UNIVERSITY OF OXFORD

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1 UNIVERSITY OF OXFORD FHS IN BIOLOGICAL SCIENCES UNDERGRADUATE PROJECT REPORT PROJECT DISSERTATION SUBMITTED AS PART OF THE FINALS EXAMINATION IN THE HONOURS SCHOOL IN BIOLOGICAL SCIENCES PLEASE ENTER YOUR CANDIDATE NUMBER ELECTRONICALLY IN THE BOX BELOW Candidate Number COVER SHEET PAGE 1

2 Project Supervisor Word Count (Maximum 7,000) A D R I A N T H O M A S 6, TITLE: Maximum force output from flying insects, variations in body mass, flight muscle mass, wing area, and aspect ratio, and an experimental analysis of the effects of desiccation on load carrying capacity in the blowfly (Calliphora vicina) COVER SHEET PAGE 2 2

3 Abstract Animal flight performance can be evaluated using load lifting experiments which are used to infer the upper limits to aerodynamic force output. Insect data from Marden s (1987) seminal comparative load lifting study was reanalysed here using appropriate controls for mass dependence and phylogenetic non-independence. Flight muscle mass was found to be the most important parameter determining maximum lift force and was found to fully account for the effects of body mass on lifting capacity. In contrast to Marden s findings, wing area and aspect ratio were both found to significantly affect maximum force output. A desiccation treatment was adopted in order to assess the effect on load carrying capacity of varying body mass in blow flies (Calliphora vicina). Flies subject to desiccation, and therefore an increased ratio of flight muscle mass to body mass, showed a 3.12% increase in maximum body weight-specific lift compared with initial lifting attempts. This experimental result confirms the conclusions from Marden s comparative approach that flight muscle ratio is positively correlated with maximum body weight-specific lift force. This interspecific analysis also provided an opportunity for allometric comparisons with Marden s interspecific data, despite the small range of body masses represented in this sample, indicating subtle differences in the scaling of lift force within and between species. 3

4 Table of Contents Abstract 3 Introduction 5 Load lifting experiments 7 Experimental approach: a desiccation treatment 8 Materials and methods 9 Analysis of Marden s data 9 Blowfly load lifting 12 Specimen rearing 12 Load lifting setup 12 Desiccation treatment 14 Measurements and data processing 14 Results 15 Reanalysis of Marden s data 15 Morphological parameters individually 15 Full model: body mass, flight muscle mass, aspect ratio and wing area 16 Morphological parameters controlling for body mass 17 Blowfly experimental results 18 Effect of desiccation treatment on load lifting capacity 19 The effect of intraspecific morphological variation on maximum lift force 20 Discussion 21 Statistical considerations 21 Mass dependence 21 Model justification and multiple testing 22 Phylogenetic control 22 Morphological variation and maximum lift force 24 Flight muscle mass 24 Body mass 24 Wing morphology 25 Wingbeat type 26 Experimental manipulation of body mass in the blowfly 27 The effects of descreased body mass on load lifting capacity 27 Additional effects of a desiccation treatment 28 Conclusions and future directions 29 Acknowledgements 30 Appendices 31 Marden s load lifting data 31 Blowfly desiccation data 33 Work cited 34 Safety registration form 38 Management report 40 Gnatt chart of project time management 42 4

5 Introduction The ability to fly has given insects a myriad of ecological opportunities and arguably played a key role in their diversification. This ability shows huge variation across class insecta. An understanding of the biomechanical limits to flight performance can help inform further aspects of behaviour, ecology and evolution of volant taxa. A number of studies have attempted to explain variation in flight performance by examining the effects of interspecific morphological variation, most notably Marden (1987, 1989, 1990). However, few studies (Mountcastle & Combes 2013) have used experimental manipulation of morphological characters to test for the effects on insect flight performance. Here, I reanalyse Marden s data incorporating phylogenetic control and then adopt an experimental approach to examine the effect of decreasing body mass on load lifting capacity in blowflies (Calliphora vicina). The study of insect flight and its relationship to morphology relies on the quantification of flight performance parameters. Vertical force production is a key component of locomotion in three dimensions and is required to counteract the gravitational force acting on the bodies of volant taxa. The maximum lift generated during take-off is therefore an important factor in the study of animal flight performance. Maximum lift production is proportional to take-off velocity and acceleration (Vogel, 1966) and is therefore closely linked to predation risk and survival (Marden & Chai, 1991). In addition, lift production often correlates with reproductive success (Marden, 1989) making it a useful animal flight metric with important evolutionary consequences. Identification of the principle parameters determining vertical force production in insects is not only of interest in the fields of biomechanics and ecology but also has biomimetic application in the design of micro aerial vehicles. Several theoretical predictions have been made regarding the relationship between morphology, take-off ability, lift production and power output based on general aerodynamic principles for birds, bats and insects. Animal flight performance has been suggested by 5

