Draft · 2015. 6. 19. · Draft 2 16 Abstract 17 Wing wear reflects the accumulation of irreversible damage to an insect’s wings over its 18 lifetime, and this damage should influence

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Shape of wing wear fails to affect load lifting in bumble

bees with experimental wing wear

Journal: Canadian Journal of Zoology

Manuscript ID: cjz-2014-0317.R1

Manuscript Type: Article

Date Submitted by the Author: 28-Apr-2015

Complete List of Authors: Roberts, Jordan; University of Calgary, Biological Sciences Cartar, Ralph; University of Calgary, Biological Sciences

Keyword: Bombus impatiens, bumble bees, insect flight, insect wing, load lifting, wing shape, wing wear

https://mc06.manuscriptcentral.com/cjz-pubs

Canadian Journal of Zoology

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Shape of wing wear fails to affect load lifting in bumble bees with experimental wing wear 1

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Jordan C. Roberts & Ralph V. Cartar 3

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Author for correspondence 5

Jordan C. Roberts, Department of Biological Sciences, University of Calgary 6

2500 University Drive N.W., Calgary, AB, Canada, T2N 1N4 7

Phone: (403) 220-3555 8

Fax: (403) 289-9311 9

[email protected] 10

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Ralph V. Cartar, Department of Biological Sciences, University of Calgary 12

2500 University Drive N.W., Calgary, AB, Canada, T2N 1N4 13

[email protected] 14

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Abstract 16

Wing wear reflects the accumulation of irreversible damage to an insect’s wings over its 17

lifetime, and this damage should influence flight performance. In the case of bumble bees, flight 18

seems robust to variation in wing area asymmetry and air pressure, but not to loss of wing area. 19

However, how the pattern of wing wear affects flight performance remains unstudied. In nature, 20

wing wear typically occurs in a ragged and haphazard pattern along the wing’s trailing margin, a 21

shape strikingly different from the straight cut applied in past studies. In this study, we test if 22

shape of wing wear (implemented as 4 distinct treatments plus a control) affects maximum load 23

lifting capabilities and wingbeat frequency of worker bumble bees (Bombus impatiens Cresson 24

1863). We found that shape of wing wear of 171 mg bees had no detectable effect on maximum 25

load lifting capability (detectable effect size = 18 mg) or on wingbeat frequency (detectable 26

effect size = 15 Hz), but that loss of wing area reduced load lifting capability and increased 27

wingbeat frequency. The importance of wing area in explaining the load lifting ability of bumble 28

bees is reinforced in this study. But, paradoxically, shape of wing wear did not detectably affect 29

lift generation, which is determined by unsteady aerodynamic forces in these lift-reliant insects. 30

31

Key words: 32

Bombus impatiens; bumble bees; insect flight, insect wing; load lifting; wing shape; wing wear. 33

Header: 34

Jordan C. Roberts & Ralph V. Cartar, Load-lifting capability in bumble bees is insensitive to 35

shape of wing wear 36

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Introduction 38

Unlike birds, which can preen misaligned feather barbs or regrow damaged feathers, 39

insects lack a mechanism for wing repair. This means that damage resulting from collisions 40

(Higginson and Gilbert 2004), fighting (Alcock 1996), predation attempts (Benson 1972), and 41

prolonged use (Allsopp 1985) will accumulate through an insect’s life. For bumble bees 42

(Hymenoptera: Bombus spp.), wing wear is primarily caused by collisions with foliage during 43

foraging bouts (Foster and Cartar 2011a). Experimentally-induced wing wear in bumble bees 44

results in increased mortality (Cartar 1992) and decreased load lifting (Johnson and Cartar 2014), 45

but with little effect on metabolic rate (Hedenstrom et al. 2001) or on flight trajectories while 46

traveling between flowers with unobstructed flight paths (Haas and Cartar 2008). 47

Experimental studies of wing wear and flight capabilities of bees have typically simulated 48

wing wear by clipping a straight strip along the trailing edge of the forewing (Cartar 1992; 49

Hedenstrom et al. 2001; Haas and Cartar 2008; Johnson and Cartar 2014; Vance and Roberts 50

