Figures and data in Adaptations in wing morphology rather than wingbeat kinematics enable flight in small hoverfly species

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Tables
Additional files

7 figures, 3 tables and 7 additional files

Figures

Figure 1 with 1 supplement

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The studied hoverfly species shown with their phylogenetic relationships.

Sample size as number of individuals for each species is in parentheses. Species marked with coloured circles are displayed on the right, and coloured circles with black outlines are of species for which both morphology and flight kinematics were quantified. Body mass is presented as mean values and standard deviation. Phylogeny was obtained from Wong et al., 2023.

Figure 1—figure supplement 1

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The body mass of museum specimens was approximated using the relationship between thorax width and the fresh mass in wild-caught specimens.

(A) A cubic polynomial regression model was fitted to the data from wild-caught specimens. (B) The equation of the fitted model was used to estimate body mass from thorax width in museum specimens.

Figure 2

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Quantifying the in-flight wingbeat kinematics and wing morphology of hoverflies.

(A) Hoverflies were released in an octagon-shaped flight arena. We recorded stereoscopic high-speed videos of the flying hoverflies using three synchronised high-speed video cameras; from the videos, we reconstructed the three-dimensional body and wingbeat kinematics. Infrared light panels positioned as the bottom of the arena enabled high contrast between the flying insect and the background. (B) Conventional wing angles were measured at each time step (t=0.4 ms) in the body reference frame. ϕ, wing stroke angle within the stroke-plane; η, wing deviation angle out of the stroke-plane; θ, wing rotation angle along the spanwise axis; $\vec{u}$ , air velocity vector relative to the wing; α, angle-of-attack of the wing. (C) Wing morphological parameters including their definitions: wingspan R, wing surface area S, radial position along the span r, local wing chord c at distance r, the second-moment-of-area $S_{2}$ , and its dimensionless homologue $S_{2}^{*}$ .

Figure 3 with 1 supplement

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Wingbeat kinematics during hovering flight of the eight studied hoverfly species.

(**A–E**) Temporal dynamics of the wingbeat kinematics throughout the wingbeat cycle of all digitised wingbeats. Separate wingbeats are colour-coded by body mass (see legend on top), and the black lines show the average wingbeat kinematics for all wingbeats combined. (**A–C**) Temporal dynamics of the three conventional wingbeat kinematics angle (stroke, deviation, and rotation angle, respectively; see Figure 2 for definitions). (**D, E**) Angular speed and angle-of-attack of the wings throughout the wingbeat cycle, derived from wing stroke, deviation, and rotation angles. (**F–I**) Derived wingbeat-average wingbeat kinematics parameters for each studied species versus the body mass of that species. The kinematics parameters are wing stroke amplitude A_ϕ, wingbeat frequency f, wingbeat-average angular wing speed $\bar{ω}$ , and mean angle-of-attack at mid wing stroke $\bar{α}$ , respectively. Each data point shows mean ± standard error per species and is colour-coded according to the legend on the top. None of the wingbeat-average wingbeat kinematic parameters were significantly associated with body mass (Table 1). Horizontal dashed lines show the mean parameter values, as expected under kinematic similarity.

Figure 3—figure supplement 1

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Derived wingbeat-average wing kinematics parameters for each studied species versus the body mass of that species.

The kinematics parameters are (A) wingbeat frequency f, (B) wing stroke amplitude A_ϕ, (C) wingbeat-average angular wing speed $\bar{ω}$ , and (D) mean angle-of-attack at mid wing stroke $\bar{α}$ , respectively. Each data point shows mean±standard error per species. None of the wingbeat kinematic parameters were significantly associated with body mass, as shown by the non-significant dashed black trend lines from phylogenetic generalised least squares (PGLS) regressions. The corresponding scaling based on kinematic similarity is shown with red dashed lines, and the expected scaling for maintaining weight support across sizes, when assuming that all other parameters scale under kinematic similarity, is shown in dotted grey lines (see Table 1 for details).

Figure 4 with 1 supplement

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The scaling of wing morphology with body mass for all 28 studied hoverfly species (**A–D**), and how allometric scaling of wing morphology contributes to maintaining weight support across the hoverfly size range (**E, F**).

