compared to transgene animals with wings at aspect ratios between ~2.7 and ~3.0 [47]. While maximum forward flight speed does not increase with increasing aspect ratio, the transgene flies exhibit ~22% improved tangential acceleration and an ~10% improved deceleration capacity, they turned at higher angular rate (~10 – ~21%) and at an ~23% smaller turning radius than controls. The results suggest that in fruit flies, an increasing aspect ratio leads to an increase in agility and maneuverability. Notably, even if the GAL4-induced RNA interference selectively tackled wing shape, the above findings could also be explained by behavioral modifications because the maximum mechanical power output of the indirect flight muscles were thought to be similar in both tested groups [47].

#### **4. Functional Relevance of Three-Dimensional Wing Shape**

There is a longstanding debate on the functional relevance of three-dimensional wing shape compared to a flat wing design. It is widely accepted that the wing's three-dimensional corrugation serves as a mechanical design element to improve stiffness and thus to avoid excessive wing deformation during flight [28,132–134]. Its potential contribution to aerodynamic lift and drag production, by contrast, is less clear and apparently depends on the chosen approach for analysis. The majority of previously published studies used numerical or physical wing models at various Reynolds numbers for analysis and reported that wing corrugation either improves aerodynamic performance [56,58,65,66,118,135–137] or attenuates performance [56,59,65,66,134,137–139]. Other studies that reported little or no effect of corrugation on wing performance in beetles [55], dragonflies [140], bumblebees [141], hoverflies [142], and fruit flies [50] at Reynolds numbers between 35 and 34,000. Some studies, moreover, also reported inconsistent results on the significance of wing corrugation in dragonflies [63,64,143,144], bumblebees [54], and a generic model [59].

Although corrugation may change local wing pressure, the difference of lift and drag coefficients between corrugated and flat wings is typically not more than 5% for both lift and drag for angles of attack between 35◦ and 50◦ [141], and 17% for drag at low Reynolds number of 200 and 5◦ angle of attack [50]. A likely explanation for the latter findings is that corrugation is usually smaller than the typical flow structures at the wing, such as the leading-edge vortex and the area of flow separation. Thus small-scale corrugation produces only small local changes in both flows at the wing and aerodynamic forces [50]. As the size of flow structures depends on Reynolds number, corrugation structures should be coarser in small insect wings than in larger wings for pronounced wing-vortex interaction. In contrast to small-scale corrugation, large-scale chordwise wing camber has a pronounced effect on aerodynamics characteristics of a wing [54,55]. Upward camber and a downward oriented leading wing edge tend to create more lift than a flat wing flapping at similar angle of attack. Chordwise camber and the shape of the leading edge are thus comparable to a change in the effective angle of attack of an insect wing [56,83].

There is little difference in flow patterns between flat and three-dimensional fly wings but vortices and stagnant air cushions that are trapped in corrugation valleys of a wing may potentially improve lift production by changes in wing's effective geometry [61,135]. Evidence for trapped vortices were experimentally found in wings moving at relatively high Reynolds number [63,64], including an aerodynamic study that demonstrated vortex trapping at the wing's acceleration phase and at Reynolds numbers ranging from 34,000 to 10<sup>5</sup> , but not at 3500 [140]. The latter value is at the upper end of Reynolds numbers typical for flying insects. Studies that did not find vortex trapping attributed the absence to the elevated angle of attack in insect wings [55]. In corrugated wings of gliding dragonflies, slowly rotating vortices only develop at small angles of attack but flow broadly separates from the wing surface at larger angles (Re = 34,000 [53], Re = 1400 [136]). By contrast, a recent numerical study on root-flapping wings shows that corrugation valleys in fruit flies, house flies, and blowflies are unable to trap vortices at Reynolds numbers up to 1623 (Figure 5) [83]. Thus, small-scale corrugation, low Reynolds number, spanwise flow advecting vorticity and high angle of attack make vortex trapping less likely in flapping insect wings. Trapped flows should thus be considered as an exception rather than a common aerodynamic phenomenon in insect flight [134].

**Figure 5.** Flow pattern produced by natural wing models of three fly species. Color-coded instantaneous streamlines in (**a**) *Drosophila*, (**b**) *Musca*, and (**c**) *Calliphora*. Snapshots are taken at 1.3 (*Drosophila*) and 3.3 stroke cycle (*Musca, Calliphora*) after motion onset in natural wings [83]. Streamlines were computed from particles released in the corrugation valleys of the dorsal (upper) wing surface near the leading wing edge. Data show little spanwise vorticity inside the corrugation valley near the surface (arrows) and leading-edge vortex suction pulls the virtual particles away from the surface.