6 various authors to be strongly influenced by body mass (Norberg 1990; Ellington, 1991), however the mechanisms underlying this relationship are hard to characterise. Wing loading, the ratio of body weight to wing area, is another key parameter which can be used to make detailed predictions of flight performance (Taylor & Thomas, 2014). Animals with relatively larger wings compared to body size will take off at higher speeds and should perform a more energy efficient flight (Ellington, 1991). Aspect ratio, a dimensionless variable describing wing shape, was first demonstrated by Wenham (1866) to be an important flight performance parameter. Wings with a high aspect ratio (long narrow wings) have a better lift to drag ratio and therefore enhances lift production. Weis-Fogh (1973) and Ellington (1984) used biomechanical models to support this prediction, concluding that lift production should be positively related to wing area and aspect ratio and negatively correlated with wing loading. Weis-Fogh (1974) further noted that some insects use an unconventional lift-enhancement mechanism involving the clapping of wings together and then flinging them apart. Insects using this clap-and-fling mechanism are therefore expected to generate greater maximum lift forces. The mass of the motor generating lift (flight muscle mass) is a further parameter of obvious interest in determining maximum force output. Pennycuick (1969) presented a theoretical model to explain maximum power output in terms of muscle mass where power depends upon strain, stress and contraction frequency. It was assumed that flight muscles operate at values of stress and strain which are independent of body mass therefore implying that the power available per unit of muscle mass is proportional to the frequency of contraction. Flight muscle mass should therefore also act as a good predictor of maximum lift force during high intensity bursts of flight such as during take-off. The ratio of flight muscle mass to body mass was also identified by Hartman (1961) as a key variable affecting lift production after observations of take-off ability in a range of birds in relation to the proportion of the proportion of body mass composed of flight muscle. 6

7 Load lifting experiments Data on extreme features of locomotive performance are often difficult to obtain due to the problems in differentiating between behavioural propensity and physiological capacity to perform at maximum levels. However, in the past 3 decades load lifting experiments have enabled quantification of maximum vertical force production in a large range of volant taxa. This technique, first adopted by Marden (1987), works on the assumption that when subject to progressively increasing load, the animal will act to maximise vertical aerodynamic force production. By defining maximum load lifted as a measure of flight ability, Marden (1987) was able to conduct large scale allometric analyses of flight performance across a broad range of flying animals. Marden attempted to overcome the problem of mass-dependence and intercorrelation between the morphological variables used by comparing maximum mass-specific lift force against mass-specific morphological variables. The results of this analysis led Marden to conclude that relative muscle mass (the ratio of flight muscle mass to body mass) was the most significant determinant of body mass-specific lift. A further key finding was that take-off performance scaled isometrically with flight muscle mass. Marden found no wing characteristic variable to be significant in explaining observed variation in maximum load lifted after controlling for flight muscle mass. However, Marden s analysis found that insects with clap-and-fling wing motions achieved on average 25% more muscle mass-specific lift than did animals with other types of wingbeat. Marden s data can be analysed more powerfully by entering multiple variables into a general linear model allowing each factor to be examined once the variance due to other factors has been accounted for removing the need for comparison of mass-specific morphological variables. Felsenstein (1985) demonstrated that interspecific comparisons such as Marden s are potentially confounded by the lack of statistical independence among data points. In this 7

8 study, a method of phylogenetic control is implemented in the analysis of Marden s data making use of a generalized least squares approach to transform the data. Since Marden s initial load lifting study, a number of authors have introduced variations on the original methodology used. Chai et al. (1997) introduced an altered experimental technique involving the attachment of a beaded string to the study animal which applies an asymptotically increasing load with increasing height above the ground. As the animal ascends increasing weight is lifted off the ground until the animal transiently hovers in the air while sustaining maximum load. Direct comparison of this approach against cumulative load attachment indicates a number of reasons to favour asymptotically increasing load techniques which generally provide a better estimate of maximum force output (Dillon & Dudley, 2004). This difference results from problems in distinguishing the ground effect and initial wing flapping from vertical acceleration when using a take-off performance metric meaning that Marden s technique does not provide results which are necessarily equivalent to lift force production. However, ground effects are thought to be negligible when the animal height above the ground exceeds the wing length by a factor of 10 (Rayner, 1991), allowing hovering flight to indicate maximum vertical force production with greater reliability. In addition, the asymptotic loading technique avoids complications with fatigue allowing maximum lifting capacity to be attained with a single flight bout and provides increased experimental resolution of maximum load lifted. Experimental approach: a desiccation treatment Here, I adopt an asymptotically increasing load lifting technique to compare body weightspecific lift before and after a desiccation treatment in order to determine the effect of changing body mass on load lifting in the blowfly (Calliphora vicina). Whilst other studies (e.g. Berrigan, 1991) have examined the effects of varying flight muscle ratio on the load lifting capacity of an individual, to my knowledge none have experimentally decreased the 8