(**A–D**) Body mass (abscissa) versus on the ordinate the second-moment-of-area S₂, wingspan R, mean chord $\bar{c}$ , and normalised second-moment-of-area $S_{2}^{*}$ , respectively. Each data point shows a species average value. Data points of species for which flight was studied are colour-coded (see top row), and species with only quantified morphology are shown in grey (see the corresponding individual-specific data in Figure 4—figure supplement 1). The black, red, and grey trendlines show the best fitting line from a phylogenetic generalised least squares (PGLS) regression, isometric scaling, and the expected scaling for metric-specific maintenance of weight support, respectively (see legend above A). All fitted PGLS regression slopes, except for wing chord, are significantly lower than expected under geometric similarity, suggesting negative allometric scaling of wing size and shape with respect to body mass (see also Table 1). (**E, F**) The relative contributions of different wing morphology metrics to maintaining weight support across the studied range of hoverfly sizes, expressed by the relative allometric scaling factor a*. (E) The relative allometric scaling factor for the second-moment-of-area S₂ and (F) the relative allometric scaling factor for the separate morphological components of S₂: wingspan R, mean chord $\bar{c}$ , and normalised second-moment-of-area $S_{2}^{*}$ .

Figure 4—figure supplement 1

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Wing morphology parameters versus body mass for all studied specimens.

(**A–D**) Body mass (abscissa) versus on the ordinate the second-moment-of-area S₂, wingspan R, mean chord $\bar{c}$ , and normalised second-moment-of-area $S_{2}^{*}$ , respectively. Each circle shows data for a different individual. Species for which both flight and morphology were studied are colour-coded (see top row), whereas species with only quantified morphology are shown in grey.

Figure 5 with 2 supplements

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Changes in wing shape and size associated with body mass variation.

Each data point shows a species-average value (see the individual-specific data in Figure 5—figure supplement 2), and is colour-coded for species of which both flight and morphology were studied (see right column of B), and in grey for species with only morphology quantified. (A) Normalised second-moment-of-area ( $S_{2}^{*}$ ) versus the primary principal component (PC1) of the phylogenetic principal component analysis (phyloPCA) performed on the mean wing shape coordinates of all 28 studied hoverfly species. On the right, we show the 28 wing outlines colour-coded and normalised with body mass (with coordinates X^∗=*X/m*¹^/³). (B) Body mass (m) versus PC1 (left), and mass-normalised wing outlines versus body mass for the eight species used in our flight experiments (right). The left and right gritted wing shapes on the PC1 axis show the theoretical wing shapes at maximum and minimum value of PC1. PC1 explains 65.21% of the variations in wing shape (see also Figure 5—figure supplements 1 and 2). (**A, B**) The combined results show that in larger species, wing surface area was located more proximally (lower PC1 and $S_{2}^{*}$ values) than in smaller species, in which wing area tended to be located more distally (higher PC1 and $S_{2}^{*}$ values). Combined with the changes in wing shape (left), weight-normalised wingspan (R^∗) and mean chord ( $\bar{c}$ ) tend to be larger in smaller species (right).

Figure 5—figure supplement 1

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Result of geometric morphometrics analysis on the wing outlines of 28 hoverfly species; data per species.

Species for which both flight and morphology were studied are colour-coded (see top row), whereas species with only quantified morphology are shown in grey. (A) The first two principal components (PC1 and PC2) from the phylogenetic principal component analysis (phyloPCA) on the geometric morphometrics data, along with the associated shape changes and the percentage of variation explained by these principal components. Shown wing shapes represent the extreme values associated with each PC axis. (B) PC1 and PC2 (first and second row, respectively) plotted against body mass, highlighting that the change in wing shape carried on PC1 is associated with variations in body mass.

Figure 5—figure supplement 2

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Result of geometric morphometrics analysis on the wing outlines of 28 hoverfly species; data per individual.

