Nathan P. Myhrvold Growth and Metabolism Are Properties of In- Dividual Species

RESEARCH

◥ appropriately included Archaeopteryx as a dino- TECHNICAL COMMENT saur; it is taxonomically a bird, and its age-mass data require different treatment (6). It also has a disproportionate impact: minus Archaeopteryx, DINOSAUR PHYSIOLOGY r2 = 0.386 for dinosaurs. The analyses of Grady et al.(1) and Case (2) were based entirely on robust correlation in these Comment on “Evidence for regressions. However, the shear transformation creates an illusion; in reality, dinosaur data overlap every group except birds. Many extant groups mesothermy in dinosaurs” also overlap, including endotherms and ectotherms (Fig. 1). Nathan P. Myhrvold Growth and metabolism are properties of individual species. Classifying them by group av- Grady et al. (Reports, 13 June 2014, p. 1268) studied dinosaur metabolism by comparison erages (i.e., regression)—especially when r2 = of maximum somatic growth rate allometry with groups of known metabolism. They 0.386—commits a fundamental error in inference concluded that dinosaurs exhibited mesothermy, a metabolic rate intermediate between known as the “ecological fallacy” (7). endothermy and ectothermy. Multiple statistical and methodological issues call into Grady et al.(1) argued that Gmax determines question the evidence for dinosaur mesothermy. Maximum Growth Rate BMR [Case was skeptical (8)] and offered three lines of support. First, regressions of Gmax versus rady and co-workers (1) followed the meth- many species, they assume a value for M rather M seemed to classify endotherms and ectotherms; Nathan P. Myhrvold od of Case (2) to investigate dinosaur than using regression to estimate it, and/or they this is a fallacy, as discussed above. Second, meta- metabolism by using allometric scalingDoesadd hypothetical dataNot points for neonates. Determine Either bolic scaling theory predicts it; empirical evi- Dinosaur Metabolism of maximum growth rate Gmax with max- practice could distort estimates of Gmax and k. dence contradicts this theory, however (9). Third, imum body mass M to estimate basal Regression of Gmax versus M is inappropriate “[e]mpirical evidence (13) indicates that Gmax scales Gmetabolic rate BMR. They determined G for because kM/e has M as a factor. On a log-log similarly to B, where G = G Ma.” This suggests max max 0

extant and extinct species by fitting Gompertz scale, this relationship amounts to the geometric that BMRºGmax and thus that metabolic rate on October 6, 2015 −k t−t growth models m t Me−e ð 0Þ to age-mass shear transformation y → x + y, which com- may be inferred from growth (1). Statistical cor- ð Þ¼ data; k is a growth rate parameter, t0 is the in- presses data points along the line y = x (Fig. 1). relation, however, is not transitive (10), as a simple flection point, and Gmax = kM/e. Log-log regres- High correlation and low scatter is a geometric test reveals. Moreover, a comparison of the growth rates obtained from these data ries (fig. 6). This result challenges the idea that dinosaurs exhibited a meta- Abstract Statistical Problems b Biological Problems sions of Gmax versus M show little scatter and artifact of their chosen regression variable. It is well known (9) that BMR º M ,0:6 ≤ sets reveals a pronounced degree of overlap among dinosaurs and other an- bolic mode distinct from extant species. 2 imals groups in both the endothermic and ectothermic metabolic catego- Many previous studies have used growth rates to determine dinosaur correlation, which occurs because Gmax has M as an explicithigh rfactor.[Fig. 1 and fig. S1In in studies (1)], that classifying have claimed ex- to findThat evidence choice for isdinosaur unnecessary. mesothermy Grady et alpied. propose an intermediateb ≤ position,0:85. Regression which researchers of BMR interpretedand asG maxmesothermy.is thus In addition to statistical issues, studies of dinosaur metabolism face substan- biological problems in particular undermine confidence in the prior con- a a−1 metabolism. These studies compared the allometric scaling of maximum I show that when the correct variable (i.e., maximumtant mass-specific groups by endothermic[6, 7], or investigators ectothermic regressed me- averagesGmax of= GcMmax versus, in which averages case of Mk for cMpoly- . OneHowever, should my confoundedreanalysis of this because approachG andmax thehas underlyingM as a factor.data sets In- tial challenges imposed by fundamental constraints of biology. Three clusions about the metabolism of dinosaurs. ¼ k/e (1/y) k/e (1/y) growth rate (Gmax) as a function of maximum body mass (M) for dinosaurs growth rate rather than Gmax) is used in the regression,tabolism. available data The show dinosaur regressionphyletic groups falls of betweenspecies. They foundregress thatG themax endothermic= k/e (i.e., mass-specificgroups cluster rate)has identified versus severalstead, serious we muststatistical pair problemsBMR withthat callk/ ethese. I performed conclusions A 10-1 100 101 102 B 100 101 102 with the scaling for extant groups in order to classify dinosaur metabolism no correlation between growth rate and BMR. Moreover,these the practice two groups, of using which separately they call from mesothermy. ectothermic groupsM onto log-log estimate charts;c and dinosaura and groups to test occu this- hypothesis.into question [8, pairwise9]. Four distinct regressions kinds of statistical of k/e, M error, and are BMRinvolved., using 1 Metabolism cannot depend on the average of a polyphyletic group. as endothermic, ectothermic, or something in between (mesothermic). regressions across dinosaur taxa as a means to classify allGrady dinosaurset is al not. deviated from accepted statisti- This method, which predates Case (4) and is com- data sets from Grady et al.(1). The regressions of Birds (altricial)