9 ratio of flight muscle to body mass and have relied instead on naturally occurring variation in body mass or addition of weights. The desiccation treatment adopted exploits the vulnerability and tolerability of insects to water loss by subjecting them to low relative humidity and causing desiccation and therefore a decline in body mass. Water loss is presumed to be primarily from the hemolymph, as this is the largest pool of extracellular water within the insect body (Folk, et al., 2001). Muscle cells are assumed to remain hydrated throughout mild desiccation as they draw on extracellular water stores and therefore muscle mass is expected to decrease at a rate slower than total body mass. Calliophora are known to be able to tolerate considerable variations in water content, resulting in changes in the concentration of their hemolymph, without apparent ill effects (Barton-Browne, 1964). Given that Marden found the ratio of flight muscle mass to body mass to positively predict maximum body mass-specific lift, a treatment which decreases body mass relative to flight muscle mass is expected to result in an increased in maximum body weight-specific lift force. The loss of body mas during desiccation is compensated by the ability to lift additional load as the flight muscle mass remains relatively constant. Therefore after desiccation, whilst the total load lifted (body mass + additional load) may decrease due to other adverse effects on flight function relating to treatment, the maximum load which can be sustained relative to body mass is predicted to increase. Materials and methods Analysis of Marden s data Marden s (1987) data was reanalysed in MATLAB using a custom-written package for phylogenetic control (Taylor & Thomas 2014). Bird and bat data was excluded from the 9

10 analysis due to their phylogenetic disparity with insects and because they produce large relative forces giving them undue weight in regression analysis. For each specimen, this dataset consisted of a measurement for body mass (m), flight muscle mass (m mus ), wing area (S), wingspan (b) and maximum lift force (F vert ). Species means were taken of all morphological variables where more than one specimen had been recorded from the same species leaving 48 insect species in the analysis. Aspect ratio (AR) was calculated as b 2 /S and wing loading (p w ) was calculated as M b /S for each species. All continuous independent variables, as well as maximum lift, the dependent variable, were log e transformed prior to analysis. This transformation is appropriate in this analysis of morphometric data spanning multiple orders of magnitude as it enables allometric scaling effects to be examined. Species were also categorised discretely according to their wingbeat type as either conventional or clap-and-fling as this was a variable of specific interest to Marden in his analysis. The phylogenetic relationships between the insect species under investigation (Fig. 1) were determined primarily using Tree of Life ( Recent molecular phylogenies were consulted when resolving disputed relationships and the topology of closely related taxa (see Fig. 1 for sources). Where relationships remained unknown or highly disputed, multiple branches were taken to stem from the same node. This phylogeny was coded using CAIC format, where each letter in a string represents different branches at each node. A method of generalized least squares was used to transform the data associated with each species using the error covariance structure specified by the phylogeny. The transformed data was then analysed using least squares techniques. 10

11 Sphingidae (Kitching, 2003) Lepidoptera (Wiegann, et al., 2002) Hymenoptera (Sharkey, 2007) Endopterygota (Giribet et al., 2013) Coleoptera (Beutel et al., 2010) Hemiptera (Cryan and Urban. 2012) Ondonta (Hasegawa & Kasuya, 2006) Figure 1 Composite Phylogeny for the insects used in Marden 1987, with sources for the phylogenetic relationships used in the phylogenetically controlled generalised least squares regression analysis reported here. Where specimens were not classified at the species level, higher level classifications are given with arbitrary species identifiers. 11

12 Blowfly load lifting Specimen rearing Blowfly (Calliphora vicina) pupae were purchased from a local fishing supplier (Fat Phil s, Oxford, United Kingdom) on 5 May 2013 and placed in plastic containers with sawdust until eclosion. Adult flies were housed in 35 x 35 x 145 cm nets and fed mashed banana and milkbased infant formula powder. Both rearing and experiments were carried out at 20 o C, on a 10:14 light:dark regime. Individual blow flies were selected without conscious bias from a total of about 3000 flies 2 8 days after eclosure. Loading lifting setup Pilot studies were conducted to determine the optimal amount of time for anesthetisation and desiccation treatment. Lift production was evaluated using an asymptotic loading technique similar to that described above of Chai et al. (1997). Lift trials were conducted in an open chamber measuring 45 x 65 x 50 cm constructed using white foam board (see Fig. 2). Flies were cold-anesthetized at -15 o C for 4 min until quiescent and weighed using a UMX2 Ultramicrobalance to the nearest 0.1 mg. A monofilament thread, with a linear mass density of 0.12 mg cm 1, was attached to the dorsal surface of each fly abdomen using high viscosity cyano-acrylate glue below the expected centre of gravity for hovering flight in an attempt to minimise pitching torque. Beads, weighing 2.8 ± 0.8 mg, were attached every 15 mm along the thread with the first bead 25 mm from the point of attachment in an attempt to increase maximum height and reduce ground effects. Flies were allowed to recover for 30 minutes before being released in the flight chamber. The flies flew erratically at first but would generally settle on the centre of the chamber floor within a few minutes of being released. Mechanical stimulation then caused the flies to take-off towards a lamp positioned above the chamber progressively lifting more beads until the maximum weight was sustained. The greatest height for each lifting attempt was taken to represent the maximum hovering performance. Flies were allowed 3 lift attempts with 3 minutes recovery time in an opaque 12

