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Supplemental Information: 150 million years of sustained increase in flight efficiency

Chris Venditti, Joanna Baker, Michael J. Benton, Andrew Meade and Stuart Humphries

Supplemental Table 1 Table S1. Species included in analyses.

Wingspan

Data

Phylogenetic inference

from

from

Henderson [S1]

Benson Species Name

et al. et

[S2]

Dimorphodon macronyx ranzii ningchengensis buffarinii muensteri pilosus santanae weii longiceps Pterodactylus antiquus guinazui northropi* longicristatus Eudimorphodon rosenfeldi Campylognathoides liasicus Campylognathoides zitteli crassirostris Darwinopterus modularis Wukongopterus lii Pterorhynchus wellnhoferi Elanodactylus prolatus Eosipterus yangi chenianus Boreopterus cuiae Cycnorhamphus suevicus Ardeadactylus longicollum Pterodactylus kochi cristatus Germanodactylus rhamphastinus Haopterus gracilis Huaxiapterus corollatus Eopteranodon lii Huaxiapterus jii dongi Chaoyangopterus zhangi Jidapterus edentus Eoazhdarcho liaoxiensis Shenzhoupterus chaoyangensis Eudimorphodon cromptonellus Peteinosaurus zambellii schesaplanensis filisurensis Austriadactylus cristatus Parapsicephalus purdoni Sericipterus wucaiwanensis Angustinaripterus longicephalus Harpactognathus gentryii Cacibupteryx caribensis Qinglongopterus guoi Nesodactylus hesperius banthensis Changchengopterus pani volans ammoni Dendrorhynchoides curvidentatus Kryptodrakon progenitor subulatus Gnathosaurus macrurus Plataleorhynchus streptophorodon quingyangensis Moganopterus zhuiana Kepodactylus insperatus elegans Ctenochasma porocristata Gegepterus changae youngi Gallodactylus canjuersensis Normannognathus wellnhoferi Anhanguera piscator Anhanguera blittersdorffi Anhanguera araripensis Liaoningopterus gui mesembrinus clavirostris simus araripensis sibbicki Guidraco venator Zhenyuanopterus longirostris atrox Hongshanopterus lacustris Lonchodectes compressirostris Nurhachius ignaciobritoi Liaoxipterus brachyognathus sinensis Istiodactylus latidens Longchengopterus zhaoi Pteranodon sternbergi gracilis Nyctosaurus lamegoi Muzquizopteryx coahuilensis navigans Tupandactylus imperator Bakonydraco galaczi Europejara olcadesorum Huaxiapterus benxiensis Sinopterus gui crypticus Bennettazhia oregonensis Domeykodactylus ceciliae Noripterus parvus Noripterus complicidens Tupuxuara leonardii sethi linhaiensis Azhdarcho lancicollis Arambourgiania philadelphiae * Removed from main analyses (see main text).

Supplemental Table 2

Table S2. Parameters for the flight model. Parameters Value and/or units Source

Wingspan, b m Data

Body mass, M kg Data

2 Projected frontal area of body, Sbody m Data

2 Wing area, Swing m Data

Body drag coefficient, Cd 1.25 Flight v1.25 [S3]

Flight muscle efficiency, EFM 0.23 Flight v1.25 [S3]

Induced power factor, k 1.2 Flight v1.25 [S3]

0.624 -1 Metabolic power, PBMR 3.277 x M W (J s ) London et al 2014 [S4]*

Constants

Air density, ρ 1.23 kg m−3

Gravitational acceleration, g 9.81 m s-2

*OLS regression of Log(PBMR) on Log(M) using their full dataset (n = 526 observations of 491 species, r2 = 0.904, p < 0.0001).

Supplemental Experimental Procedures

Phylogenetic Inference

All morphological data was obtained from the phylogenetic character matrix of Andres et al. [S5]. However, we retained only discrete morphological characters, excluding all continuously varying morphology and treating all ordered characters as unordered, resulting in a total of 185 discrete morphological characters coded for 109 pterosaur species.

We constructed a posterior sample of time-calibrated phylogenetic trees for using the birth-death serial-sampling model [S6, S7] as implemented in BEAST v2 [S8] which allows for simultaneous estimation of both the topology and divergence times. For each species, we tip-dated using the midpoint of the stratigraphic age representing the first appearance of each species using the time intervals summarized by Benson et al. [S2] (stratigraphic age for Kryptodracon progenitor was taken from Andres et al. [S5]). The origin of the birth-death process was estimated from a uniform prior distribution ranging from the age of the youngest species in the tree (Eudimorphodon rosenfeldi) and an arbitrary upper limit of 350 Ma.

Owing to the lack of information about speciation and rates in the pterosaur literature we took a conservative approach by placing a wide uninformative prior distribution (uniform ranging between 0 and infinity) on both the effective reproductive number (the birth- death ratio) and the “become uninfectious rate” (total death rate). Similarly, we placed an uninformative uniform prior between 0 and 1 on the sampling proportion. Together, these parameters enable direct estimation of the birth-death rates throughout the phylogenetic tree [S6, S9].