Aerodynamic studies on fly wings with genetically modified corrugation and camber patterns are missing and thus is the exact significance of wing corrugation in flies for aerodynamic performance and efficiency. This difficulty was recently circumvented by a numerical study using computational fluid dynamics on three differently-sized fly species (*Drosophila melanogaster*, *Musca domestica*, and *Calliphora vomitoria*) [83]. The wing models were reconstructed from high-resolution scans [75] and corrugation and camber numerically removed afterwards. The study allowed a direct comparison of air flow structures, force production, power requirements, and propulsion efficiency of a natural, cambered, corrugated and flat wing design. The findings suggest that three-dimensional corrugation of fly wings has no significant effect on mean aerodynamic force production compared to a flat wing at the tested Reynolds numbers for wing motion between 137 and 1623 [83]. This result is consistent with a previous study on bumblebee model wings that reported less than 5% change in aerodynamic force production of four differently-corrugated wings [141]. Our data, instead, suggest that corrugation may alter the temporal distribution of forces within the stroke cycle.

The three-dimensional camber of rigid fruit fly-, housefly-, and blowfly-wings also has no significant benefit for lift production but attenuates Rankine-Froude flight efficiency by up to ~12% compared to a flat wing [83]. This is different from previous findings on deforming wings in hoverflies, which is discussed in chapter 5 [145]. The computed flight efficiencies in rigid wings of 17–23% were somewhat below the experimentally derived estimates that range from 26–32% in various species of fruit flies to 37–55% in large crane flies, beetles and bees [23]. A potential explanation for this discrepancy is that many of the experimental studies used Ellington's quasi-steady model for flight power [128], while the numerical model solved the Navier–Stokes equations for fluid motion. Altogether, the above results make it more likely that 3-dimensional corrugation and camber have been selected according to mechanical rather than aerodynamic constraints. Even though there are some energetic costs for wing flapping associated with three-dimensional wing shape, the increased stiffness and change in force distribution in corrugated and cambered insect wings might be of advantage during elevated wing loading—conditions that occur during maneuvering and flight under turbulent environmental conditions.

#### **5. Wing Sti**ff**ness and Benefits of Elastic Wing Deformation**

Wing joints, the cuticular composition of proteins and chitin fibers, and elastic proteins such as resilin allow wings to elastically deform during flapping motion in response to inertial and aerodynamic loads [24,146–156]. Elastic wing deformation alters flight in two ways: first, it smooths out and thus lowers sudden acceleration of local wing mass, and consequently maximum instantaneous inertial costs [116,157–159], and second, it changes flow conditions due to changes in local angle of attack, and thus the direction of flow [79,160]. In hoverflies, these effects appear to be negligible, as the time courses of lift, drag and aerodynamic power are similar in deforming (camber deformation, spanwise twisting) and rigid flat-plate wings [145]. Part of the potential energy stored in a deformed wing might not be elastically recycled throughout the stroke cycle, which results in plastic deformations and stress on the cuticle [161]. Moreover, the energy loss stresses the total energy budget for flight and thus leads to a reduction of propulsion efficiency. Measurements in wings of fruit flies, house flies and blowflies suggest that only 77–80% [161] and 87–93% [75] of the elastic potential energy is recycled during a full deformation–relaxing cycle. However, the significance of the relative loss in elastic potential energy depends on how much the wing deforms during flight. For example, at the end of each half stroke, aerodynamic and added mass reaction force partly cancel out wing mass-induced moments [161]. Total elastic potential energy is thus small at the end of upstroke and downstroke, and so is energy loss. Consequently, the elastic structures of the wing may not be able to recycle much kinetic energy gained from a preceding half stroke and thus contribute only slightly to the recycling of kinetic energy at the stroke reversals. By contrast, a larger amount of elastic potential energy is stored at the beginning of each half stroke and subsequently released throughout the wing translation phase in flies [161].

To avoid wing bending at elevated wing loading, spring and flexural stiffness of insect wings typically increase with increasing body size [29]. This finding also holds for fruit flies, house flies and blowflies, in which median spring stiffness along an aerodynamic characteristic beamline is ~0.024, 0.63, and 1.76 Nm−<sup>1</sup> , and median flexural stiffness is 4.86 × 10−11, 9.73 × 10−<sup>9</sup> , and 1.33 x 10−<sup>7</sup> Nm<sup>2</sup> , respectively [75]. Due to these elevated stiffness values, fly wings deform only little in spanwise direction during wing flapping. Nevertheless, the distribution of local spatial stiffness in fly wings varies between species. In response to point loads at 11 characteristic points on the wing surface, for example, the average spring stiffness of bending lines between wing hinge and point load varies ~77-fold in fruit flies and ~44-fold in house flies but only ~28-fold in large blowflies [75]. This suggests that wings of larger flies behave more like a homogenous material with uniform thickness compared to smaller flies. As this property determines how inertial and aerodynamic forces deform a flapping wing, the stiffness variability could reflect the differences in local aerodynamic forces in different species.