Each data point shows a different individual value. Species for which both flight and morphology were studied are colour-coded (see top row), whereas species with only quantified morphology are shown in grey. (A) The two first principal components (PC1 and PC2) of the phylogenetic principal component analysis (phyloPCA), together with the associated shape changes and percentage of the variation explained by the principal components. Shown wing shapes represent the extreme values associated with each PC axis. (**B, C**) Body mass and versus PC1 and PC2, respectively. This shows that changes in wing shape carried on PC1 is are associated with variations in body mass, while this is less so for PC2.

Figure 6 with 1 supplement

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Aerodynamic forces produced by hovering hoverflies, as estimated using computational fluid dynamics (CFD) simulations.

(**A, B**) For our simulations, we used the species-specific wing shapes and sizes (top row), but average wingbeat kinematics and frequency ( $\bar{f}$ ) across all eight studied hoverfly species (**A, B**). (C) The resulting temporal dynamic of vertical forces throughout the wingbeat cycle, coloured by species (see legend on top). (D) The wingbeat-average vertical force versus body mass, for all simulated hoverfly species operating at the average wingbeat frequency for all species $\bar{f}$ (square data points and dashed trend line), and forces scaled to the species-specific wingbeat frequency f (round data points in B and D, and solid trend line). The trendline for weight support (*F=mg*) is shown with a grey dashed line. With the species-specific wingbeat frequency f (solid trend line and circles in B and D) hoverflies are closer to producing weight support than for the simulations at the average wingbeat frequency $\bar{f}$ (dashed lines in B and D).

Figure 6—figure supplement 1

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Temporal dynamics of the vertical aerodynamic forces produced during the wingbeat of the eight studied hoverfly species, estimated using computational fluid dynamics (CFD) simulations.

Data for the eight species are colour-coded according to the legend on the top. All simulations were run with the mean wingbeat kinematics of all hoverflies combined (Figure 6A and B), but with species-specific wing morphology (see legend on top). The aerodynamic forces in the different panels are scaled and normalised using four different methods: (A) aerodynamic forces as directly estimated using the CFD simulations, and where all wings operate at the mean wingbeat frequency of all hoverflies ( $\bar{f}$ ); (B) aerodynamic forces as produced by each hoverfly beating its wings at the species-specific wingbeat frequency f; (C) aerodynamic forces normalised with its wingbeat-average force, $F^{*} = F / \bar{F}$ ; (D) aerodynamic forces produced using the species-specific wingbeat frequency and normalised with the mean weight of the specific hoverfly species F/mg.

Figure 7

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The relative contribution of allometric variations in wing morphology and wingbeat kinematics to computational fluid dynamics (CFD)-derived vertical aerodynamic force production, and how this contributes to maintaining in-hovering weight support across the sampled range of hoverfly sizes.

(**A–C, E–G**) Wingbeat-average vertical force at species-specific wingbeat frequency f (abscissa) versus on the ordinate various wing morphology and kinematics traits. In each panel, data points are results for different species, colour-coded according to the legend on the top. The solid and dashed black lines show the significant and non-significant ordinary least squares (OLS) regression fits, respectively. The dashed red and grey lines show the expected slopes for scaling under morphological and kinematic similarity and for 100% metric-specific weight support, respectively. (**D, H**) The relative contributions of allometric variations in wing morphology and kinematics to maintaining weight support across the studied range of hoverfly sizes, expressed by the relative allometric scaling factor a* (Equation 3). Contributions based on significant and non-significant OLS regressions are shown in dark and light grey, respectively. (A) The wingbeat-average vertical force scales linearly with the product of second-moment-of-area and wingbeat-average angular speed squared (Equation 1: $F \sim S_{2} {\bar{ω}}^{2}$ ), resulting in weight support across all sizes. (**B–D**) Separating this product into its main components (B and C, respectively) shows that the second-moment-of-area and wingbeat frequency contribute 81% and 22% to maintaining weight support across sizes, respectively (D). (**E–H**) Parting the contribution of second-moment-of-area into its components (**E–G**) shows that allometric variations in wingspan, mean chord, and normalised second-moment-of-area contribute 55%, 19%, and 9% to maintaining weight support across sizes, respectively (H).