2014), or by removing the hind wing (Buchwald and Dudley 2010). In nature, wing wear occurs 51

more stochastically, often in a haphazard and ragged pattern along the distal edge of the forewing 52

or involving small punctures, not a clean shear (Mueller and Wolf-Mueller 1993; Mountcastle 53

and Combes 2014; Fig. 1). It is therefore possible that inferences about effects of wing wear on 54

flight and mortality that use a straight cut might be limited in applicability to wing wear in 55

nature. In this study, we test the hypothesis that the shape of wing wear affects the flight 56

capability of bumble bees, in addition to area and asymmetry. 57

Natural ragged and artificially straight-clipped wing edges might differ in their 58

aerodynamic performance. One mechanism for diminution of flight performance in naturally-59

worn wings is the presence of “flaps” (i.e., protruded tips) unsupported by adjacent wing 60

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membrane. While spanwise flexion of wings may be important in the production of lift during 61

bumble bee flight (Mountcastle and Combes 2013), the “flaps” of a ragged edged, naturally-62

worn wing (Fig. 1) may be too flexible and generate little or no lift during flight, partially 63

through the loss of induced camber,and may be affected by any supporting wing veination (e.g., 64

Fig. 2E, arrow). Wing flexion is important in insect flight (Wootton 1992), with induced camber 65

being particularly important for generating lift (Young et al. 2009). A wing edge with flaps 66

might therefore generate less lift than expected simply on the basis of area, particularly if the 67

flaps are not braced by wing veination. 68

A ragged edge may also increase the turbulent vorticity experienced by a wing in flight, 69

increasing drag. However, to our knowledge, no studies have examined shape of wing wear and 70

aerodynamics in insects. To stretch the comparison, we have drawn on knowledge from bird 71

moulting and battle damage in aircrafts as a source of comparison. In simulations of bird flight 72

using theory for fixed-wing aircraft, wing shape mattered: lift to drag ratios were lower in 73

moulting rectangular wings than in intact rectangular wings, and gap size and position affected 74

performance (Hedenstrom and Sunada 1999). Similarly, aircraft with simulated battle damage at 75

mid-length distances on the airfoil, at angles of attack > 8°, suffered major decreases in their 76

coefficient of lift and increases in their coefficients of drag (Irwin 1999). Despite differences in 77

Reynolds number and in kinematics (fixed-wing aircraft vs. bees with a semi-circular wingbeat 78

at ~180 Hz), damage-induced disruption of airflow patterns may to some extent be shared 79

between worn bee wings and moult- and battle-damaged plane wings, and suggest that irregular 80

wing shape can be detrimental to generation of lift . Thus, deep valleys of ragged wing wear and 81

holes in the wing may disturb airflow over the wing, lowering lift to drag ratios. 82

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Among bees, wing wear is manifested in several qualitatively different shapes that we 83

attempt to independently simulate in this paper: flaps (Fig. 1A,B), valleys (Fig. 1A,B) (supported 84

by distal venation and unsupported), holes (Fig. 1B,C), and raw area loss (Fig. 1D). The valleys 85

of wing wear can produce deep span-wise damage from the trailing wing edge. Raggedness 86

produces flaps (supported or unsupported by wing veination). Holes can also produce damage at 87

many points along the length and chord of the wing, but generally only involve the loss of a 88

small amount of wing membrane. We compare the performance of wings damaged according to 89

these classes of wear shape (Fig. 2A,B,C) with the performance obtained from straight clipping 90

along the wing margin (Fig. 2D) used in previous experiments (Cartar 1992; Hedenstrom et al. 91

2001; Haas and Cartar 2008; Vance and Roberts 2009; Johnson and Cartar 2014), or no wear 92

(controls; Fig. 2E). We measure flight performance as the maximum load lifting capabilities of 93

bees during hovering flight (Dillon and Dudley 2004; Buchwald and Dudley 2010). 94