Basalwww.sciencemag.org metabolic rate (BMR) is a characteristic inherent to an individual spe- average of growth rates spanning broad taxonomic groups such as families b cal practice in estimating G . Model selection mon in growth rate studies (5), yields identical k/e and M, and of BMR and M, yield moderately Kleiber’s Law holds that basal metabolic rate BMR = a M . Previous valid, for both statistical and biological reasons. max cies or taxon. The parameter has no valid meaning when estimated from an or orders. Birds (altricial) d studies have shown that, with reasonably high correlation, Gmax = c M with My reanalysis of previously published data sets inshould fact finds be that done the on a data set (species) basis (3); values for c and a but with much weaker correla- strong correlations, but effectively no correla- Birds (precocial) 2 roughly similar exponents 0.6 < b, d < 0.9, depending on the taxonomic growth rates of dinosaur taxa overlap with those of bothinstead endothermic they chose and a model1 by Choosing the mean Akaike thetions. wrong For example, regressionr = 0.798 for precocial variables birds yieldstion appears misleading between k/e and BMR results.(Fig. 2). 2 Growth rate can determine metabolism only at the level of species. group. It does not follow that Gmax is related to BMR, however, because ectothermic extant animals. I conclude that one cannotinformation determine the criterion across all species. For when using Gmax, but 0.513 when−1 using k/e. In conclusion, one cannot classify dinosaurs Birds (precocial) The maximum growth rate is obtained by using the equationG max = k M e , In fact, using M in the regression effectively applies a geometric shear Eutherians statistical correlation is not transitive. Prior studies used inappropriate regres- metabolism of either dinosaur or extant animal species by using growth- Using k/e with the dinosaur data in (1) yields as mesotherms on the basis of growth rate al- Animal species show a wide diversity of metabolic rates, and by definition There exists no mechanism by which the metabolic rate of an extant species where k is a growth-rate parameter.2 M is an inappropriate choice of regres- transformation, which produces high correlation and low scatter as an this diversity cannot be “inherited” by a broad taxonomic group over mil- can reach back through time to inform, via some shared ancestor, the meta- sion variables that confounded this relationship by introducing a spurious rate studies alone. Intellectual Ventures LLC, Bellevue, WA 98005, USA. r = 0.549. I found 11 errors in these dinosaur lometry. The growth rates of the dinosaur taxa sion variable because it is a factor in this equation and is thus inextricably2 artifact (fig. 1B). The inappropriate choice of regression variable thus con- Marsupials *E-mail: [email protected] data; when corrected, r = 0.514. Grady et al. in- studied by Grady et al.(1) match those of both lions of years of evolution—diversity means interspecies variation. bolic rate of a species on some other branch of the phylogenetic tree. Eutherians linked to Gmax. founds the analysis. Dinosaurs

Fig. 1. Data ranges 3Downloaded from The metabolic theory of ecology is not supported by empirical data. A B Crocodiles Marsupials Prior Work Built on “Case’s Method”—A Method Case forRejected taxonomic 9 The metabolic theory of ecology, widely applied in these studies, assumes Moreover, when empirical data for BMR and M are plotted on a semilog letters to nature 10 b Dinosaurs 21. Shipboard Scienti®c Party. Explanatory notes. Proc. ODP Init. Rep. 144, 20 (1995). substantially different rates12,13 and the relationship between local- groups. The convex GmaxGmax = = M M k/e k/e Squamates 22. Crowley, T. J. & Zachos, J. C. in Warm Climates in Earth History (eds Huber, B. T., MacLeod, K. G. & that a simple power law, such as BMR = a M , relates metabolism to maxi- chart, often the result is a complex curve, not the straight line that a power Wing, S. L.) 50±76 (Cambridge Univ. Press, Cambridge, 2000). ized measures of tissue formation rates and overall body growth are 14 BirdsAltricial( (altricial)a Birds 23. Sarmiento, J. L., Herbert, T. D. & Toggweiler, J. R. Causes of anoxia in the world ocean. Glob. untested for nearly all skeletal elements . Broader studies have Biogeochem. Cycles 2, 115±128 (1988). combined histological age assessments with size indices, but lacked Nearly all previous studies that use growth rates to analyze dinosaur metab- 24. Wolff, T., Mulitza,In