13 container between attempts. Given the focus on maximum performance, only the greatest of the lifting attempts was used in subsequent analyses. Flights in which the insect approached the chamber boundaries were not recorded. The minimum hovering height was 50 mm above the ground which corresponded to more than 5 wingspans for this individual, therefore precluding potential ground effects (Rayner, 1991). Light source NOT TO SCALE String glued to fly abdomen White foam board Monofilament with beads attached every 15 mm Video camera (25 fps) 50 cm Figure 2 - Load lifting assay used to determine maximum lift force for blowflies 13

14 Desiccation treatment Following initial lifting measurements, each individual was placed in a sealed container with the beaded thread still attached. 3g of fresh desiccant (Drierite, purchased from was placed into the container, separated from the fly using a sponge where the flies remained for 5 hours. The calcium sulphate in this desiccant generates 0% RH resulting in diffusion of water through the arthropod cuticle allowing for controlled water loss (Toolson 1978). Flight trials were then repeated, again recording 3 lift attempts for each individual. Measurements and data processing Within 5 minutes of the final lifting attempt the flies were frozen allowing the beaded string and any remaining glue to be removed and the desiccated body mass to be measured. Flight trials were recorded using a video camera (Sony CMOS HD) mounted at the side of the flight chamber and video sequences were imported to a computer and inspected to determine the number of beads lifted for each lifting attempt. The mass lifted for each attempt was then estimated as the sum of number of beads lifted multiplied by the average bead mass and the mass of the filament and the adhesive. Maximum vertical aerodynamic force (F vert ) production was calculated for each individual s maximum load lifted as the product of the total load lifted (body mass + additional load) and acceleration due to gravity (g) (9.81 m s -2 ). Maximum body weight-specific lift (F vert /mg) was also calculated for each lift attempt as this dimensionless variable allows comparison of relative force production before and after desiccation. Flies were frozen for 2 hours and pinned to a foam board with wings outstretched and then scanned on a Plustek Opticbook 3800 scanner at 300 d.p.i. ImageJ (v1.47) was used to determine the wingspan, as double the maximum length from the wing base to the furthest point at the wingtip of a single wing, and the wing area, by drawing polygons around a single 14

15 wing and doubling it. These measurements in pixels were converted into millimetres using a ruler scanned for calibration. Paired t- tests and ordinary least squares regression models were run in JMP 10. Histograms of differences were examined to detect departures from normality for paired data and residual plots were examined to verify regression assumptions. Results Reanalysis of Marden s Data Morphological parameters individually against lift force Mean lift production and morphological data was analysed from 48 insect species presented in Marden s (1987) seminal load lifting study (Appendix 1). Variable R 2 p value AdjSS F ratio Coefficient 95% CI ρ Body mass (g) < 0.001* , Flight muscle <0.001* x , mass (g) Wing area <0.001* , (mm 2 ) Aspect Ratio , Wing span <0.001* , (mm) Wing loading * , (g mm -1 ) Wingbeat type , Table 1 Output from a regression of each variable against maximum lift force, Fvert (mn), including coefficients of determination and allometric exponents with 95% confidence intervals. Specifically, values reported here are for log e transformed maximum vertical lift force, on log e transformed morphological variables and wingbeat type for 48 insect species using phylogenetic control. The phylogenetic distortion parameter (ρ) is given for each model. Asterisks indicate significant p values when the expected False Discovery Rate is 5%. 15

16 There is a significant correlation between maximum lift force and each individual variable apart from aspect ratio (p = 0.794) and wingbeat type (p = 0.773) when the false discovery rate is controlled to deal with inflated Type I error (see Benhamini and Hochberg 1995). Wing loading is not significant after the more conservative Bonferroni correction (critical p value = , for 17 tests). Body mass alone was found to strongly predict log maximum lift force (R 2 = 0.939, p < 0.001). Maximum lift force scaled allometrically with body mass (F vert = 0.547m ) with the exponent differing significantly from one (p = , t = 2.49, df = 46). The phylogenetic distortion parameter from this model output (ρ = 0.344), indicates that a large proportion of the remaining variation in maximum lift force can be accounted for by the error covariance structure based on the phylogeny in Fig. 1. Maximum lift force scaled with wing area with the allometric exponent which does not differ significantly from (p = 0.679, t = 0.417). The phylogenetic distortion parameter is greatest for wing area (ρ = 0.487) indicating that this parameter shows the most systematic variation in its effect on along phylogenetic lines. Full model: body mass, flight muscle mass, aspect ratio and wing area A phylogenetically controlled ordinary least squares multiple regression model fitted with four loge transformed morphological variables (Table 2) was found to very strongly predict log e transformed maximum lift force when controlled for phylogeny (R 2 = 0.989, p < 0.001). 16

