Population and Conservation Biology, Department of Ecology and Genetics, Evolutionary Biology Centre, Uppsala University, Norbyvägen 18D, 75236, Uppsala, Sweden

Department of Ecology, Evolution, and Organismal Biology, Iowa State University, 241 Bessey Hall, Ames, IA 50011, USA

Abstract

Background

Wing size and shape have important aerodynamic implications on flight performance. We explored how wing size was related to wing shape in territorial males of 37 taxa of the damselfly family Calopterygidae. Wing coloration was also included in the analyses because it is sexually and naturally selected and has been shown to be related to wing shape. We studied wing shape using both the non-dimensional radius of the second moment of wing area (RSM) and geometric morphometrics. Lower values of the RSM result in less energetically demanding flight and wider ranges of flight speed. We also re-analyzed previously published data on other damselflies and dragonflies.

Results

The RSM showed a hump-shaped relationship with wing size. However, after correcting for phylogeny using independent contrast, this pattern changed to a negative linear relationship. The basal genus of the study family,

Conclusions

We found that RSM showed a complex relationship with size in calopterygid damselflies, probably as a result of other selection pressures besides wing size

Background

Flight performance is a result of complex interactions between body morphology (i.e., wings, tails), behavior and the biological and physical environment

Apart from body size, other variables might also affect the optimal wing shape, for example flight behavior

In this study, we explore how wing shape is related to wing size (used as a proxy of body size), and discuss its implications on flight performance. For that purpose we compare males of damselfly taxa within the family Calopterygidae. These species display territorial behavior

We studied wing shape using uni- and multivariate methods. First, we quantified wing shape using the non-dimensional radius of the second moment of wing area

In the present work, we specifically studied 37 taxa of male calopterygid damselflies that differ in wing shape, wing size and wing coloration patterns. We first explored the allometry of wing shape (using the RSM and geometric morphometrics) and the effect of wing coloration. We then compared wing shape captured by the RSM and by geometric morphometrics. We also investigated how the RSM and body length were related in a larger sample of both dragonflies and damselflies, by re-analyzing previously published data. Finally, we also performed independent contrasts for taking into account the evolutionary relationships of our study taxa.

Results

RSM and size

Before correcting for phylogenetic effects, the RSM was related in a quadratic way to wing centroid size in both fore- and hindwings (Figure ^{2} = 0.013, _{1,35} = 0.457, ^{2} = 0.424, _{2,34} = 12.520, ^{2} = 0.151, _{1,35} = 6.246, ^{2} = 0.435, _{2,34} = 13.094,

Relationship between wing shape, measured as the non-dimensional radius of the second moment of wing area (RSM), and wing centroid size (A: forewings; B: hindwings)

**Relationship between wing shape, measured as the non-dimensional radius of the second moment of wing area (RSM), and wing centroid size (A: forewings; B: hindwings).** Wing shape variation is shown as deformation grids obtained from geometric morphometrics. The deformation grids are based on certain taxa contained in circles and numbered. Data are grouped into the different coloration groups (see Methods; group 1: filled circles; group 2: triangles; group 3: inverted triangles; group 4: rhombuses; group 5: crosses; group 6: open circles).

The RSM showed a linear relationship with wing shape estimated from geometric morphometric methods as shape scores, both for fore- and hindwings (Figure _{20,52} = 13.984, _{20,52} = 72.692,

Relationship between wing shape expressed as shape scores, and wing shape measured as the non-dimensional radius of the second moment of wing area (RSM) (A: forewings; B: hindwings)

**Relationship between wing shape expressed as shape scores, and wing shape measured as the non-dimensional radius of the second moment of wing area (RSM) (A: forewings; B: hindwings).** The symbols indicate the different coloration groups (see Methods; group 1: filled circles; group 2: triangles; group 3: inverted triangles; group 4: rhombuses; group 5: crosses; group 6: open circles).