S., Ruhlemann, fact, C. & Wefer, G. Response ofCase the tropical Atlantic thermocline was to late reliable troubled means to evaluate developmental bodyby mass 15.the fact that empirically there seemed to be 8 Quaternary trade wind changes. Palaeoceanography 14, 374±383 (1999). hulls of data points 25. Gale, A. S., Kennedy, W. J., Burnett, J. A., Caron, M. & Kidd, B. E. The late Albian to Early Cenomanian In most extant animals, mass changes with respect to age show 16 10 mum body mass. But the value of the exponent b used in published studies law should produce (fig. 4). succession at Mont Risou near Rosans (Drome, SE France): an integrated study (ammonites, sigmoidal patterns . Standardized comparisons of maximum Reptiles inoceramids, planktonic foraminifera, nannofossils, oxygen and carbon isotopes. Cret. Res. 17, 515± growth rates among phylogenetically and morphologically diver- 606 (1996). Sharks gent taxa can be made using values from the exponential stage of olism use methods that build on pioneering work by Ted J. Case [1], which no26. Stoll, H. M. &universal Schrag, D. P.High-resolution stable isotope records from thelaw Upper Cretaceous rocksrelating of 17,18 metabolic rate and body size—nor has one been development . Analyses of exponential growth among the major Italy and Spain: Glacial episodes in a greenhouse planet? Geol. Soc. Am. Bull. 112, 308±319 (2000). letters to nature from Grady et al.(1) 27. Smith, A. G., Smith, D. G. & Funnell, B. M. Atlas of Mesozoic and Cenozoic Coastlines (Cambridge groups of extant vertebrates indicate that rates absolutely increase varies considerably; it is now clear that no single value applies universally. Univ. Press, Cambridge, 1994). with respect to body mass and that each clade has characteristic 1 7 13 28. Hofmann, P.,Ricken, W., Schwark, R. L. & Leythaeuser, D. Carbon-sulfur-iron relationships in d C of 17 organic matter from late Albian sedimentary rocks from the North Atlantic Ocean: palaeoceano- rates . associated error as the sum of terms arising from nonlinear interactions between Acknowledgements We thank A. Thorpe and M. Allen for encouraging the development of this these later studies cite (fig. 1). Case’s own papers make clear, however, that he foundgraphic implications. Palaeogeogr. in Palaeoclimatol. the Palaeoecol. 163, 97±113 years (2000). since.To compare whole-body growth rates between the Dinosauria 10 10 29. Bemis, B. E., Spero, H. J., Bijma, J. & Lea, D. W. Reevaluation of the oxygen isotopic composition of and extant vertebrates, similarparameter quanti®ed perturbations data are and needed. noise This (natural variability) in the model simulations used to project. We also acknowledge many Hadley Centre colleagues for their advice on model planktonic foraminifera: Experimental results and revised palaeotemperature equations. Palaeocea- are plotted in terms requires growth series representingconstruct the the full predictions. range of dinosaur Both error size, terms were assumed to be independent of location in parameters and their uncertainty ranges, and for comments on earlier versions of the manuscript. nography 13, 150±160 (1998). shape and phylogeny, and accurate age and mass assessments at all 30. Poulsen, C. J., Barron, E. J., Peterson, W. H. & Wilson, P. A. A reinterpretation of mid-Cretaceous parameter space (and hence climate sensitivity). The first term was estimated by verifying This work was supported by the UK Department of the Environment, Food and Rural Affairs. Teleosts Fish shallow-marine temperatures through model-data comparison. Palaeoceanography 14, 679±697 (1999). ontogenetic stages. To ourour knowledge, statistical no predictionsstudy of growth against rates simulations has made with 13 model versions containing D.A.S. was funded by the NERC COAPEC thematic programme. BirdsBiPrecocial (precocial) Birds did not believe that metabolism can be deduced from growth rates (fig. 2). fully met these requirements. However, recent merging of bone multiple parameter perturbations and simulating climate sensitivities in the range 6 Acknowledgements histology and scaling principles has provided the requisite tools and of (A) k/e and (B) data for a single dinosaur (Psittacosaurus3.1–4.9 8C. The mongoliensis second term)14. At was last, estimated the from the long STD experiment (See Competing interests statement The authors declare that they have no competing financial We thank M. Cooper, M. Hall and K. Davis for laboratory assistance and manuscript 6 10 production; M. Arthur and E. Barron for comments on the manuscript; and D. Kroon, pieces are in place to assessSupplementary how dinosaurs reallyInformation). grew. Each of our 21 4 10 predictions of l was then interests. £ £ H. Elder®eld, J. Erbacher, B. Huber, L. Kump, B. Opdyke, C. Poulsen, G. Ravizza, We studied genera of non-avianexpressed dinosaurs as a gaussian that span distribution a diversity ofaccounting for its expected error. A PDF of feedback E. Rohling and N. Shackleton for support and discussions. This work was supported by a phylogeny, size and shape (Fig. 1). We included representatives from 6 NERC post-doctoral research fellowship and a UK ODP rapid