17 Variable p value AdjSS F ratio Coefficient 95% CI Model R 2 Model ρ Body mass , <0.001 (g) Flight muscle <0.001* , 1.00 mass(g) Aspect ratio * , Wing area (mm 2 ) <0.001* , Table 2 Multiple regression describing the effects of log e transformed body mass, flight muscle mass, wing area and aspect ratio on log e transformed maximum lift production for 48 insect species using phylogenetic control. Asterisk indicates significant p values when the expected false discovery rate is 5%. Flight muscle mass was the strongest predictor of maximum lift force (F 1, 42 = 98.9, p < 0.001). When the effects of body mass and wing morphology are controlled, maximum lift production was proportional to m mus. This exponent does not differ significantly from one (p = , t = 1.99, df = 46) indicating isometric scaling of maximum lift force with flight muscle mass. In this model, wing area was found to be highly significant (F 1, 42 = 29.3, p < 0.001). Aspect ratio was found to significantly predict maximum lift force (F 1, 42 = 6.51, p = ) only when false discovery rate is controlled at 5% (critical p value = ) but not when the more conservative Bonferroni correction is applied (critical p value = , for 17 tests). Body mass was found not to significantly predict maximum lift force when controlled for flight muscle mass and wing morphology (F 1, 42 = 0.521, p = 0.474). This result suggests that the effect of body mass on maximum lift force seen in the above model is due almost entirely to scaling effects of body mass with wing area, aspect ratio and flight muscle mass. Further statistical models were used to dissect this relationship, presented below. The phylogenetic distortion parameter for the model in Table 2 has been reduced almost to zero (ρ < 0.001) which indicates that these 4 variables together account for almost all of the equation error which would otherwise be accounted for by the error covariance structure defined by the phylogeny in Fig

18 Morphological parameters controlling for body mass Each variable in the full model above was entered into a regression model with body mass as a covariate in order to determine which parameter is accounting for the effects of body mass on maximum lift force. Variable p value AdjSS F ratio Coefficient 95% CI Model R 2 Model ρ Flight muscle <0.001* , mass (g) Body mass x , (g) Aspect radio , Body mass (g) Wing area (mm 2 ) Body mass (g) <0.001* , <0.001* , <0.001* , Table 3 - The effects on maximum lift force of flight muscle mass, aspect ratio and wing area each controlled for the effects of body mass with phylogenetic control. All variables were log e transformed prior to analysis. Asterisk indicates significant p values when the expected false discovery rate is 5%. Flight muscle mass, aspect ratio and wing area were each run separately against maximum lift force in a model controlling for body mass (Table 3). Residual body mass significantly predicts maximum lift force in models with both aspect ratio and wing area (p < 0.001, p < 0.001). However, the effects of body mass complete disappear when entered into a model with flight muscle mass (p < 0.843). Therefore the effects of flight muscle mass on maximum lift force almost entirely account for the apparent effect of body mass. Blowfly experimental results The maximum of 3 lift attempts was analysed for a total of 30 individual blow flies for both the desiccation treatment and the control (see Appendix 2). Desiccation treatment resulted in a significant decrease in body mass (paired t-test: t = -13.9, df = 29, p < 0.001) with a mean decrease of 5.75%. The average rate of water loss was therefore mg hr -1 which is 18

19 within the range expected for mesic insect species of this size (Addo-Bediakoa, et al., 2001). There is likely to be significant and heritable variation in load lifting ability between individuals and therefore each fly was compared against its own performance before and after desiccation in a paired design in an attempt to minimise extraneous variation. The effect of desiccation on load lifting capacity The desiccation treatment was found to result in an increase in maximum body weightspecific lift (F vert /mg) (paired t-test: t = 2.94, df = 29, p = ). Fig. 3 shows the difference in body weight-specific lift before and after desiccation. Prior to desiccation, flies lifted on average 34.6% of their body weight but after the treatment could lift 38.8% of their body weight. The maximum additional load which could be sustained after desiccation increased relative to the control, however this effect was not significant (paired t-test: t = 1.46, df = 29, p = 0.156). Desiccated flies were found to lift a maximum additional load on average 1.6 mg greater than the maximum load sustained prior to desiccation. Change in body mass after desiccation was found to significantly predict the change in additional load lifted (R 2 = 0.351, p = ). Despite the body-weight specific increase in lift production, the absolute maximum lift force produced after desiccation shows a decreased compared with the initial maximum lift (paired t-test: t = -2.57, df = 29, p = ) with a mean difference of mn. 19

20 Desiccated bodyweight specific lift Initial bodyweight specific lift Paired mean body-weight specific lift Figure 3 Difference in body-weight specific lift before and after a desiccation treatment in blowflies. The solid blue line represents the mean difference with the 95% confidence interval above and below shown as dotted lines. The confidence region does not include zero indicating a significant difference between initial and desiccated lifts when α = The effect of intraspecific morphological variation on maximum lift force A model was run similar to the interspecific model of Marden s insects in the analysis above to examine the effects of log e transformed body mass, wing area, aspect ratio on log e transformed maximum lift force prior to desiccation within blowflies (R 2 = 0.241). Body mass was found to significantly predict the maximum lift force when controlled for the effects of wing morphology (p = ). In this model, maximum lift production was proportional to m This exponent does not differ significantly from one (p =0.110,t = 1.65,df = 28) indicating isometric scaling of maximum lift force with body mass. Neither wing area nor 20