Besides elastic energy recycling, dynamic deformations in span- and chordwise direction alter the wing's aerodynamic performance throughout the stroke cycle [162–164] and may help to stabilize flight [165]. Findings on the aerodynamics of flexible wings have recently been summarized in a comprehensive review [5]. For example, Du and Sun [145] found that camber deforming and spanwise twisting wings of hoverflies produce ~10% more lift at ~17% less aerodynamic power expenditures than a flat rigid wing. The authors suggest that this benefit in lift production is mainly caused by the dynamic changes in wing camber, while the difference in power is mainly due to spanwise twist [145]. More lift at reduced costs results in an increase in flight efficiency, which in turn reduces the metabolic cost for wing flapping and may eventually enhance the animal's fitness. Notably, this conclusion runs counter to the study on rigid fly wings that found a decrease in Rankine–Froude efficiency in cambered compared to flat wings (see chapter 4) [83]. Other examples on the significance of dynamic camber and spanwise twist include beetles and moths. Owing to force-induced deformation, wing camber in beetles is inverted (downward camber) during the upstroke that improves aerodynamic performance compared to a non-deforming wing [55]. Aerodynamic details of wings with different geometry including twist, leading edge details, and camber in hawkmoth-like revolving wings [86] show that flow separation at the leading edge prevents leading-edge suction and thus allows a simple geometric relationship between forces and angle of attack. The force coefficients in these experiments appear to be remarkably invariant against alterations in leading-edge detail, twist and camber. In general, our knowledge on the aerodynamic significance of three-dimensional wing structure and flexing in insect flight is still limited and largely stems from studies on simplified flight models

such as two-dimensional computational simulations, rectangular flat wing planforms, simplified three-dimensional extrusions of two-dimensional profiles, and also from work at inappropriately large Reynolds number [54,58,59,65,118,135,136,138].

#### **6. Conclusions**

In conclusion, wings of insects and wings of flies (in particular) are complex, three-dimensional body appendages with elevated spanwise and comparatively little chordwise stiffness. Their tapered shape improves span efficiency during root-flapping but genetic modifications of wing shape has questioned that the current shape solely results from a evolutionary selection process towards maximum aerodynamic performance [47]. The three-dimensional corrugation pattern of veins and membranes forms valleys that channel axial flow components, following the pressure gradient from the wing hinge to the tip, but does not trap vortices for lift-enhancement as previously suggested for the more corrugated wings of dragonflies [28,61,83,135]. Fly wings also have the ability to store elastic potential energy during wing deformation, but analyses using static loadings suggest that up to ~20% of this energy might be lost due to plastic or viscoelastic deformation. Nevertheless, the exact benefits of three-dimensional wing design for locomotor capacity, flight efficiency and body posture control in insects are still under debate [166]. These data, however, are highly welcome not only by biologists working on insect flight, but also by engineers working in the area of bionic propulsion and on the development of the next generation of man-made flapping devices.

**Supplementary Materials:** Detailed descriptions on the calculation of spanwise circulation and wing shape in revolving wings are available online at http://www.mdpi.com/2075-4450/11/8/466/s1.

**Author Contributions:** S.K. prepared an early draft of the review; M.C. calculated the ideal wing profile for a rotating wing; T.E. performed the numerical calculations; H.-N.W. revised the draft and prepared references; F.-O.L. improved the manuscript. All authors equally contributed to editing of this review. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Acknowledgments:** The authors thank the referees for their helpful comments on this manuscript.

**Conflicts of Interest:** The authors declare no conflicts of interest.

#### **References**


© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

*Article*

## **Comparison of Wing, Ovipositor, and Cornus Morphologies between** *Sirex noctilio* **and** *Sirex nitobei* **Using Geometric Morphometrics**

**Ming Wang 1,2 , Lixiang Wang <sup>3</sup> , Ningning Fu 1,2, Chenglong Gao 1,2, Tegen Ao <sup>4</sup> , Lili Ren 1,2,\* and Youqing Luo 1,2,\***


Received: 31 December 2019; Accepted: 21 January 2020; Published: 24 January 2020

**Abstract:** *Sirex noctilio* F. (Hymenoptera: Siricidae) is an invasive woodwasp from Europe and North Africa. Globalization has led to an expanding global presence in pine forests. *S. noctilio* has been previously introduced outside of its native range and now co-occurs in trees with native *S. nitobei* Matsumura (first discovered in 2016). Damage to *Pinus sylvestris* var. *mongolica* Litv in northeast China can be attributed to two types of woodwasp. To distinguish the two species by the traditional taxonomic morphology, we mainly differentiate the color of the male's abdomen and the female's leg. There remains intraspecific variation like leg color in the delimitation of related genera or sibling species of *Sirex* woodwasps. In this study, we used landmark-based geometric morphometrics including principal component analysis, canonical variate analysis, thin-plate splines, and cluster analysis to analyze and compare the wings, ovipositors, and cornus of two woodwasps to ascertain whether this approach is reliable for taxonomic studies of this group. The results showed significant differences in forewing venation and the shapes of pits in the middle of ovipositors among the two species, whereas little difference in hindwings and cornus was observed. This study assists in clarifying the taxonomic uncertainties of Siricidae and lays a foundation for further studies of the interspecific relationships of the genus *Sirex*.