response grant. strength was derived by combining the resulting 21 4 10 distributions, each weighted Correspondence and requests for materials should be addressed to J.M.M. most major dinosaurian clades, as well as taxa ranging in size from £ £ G . The blue grid Marsupialssupialsupials according to the probability of the relevant value of l .This was converted into a PDF of (james.murphy@metoffice.com). Correspondence and requests for materials should be addressed to P.A.W. tiny bipedal theropods to enormous quadrupedal sauropods. std max (e-mail: [email protected]). D D l Results climate sensitivity using T Q/ , giving the blue PDF in Fig. 3. The red PDF was 5 Notably, our sample also spans nearly the entire temporal¼ range 2 for non-avian dinosaurs,derived with the in the inclusion same manner, of taxa except from thatthe a further weighting of exp(20.5CPI ) was applied 10 -2 -1 0 1 2 3 4 5 -2 0 2 4 6 Early Jurassic to Late Cretaceousto each of periods. the gaussian We previously distributions gener- of l. Results from our 13 verifying multiple ated histological samplesperturbation and longevity experiments data for two showed dinosaurs that our statistical predictions of CPI were close to the illustrates the shear 6 14 ...... (Apatosaurus excelsus andsimulatedPsittacosaurus values and mongoliensis that the predictions), and of l carried a standard error of about SquamatesSququamuamatesess Log k/e (1/y) Log k/e (1/y) supplemented these data with histological22 21 growth series from ...... 0.15 Wm 3 K , arising mainly from4 the nonlinear effects of combining parameter Dinosaurian growth patterns the literature (Syntarsus rhodesiensis , Massospondylus29 carinatus and Maiasaura peeblesorumperturbations7). We also generated. a histological Gigantism and comparative 0 4 A reanalysis of the data on dinosaur growth and mass previously used to (fig. 5). Other researchers have similarly concluded that body mass and me- growth series for Shuvuuia deserti, a small, highly derived transformation that (1/y) and rapid avian growth rates Received 29 March; accepted 16 June 2004; doi:10.1038/nature02771. maniraptoriform theropod (Fig. 1)19. We assessed age from 10 (g/y) 10 Figure 6. Large groups of taxa do not divide cleanly into metabolic groups by growth rate. These (A) ref [1] and (B) ref [6]. Mean values for each group are indicated by capped bars. Shaded bands ² ³

Gregory M. Erickson*, Kristina Curry Rogers & Scott A. Yerby growth lines in histologically1. Gordon, prepared C. et specimens al. The simulation (Fig. 1) of SST, and sea ice extents and ocean heat transports in a version of the life-history parameters of e obtained mass estimates through the application of scaling Hadley Centre coupled model without flux adjustments. Clim. Dyn. 16, 147–168 (2000). / support claims of mesothermy [6, 7] finds that, when the errors mentioned tabolism are unrelated [11]. * Department of Biological Science and College of Medicine, Florida State techniques (see Methods).2. A Giorgi, sigmoidal F. & Francisco, equation R. Evaluating was used uncertainties to in the prediction of regional climate change. University, Tallahassee, Florida 32306-1100, USA model the growth of each species and least-squares regression tyrannosauridrelates dinosaursk/e to Gmax. k Geophys. Res. Lett. 27, 1295–1298 (2000). max histograms of mass-adjusted growth rates assume a fixed exponent of ¾ for data sets from highlight the growth rates that overlap among extant endotherms and ectotherms. Figure from ref. [4] ² Science Museum of Minnesota and Macalester College, analysis was used to ®t the curves to these data. Exponential PlacentalEutheriansEuthe Mammals 3. Allen, M. R. & Ingram, W. J. Constraints on future changes in climate and the hydrological cycle. 3 120 W. Kellogg Boulevard, St Paul, Minnesota 55102, USA stage growth rates were converted to daily growth rates using the Gregory M. Erickson1,2, Peter J. Makovicky3, Philip J. Currie4, ³ Department of Biomechanical Engineering, Stanford University, Stanford, Nature 419, 224–232 (2002).20 G appropriate number of days in the Mesozoic era . A regression 2 5 6 k/e (1/y) above are corrected, no meaningful correlation exists between max and California 94305, USA 10 G M line was ®tted to the maximum4. Cubasch, growth U. rateset al. in forClimate the dinosaurs Change 2001, to The Science of Climate Change Ch. 9 (eds Houghton, J. T. MarkThe A. Norell , Scott solid A. Yerby & Christopher black A. Brochu out- ...... enable comparisons with dataet al. from) 527–582 the (Cambridge literature Univ. for extant Press, Cambridge, 2001). 17,18 1 Gmax (g/y) Did dinosaurs grow in a manner similar to extant reptiles, vertebrates . 5. Allen, M. R., Stott, P. A., Mitchell, J. F. B., Schnur, R. & Delworth, T. L. Quantifying the uncertainty in Department of Biological Science, Florida State University, Tallahassee, Florida mammals or birds, or were they unique1? Are rapid avian Our analysis revealed that sigmoidal equations (Fig. 2) accu- forecasts of anthropogenic climate change. Nature 417, 617–620 (2000). 