21 aspect ratio significantly predicted maximum lift force when controlled for the effects of body mass (p < 0.613, p < 0.972). The maximum force output recorded here for blowflies is comparable to Berrigan s (1991) dipteran load lifting study on flesh flies (Neobellieria bullata). The mean body weight-specific lift (F vert /mg) for flesh flies was found to be 1.21 ± whilst with the mean body weightspecific lift recorded for blowflies in this study prior to desiccation was 1.35 ± The difference in these values will reflect the different load lifting techniques used as well as the differences in morphology between these two dipertan species. Discussion Statistical considerations This analysis of maximum lift force data was more appropriate than Marden s (1987) initial analysis of this dataset for a number of reasons aided by the development of improved statistical techniques in the decades since Marden s work was published. Mass dependence Marden was limited in his initial analysis by the availability of statistical techniques allowing multiple independent variables to be analysed simultaneously and attempted to control for mass dependency by analysing mass-specific morphological variables against mass-specific lift force. However, this does not allow the relationships between explanatory variables and the effects of scaling to be fully dissected. Mass dependency can be better controlled by entering all the variables of interest into a general least squares regression model as was done in this analysis. This covariance analysis has advantages over the use of ratios as it 21

22 does not make the restrictive assumption that the variables scale isometrically and can also provide important information about the data which is otherwise lost with the use of ratio variables. Model justification and multiple testing Flight parameters were selected to be entered into the regression model based on predictions from first principles and on Marden s key findings. The shape of a wing planform can be described using any pair of the following parameters; wing span, wing area and aspect ratio. Aspect ratio and wing area both appear in equations for lift and drag coefficients and so it is logical for these two parameters to be entered into the model. Marden found flight muscle ratio to be the most important variable in predicting maximum mass-specific lift force and therefore flight muscle mass and body mass are also entered also into this model. The false discovery rate, the expected proportion of erroneous rejections among all rejections, was used to deal with the inflated risk of type I error arising from multiple testing. This simple approach, first presented by Benjamini and Hochberg (1995), exerts a less stringent control over false discovery in comparison to familywise error rate procedures such as the widely used Bonferroni correction. This results in increased statistical power at the cost of increasing the type I error rate and is appropriate here where test statistics are unlikely to be independent. Phylogenetic control The use of techniques controlling for non-random species associations in this analysis was found to be of value when analysing variables separately or when controlling for body mass alone. The full model containing body mass, flight muscle mass, aspect ratio and wing area showed little difference in output between a model run with and without phylogenetic control. This means that these variables which have been identified are the real parameters which determine lifting capacity rather than other unidentified factors which vary systematically 22

23 along phylogenetic lines. The majority of deterministic variation in maximum lift force which can be accounted for using the error covariance structure based on the phylogeny in Fig. 1 is explained by flight muscle mass and wing area. This means that flight muscle mass explains most of the systematic variation in maximum lift force along phylogenetic lines. Whilst well resolved phylogenetic information is not available for many taxonomic groups, the data which is currently available from molecular phylogenies can be useful for comparative allometric studies such as this in controlling for local systematic variation not explained by measured independent variables. In failing to account for the phylogenetic nonindependence of species level data, comparative studies such as Marden s original analysis will suffer from inflated Type I error rates arising from the use of biased estimates of the standard error of any parameters estimated. The analysis in this study uses a generalized least squares method, first outlined by Grafen (1989), to minimise the problems arising from the use of species level data. This method is a generalization of Felsentein s (1989) independent contrasts method and will yield identical results to independent contrast models given the same phylogenetic information and assumed model of evolution (Garland, et al., 2005). However, this approach has advantages over Felsenstain s (1985) widely used approach of independent contrasts because it does not require an explicit model of trait evolution and can also be applied to categorical variables. This method is therefore appropriate for the dataset analysed in this study where it is not possible to obtain detailed information on divergence times of each species. Instead, a branch length transformation optimised to fit the tree to tip data, first proposed by Grafen (1989), is employed meaning that no branch length information was required for this analysis, only a topology of species relationships. The analysis of Marden s data in this study treated mean values for species as if they were estimated without error which can lead to problems in the calculation of slope coefficients. 23

24 Whilst for the purposes of this study this issue is unimportant, a more rigorous analysis might incorporate information on within-species variation by employing measurement error models such as those used by Fuller (1987). Morphological variation and maximum lift force lift force Flight muscle mass This analysis of Marden s insect data using phylogenetic control confirmed the original conclusion of Marden s (1987) study that after controlling for body mass, flight muscle mass is the most important flight related morphological variable in predicting the maximum vertical lift force. This analysis confirmed isometric scaling of maximum lift force with flight muscle mass reported in Marden s original analysis by demonstrating that the relationship can be described by a single scaling equation in which the muscle mass-specific force is 59.9 ± 8.32 N kg 1 (mean ± S.D.). Further analyses by Marden & Allen (2002) have demonstrated the generality of this relationship finding that maximum force output by any rotary motors ranging from myosin to jet engines scale as motor mass 1.0 with a motor mass-specific force of 57±14 N kg 1. Body mass Marden s result that body mass alone significantly predicts the maximum lift force was also confirmed by my reanalysis of Marden s data using phylogenetic control. Body mass was also found to predict lift force within blowflies, although this effect was weak presumably owing to the limited range of body masses represented in the blowfly data. When using ordinary least squares without controlling for phylogeny, the coefficient of determination for body mass alone (R 2 = 0.922) is smaller than that calculated for log body mass against maximum lift by Marden (R 2 = 0.972). This is likely to reflect the smaller 24