Tables

Table 1

Results of phylogenetic generalised least squares (PGLS) regressions of the log10-transformed morphological and wingbeat kinematic parameters from the aerodynamic model (Equations 1 and 2) relative to log10-transformed body mass.

Estimated scaling factors of which the 95% confidence interval exclude the scaling factor for geometric similarity are indicated in bold and with a star, suggesting allometric scaling of that metric (see last column). The preceding two columns show the scaling factor for geometric or kinematic similarity, and the scaling factor for maintaining weight support across sizes via allometric changes of the specific parameter, assuming all other parameters scale under geometric and kinematic similarity.

	n	p	R²	Intercept	Scaling factor estimate [95% CI]	Scaling factor for similarity	Scaling factor for single-metric weight support	Allometry
Wing morphology
Second-moment-of-area S₂	28	<0.001	86%	–2.949	1.008 [0.767 - 1.250] *	4/3=1.33	1	Negative
Wingspan R	28	<0.001	84%	–0.479	0.255 [0.192 - 0.317] *	1/3=0.33	2/9 = 0.22	Negative
Wing chord c̄	28	<0.001	88%	–1.145	0.294 [0.229 - 0.359]	1/3=0.33	0	Isometry
Normalised second-moment-of-area S₂*	28	<0.001	34%	–0.413	–0.034 [–0.051 - –0.018] *	0	–1/3 = –0.33	Negative
Wingbeat kinematics
Wingbeat frequency f	8	0.427	9%	2.343	–0.084 [–0.161 - –0.063]	0	–1/6 = –0.17	–
Stroke amplitude $A_{Φ}$	8	0.785	1%	2.041	–0.017 [–0.134 - –0.101]	0	–1/6 = –0.17	–
Wing angular speed $\bar{ω}$	8	0.225	0%	10.161	–0.101 [–0.249 - –0.046]	0	–1/6 = –0.17	–
Angle-of-attack $\bar{α}$	8	0.105	22%	3.947	–0.085 [–0.174 - –0.002]	0	–1/3 = –0.33	–

Table 2

Results of ordinary least squares (OLS) regression between the log10-transformed vertical aerodynamic force estimated from computational fluid dynamics (CFD) and log10-transformed morphological and kinematics parameters, for all eight hoverfly species studied using CFD.

OLS regressions for metrics that scale significantly with aerodynamic force magnitude are indicated with a star, and have p-values in bold (p<0.05). For each tested parameter, we estimated its relative contribution to maintaining weight support across sizes using the relative allometric scaling factor a* (Equation 3), based on the estimated scaling factor, the scaling factor for geometric or kinematic similarity, and the expected scaling for maintaining metric-specific weight support.

	n	p	R²	Intercept	Scaling factor estimate [95% CI]	Scaling factor for similarity	Scaling factor for metric-specific weight support	Relative allometric scaling factor a*
$S_{2} \cdot {\bar{ω}}^{2}$	8	<0.001*	100%	3.593	0.989 [0.974 - 1.005]	4/3 = 1.33	1	103%
Second moment of area S₂	8	<0.001*	88%	–0.844	1.063 [0.667 - 1.461]	4/3 = 1.33	1	81%
Wingbeat frequency f	8	0.667	3%	2.218	–0.037 [–0.238 - 0.164]	0	–1/6 = –0.17	22%
Wingspan R	8	<0.001*	88%	0.058	0.272 [0.173 - 0.371]	1/3 = 0.33	2/9 = 0.22	55%
Wing chord c̄	8	0.001*	83%	–0.525	0.271 [0.147 - 0.394]	1/3 = 0.33	0	19%
Normalised second moment of area S₂*	8	0.055	48%	–0.504	–0.031 [–0.061 - 0.000]	0	–1/3 = –0.33	9%