In challenging flight circumstances such as following experimentally induced wing wear, 95

bees may attempt to increase their lift production by altering their wingbeat kinematics. Two 96

ways this could be accomplished are through an increased wingbeat frequency, or an increased 97

stroke amplitude. In low pressure conditions simulating high altitude, bees compensate by 98

increasing their stroke amplitude, rather than increasing their wingbeat frequency (Altshuler et 99

al. 2005; Dillon and Dudley 2014). However, honey bees Apis mellifera (Linnaeus 1758) with 100

asymmetrical and symmetrically induced wing wear (of the straight edge variety) increased both 101

their stroke amplitude and (to a lesser extent) their wing beat frequency (Vance and Roberts 102

2014). Carpenter bees Xylocopa varipuncta (Patton 1879) hovering in lower density gas mixtures 103

also use both strategies to generate lift (Roberts et al. 2004). We therefore also examine how 104

wing beat frequency varies with shape of wing wear. The typical outcome of loss of wing area is 105

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an increase in wingbeat frequency, so we expected an increase in wingbeat frequency at higher 106

levels of wear. We also expected a greater increase in stroke amplitude in the treatments 107

hypothesized to have the largest impact on flight performance (i.e., unsupported flaps and holes), 108

but could not test this hypothesis, as we did not measure stroke amplitude. 109

In this experiment, we examine how shape of simulated wing wear affects maximum load 110

lifted and wingbeat frequency of flying bumble bees. If location of wear affects flight 111

performance, then each treatment tests a particular mechanism which may affect lift producing 112

capabilities, related to length of the intact wing (the valley treatment), support from adjacent 113

wing membrane (the flapped treatment), and air pressure between top and bottom wing surface 114

(the hole treatment). We test these hypotheses with bumble bees, using the asymptotic loading 115

method for estimating maximum capacity for load lifting (Buchwald and Dudley 2010). 116

Materials and methods 117

The experiment was conducted on bees from a commercially raised colony of Bombus 118

impatiens (Cresson 1863), obtained from BioBest (Leamington, ON, Canada). Assessments were 119

carried out in November 2013 and December 2013. The colony was provided with a nectar 120

solution and a pollen paste ad libitum. 121

Prior to wing alteration, bees were anesthetized in a -20°C freezer for (mean ± SD) 5.97 ± 122

1.45 min, until the subjects were unable to flap their wings. Three bees that were unable to fly or 123

resume coordinated movement following being removed from the freezer were excluded from 124

analysis, as their behaviour suggested they suffered damage from the anesthesia. Time in freezer 125

was not significant in statistical models explaining load lifting or wingbeat frequency, and 126

therefore not included in fitted models. 127

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Several types of wing shape were experimentally applied (Fig. 2A-E) using a fine pair of 128

scissors. Bees with intact wings (Fig. 2E) served as controls. Control bees were handled in an 129

equivalent manner to those with wing manipulations applied. Straight-clipped wing treatments 130

were cut in a similar fashion to those of previous experiments: a thin strip was cut parallel to the 131

distal edge of the wing (Fig. 2D; Cartar 1992; Hedenstrom et al. 2001; Haas and Cartar 2008). 132

To produce a flapped wing edge, two V-shaped areas were cut from the distal edge of the wing, 133

placed such that the area between formed a triangular flap (Fig. 2A) In the hole treatment, wings 134

were pierced with a 1 mm diameter probe, scraping against the wing in a circular arc to remove 135

area, rather than simply puncturing the membrane (Fig. 2B). The hole treatment was used to 136

determine the effect of wear at a specific point, with minimal impact on area loss, as well to 137

allow wing damage away from the wing’s trailing edge, a wear feature that occurs naturally (Fig. 138

1B, C). In the valley treatment (with one “V” shape removed), we removed a singular wide “V”, 139

with its apex approximately at mid chord (Fig. 2C). 140

Bumble bees used in this study (n=57) ranged in mass from 90 to 288 mg (mean ± SD: 141

171.4 ± 44.1 mg) with mean marginal cell length (± SD) of 2.71 ± 0.25 mm. For the treatments 142

with major area loss (i.e., not the control or hole treatment), the mean area losses (%) were: 143

flapped treatment 11.2 ± 3.8 % (n=19), valley treatment 12.5 ± 3.3 % (n=9), and straight cut 144

treatment 23.4% ± 4.4 % (n=10). Bees with the straight cut treatment had the most wing area 145

removed, with 3 distinct wing loss groupings (Tukey HSD P < 0.05 contrasts: control = hole < 146

flapped = valley < straight cut) flapped and valley were statistically indistinguishable). Lengths 147

of mid-flaps of the flapped treatment, measured from the flap centre, were (mean ± SD) 1.11 ± 148