25 sample size and smaller range of body masses used in this analysis which includes only insects, a subset of Marden s original data. An interesting result arising from my analysis of flight muscle mass after controlling for the effects of body mass rather than the use of flight muscle ratio was that body mass had no effect on maximum lift force when controlled for flight muscle mass. This suggests that correlation between body mass and flight muscle mass is almost entirely responsible for the apparent effects of body mass on lift force and that scale effects with other flight related morphological variables are relatively unimportant. Whilst the additional load lifted by insects in lifting experiments might easily be independent of body mass, the maximum lift force is a function of the total load lifted making this a surprising result. In contrast to Marden s finding that maximum force output scales isometrically with body mass, this analysis of Marden s insects found body mass to show a slight negative allometric scaling with maximum lift force. Despite the small range of body masses represented in the blowfly sample, this data presents an opportunity to compare intraspecific allometric exponents with those calculated from Marden s interspecific data. For Calliphora vicina, body mass was found to scale isometrically with maximum lift force prior to desiccation. Wing morphology My analysis also found wing morphology to significantly predict maximum lift force when controlled for the effects of flight muscle mass, a conclusion not reached by Marden in his original analysis of the same data. Both aspect ratio and wing area significantly predict takeoff ability when controlled for the effects of body mass and flight muscle mass when the false discovery rate is set to 5%. If the Bonferroni correction is used however, aspect ratio is not found to be significant. In a model of wing area controlling for the effects of body mass, both parameters are highly significant in predicting maximum load lifted. This is a result which 25

26 Marden did not find when controlling for mass dependence using ratios but one which is in line with theoretical predictions regarding wing loading. Neither wing area nor aspect ratio was found to significantly predict maximum lift force within blowflies in this study. This assay of load lifting capacity may not be sensitive enough to detect the effects of small deviations in wing characteristics represented in this sample over a small range of wing morphologies. More recent load lifting studies examining the effect of both interspecific (Buchwald & Dudley, 2010) and intraspecific (Dillon & Dudley, 2004; Berrigan, 1991) variation in wing morphology report a similar conclusion to my analysis of Marden s data finding aspect ratio to have a very weak or insignificant effect on maximum lift force but find wing area to strongly predict maximum lift force. This finding that lift is dependent on wing area to a greater extent than wing shape is in line with aerodynamic predictions (Ellington, 1991). The scaling of maximum lift force with wing area 2/3 in my analysis of Marden s data is a result expected from basic scaling principles of surface area with a volume and is supported by a number of other studies (e.g Dudley & Srygley, 1994). Wingbeat type Marden identified wingbeat type as an important variable in his original analysis finding species defined as clap-and-fling to provide 25% more mass-specific lift than those defined as having conventional wingbeats. However, in direct contrast my analysis of the same data found no significant difference between these discrete categorisations of wingbeat mechanism. With the same wingbeat frequency, amplitude and area clap-and-fling wingbeats would be expected to produce greater lift than conventional flapping mechanisms. However, these results may reflect a tendency of insects which don t adopt a clap-and-fling mechanism to have larger wings with greater wingbeat frequencies and stroke amplitudes 26

27 making this effect hard to dissect statistically. Dudley (2002) suggests that Marden s discrete categorisation of insects as clap-and-fling or conventional fliers does not accurately characterise the continuum of contralateral wing separation observed in flapping flight particularly during load carrying when wing proximity may be more pronounced. The exclusion of bird and bat data, and the use of phylogenetic control may further explain this contrasting result to Marden s initial analysis as wingbeat type varies systematically along phylogenetic lines. Experimental manipulation of body mass in the blowfly The effects of decreased body mass on load lifting capacity The experimental methodology used in this study allows body mass to be manipulated whilst holding all other flight related morphological variables constant providing an important experimental control which is not possible in Marden s comparative approach. Crucially, it allows manipulation of the association between flight muscle mass and body mass in their effects on maximum lift force. Experimental manipulation of blowfly body mass with a desiccation treatment found the maximum body weight-specific lift force to increase when body mass is reduced. The desiccation treatment was found to result in an increase in the maximum additional load which could be sustained during hovering flight; however this effect was not statistically significant. Given that the effects typically associated with desiccation in insects, discussed below, all adversely affect locomotor performance, the direction of this result is an interesting finding despite not being statistically significant. Whilst the absolute flight muscle mass will remain constant, or show a slight decrease, the increased flight muscle ratio has resulted in an increased maximum body weight-specific lift, as predicted by Marden s original analysis. 27