**Keywords:** cornus; geometric morphometrics; ovipositor; Siricidae; taxonomy; wing

#### **1. Introduction**

Siricidae is a small group of species, in which individuals are relatively large with a clean body surface and easily identifiable morphological features. One of the most striking features of Siricidae is what appears to be incredible variation in wing venation, including the appearance or the disappearance of veins symmetrically or asymmetrically on either wing. Such variation is very rarely seen in other Hymenoptera, a group where wing veins are important for classification [1]. The wing characteristics of Siricidae are unstable and seldom used in taxonomic studies. In general, the classification and identification of this group is based mainly on the structure of the thorax and abdomen. However, these structures are very similar in closely related species; thus, it is difficult to accurately identify species in some cases. Interestingly, geometrics, as a new classification method, has been recently applied in many classification studies of Hymenoptera [2].

It is well known that insect wing shape can exhibit a high heritability in nature [3,4]. Thus, wing morphology is of primary importance to entomologists studying systematics. Since the 1970s, several investigators have used the two-dimensional characteristics of insect wings to advance the fields of systematics and phylogeny [5,6]. Geometric morphometrics utilizes powerful and comprehensive statistical procedures to analyze the variations in shape using either homologous landmarks or outlines of the structure [6–8], and it is currently considered to be the most rigorous morphometric method. Wings are excellent in studies that define morphological variations because they are nearly two-dimensional and their venation provides many well-defined morphological landmarks [9]. For instance, vein intersections are easily identifiable, which enables the general shape of the wing to be captured [10]. The use of geometric morphometrics to study wing venation has also been useful in insect identification at the individual level [11], in differentiation between sibling species [12,13], and in delimitation among genera. However, thismethodology has not yet been applied in studies of woodwasps.

The wood-boring wasp, *Sirex noctilio* Fabricius (Hymenoptera: Siricidae), is an invasive pest of numerous species of pine tree (*Pinus* spp.) worldwide and most of the destruction from *S. noctilio* is in commercial plants [14,15]. In August 2013, woodwasps were detected as a pest of Mongolian pine (*Pinus sylvestris* var. *mongolica*) in the Duerbote Mongolian Autonomous County, Heilongjiang Province, China [16]. In 2016, two morphologically similar woodwasps were found to damage *P. sylvestris* var. *mongolica* in Jinbaotun forest farm, Inner Mongolia, causing a lot of pine forests to weaken and die. After morphological comparison and molecular identification, the two woodwasps were *S. noctilio* and *S. nitobei* [17]. Each have two pairs of large, transparent-film wings with visible mesh veins. As the insect wing is a planar structure, it is relatively easy to acquire two-dimensional images, and it is difficult to unintentionally distort the structure. Unfortunately, it is rather difficult to identify *S. noctilio* and *S. nitobei* wing vein characteristics with the naked eye, and these two species display unstable vein patterns, which means that the use of geometric morphometrics is appropriate [18].

In previous studies, the pits on the ventral portion (lancet) of the ovipositor have been consistently used as an identifying structure. The lancets of the ovipositor independently slide back and forth to move the egg and to penetrate wood. This characteristic was used for the first time by Kjellander (1945) to segregate females of *S. juvencus* from those of *S. noctilio*. Furthermore, the size, shape, and number of pits on the ovipositors can be used as distinguishing features for the identification of most species [15]. This also holds true for *Sirex*, in which the most important distinguishing characteristics on the ovipositor are pits located from the base to approximately the middle of the lancet, although the apical teeth segments usually do not show distinct differences [15]. Another striking diagnostic feature is the large hornlike projection, called the cornus, on the last abdominal segment of the females. The cornus is thought to help the larvae pack the frass in the tunnel. The cornus varies in shape (the shape of the female cornus does not vary with size for most species), although their distinguishing features remain poorly characterized. These difficulties underline the need for further studies to clarify the taxonomy of woodwasps, either by searching for new morphological characteristics with clear distinguishing variations or applying alternative effective methods to provide a basis for studying flight and reproductive behavior.