0.438 mm. For the valley treatment, the depths of the removed areas (mean ± SD) were 1.53 ± 149

0.31 mm. 150

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We used an asymptotic lifting mechanism (Chai et al. 1997; Dillon and Dudley 2004; 151

Buchwald and Dudley 2010; Johnson and Cartar 2014) to determine the maximal load lifting 152

capabilities of bumble bees. A beaded string was tied with a noose knot around the petiole, 153

which is near their centre of mass (Dudley and Ellington 1990). The beads were placed in sets of 154

two at known distances and weights. Bees were compelled to vertically ascend by an overhead 155

13 W ultraviolet light (Blue Planet, Trileaf Distribution, Trifeuil, Toronto, ON, Canada) 156

positioned 48 cm above the test arena. Each bee rose to a height at which it could not lift the next 157

bead set. The most proximal bead sets were place approximately 5cm from the noose and 158

following this set, bead sets were placed 2cm apart. The average bead set weighed (mean ± SD) 159

15.9 ± 4.8 mg. The maximum load lifted was calculated as the total bead and string weight lifted 160

by the bee. Bees completed flight trials in a small clear plexiglas box (29x29x20 cm) open at its 161

top and filmed directly overhead by a Panasonic Lumix-DMC-FZ200 at 30fps mounted 65 cm 162

above the chamber. A mirror was placed at a 45° angle at the bottom of the flight chamber, and a 163

vertical scale placed on the wall opposite to the mirror, so height could be determined from the 164

overhead recording. The maximal load lifted during the 15-minute flight trial was the flying bout 165

where the bee lifts the most bead sets. Flying bouts where bees lifted off towards the wall of the 166

experimental arena within 2 cm, or where bees ascended while within 2 cm of the walls were not 167

counted. This was done to avoid the complication of boundary effects on flight (Rayner and 168

Thomas 1991). During the trials bees were largely left alone. However, if bees were consistently 169

lethargic, they were encouraged to fly by a gentle puff of human breath, or by gentle prodding. In 170

cases where the noose knot of the beaded string was clearly impeding movement, the knot was 171

rearranged to a more favourable position. 172

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Following each trial, bees were sacrificed (by freezing), weighed and their forewings 173

removed and photographed (Olympus E-420 Zuiko Digital). Wing area loss was determined 174

using ImageJ v 1.47 (Rasband, NIH, MD, USA, 2014). Trials occurred in temporal blocks 175

(n=10) with every treatment occurring in random order in each block. Bees were haphazardly 176

selected from the colony to participate. Each bee received only one treatment as repeated 177

anesthesia affects a bee’s flight, independent of wing alteration (personal observation). 178

To explore the compensation mechanisms of bees with wing wear, the wingbeat 179

frequencies of bees were determined from the sound files associated with the flight trials. Audio 180

tracks were exported from a short period of flight using SimplemovieX v 3.12 (Aero Quartet, 181

Spain, 2010). Pitch was quantified as the dominant frequency assumed to correspond to the wing 182

beat frequency of the bee. We examined for a dominant frequency in the range 150 to 250 Hz for 183

each bee using Praat v 5.3.56 (Boersma and Weenink, Institute of Phonetic Sciences, 2005). 184

Audio was selected from the trials for clarity and consistency, using steady (non-erratic) flight 185

bouts, to avoid Doppler effects of rapid bee movements and changes to wingbeat frequency due 186

to maneuvering. Several flight trials (n=10) contributed no data on dominant frequency. These 187

tended to be when bees only achieved short flight periods, or with high background noise. We 188

extracted frequencies from the “voiced” frames in Praat, which are the audio frames in which a 189

dominant frequency can be determined. 190

Statistical analyses were completed using JMP v11.0 (SAS institute Inc, Cary, NC, 191