We modelled rate heterogeneity across lineages using an uncorrelated relaxed morphological clock [S10]. We placed an exponential prior (mean = 1) on the mean of the lognormal distribution from which the branch-wise clock rates are drawn, and a gamma prior (α = 0.5396, β = 0.3819) on the standard deviation. Characters were partitioned on the basis of the number of discrete states, and Lewis’ Markov k (Mk) model of morphological character evolution [S11] was applied across all partitions, estimating a shared gamma shape parameter (Γ4) [S12] using an exponential prior distribution with mean = 1.

The MCMC chain was run for 1 billion iterations, sampling every 100,000 iterations after convergence. To produce the posterior sample of 1,000 phylogenetic trees used in the main analyses, we randomly sampled 1,000 iterations from this chain, ensuring that all parameters had an effective sample size of >750, calculated using Tracer v1.6 [S13]. We ensured that all parameters that were estimated using a uniform uninformative prior (origin, effective reproductive number, become uninfectious rate, and the sampling rate) returned a posterior distribution of estimates that differed from the prior. The analysis was repeated multiple times to ensure convergence was reached. All chains were inspected visually using Tracer v1.6 [S13].

After constructing our posterior sample of phylogenetic trees, we extended the terminal branches to correspond with the midpoint of the last appearance interval for each species. Our first-appearance dating approach coupled with this post-hoc extension of lineages ensures that our branch lengths represent the full known range of every species in the tree. The full sample is visualized in Figure 1A as a density tree produced in R [S14] using functions available in the package phangorn [S15], and is available to download in nexus format as Supplementary Data 1 of this article.

Imputation of pterosaur measurements

To calculate our efficiency index (see below) we require mass, frontal area and wing area for adult pterosaur species. Estimates for these are available for 12 species (Table S1 and Henderson [S1]). Adult wingspan is available for these 12 species plus an additional 26 species [S2; Table S2]. Using the phylogenetic method outlined in Organ et al 2007 [S16] we imputed a posterior sample of 1000 estimates of mass, frontal area and wing area for these 26 species (Table S1) based on each morphology’s relationship with wingspan (i.e. using a phylognetic regression of each morphology against wingspan).

Estimation of energetic efficiency

A number of energetic efficiency measures exist [S17] but one useful proxy is the inverse of the mass specific Cost of Transport (CoT, the energy required to move a unit mass a unit distance, independent of the time taken to do so). We estimate CoT as PBMR/(V x M) where V is the least energetically expensive travel speed (i.e. Vmp) and other parameters are as in Table S2.

For the 12 species with available data (Table S1 and Henderson [S1]) we produce a single estimate of CoT-1 using the above formula. For each of the 26 species for which we imputed mass, frontal area and wing area (Table S1 and above), we use the full sample of our imputed values to produce a posterior sample of 1000 estimates of CoT-1.

As formulated, CoT accounts for mass, however, as energy efficiency appears to increase with body size [S18, S19] we included size in our regression model of CoT-1 through time (main text and see below) to account for this.

Flight energetics model

Animal powered flight energetics, while perhaps kinematically different for bats, birds and pterosaurs are still ultimately constrained by physics. It has previously been demonstrated that it is possible to infer flight performance of pterosaurs [S20] using biophysical models of flight in combination with metabolic scaling estimates from birds. Here we used an actuator- disc based model owing to the pedigree of this approach and because more complex wake dynamics models and computational approaches are particularly difficult to parameterize, and require a number of kinematic parameters such as wingbeat frequency that are impossible to infer from fossil material. We used a modified version of Pennycuick’s Flight model (v1.25; [S3]) that we developed from Humphries et al. [S20] and implemented in Matlab® [S21], and which includes parasite power estimates from Ward et al. [S22]. The model produces a U-shaped power to airspeed relationship, from which a minimum power speed (Vmp) can be calculated. This Vmp is the least energetically expensive flight speed and so provides a useful proxy for efficiency [S17] when incorporated into the CoT.

We used the model to estimate the metabolic and mechanical power required for powered (flapping) flight given information on a minimal set of morphological traits and estimates of physiology, as well as aerodynamic constants (Table S2). The intersection of the power curve with an ’s available metabolic power (calculated from mass and estimated basal metabolic rate, BMR) allows us to characterise flight ability [S3, S23]. Consistent with current thought [S24, S25], and in line with previous studies [S20], we assume that pterosaurs had a BMR similar to that of birds.

Phylogenetic regression models testing temporal trends in mass and efficiency

To test the evolutionary trajectories of pterosaur mass and CoT-1 through time we use phylogenetic generalized least squares [S26, S27] multiple regression models in a Bayesian framework. We assessed the significance of regression parameters using the proportion of the posterior distribution that crosses zero, 푃푥, where we consider 푃푥 < 0.05 as significant. In addition to the 12 species for which we have single estimates of body mass and CoT-1 [S1], in all of our models we include the full set of posterior estimates of both body mass and CoT-1 for the 26 species for which the data are imputed. These values are sampled in proportion to their probability during the running of the MCMC chain. This allows us to incorporate information about the variance of our imputations, avoiding problems associated with summarizing the posterior distribution into a single point estimate.