Geometric morphometrics [6,19,20] overcomes the shortcomings of conventional morphological analysis and focuses on the topological information of the organic form [18]. In addition, as it is not affected by various factors, such as size and shape, this method has the potential to be more widely used in the identification of insects, resulting in automatic insect recognition system that is continually updated and improved [3]. In taxonomy and other fields, genetics and morphometrics are complementary tools that are often used to understand the origins of phenotypic differences. The application of marker points in biology can be divided into three categories [21]. In this study, we focused on two of these categories, namely (i) the common points that can be accurately found on each specimen based on the anatomical features, which is a mathematical point supported by substantial evidence between homologous subjects [22], such as structural intersections (the basis for marking points on wings); and (ii) the mathematical point for homologous subjects, which is supported

by geometrical rather than histological evidence, such as depressed or convex points (the basis for marking points on ovipositors and cornus). Platts analysis was used to superimpose the marker points and minimize the deviation of the marker points. In the same coordinate system, the influence of non-morphological factors in morphological information analysis was eliminated, and the average contour of each population was obtained. Thus, in the present study, we applied landmark-based geometric morphometrics to quantify and analyze wing, cornus, and ovipositor morphologies of two *Sirex* species that have not been previously characterized. We explored the similarities between these species to strengthen the available quantitative research data that form the basis of species identification and to provide new insights for automatic insect identification systems.

#### **2. Materials and Methods**

#### *2.1. Ethics Statement*

This study did not involve endangered or protected species. No specific permits were required for this study.

#### *2.2. Insects*

Insect samples were collected from the Jinbaotun Forest in Tongliao City, Inner Mongolia, from June 2016 to September 2017. Trees were felled in early summer, and insects were collected at emergence. Insects were collected from different, unrelated plots. Sirex specimens were structurally analyzed (Table 1). Prior to geometric morphometric analysis, specimens were identified using adult morphological characteristics, including the color of their thoracic legs, abdomen [1,23].


**Table 1.** The *Sirex* specimens collection information in this study.

#### *2.3. Insect Processing and Image Acquisition*

The front and rear wings of each specimen were cut off from the body. Rohlf et al. suggested using only one side of each paired organ or limb to avoid asymmetry bias between the two halves [24]. In this study, only the left wings of specimens were used, which were ultrasonically cleaned with 75% alcohol for 90 s to remove impurities. Thereafter, specimens were dehydrated with an ascending series of ethanol washes (75%, 80%, 85%, 90%, 95%, 100%, and 100%) for 20 min each. Specimens were softened with xylene, placed on glass slides that were previously wiped clean with a lens tissue, and then mounted in neutral balsam.

Ovipositors and cornus were dissected from the *Sirex* specimens, and the remaining parts were stored at −20 ◦C. We used ten individuals of each species to examine the pits and cornus. Impurities were removed from the specimens by ultrasonic cleaning (Skymen, JP-1200, Shenzhen, China) or brushing. The specimens were then placed face up on clean glass slides and mounted in neutral gum (Coolaber, Beijing, China). All specimens were numbered.

A light microscopy (Leica, S4E, Wetzlar, Germany) was performed to determine the number and distribution of pits on ovipositors. Images were captured with a Nikon camera (Nikon D90, Tokyo, Japan). Each image was saved as a 24-bit. bmp image, and original stored images were used in subsequent analysis rather than compressed files. The directions and positions of the specimen images were readjusted with Photoshop CC2015 software (Adobe Systems, San Jose, USA).

#### *2.4. Standardization of Data and Statistical Analysis*

The TPS files were maked from selected images of wings, ovipositors, and cornus using TpsUtil software (tpsUtil 1.47, [24]). The landmarks in each image were recorded as the central location point of each specimen and digitized using TpsDig2 software (New York, NY, USA) [24]. For each. Tps file, the landmarks were scanned in the same order, and the scale factor was set for each image. Therefore, 20 landmarks from the forewing, 11 landmarks from the hindwing (Figure 1a), nine landmarks (Figure 2) from the ovipositor (from the base to the middle pits, Nos. 14, 15, 16), and five landmarks from the cornus (Figure 3) were digitized.

**Figure 1.** Description of the landmarks used in geometric morphometric analysis. (**a**) Locations of the 20 landmarks on the forewing of *Sirex* considered in the geometric morphometric analysis, locations of the 11 landmarks on the hindwing of *Sirex* considered in the geometric morphometric analysis; (**b**) The black wing image which was converted to binary.

**Figure 2.** Position of 9 type landmarks on the ovipositor of *Sirex* considered in the geometric morphometric analysis.

**Figure 3.** Position of 5 type landmarks on the cornus of *Sirex* considered in the geometric morphometric analysis.

After the. Tps files were converted into nts files using TpsUtil software and the marker information was saved, the images were processed with MorphoJ software [25,26]. The variations in shape were assessed by principal component analysis. To better visualize the variations in shape, we determined the average configuration of landmarks for each species. Deformation grids were used to show the variations. The relative similarity and discrimination of the species was analyzed using canonical variate analysis, which identified changes in shape using mean values of the two groups by assuming that covariate matrices were identical [27]. Canonical variate analysis is a reliable method for identifying differences among taxa. Procrustes ANOVA (Analysis of Variance) [25,28] was utilized to determine significant differences among species [29]. Furthermore, PAST software [30,31] was used to generate phenograms by cluster analysis that utilized Euclidean distances calculated from the matrix of the Procrustes shape coordinates. ImageJ software [32] was used to calculate the wing area. All images were converted into binary files, and the background was removed, which resulted in a black wing surrounded by a white space (Figure 1c). The wing outline was assessed, and minor damage to the wing outline was eliminated. The pixels per mm were calculated using a ruler of known scale, and the wing area was obtained.