32306-1100, USA RESEARCH | REPORTS growth rates an innovation unique to birds, or were they inherited rately describe the growth data for the six dinosaurs we tested 2 from dinosaurian precursors2? We quanti®ed growth rates for a (0.885 # r2 # 1.0). Exponential-stage6. Mearns, growthL. O. et al. ratesin Climate ranged Change from 2001,3.4 The Science of Climate Change Ch. 13 (eds Houghton, J. T. Division of Paleontology, American Museum of Natural History, Central Park 2 A B 1 line encompasses all group of dinosaurs spanning the phylogenetic and size diversity to 14,460 g day- , with valueset positively al.) 739–768 correlating (Cambridge with Univ. increased Press, Cambridge, 2001). West at 79th Street, New York, New York 10024-5192, USA areas of downwelling across the 660 is consistent REFERENCES AND NOTES 27. T. J. Tenner, M. M. Hirschmann, A. C. Withers, P. 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Hirschmann, T. Tenner, C. Aubaud, A. C. Withers, 13 March 2014; accepted 12 May 2014 growth rates beyond that of its closest relatives. 10 10 10 tial melt at 410 km is expected (26, 27) where the 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 Phys. Earth Planet. Inter. 176, 54–68 (2009). 10.1126/science.1253358 Allometries of Maximum Growth Rate versus22. Gregory, Body J. M., Stouffer, Mass R. J., Raper, S. C. B., Stott, P. A. & Rayner, N. A. An observationally based Was Dinosaurian Physiology Inherited by Birds? partition coefficient of H2O between wadsleyite Stemming from more than a century of investigation, consider- and olivine is at least 5:1 (11). We can expect at at Maximum Growth Indicate That Non-Avianestimate ofDinosaurs the climate sensitivity. J. Clim. 15, 3117–3121 (2002).amining growthable setsrates understanding of of overlapvarious tyrannosaurid species osteology4, every myology (top5, neurol- 23. Anderson, T. L. et al. Climate forcing by aerosols—a hazy picture. Science 300, 110–111 (2003). Reconciling Slow Growth in Archaeopteryx least 5% partial melt in a bulk 1 wt % H2O perid- 6 7,8 3,9 10,11 otite system where the partition coefficient between 24. Barnett, T. P., Pierce, D. W. & Schnur, R. Detection of anthropogenic climate change in the world’s ogy , behaviour , physiology , physical capabilities and 1,6 2 3 4,6 1 Had Growth Rates Typical of Fast Growing Ectothermic Marsupials DINOSAUR PHYSIOLOGY 12,13 Gregory M. Erickson *, Oliver W. M. Rauhut , Zhonghe Zhou , Alan H. Turner , Brian D. Inouye , ringwoodite and silicate perovskite is 15:1 (11). Thus, oceans. Science 292, 270–274 (2001). phylogeny have been gained. Lacking are empirical data on MM (g)(g) MM (g) (g) 5 6 ) suggested possible connections between Dongyu Hu , Mark A. Norell production of up to 1% melt by dehydration melt- Sauropsids 25. Boer, G. J. & Yu, B. Dynamical aspects of climate sensitivity.leftGeophys. Res. Lett. 30, 1135 (2003). tyrannosaurid life history such as growth rates, longevity and 1 Birds (precocial) ¨ ¨ ing of hydrous ringwoodite viscously entrained into group except birds. 1 Department of Biological Science, Florida State University, Tallahassee, Florida, United States of America, 2 Bayerische Staatssammlung fur Palaontologie und Geologie 26. Stouffer, R. J. & Manabe, S. Response of a coupled ocean-atmosphere model to increasing 10 and Department of Earth and Environmental Sciences, LMU Munich, Mu¨nchen, Germany, 3 Key Laboratory of Evolutionary Systematics of Vertebrates, Institute of Jan Werner*, Eva Maria Griebeler somatic maturity (adult size) from which the developmental pos- the lower mantle is feasible. Evidence for mesothermy atmospheric carbon dioxide: sensitivity to the rate of increase. J. Clim. 12, 2224–2237 (1999). Vertebrate Paleontology & Paleoanthropology, Chinese Academy of Science, Beijing, China, 4 Department of Anatomical Sciences, Stony Brook University, Stony Brook, Birds (altricial) The density of hydrous melt near the top of Department of Ecology, Zoological Institute, University of Mainz, Mainz, Germany 27. Watterson, I. G. Interpretation of simulated global warminggrowth using a simple model. J.rate Clim. 13, andsibilities metabolism, for how T. rex attained but gigantism concluded can be formally tested. New York, United States of America, 5 Paleontological Institute, Shenyang Normal University, Shenyang, China, 6 Division of Paleontology, American Museum of Natural the lower mantle is uncertain, but it is likely Crocodiles History, New York, New York, United States of America in dinosaurs 202–215 (2000). Recent advances in techniques for determining the ages at death Figure 3. A convex hull surrounding data points published for several groups of animal species [1] But the choice of as a regression variable is inappropriate because regressing versus effectively buoyant with respect to the top of the lower M Gmax M 28. Senior, C. A. & Mitchell, J. F. B. The time-dependence of climate sensitivity. Geophys. Res. Lett. 27, (Not shown: monotremata3,14 and testudines.) 