USA). ANCOVAs were fit explaining maximum load lifted (g0.5) and wingbeat frequency (Hz) 192

from treatment (5 states), area loss (%), and marginal cell length (a proxy measurement for bee 193

size; Fig. 2E). Maximum loads lifted were squareroot transformed to meet the assumptions of 194

our analyses (i.e., normal and homogeneous residuals). Marginal cell length is commonly used as 195

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a measure of bee size (e.g., Plowright and Jay 1968; Goldblatt and Fell 1987; Owen 1988). 196

Marginal cell length was used as a measurement of size in preference to bee mass, since nectar 197

crops were not cleared prior to trials and mass may therefore be a less reliable measurement of 198

bee size. Marginal cell length in the subjects used in this experiment was strongly correlated with 199

intact wing area (r = 0.982), and wing area is strongly correlated with bee mass, at least 200

interspecifically (Bullock 1999). As well, we found marginal cell length (ln[mm]) and bee mass 201

(ln[g]) were strongly correlated in our subjects (r = 0.904). We expect the loss of precision is due 202

to nectar load in our subjects. Therefore the use of marginal cell length is likely an appropriate 203

size measurement for bees. Area loss (%) and the treatments were highly correlated (variance 204

inflation factors >8), so these two variables were analyzed in separate models as well (i.e., new 205

models either included treatment or area loss). None of the “nuisance” variables (time in freezer, 206

block, or specific beaded string used) were significant in the models explaining lift and they were 207

therefore excluded from the models presented. In the analysis of wingbeat frequency, block was 208

included as a random effect, as it explained a small portion of the variance (11.3% in the 209

saturated model, 4.0 % in the treatment model, and 7.3 % in the area loss model). 210

Results 211

The saturated model explaining maximum load lifted with all of the explanatory variables 212

(treatment (5 states), area loss (%), and marginal cell length) showed area loss and marginal cell 213

length had a significant effect on maximum load lifting capability (Table 1). Larger bees lifted 214

larger loads, and those with greater area loss lifted less. Wing shape did not affect load lifting 215

ability (Table 1). The same conclusion is obtained from models in which wing area loss and 216

treatment are considered in isolation, along with bee size. For the treament model, all treatments 217

(including controls) still had statistically indistinguishable load lifting abilities (Fig. 3a; Table 1), 218

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but larger bees lifted bigger loads (Fig. 3b; Table 1). In contrast, area loss again reduced 219

maximal load lifting capability (Fig. 4a; Table 1), while larger bees still lifted bigger loads (Fig. 220

4b; Table 1). Taking these three model fits together, load-lifting was affected by area loss, not by 221

treatment. 222

The saturated mixed effects model explaining wing beat frequency found larger bees had 223

lower wing beat frequencies, but that. area loss and treatment were insignificant. But results 224

were different when wing area loss and treatement were considered in isolation, along with bee 225

size. In the treatment model of wingbeat frequency, wingbeat frequency was unaffected by 226

treatment (Fig. 5a; Table 1), but larger bees had lower wingbeat frequencies (Fig. 5b; Table 1). 227

In the area loss model, area loss (%) had a significant positive effect on wingbeat frequency (Fig. 228

6a; Table 1), and bigger bees had lower wingbeat frequencies (Fig. 6b; Table 1). Hence, 229

wingbeat frequency was affected by area loss, not treatment. Taking these three model fits 230

together, wing beat frequency is affected by wing area loss, but not by shape of wing damage 231

(i.e., treatment). 232

The detectable effect size for the load lift capabilities using the treatment model, with a 233

power of 0.95, an α of 0.05, n=57, and the observed sample variance, was 0.135 g0.5 or ~18.2 mg. 234

That is, our conclusion of no effect of wing shape on load lifting means that differences among 235

treatments in load lifting that were within 18.2 mg qualify for us as having “no effect”. For 236

wingbeat frequency, we calculated detectable effect size using a ANCOVA (power analysis is 237

not possible in a mixed effects model. In the resulting model, using a power of 0.95, α = 0.05, n 238

= 47, and the observed sample variance, the detectable effect size was 15.5 Hz. Hence, our 239

conclusion of no effect of wing shape on wingbeat frequency can be qualified in that treatments 240