28 The change in body mass after desiccation was found to predict the change in additional load lifted. This indicates that it is the desired effect of the desiccation treatment which is influencing load carrying capacity rather than other associated factors of the treatment which might be increasing load lifting ability relative to body mass. This is comparable to the results of Berrigan s (1991), study which found that increases in body mass during ovarian development correlated with the decrease in additional mass lifted. However, similarly to the desiccation treatment in this study, the total mass lifted by gravid females was significantly lower than the total mass lifted prior to egg development suggesting that ovarian development, like desiccation, affects flight performance in ways other than simply altering body mass relative to flight muscle mass. Additional effects of a desiccation treatment The total load lifted (body mass + additional load), and therefore also the maximum lift force produced, decreased after desiccation. This result is expected given the range of adverse effects on locomotor performance typically associated with this treatment. Fluid loss will result in changes in cellular ion concentrations which can have a myriad of implications for metabolic systems. Nervous and muscular systems will also be adversely affected and the oxygen-transporting abilities of the hemolymph will be reduced (Gefen & Ar 2005). Whilst mesic insects are known be able to tolerate a range of internal water concentrations, flight is an extremely sensitive form of locomotion and therefore flight performance is likely to decline rapidly when internal conditions are sub-optimal. Insect wings, which rely on cuticular hydration, will show a decrease in flexibility when water is lost (Mengesha, et al., 2011). This increase in wing stiffness is has been found in other load lifting studies to decrease load lifting capacity (Mountcastle & Combes, 2013). An additional issue associated with the application of a desiccation treatment is access to food which in this study was limited to a period preceding the initial load lifting attempt. The 28

29 flies were not given access to the sugar solution during or after desiccation as this would have counteracted the effects of the treatment in decreasing body mass. Like the factors highlighted above, this effect should result in a reduction in flight performance and is therefore has been counteracted in this study by the effects of reduced body mass on additional load carrying capacity. A further methodological point for consideration in this study is that flies were weighed before attachment of the beaded string and initial lifting trials and then after the string had been removed following desiccation and subsequent lifting attempts. As a result, the initial mass recorded is likely to be greater than the actual mass at initial lifting attempts whilst the final mass recorded is likely to be lower than the actual body mass at desiccated lifting attempts. This could lead to an overestimation of the difference in body weight-specific lift before and after desiccation. Conclusions and future directions This study has found flight muscle mass to be the principle morphological determinant of flight performance, as defined by load lifting capacity. Despite providing no additional explanatory effects after controlling for the effects of flight muscle mass, body mass is a useful parameter in the study of flight performance. For many insects, the flight muscle ratio is relatively constant meaning that in most cases, body mass provides a convenient and accurate means of predicting flying ability. This is particularly useful in ecological studies of escape responses and foraging ability where flight muscle mass might not easily be measured. However, a description of wing area and flight muscle mass (motor mass in general) is required in order to more accurately characterise flight performance and it is therefore these parameters which should be of specific interest in the design of micro aerial vehicles. 29

30 Future work on insect flight performance would do well to focus specifically on the differences between inter- and intra-specific scaling of load lifting, applying asymptotic loading techniques and methods of phylogenetic control for between species comparisons. New imaging techniques, such as X-ray microtomography, may in the future provide a more accurate and pragmatic method for measuring the mass of specific flight muscles, allowing the effect of these motors on maximum force output to be dissected further in comparative studies. Experimental manipulation of flight related morphological parameters is problematic as treatments will often have multiple effects on locomotor performance. However, they can provide important information to complement comparative results and treatments such as the manipulation of wing area could prove informative in future work. Acknowledgements I would like to thank Adrian Thomas for his supervision and advice throughout this project. I would also like to thank Graham Taylor whose MATLAB software and guidance made the phylogenetically controlled analysis possible. This project will be submitted for publication, co-authored by Prof. Thomas and Dr. Taylor, in February Beth Mortimer and Alex Greenhalgh from the Oxford Silk Group were extremely helpful in assisting me in the rearing of my fly pupae and by lending me the necessary equipment. 30

31 Appendices Appendix I: Marden s load lifting data Mean values for morphological variables and maximum lift data for 48 insect species, taken from Marden (1987). Where specimens were not identified at the species level, higher level classifications are given with arbitrary species identifiers. Species Body mass (g) Flight muscle mass (g) Wing area (cm 2 ) Wing span (cm) Wing loading (g/cm 2 ) Aspect ratio Maximum lift force (mn) Danaus plexippus Pieris rapae Phoebis argante Heliconius cydno Heliconius erato Parides sesostris Papilio sp Hesperiidae sp Hesperiidae sp Lycaenidae sp Ascalapha odorata Rothschildia lebeau Tiltaea tamerlan Xylophanes tersa Xylophanes sp Xylophanes sp Manduca sp Pachylia ficus Enyo sp Agnus cingulatus Sphingidae sp Sphingidae sp Sphingidae sp Sphingidae sp Sphingidae sp Sympetrum sp Anax junius Aeshna canadensis Aeshna sp Libellula pulchella Libellula sp Megaloptera sp