1 2,3 1 Abstract of dinosaurs by using skeletal growth line counts , coupled with mantle (28). Hence, we expect that the velocity John M. Grady, * Brian J. Enquist, Eva Dettweiler-Robinson, (w) (w) Crocodiles 3 BMR BMR 2685–2689 (2000). Abstract decreases imaged beneath the 660 are transient Natalie A. Wright,1 Felisa A. Smith1 We tested if growth rates of recent taxa are unequivocally separated between endotherms and ectotherms, and compared that the relationshipdevelopmental was size estimates unreliable, make quantitative on both growth-curve features resulting from ongoing downward flow these to dinosaurian growth rates. We therefore performed linear regression analyses on29. the Stainforth, log-transformed D. A. et maximum al. Evaluating uncertainty in the climate response to changing levels of greenhouse seems to show that data sets for dinosaurs ( ) overlap with several extant groups, whether adds an unnecessary shear transformation ( ) that artificially reduces scatter and inflates the reconstructions for dinosaurs feasible. These methods have been black outline blue grid in B BMR Background: Archaeopteryx is the oldest and most primitive known bird (Avialae). It is believed that the growth and through the 660 that is driven by sinking slabs Were dinosaurs ectotherms or fast-metabolizing endotherms whose activities were growth rate against log-transformed body mass at maximum growth for extant altricial birds,gases. precocialNature birds,(submitted). eutherians, energetic physiology of basalmost birds such as Archaeopteryx were inherited in their entirety from non-avialan dinosaurs. marsupials, reptiles, fishes and dinosaurs. Regression models of precocial birds (and fishes) strongly differed from Case’s in the lower mantle. Eventually, the slightly unconstrained by temperature? To date, some of the strongest evidence for endothermy 30. Allen, M. R. & Stainforth, D. A. Towards objective probabilistic climate forecasting. Nature 419, 228 used to study growth rates in two small theropods, a small and a This hypothesis predicts that the long bones in these birds formed using rapidly growing, well-vascularized woven tissue study (1978), which is often used to compare dinosaurian growth rates to those of extant vertebrates. For all taxonomic buoyant hydrous melt would percolate upward, comes from the rapid growth rates derived from the analysis of fossil bones. However, theoretical and empirical grounds (fig. 2). Nev- typical of non-avialan dinosaurs. groups, the slope of 0.75 expected from the Metabolic Theory of Ecology was statistically supported.(2002). To compare growth large ornithischian and a medium-sized and a gigantic sauropodo- 0 returning H2O to the transition zone (4). Dehy- these studies are constrained by a lack of comparative data and an appropriate energetic rates between taxonomic groups we therefore used regressions with this fixed slope and group-specific intercepts. On morph3. These data were used to derive a regression of body mass plotted in terms of k /e(A) or in terms of Gmax (B), where Gmax = M k/e. apparent correlation. Figure from ref. [8] Methodology/Principal Findings: We report that Archaeopteryx long bones are composed of nearly avascular parallel- dration melting has also been suggested to oc- framework. Here we compile data on ontogenetic growth for extant and fossil vertebrates, average, maximum growth rates of ectotherms were about 10 (reptiles) to 20 (fishes) times (in comparison to mammals) or 10 fibered bone. This is among the slowest growing osseous tissues and is common in ectothermic reptiles. These findings cur where hydrous wadsleyite upwells across including all major dinosaur clades. Using a metabolic scaling approach, we find that even 45 (reptiles) to 100 (fishes) times (in comparison to birds) lower than in endotherms.Supplementary While on average Information all taxa wereaccompanies the paper on www.nature.com/natureertheless,. manyagainst recent growth rate studies and to generalize on the broadly growth about non-avian Squamates Sharks Marsupials dispute the hypothesis that non-avialan dinosaur growth and physiology were inherited in totality by the first birds. the 410 and into the olivine stability field (3, 27). growth and metabolic rates follow theoretical predictions across clades, although some clearly separated from each other, individual growth rates overlapped between several taxa and even between endotherms Examining these findings in a phylogenetic context required intensive sampling of outgroup dinosaurs and basalmost birds. Experiments indicate that hydrous melt is grav- groups deviate. Moreover, when the effects of size and temperature are considered, and ectotherms. Dinosaurs had growth rates intermediate between similar sized/scaled-up772 reptiles and mammals, but a NATURE | VOL 430 | 12 AUGUST 2004 | www.nature.com/nature Our results demonstrate theThis presence content downloaded of a scale-dependent from 128.95.104.66 maniraptoran on Fri, 5 Dec histological 2014 12:42:56 continuum PM that Archaeopteryx and © 2004 Nature Publishing Group itationally stable atop the 410 (28), so once melt is dinosaur metabolic rates were intermediate to those of endotherms and ectotherms and much lower rate than scaled-up birds. All dinosaurian growth rates were within the range of extant reptiles and mammals, other basalmost birds follow. Growth analysisAll use forsubjectArchaeopteryx to JSTOR Termssuggests and Conditions that these animals showed exponential