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that were no more different than 15.5 Hz (i.e., ~8% of an average control bee’s wingbeat 241

frequency of 190 Hz) are statistically indistinguishable. 242

Discussion 243

In analyses of both maximum load lifting capability and wingbeat frequency, treatments 244

that varied the shape of wing wear had no detectable effect on the outcomes. For bumble bees, 245

the shape of area loss is apparently inconsequential to load lifting capability. Area loss however 246

is a major determinant of load lifting capability. Hence, the mechanisms by which we proposed 247

different shapes of wing wear to be affecting aerodynamic capabilities are likely not having a 248

major impact on lift-producing capabilities. 249

The detectable effect size of these results on load-lifting capabilities (roughly 18 mg) is 250

approximately 1/5 of of a 170 mg bumble bee worker’s hourly foraging rate (Spaethe and 251

Weidenmuller 2002), and roughly 1/3 of a 162 mg bumble bee worker’s foraging load size 252

(Johnson and Cartar 2014). Thus, if there are indeed differences in load-lifting ability among 253

wing wear shapes, they likely reflect a fraction of an individual’s foraging capabilities. A bigger 254

sample size and a more controlled means of adjusting wing shape could distinguish more subtle 255

differences in load lifting that may exist between shapes of wing wear. 256

Our results are congruent with the noneffect of asymmetry of wing wear on flight capability 257

(Johnson and Cartar 2014). However, they are in some ways contrary to those of Hedenstrom 258

and Sunata (1999), who modeled flight capabilities of moulting birds, and found the location of 259

missing feathers important to lift capabilities. Hedenstrom and Sunata (1999) used steady-state 260

aerodynamics in their model, which might poorly reflect unsteady state dynamics acting on an 261

insect wing in flight (Dickinson et al. 1999, Hedrick et al. 2014). To our knowledge, there has 262

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been no analysis of worn-winged insect flight that uses unsteady state mechanisms, and from the 263

current study these mechanisms (reviewed by Hedrick et al. 2014) would appear to be necessary 264

to explain our results. Through the use of modeling and particle image velocimetry, it should 265

now be feasbile to study the unsteady aerodynamics involved in a damaged insect wing during 266

flight (Hedrick et al. 2014). 267

It also appears that bees do not compensate for wing wear shape by changing wingbeat 268

frequency. Either this is because there is truly little effect of wing wear shape on aerodynamic 269

performance, or because bees increase their stroke amplitudes (not measured by us) in 270

compensating for the changes in shape (Altshuler et al. 2005; Dillon and Dudley 2014; Vance 271

and Roberts 2014). Bees increase their wingbeat frequency at higher levels of wear. This likely 272

has to do with the decreased inertia in flapping smaller, lighter wings (Vance and Roberts 2014). 273

It is difficult to say whether the increased wingbeat frequency in bees with higher area loss 274

serves as the primary aerodynamic compensation, without knowing the stroke amplitudes of 275

these bees. Honey bees with worn wings (straight cut) increased their stroke amplitude with 276

increased wing wear (Vance and Roberts 2014). 277

Maximal lift capability is but one factor of a bee’s flight. Others aspects of flight may be 278

more impacted by changes to shape of wing wear. In very simple foraging scenarios, bumble 279

bees suffer minor losses in flower-to-flower flight capabilities with major wing wear (Haas and 280

Cartar 2008). However, in more complex foraging scenarios, where a bee must fly between 281

flowers in an inflorescence, or change altitude in order to land on the next set of flowers, more 282

complex and difficult maneuverability must be implemented (speculated by Higginson and 283

Barnard 2004). Bumble bees make foraging choices in the field that depend on their wing wear 284

(Foster and Cartar 2011b). As such, it is worthwhile to examine the effect of shape of wing wear 285

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in natural circumstances, to determine the effect of wing shape on maneuverability. Similarly, 286

Lepidoptera with experimentally removed hindwings have severely reduced maneuverability, 287

while still being able to fly (Jantzen and Eisner 2008). Among Drosophila, the complex 288

maneuvers involved in predator avoidance are controlled by subtle changes to the wing 289

kinematics (Muijres et al. 2014). Maneuverability, again, may depend on wing shape. 290