Supplemental References S1. Henderson, D.M. (2010). Pterosaur body mass estimates from three-dimensional mathematical slicing. J. Vert. Paleont. 30, 768-785. S2. Benson, R.B.J., Frigot, R.A., Goswami, A., Andres, B., and Butler, R.J. (2014). Competition and constraint drove Cope's rule in the evolution of giant flying reptiles. Nat. Commun. 5. S3. Pennycuick, C.J. (2008). Modelling the Flying Bird, Volume 5, (Canada: Elsevier). S4. Londoño, G.A., Chappell, M.A., Castañeda, M.d.R., Jankowski, J.E., and Robinson, S.K. (2014). Basal metabolism in tropical birds: latitude, altitude, and the ‘pace of life’. Funct. Ecol. 29, 338-346. S5. Andres, B., Clark, J., and Xu, X. (2014). The earliest pterodactyloid and the origin of the group. Curr. Biol. 24, 1011-1016. S6. Stadler, T. (2010). Sampling-through-time in birth–death trees. J. Theor. Biol. 267, 396-404. S7. Stadler, T., Kühnert, D., Bonhoeffer, S., and Drummond, A.J. (2013). Birth–death skyline plot reveals temporal changes of epidemic spread in HIV and hepatitis C virus (HCV). Proc. Natl. Acad. Sci. U.S.A. 110, 228-233. S8. Bouckaert, R., Heled, J., Kühnert, D., Vaughan, T., Wu, C.-H., Xie, D., Suchard, M.A., Rambaut, A., and Drummond, A.J. (2014). BEAST 2: a software platform for Bayesian evolutionary analysis. PLoS Comput. Biol. 10, e1003537. S9. Stadler, T., Kouyos, R., von Wyl, V., Yerly, S., Böoni, J., Bürgisser, P., Klimkait, T., Joos, B., Rieder, P., and Xie, D. (2011). Estimating the basic reproductive number from viral sequence data. Mol. Biol. Evol. 29, 347-357. S10. Drummond, A.J., Ho, S.Y.W., Phillips, M.J., and Rambaut, A. (2006). Relaxed phylogenetics and dating with confidence. PLoS Biol. 4, e88. S11. Lewis, P.O. (2001). A likelihood approach to estimating phylogeny from discrete morphological character data. Syst. Biol. 50, 913-925. S12. Yang, Z. (1994). Maximum likelihood phylogenetic estimation from DNA sequences with variable rates over sites: approximate methods. J. Mol. Evol. 39, 306-314. S13. Rambaut, A., Suchard, M.A., Xie, D., and Drummond, A.J. (2015). Tracer v1. 6. 2014. S14. R Core Team (2015). R: A language and environment for statistical computing. (R Foundation for Statistical Computing). S15. Schliep, K.P. (2011). phangorn: phylogenetic analysis in R. Bioinformatics 27, 592- 593. S16. Organ, C.L., Shedlock, A.M., Meade, A., Pagel, M., and Edwards, S.V. (2007). Origin of avian genome size and structure in non-avian dinosaurs. Nature 446, 180-184. S17. Taylor, G., and Thomas, A. (2014). Evolutionary biomechanics: selection, phylogeny, and constraint, (New York, USA: Oxford University Press). S18. Alexander, R.M. (2005). Models and the scaling of energy costs for locomotion. J. Exp. Biol. 208, 1645-1652. S19. Bale, R., Hao, M., Bhalla, A.P.S., and Patankar, N.A. (2014). Energy efficiency and allometry of movement of swimming and flying . Proc. Natl. Acad. Sci. U.S.A. 111, 7517-7521. S20. Humphries, S., Bonser, R.H.C., Witton, M.P., and Martill, D.M. (2007). Did pterosaurs feed by skimming? Physical modelling and anatomical evaluation of an unusual feeding method. PLoS Biol. 5, e204. S21. MATLAB R2017a (2017). The MathWorks Inc., (Natick, MA). S22. Ward, S., Möller, U., Rayner, J.M., Jackson, D.M., Bilo, D., Nachtigall, W., and Speakman, J.R. (2001). Metabolic power, mechanical power and efficiency during wind tunnel flight by the European starling Sturnus vulgaris. J. Exp. Biol. 204, 3311- 3322. S23. Pennycuick, C.J. (1989). Bird Flight Performance, (Oxford University Press, USA). S24. Clarke, A. (2013). Dinosaur Energetics: Setting the Bounds on Feasible Physiologies and Ecologies. Am. Nat. 182, 283-297. S25. Pontzer, H., Allen, V., and Hutchinson, J.R. (2009). Biomechanics of running indicates endothermy in bipedal dinosaurs. PLoS ONE 4, e7783. S26. Pagel, M. (1997). Inferring evolutionary processes from phylogenies. Zoologica Scripta 26, 331-348. S27. Freckleton, R.P., Harvey, P.H., and Pagel, M. (2002). Phylogenetic analysis and comparative data: A test and review of evidence. Am. Nat. 160, 712-726.