growth and were lower than those of birds. Under the assumption that growth rate and metabolic rate are indeed linked, our sciencemag.org 29 MAY 2015 VOL 348 ISSUE 6238 generated, it may remain or spread laterally rather closest to those of extant mesotherms. Our results suggest that the modern dichotomy of SCIENCE • 982-c rates like non-avialan dinosaurs, three times slower than living precocial birds, but still within the lowermost range for all results suggest two alternative interpretations. Compared to other sauropsids, the growth rates of studied dinosaurs clearly and metabolism of dinosaurs have built upon endothermic vertebrates. than maintaining a clear correlation with ongoing endothermic versus ectothermic is overly simplistic. indicate that they had an ectothermic rather than an endothermic metabolic rate. Compared to other vertebrate growth vertical flow patterns. Seismic detections of a low- rates, the overall high variability in growth rates of extant groups and the high overlap between individual growth rates of Conclusions/Significance: The unexpected histology of Archaeopteryx and other basalmost birds is actually consistent with velocity layer atop the 410 are common but lateral- ver the past few decades, the original char- cally similar to endothermic mammals and birds endothermic and ectothermic extant species make it impossible to rule out either of the two thermoregulation strategies retention of the phylogenetically earlier paravian dinosaur condition when size is considered. The first birds were simply ly sporadic beneath North America and globally acterization of dinosaurs by early paleon- (1–3). This debate is of more than heuristic inter- for studied dinosaurs. Case’s method, on the faulty assumption that it feathered dinosaurs with respect to growth and energetic physiology. The evolution of the novel pattern in modern forms Sharks (29, 30). The combination of dehydration melting tologists as lumbering, slow-metabolizing est; energy consumption is closely linked to life occurred later in the group’s history. –1 driven by downwelling across the 660 and up- ectotherms has been challenged. Recent history, demographic, and ecological traits (4). Citation: Werner J, Griebeler EM (2014) Allometries of Maximum Growth Rate versus Body Mass at Maximum Growth Indicate That Non-Avian Dinosaurs Had 10 welling across the 410 could create a long-term studies propose that dinosaurs were ca- Extant endothermic mammals and birds pos- Growth Rates Typical of Fast Growing Ectothermic Sauropsids. PLoS ONE 9(2): e88834. doi:10.1371/journal.pone.0088834 Citation: Erickson GM, Rauhut OWM, Zhou Z, Turner AH, Inouye BD, et al. (2009) Was Dinosaurian Physiology Inherited by Birds? Reconciling Slow Growth in H O trap in the transition zone (4). Opable of an active lifestyle and were metaboli- sess metabolic rates ~5 to 10 times higher than Editor: Andrew A. Farke, Raymond M. Alf Museum of Paleontology, United States of America 2 has been proven to apply universally. Archaeopteryx. PLoS ONE 4(10): e7390. doi:10.1371/journal.pone.0007390 Received April 24, 2013; Accepted January 17, 2014; Published February 25, 2014 Editor: Robert DeSalle, American Museum of Natural History, United States of America Copyright: ß 2014 Werner, Griebeler. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits Received June 6, 2009; Accepted September 16, 2009; Published October 9, 2009 1268 13 JUNE 2014 • VOL 344 ISSUE 6189 sciencemag.org SCIENCE unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Copyright: ß 2009 Erickson et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits 2 Funding: The project was financed by the 421 German Research Foundation (grant GR 2625/2-2). The funders had no role in study design, data collection and unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. analysis, decision to publish, or preparation of the manuscript. Regression is not transitive. Funding: This research was generously funded by an DFG grant RA 1012/4 to OWMR, NSF DBI 0446224 and EAR 04418649 grants to GME, an NSF ATOL 0228693 Competing Interests: The authors have declared that no competing interests exist. Teleosts grant to MAN, and the Major Basic Research Projects [2006CB806400] of MST of China to ZZ. The funders had no role in study design, data collection, and analysis, Teleosts decision to publish, or preparation of the manuscript. * E-mail: [email protected] Competing2009: Interests: The authors haveErickson, declared that no competing interests Rauhut exist. et al. [5] 2014: Grady, Enquist et al. [6] 2014: Werner & Griebeler [7] * E-mail: [email protected] –2 Introduction (mainly mammals and birds) were studied and compared to Case’s Some prior studies assume implicitly that regression is transitive: i.e., that known in statistics [10]. In the case of dinosaur data, results of regression / (1/y) / (1/y) 10 regression models [10,12,14]. However, different mathematical k e k e How fast does an organism grow? This is an important question methods were used to calculate growth rates of individuals; for this Avialae as a whole. (Although, whether that condition was Squamates Introduction because individual growth is