Bees use some mechanisms for avoiding wear during flight, which likely involve the span-291

wise flexion and flexural stiffness of the wing (Mountcastle and Combes 2014). Regardless of 292

the mechanisms, our study suggests bees are likely more dependent on preventing loss of wing 293

area, rather than conserving wing shape. Along with providing support, the venation of the wing 294

appears to be more resilient to wing wear. But the trailing, distal edge of bee wings lacks 295

venation and closed cells. This may indicate the mass and rigidity associated with venation is 296

more costly to flight than is wing wear in the distal portions of the wing. 297

Overall, the shape of wing wear appears not to be important in affecting a bee’s load lifting 298

capabilities. This research adds wear shape to the category of traits to which a bee’s flight 299

capabilities are resilient, along with bees’ ability to forage with wing wear, resist the pitfalls of 300

asymmetric damage, and fly at low air pressures (Haas and Cartar 2008; Johnson and Cartar 301

2014; Dillon and Dudley 2014). Clearly, bumble bees are capable of accommodating a wide 302

array of wing injuries during flight: apparently all but loss of wing area. 303

Acknowledgements 304

We thank two anonymous reviewers for their helpful and constructive comments, and Sarah 305

Johnson for advice. We thank Mary Reid for the loan of her video camera. 306

307

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Tables 402

Table 1. Results of ANCOVAs regressions explaining maximum load lifted and wing beat 403

frequency using all variables (Saturated model), and one variable at a time (Treatment and Area 404

loss models). The analyses of wingbeat frequencies used the blocking variable order as a random 405

effect. The first 4 rows show overall model fit. A (+) or (-) following the p values indicate the 406

direction of the relationship. Variance Inflation factors for wing area removed in the saturated 407

models are 8.2 for load lifted, and 9.0 for wingbeat frequency, suggesting that the “saturated 408

models” should be regarded with skepticism. 409

410

Model Saturated model Treatment model

Area loss model

Trait Maximum

Load lifted

Wingbeat

frequency

(Hz)

Maximum

Load lifted

Wingbeat

frequency

(Hz)

Maximum

Load lifted

Wingbeat

frequency

(Hz)

Model R2 0.22 0.38 0.122 0.379 0.143 0.379

Model F 2.29 1.417 4.514

Model dfs 6,50 5,51 2,54

Model (p)

0.0497

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Figure Captions 413

Fig. 1. Examples of natural wing wear in wild-foraging bumble bees in SW Alberta, Canada. 414

Flaps are denoted with thick arrows, and valleys with thin arrows. A) Valley & flapped (B. 415

mixtus), B) Valley and flapped and hole, (B. flavifrons), C) Hole and area loss (B. perplexus), 416

D) Area loss (B. mixtus). 417

Fig. 2. Treatments applied to bee wings (B. impatiens). A. Flapped; B. Hole; C. Valley; D. 418

Straight cut; E. Control, indicating length of the marginal cell (solid line) and the distal wing-419

thickening that potentially provided support for marginal flaps (arrow). 420

Fig. 3. Relationship between maximum load lifting capability and: A. wing treatment (control 421

(n=10), straight cut (n=10), flapped (n=19), hole (n=9), and valley (n=9)), B. bee size 422

(marginal cell length). Least square means (± 1 SE) and leverage plots are based on the model 423

reported in Table 1 (column 3). 424

Fig. 4. Relationship between maximum load lifting capability and: A. wing area removed, B. bee 425

size (marginal cell length). Leverage plots are based on the model reported in Table 1 426

(column 5). 427

Fig. 5. Relationship of wingbeat frequency and: A) wing treatment (control (n=8), straight cut 428

(n=9), flapped (n=14), hole (n=8), and valley (n=8)), B) bee size (marginal cell length). Least 429

square means (± 1 SE) and leverage plot are based on the mixed effects model reported in 430

Table 1 (column 4) 431

Fig. 6. Relationship of wingbeat frequency and: A) wing area removed, B) bee size (marginal 432

cell length). Leverage plots are based on the mixed effects model reported in Table 1 (column 433

6). 434

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Draft · 2015. 6. 19. · Draft 2 16 Abstract 17 Wing wear reflects the accumulation of irreversible damage to an insect’s wings over its 18 lifetime, and this damage should influence