#### **3. Results**

#### *3.1. Shape Variables of the Wings in the Genera of S. noctilio and S. nitobei*

#### 3.1.1. Analysis of Female Forewings

Principal component analysis showed shape variations in *S. noctilio* and *S. nitobei* wings (Figure 4a). The results of Procrustes ANOVA explained 42.79% of the intergroup variations in *S. noctilio* and *S. nitobei* female forewings. Significant differences in the forewings were observed between the two species by principal component analysis (Figure 4a) and cluster analysis (Figure 4d). Mahalanobis distances between *S. noctilio* and *S. nitobei* female wings are significantly different in comparisons (*p* < 0.05), and Procrustes distances (*p* < 0.05) are similar (Table 2).

**Figure 4.** Shape variables of the female forewings of *S. noctilio* and *S. nitobei* (**a**) principal component analysis-(**b**) Transformation grids for visualizing a shape change (for the first two principal component, in this case)-(**c**) The Tps grids of Canonical Variate-(**d**) Phenogram of cluster analysis.


**Table 2.** Differences in the female wings shapes among the species of Mahalanobis distances (left) & Procrustes distances (right): *p*-values (above); distances between populations (below) (10,000 permutation rounds).

The lollipops and deformation grids indicated the direction and magnitude of the shape variations by principal component analysis (Figure 4b) and canonical variate analysis (Figure 4c). The deformation grids of the first between-group principal component revealed differences in the junction (No. 5) of Cu and 2m-cu, the junction (No. 16) of R1 and Rs2, the vannal region (Nos. 1, 3, 4) of 2A and 2cu-a, 2A and a, 1A and a. The deformation grids of the second between-group principal component revealed differences in the Rs and 2r (No. 19) and the region (around junctions Nos. 10, 17, 2). The deformation grids of the first between-group canonical variate showed that contributing most to the shape differences between them was the junctions of Cu and 2m-cu etc. (Nos. 5, 16, 3, 4, 12) (Figure 4c) (Table 3).


**Table 3.** Landmarks of forewing (according to veins nomenclature system by Ross (1937).

#### 3.1.2. Analysis of Female Hindwings

The results of Procrustes ANOVA explained 43.71% of the intergroup variations in *S. noctilio* and *S. nitobei* female hindwings. There was also significant difference between two groups in principal component analysis (Figure 5a) and cluster analysis (Figure 5d). The deformation grids of the first principal component revealed differences in the junction (No. 2) of 1A and 2A (Figure 5b). Also, the junctions of Cu and m-cu, Cu and cu-a, C (costa) and R1 (Nos. 3, 4, 11) appeared variable in species, whereas those of the second principal component revealed differences in the remigium (Nos. 7, 5, 11, 2, 8, 10) (Figure 5b). The deformation grids of the first canonical variate showed significant differences in the region of vannal fold (Nos. 2, 3, 4) (Figure 5c) (Table 4).

**Figure 5.** Shape variables of the female hindwings of *S. noctilio* and *S. nitobei* (**a**) principal component analysis-(**b**) Transformation grids for visualizing a shape change (for the first two principal component, in this case)-(**c**) The Tps grids of Canonical Variate-(**d**) Phenogram of cluster analysis.


**Table 4.** Landmarks of hindwing (according to veins nomenclature system by Ross (1937).

#### 3.1.3. Analysis of Male Forewings

The results of Procrustes ANOVA explained 35.29% of the intergroup variations in *S. noctilio* and *S. nitobei* male forewings. Significant differences in Mahalanobis distances of the male wings were observed between the two species (*p* < 0.0001, Table 5). These findings were consistent with those of principal component analysis (Figure 6a) and cluster analysis (Figure 6d or Figure 7d).

**Table 5.** Differences in the male wings shapes among the species of Mahalanobis distances (left) & Procrustes distances (right): *p*-values (above); distances between populations (below) (10,000 permutation rounds).


**Figure 6.** Shape variables of the male hindwings of *S. noctilio* and *S. nitobei* (**a**) principal component analysis-(**b**) Transformation grids for visualizing a shape change (for the first two principal component, in this case)-(**c**) The Tps grids of Canonical Variate-(**d**) Phenogram of cluster analysis.

**Figure 7.** Shape variables of the male hindwings of *S. noctilio* and *S. nitobei* (**a**) principal component analysis-(**b**) Transformation grids for visualizing a shape change (for the first two principal component, in this case)-(**c**) The Tps grids of Canonical Variate-(**d**) Phenogram of cluster analysis.