Key resources table

Reagent type (species) or resource	Designation	Source or reference	Identifiers	Additional information
Biological sample (Ceriana conopsoides)	4 individuals	Leiden Biodiversity Center
Biological sample (Dorylomorpha sp.)	3 individuals	Leiden Biodiversity Center
Biological sample (Episyrphus viridaureus)	3 individuals	Wild (Wageningen University surroundings)
Biological sample (Eristalinus aeneus)	4 individuals	Leiden Biodiversity Center
Biological sample (Eristalis tenax)	10 individuals	Wild (Wageningen University surroundings)
Biological sample (Eupeodes nielseni)	4 individuals	Wild (Wageningen University surroundings)
Biological sample (Helophilus pendulus)	4 individuals	Leiden Biodiversity Center
Biological sample (Leucozona lucorum)	4 individuals	Leiden Biodiversity Center
Biological sample (Leucozona nigripila)	4 individuals	Leiden Biodiversity Center
Biological sample (Melangyna guttata)	4 individuals	Leiden Biodiversity Center
Biological sample (Melangyna lasiophthalma)	4 individuals	Leiden Biodiversity Center
Biological sample (Melanostoma dubium)	3 individuals	Leiden Biodiversity Center
Biological sample (Melanostoma mellinum)	10 individuals	Wild (Wageningen University surroundings)
Biological sample (Microdon analis)	3 individuals	Leiden Biodiversity Center
Biological sample (Myolepta dubia)	4 individuals	Leiden Biodiversity Center
Biological sample (Neoascia annexa)	4 individuals	Leiden Biodiversity Center
Biological sample (Neoascia geniculate)	4 individuals	Leiden Biodiversity Center
Biological sample (Pipizella viduata)	4 individuals	Leiden Biodiversity Center
Biological sample (Pipunculus campestris)	3 individuals	Leiden Biodiversity Center
Biological sample (Platycheirus albimanus)	4 individuals	Leiden Biodiversity Center
Biological sample (Platycheirus clypeatus)	3 individuals	Wild (Wageningen University surroundings)
Biological sample (Psilota atra)	4 individuals	Leiden Biodiversity Center
Biological sample (Senaspis elliotti)	3 individuals	Leiden Biodiversity Center
Biological sample (Sphaerophoria scripta)	4 individuals	Wild (Wageningen University surroundings)
Biological sample (Syrphus nigrilinearus)	6 individuals	Wild (Wageningen University surroundings)
Biological sample (Tropidia scita)	4 individuals	Wild (Wageningen University surroundings)
Biological sample (Volucella hyalinipennis)	3 individuals	Leiden Biodiversity Center
Biological sample (Volucella inanis)	4 individuals	Leiden Biodiversity Center
Software, algorithm	R	R	RRID:SCR_001905	R version 4.1.2
Software, algorithm	MATLAB	MATLAB	RRID:SCR_001622	MATLAB version 2021b

Additional files

Source data 1 Morphological data at the individual level.: https://cdn.elifesciences.org/articles/97839/elife-97839-data1-v1.csv
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Source data 2 Temporal dynamic of individual wingbeat kinematics and corresponding flight sequence metadata; the average kinematics per species.: https://cdn.elifesciences.org/articles/97839/elife-97839-data2-v1.zip
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Source data 3 Input data for the CFD simulations, including the average wingbeat kinematics, mean wing length and wing shape of the species studied with CFD.: https://cdn.elifesciences.org/articles/97839/elife-97839-data3-v1.zip
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Source data 4 Phylogenetic trees used in the study.: https://cdn.elifesciences.org/articles/97839/elife-97839-data4-v1.zip
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Source data 5 Mean wing shape for all 28 studied species.: https://cdn.elifesciences.org/articles/97839/elife-97839-data5-v1.zip
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Supplementary file 1 Supplementary tables 1a–d. (a) Results of analyses of variance (ANOVAs) testing the effect of sex and species on wing morphology parameters. (b) Phylogenetic signal computed on morphological and flight traits. Species number in the morphology and flight dataset is 28 and 8, respectively. (c) Results from multiple regressions testing correlations between the wingbeat kinematics parameters and body kinematics, expressed by flight speed and climb angle. (d) Results of phylogenetic generalised least squares (PGLS) regressions of additional wingbeat kinematic parameters against body mass.: https://cdn.elifesciences.org/articles/97839/elife-97839-supp1-v1.docx
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MDAR checklist: https://cdn.elifesciences.org/articles/97839/elife-97839-mdarchecklist1-v1.docx
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Camille Le Roy
Nina Tervelde
Thomas Engels
Florian T Muijres

(2025)

Adaptations in wing morphology rather than wingbeat kinematics enable flight in small hoverfly species

eLife 13:RP97839.

https://doi.org/10.7554/eLife.97839.4

Figures

The studied hoverfly species shown with their phylogenetic relationships.