We also tested the relationship between the RSM and body length in a larger size range of dragonflies and damselflies, by re-analyzing previously published data _{2,104} = 812.344, _{1,104} = 0.552,

Relationship between wing shape, expressed as the non-dimensional radius of the second moment of wing area (RSM), and body length (based on the data of Serrano-Meneses et al. [32] for Odonata) (dark circles: non-calopterygid damselflies; triangles: calopterygid damselflies; white circles: dragonflies)

**Relationship between wing shape, expressed as the non-dimensional radius of the second moment of wing area (RSM), and body length (based on the data of Serrano-Meneses et al. ****for Odonata) (dark circles: non-calopterygid damselflies; triangles: calopterygid damselflies; white circles: dragonflies).** Pictures show an example of hindwings of a non-calopterygid damselfly (

After accounting for phylogenetic non-independence among our study taxa, a visual inspection of the relationship between the RSM vs. wing centroid size revealed that a quadratic term was no longer present (Figure ^{2} = 0.194, _{1,35} = 8.450, ^{2} = 0.270, _{1,35} = 12.954,

Phylogenetic independent contrasts of wing shape (measured as the non-dimensional radius of the second moment of wing area, RSM) on wing centroid size (A: forewings; B: hindwings)

**Phylogenetic independent contrasts of wing shape (measured as the non-dimensional radius of the second moment of wing area, RSM) on wing centroid size (A: forewings; B: hindwings).**

RSM and wing coloration

In a previous study using 36 taxa and geometric morphometrics, we showed that the coloration groups differed in the non-allometric component of fore- and hindwing shape before correcting for phylogeny

**Effect**

**d.f.**

**SS**

**
F
**

**
P
**

**A. Forewings**

Coloration group

5

0.00068

1.802

0.144

Log Centroid size

1

0.00005

0.633

0.433

(Log Centroid size)^{2}

1

0.00001

0.048

0.828

Error

29

0.00220

**B. Hindwings**

Coloration group

5

0.00091

2.404

0.061

Log Centroid size

1

0.00085

11.279

0.002

(Log Centroid size)^{2}

1

0.00003

0.351

0.558

Error

29

0.00219

Discussion

Our study showed a quadratic relationship between the RSM and wing centroid size, implying that small and large species have lower values of this parameter compared to intermediate-sized species. This result was somewhat surprising since a linear relationship would be expected from aerodynamic theory

When phylogeny was taken into account, the RSM tended to decrease with wing centroid size. The change in this relationship after correcting for phylogenetic effects suggests a phylogenetic signal, i.e., that more closely related species tend to resemble each other more than a randomly chosen species sampled from the phylogeny. In fact, a significant phylogenetic signal of wing shape is present in this family of damselflies

The linear negative relationship between the RSM and size was a result from small species showing a higher distribution of the wing area towards the wing apex, whereas large species showed a concentration of the wing area towards the wing base. A tendency to a higher concentration of wing area towards the wing base in the large species not only promotes less-energetically demanding flight

The genus

The lack of significant differences in the RSM of the hindwings among coloration groups after correcting for phylogeny contrasts with our previous study using geometric morphometrics, where we found significant differences

Conclusions

In this study we have shown that the relationships between wing shape and size are complex and taxon-specific, even within a group of species with similar flight behavior: territoriality. Moreover, the presence of wing coloration, a sexually and naturally selected trait, might influence the optimal wing shape within a trade-off between flight energetics and coloration display. The net selection pressures acting on flight performance, wing size, wing shape and body size probably differ among species, resulting in relationships that differ from the aerodynamic predictions alone. Experimental work in a comparative framework is needed to disentangle the role of wing morphology and size on flight performance.

Methods

Study taxa

Wing pictures of 338 males from 37 taxa of calopterygid damselflies (5–10 specimens per taxa) were collected from museum specimens (NCB Naturalis of Leiden and The Swedish Museum of Natural History, Stockholm), from colleagues or from our own samples (Table