The deformation grids of the first principal component revealed differences in the remigium (No. 16), the junction of Cu and 2m-cu, 2A and a etc. (Nos. 5, 3, 4, 18,13) (Figure 6b). These findings were similar to the deformation grids of the first canonical variate (Figure 6c). The deformation grids of the second principal component revealed differences in the junction of M and 2m-cu, 2A and 2cu-a, M and Cu1 (Nos. 12, 1, 10) (Figure 6b).

#### 3.1.4. Analysis of Male Hindwings

The results of Procrustes ANOVA explained 32.89% of the intergroup variations in *S. noctilio* and *S. nitobei* male hindwings. The principal component analysis of the two species had individual sample overlap.

The deformation grids of the first principal component revealed differences in the region (around by junctions Nos. 2, 4, 9, 8) (Figure 7b) were similar to the deformation grids of the first canonical variate (Figure 7c), whereas those of the second principal component revealed differences in the junctions of 1A and 2A, M and 1r-m, Cu and cu-a (Figure 7b).

#### 3.1.5. The Relationship between Wings and Dry Weight of Sirex

No significant differences were observed in the hindwings of the two woodborers. The total forewing area of male and female *S. noctilio* adults was significantly different from that of *S. nitobei* adults (F = 19.12; df = 3, 36; *p* < 0.0001; Figure 8). There was a positive correlation between the dry weight and forewing length between the two species (*S. noctilio*: r = 0.8588; *p* < 0.0001; S. *nitobei*: r = 0.8837; *p* <0.0001; Figure 9).

**Figure 8.** Comparison of total forewing area among two *Sirex*. Different letters indicate significant differences in total wing area among woodwasps within each sex, based on Tukey–Kramer's multiple comparison tests at the 5% significance level.

**Figure 9.** Relationship between the dry weight of body and the length of forewing (left: *Sirex noctilio*; right: *Sirex nitobei*).

#### *3.2. Shape Variables of the Ovipositors in the Genera of S. noctilio and S. nitobei*

The results of Procrustes ANOVA explained 67.94% of the intergroup variations in *S. noctilio* and *S. nitobei* female ovipositors. Mahalanobis distances between the two species were significantly different in pairwise comparisons (*p* < 0.0001), and Procrustes distances were similar (*p* < 0.0001) (Table 6). These findings were confirmed by the results of principal component analysis (Figure 10a) and cluster analysis.

**Table 6.** Differences in the ovipositor shapes among the species of Mahalanobis distances (left) & Procrustes distances (right): *p*-values (above); distances between populations (below) (10,000 permutation rounds).

**Figure 10.** Shape variables of the ovipositor of *S. noctilio* and *S. nitobei* (**a**) principal component analysis-(**b**) Transformation grids for visualizing a shape change (for the first two principal components, in this case)-(**c**) The Tps grids of Canonical Variate-(**d**) Phenogram of cluster analysis.

The deformation grids of the first principal component (Figure 10b) and first canonical variate (Figure 10c) revealed differences in the angle (1, 4, 7) of the average pit, whereas those of the second between-group principal component revealed differences in the bottom left points (2, 8).

#### *3.3. Shape Variables of the Cornus in the Genera of S. noctilio and S. nitobei*

The results of Procrustes ANOVA explained 31.24% of the intergroup variations in *S. noctilio* and *S. nitobei* cornus. Mahalanobis distances among the two species were significantly different in pairwise comparisons (*p* < 0.05), and Procrustes distances were similar (*p* < 0.05) (Table 7). These findings had differences in those of cluster analysis (Figure 11d). Cluster analysis (Figure 11d) revealed that several individuals (e.g., 9, 10, 11) could not be clustered, which might have been due to differences in the tunnel environment and ossification structure. In general, the results of quantitative geometric analysis were consistent with those obtained by the naked eye.

**Table 7.** Differences in the cornus shapes among the species of Mahalanobis distances (left) & Procrustes distances (right): p-values (above); distances between populations (below) (10,000 permutation rounds).

**Figure 11.** Shape variables of the cornus of *S. noctilio* and *S. nitobei* (**a**) principal component analysis-(**b**) Transformation grids for visualizing a shape change (for the first two principal components, in this case)-(**c**) The Tps grids of Canonical Variate-(**d**) Phenogram of cluster analysis.

#### **4. Discussion**

In recent years, we have witnessed monumental improvements in geometric morphometrics, which have enhanced the study of insect morphology. In general, these methods separate species shape from size and primarily focus on the shape as the key morphological characteristic, as few variables can reveal morphological differences between similar species. Geometric measurement methods, together with relevant mathematical models (e.g., principal component analysis, canonical variate analysis, and cluster analysis), can be used to acquire information on the morphology, genetic differentiation, development, and behavior of insects. When competing for resources on the same part of the host plant, the morphological structure of the two woodwasps may occur adaptive genetic variation. The use of geometric morphometrics allowed us to explain morphological similarities and differences between the two *Sirex* species, of which thin-spline analysis plots showed average contour distortion, and the length of the stick demonstrated the change size.