The body mass of museum specimens was approximated using the relationship between thorax width and the fresh mass in wild-caught specimens.

Quantifying the in-flight wingbeat kinematics and wing morphology of hoverflies.

Wingbeat kinematics during hovering flight of the eight studied hoverfly species.

Derived wingbeat-average wing kinematics parameters for each studied species versus the body mass of that species.

The scaling of wing morphology with body mass for all 28 studied hoverfly species (A–D), and how allometric scaling of wing morphology contributes to maintaining weight support across the hoverfly size range (E, F).

Wing morphology parameters versus body mass for all studied specimens.

Changes in wing shape and size associated with body mass variation.

Result of geometric morphometrics analysis on the wing outlines of 28 hoverfly species; data per species.

Result of geometric morphometrics analysis on the wing outlines of 28 hoverfly species; data per individual.

Aerodynamic forces produced by hovering hoverflies, as estimated using computational fluid dynamics (CFD) simulations.

Temporal dynamics of the vertical aerodynamic forces produced during the wingbeat of the eight studied hoverfly species, estimated using computational fluid dynamics (CFD) simulations.

The relative contribution of allometric variations in wing morphology and wingbeat kinematics to computational fluid dynamics (CFD)-derived vertical aerodynamic force production, and how this contributes to maintaining in-hovering weight support across the sampled range of hoverfly sizes.

Tables

Results of phylogenetic generalised least squares (PGLS) regressions of the log10-transformed morphological and wingbeat kinematic parameters from the aerodynamic model (Equations 1 and 2) relative to log10-transformed body mass.

Results of ordinary least squares (OLS) regression between the log10-transformed vertical aerodynamic force estimated from computational fluid dynamics (CFD) and log10-transformed morphological and kinematics parameters, for all eight hoverfly species studied using CFD.

Additional files

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The studied hoverfly species shown with their phylogenetic relationships.

The body mass of museum specimens was approximated using the relationship between thorax width and the fresh mass in wild-caught specimens.

Quantifying the in-flight wingbeat kinematics and wing morphology of hoverflies.

Wingbeat kinematics during hovering flight of the eight studied hoverfly species.

Derived wingbeat-average wing kinematics parameters for each studied species versus the body mass of that species.

The scaling of wing morphology with body mass for all 28 studied hoverfly species (A–D), and how allometric scaling of wing morphology contributes to maintaining weight support across the hoverfly size range (E, F).

Wing morphology parameters versus body mass for all studied specimens.

Changes in wing shape and size associated with body mass variation.

Result of geometric morphometrics analysis on the wing outlines of 28 hoverfly species; data per species.

Result of geometric morphometrics analysis on the wing outlines of 28 hoverfly species; data per individual.

Aerodynamic forces produced by hovering hoverflies, as estimated using computational fluid dynamics (CFD) simulations.

Temporal dynamics of the vertical aerodynamic forces produced during the wingbeat of the eight studied hoverfly species, estimated using computational fluid dynamics (CFD) simulations.

The relative contribution of allometric variations in wing morphology and wingbeat kinematics to computational fluid dynamics (CFD)-derived vertical aerodynamic force production, and how this contributes to maintaining in-hovering weight support across the sampled range of hoverfly sizes.

Results of phylogenetic generalised least squares (PGLS) regressions of the log10-transformed morphological and wingbeat kinematic parameters from the aerodynamic model (Equations 1 and 2) relative to log10-transformed body mass.

Results of ordinary least squares (OLS) regression between the log10-transformed vertical aerodynamic force estimated from computational fluid dynamics (CFD) and log10-transformed morphological and kinematics parameters, for all eight hoverfly species studied using CFD.

Source data 1

Source data 2

Source data 3

Source data 4

Source data 5

Supplementary file 1

MDAR checklist

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