**Taxa**

**N (fore/hindwings)**

**Coloration group (fore/hindwings)**

8/8

1/1

10/10

1/1

9/10

3/3

6/6

6/6

10/10

4/4

5/5

6/5

10/10

2/2

6/6

6/6

10/10

3/3

10/10

3/3

10/10

4/4

10/10

3/3

10/10

3/3

10/10

4/4

10/10

6/6

10/10

1/1

10/10

1/1

10/10

3/3

5/7

3/3

10/10

2/2

10/10

2/2

10/10

2/2

10/10

2/2

10/10

2/2

10/10

6/3

10/10

6/6

10/10

6/6

6/6

6/6

6/6

5/5

10/10

4/4

10/8

3/3

5/7

3/3

10/10

6/6

10/10

6/6

10/10

6/6

10/10

5/5

10/10

3/3

Because wing shape is at least partially associated to wing coloration

Wing shape analysis

We estimated shape using two different methods. First, we calculated the RSM. Second, we used geometric morphometrics techniques to study graphical changes in wing shape. The RSM has been used in the study of quasi-steady aerodynamics of hovering flight

where

Parameters used in the calculation of the non-dimensional radius of the second moment of wing area, RSM (see main text)

**Parameters used in the calculation of the non-dimensional radius of the second moment of wing area, RSM (see main text). **

We also used a geometric morphometrics approach to analyze wing shape variation. Although much more refined that the RSM, it does not provide an intuitive, quantitative estimate of wing shape as the RSM does, but it does provide an excellent visualization. In geometric morphometrics, shape is quantified from landmark coordinates after holding mathematically constant the effects of non-shape variation (position, orientation and scale)

Landmarks and semi-landmarks (*) used for the study of wing shape in the geometric morphometric approach

**Landmarks and semi-landmarks (*) used for the study of wing shape in the geometric morphometric approach.** As an example a wing of

Phylogenetic tree

We used independent contrasts to correct for the phylogenetic non-independence of our study taxa. To obtain a phylogenetic tree that included all our study taxa, we re-analyzed previously published nucleotide sequences of the following genes: 18S, 5.8S, partial 28S rDNA, and of the spacers ITS1 and ITS2 ^{7} generations and logged every 1,000 generations. The consensus tree was pruned and was then used for the independent contrasts (Figure

Phylogenetic tree used in the present study (see also [28])

**Phylogenetic tree used in the present study (see also **
**).**

Statistical analyses

For all statistical tests, species were used as our level of replicate. Hence, we calculated for each species a mean value for each variable. We performed analyses both before and after accounting for the phylogenetic relationships among taxa. The statistical analyses were carried out in SPSS (IBM Corp.), unless otherwise stated.

We first performed a regression of the values of the RSM against wing centroid size. After visual inspection of the plot, we ran both a linear and a quadratic regression of the values of the RSM on wing centroid size. To visualize how wing shape was related to the variation in the values of the RSM and to wing centroid size, we computed thin-plate spline deformation grids in tpsSplin

We also investigated how the RSM and the wing shape obtained by geometric morphometrics were related in our dataset, for fore- and hindwings separately. To do this, we first visualized this relationship by applying the approach developed by Drake and Klingenberg

To explore how the RSM was related to size over a larger size range in Odonata, we re-analyzed data published in Serrano-Meneses et al.

We also studied the relationship between the RSM and wing centroid size in our dataset using phylogenetic independent contrasts applying the method described by Felsenstein

Finally, we inspected whether there were differences among the coloration groups in the values of the RSM. We have previously shown similar results for a dataset of 36 taxa of the same family, but using geometric morphometrics approaches

Competing interests

The authors declare that they have no competing interests.

Authors’ contributions

DO coordinated sample collection, did data acquisition, analyzed data, interpreted the results and wrote the manuscript. DCA analyzed data, interpreted the results and revised the manuscript. FJ coordinated sample collection, interpreted the results and co-wrote the manuscript. All authors read and approved this paper.

Acknowledgements

We are very grateful to M. Serrano-Meneses who kindly provided us with the protocol for calculating the RSM. We thank L. Faulks and W. Kunce for useful comments on the manuscript. We also thank K. D. B. Dijkstra for his support at the NCB Naturalis of Leiden and Gunvi Lindberg for her help at The Swedish Museum of Natural History in Stockholm. We also want to thank P. Brunelle, A. Córdoba-Aguilar, R. Futahashi, D. Halstead, M. Hämäläinen, I. Santoyo, G. Sims, Y. Tsubaki, H. Ubukata and X. Yu for their help in providing us with some of the taxa. This study has been supported by a postdoc position to D. Outomuro from the Spanish Ministry of Education. D. C. Adams was supported in part by NSF grant DEB-1118884 and F. Johansson was supported by The Swedish Research Council.