Compared with conventional classification methods, geometric survey methods can identify subtle morphological differences in insects [33]. To distinguish the two species from the traditional taxonomic morphology, we mainly distinguish the color of the male's abdomen and the female's leg. However, there is intraspecific variation in color patterns on the legs, abdomen and antennae, for example, females of *Sirex californicus*, *S. nitidus*, and *S. noctilio* each have pale and dark leg color

morphs [34,35]. The results of relative warp analysis can show differences in the classification of intraspecies and interspecies [36]. In studies of morphology, the small unit on the wing is usually independent unit in the shape change, and has a certain genetic basis. Thus, different insects have different wing types and wing vein structures [3]. However, in similar species, these differences may be indistinguishable, with minor variations in the direction and branching of veins [37]. The shapes and vein profiles of insect wings contain valuable information, although it is difficult to understand the effects of behavioral and environmental factors on morphological variations using conventional classification methods [33].

Insect flight involves the first two branches of the radius vein and the thicker area of the wing film [38]), which is gradually reduced from the base to the end of the wing. *S. noctilio* woodwasps have a variable flight behavior, which relates to initial body size [39]. The body size of the *Sirex* also varies in different regions, and the two woodwasps cannot be distinguished simply by it. *Sirex* species mainly use carbohydrates for fuel during flight. The dry weight of *S. noctilio* is significantly larger than *S. nitobei* in this study. Therefore, the wing variations of both *Sirex* species in this study might explain the differences in flight ability and behavior. In addition, the ovipositor, an appendage through which females deposit eggs, plays important roles in sensing the microenvironment and initiating the laying of eggs. In this study, we observed differences in forewing and ovipositor shape, which were due to developmental plasticity. These findings provide a strong basis for further research on flight behavior and ovipositor function in various species.

In this study, we identified and classified two *Sirex* species, although the lack of inclusion of other Siricidae species was a major limitation. When species cannot be immediately identified by their appearance, landmark points can be easily extracted and analyzed. We anticipate that additional landmark points, such as those of the head, chest, and other parts, will be used in future studies [40]. Geographic distance is one of the key factors of population differentiation for widespread species. It is generally believed that the more geographically separated populations have less chance of gene exchange, resulting in morphological differences between populations. *S. noctilio* has invaded many areas in China, next we can collect samples from different regions for analysis of different geographical populations. At the same time, this paper provides basic data for the automatic recognition system of insects. Further identification of *Sirex* species will be provided. In addition, insects have a short life cycle and a fast response to the environment. Using geometric morphology can accurately analyze small changes in morphological structures and possible evolutionary trends in a short period of time.

#### **5. Conclusions**

There is species variation in the wing veins of two woodwasps. We selected the homology coordinate points for analysis. In conclusion, there were significant differences in the forewings and the pits on the ovipositor between the invasive *S. noctilio* and the native *S. nitobei*. The results showed that the taxonomic importance of hind wing venation and cornus characters was not stable for the two woodwasps. Geometric morphology can be used for morphological identification of insects of the genus *Sirex*, especially those species with variable coloration. We can distinguish the two woodwasps from the flight-related forewing veins and the reproduction-related ovipositor pits. Comparing the invasive species with their congeners can partialy avoid the bias due to taxonomical relatedness and enhance the credibility of the results. With landmark-based geometric morphometrics to quantify and analyze wing, cornus, and ovipositor morphologies of two *Sirex* species, we provide new insights for automatic insect identification systems. The currently used approach to study the morphology of wings is complicated and time consuming. This process may damage wings and several software packages cannot extract landmark points. In these cases, the user must use a computer mouse to manually select landmarks, as was performed in this study; however, measurements are affected by human factors. Further studies are needed to expand the identification system of insects by including different types of insects and performing different types of geometric morphometric analysis. New insect

identification software packages should also be developed, as they can reduce the repetitive workload for investigators working in agriculture, forestry, quarantine, and other front-line industries.

**Author Contributions:** Conceptualization, L.R. and Y.L.; data curation, M.W.; formal analysis, M.W.; funding acquisition, L.R. and Y.L.; methodology, M.W., L.R., and Y.L.; project administration, L.R. and Y.L.; resources, M.W., L.W., N.F., C.G. and T.A.; supervision, L.R. and Y.L.; writing—original draft, M.W.; writing—review and editing, M.W. and L.R. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work was supported by the National Key Research & Development Program of China "Research on key technologies for prevention and control of major disasters in plantation" (2018YFD0600200), and Beijing's Science and Technology Planning Project "Key technologies for prevention and control of major pests in Beijing ecological public welfare forests" (Z191100008519004).

**Acknowledgments:** We greatly appreciated the help from Jinbaotun Forest station in Tongliao City, Inner Mongolia and workers of the Forestry Bureau for their assistance with fieldwork.

**Conflicts of Interest:** The authors declare no potential conflict of interest.

#### **References**


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