linked to many life history traits. For reason, comparisons might be difficult between studies. Even comparable to living birds is a subject of debate [6,12–15].) example, age at sexual maturity and mortality rate in addition to within his study, Case [9] used different methods to determine The genesis of birds was a key event in vertebrate history. The We used dissecting microscopy to directly examine the long metabolic rate and reproductive output vary with age and body maximum growth rates of individuals from the studied taxonomic descendants of these animals have dominated aerial niches from bone periosteal and fracture surfaces spanning the entire size if it is valid to regress A on B and to regress B on C, then it must be valid analysis can differ greatly depending on the choice and order of the vari- mass [1–6]. The growth of an animal is determined by its energy –4 –2 –1 the Late Mesozoic until today, where they are the most speciose range of Archaeopteryx (Eichsta¨tt, Munich, Ottmann & Steil, groups. Today, more objective methods (in terms of mathematics) –3 intake (metabolic rate) and the allocation of metabolic energy to to estimate growth rates are available. 10 10 amniote clade (,10,000 species) [1,2]. Skeletal, feather, and London, and Solnhofen specimens; Table 1), the oldest known 10 10 individual growth and other demands, like maintenance and Case [9,10] used maximum absolute growth rate (AGR) to (g) behavioral evidence conclusively place birds within the evolution- bird [16]. (Note: we follow Chiappe’s (2) interpretation that all M reproduction [7,8]. Case [9,10] showed that endotherms have ary radiation of theropod dinosaurs, rightly making birds the only specimens are referable to a single species, Archaeopteryx lithographica; Figure 2. In his 1978 article,assess maximum Case growth and linkedplotted that to (asymptotic) growth body mass. rate versus body weight for species of many kinds (g) higher maximum growth rates than ectotherms, and suggested M living dinosaurs [2–4]. Growth patterns, revealed through long see Materials and Methods.) In the two largest individuals This is problematic because maximum growth can occur at to regress A on C as well. But this is demonstrably not the case, as is well ables used (fig. 6). that endothermy (in conjunction with high metabolic rates and BMR Residuals bone osteohistology can be traced phylogenetically through this different body mass (BM) proportions (e.g. at 30% and at 50% of delamination of cortical bone consistent with growth line interfaces parental care) accounts for this observation. Since Case’s [9,10] transition and used as a proxy for inferring physiological changes. asymptotic body mass) for species with similar asymptotic body –3 were found, as anticipated (Figure 2). However, all specimens papers, many studies have been released dealing with the growth Non-avialan dinosaur bones show a characteristic well-vascular- and noted substantial scattermasses. A higher that AGR of one prevents species compared to another assignment can of a simple relationship between the two. 10 unexpectedly showed exceptionally sparse longitudinal vasculari- rates of animals and an ever increasing amount of data on growth ized, rapidly formed woven-fibered matrix that is often interrupted result only because the maximum growth rate occurs at a higher zation visible on the periostal surfaces and within the semi- in extant vertebrates and non-avian dinosaurs is available today by growth lines [5–7] (Figure 1). Similar broad-scale histological transparent bones (Figure 3). Furthermore, transversely running body mass proportion, even if the relative growth rate (RGR) of –1 0 1 [11–13]. However, to the best of our knowledge, a comparison this species is the same as or lower than for the other species (RGR attributes have been reported in Mesozoic bird lineages close to fracture faces showed a circumferential fabric characteristic of the between different taxonomic groups, similar to Case [10], was 10 10 10 the base of the avialan tree [8–11] (Figure 1). This has contributed dense lamellar or parallel-fibered bone-types of living non- never done again. Only growth rates of single taxonomic groups to the paradigm that dinosaurian physiology is ancestral for dinosaurian reptiles [17].

PLOS ONE | www.plosone.org 1 February 2014 | Volume 9 | Issue 2 | e88834 C D k/e (1/y) PLoS ONE | www.plosone.org 1 October 2009 | Volume 4 | Issue 10 | e7390 2 2 why, in fact, should growth rate and R = 0.622 R = 0.034 Figure 7. BMR acts differently thanG max in that it can be cleanly separated between endothermic groups (blue in left chart, below dashed line in right chart) and exothermic groups. Figure from ref. [4] metabolic rate vary with body size at 3 Effects are not power laws. roughly the same rate? The answer is Many studies of animal metabolism assume that growth rate varies with body mass as a simple power law in which a constant exponent applies to References and Acknowledgements not at all obvious.... all organisms—or at least to all species within a broad taxonomic group. Researchers have mistakenly fit power-law functions to empirical measure- [1] T. J. Case. 1978. On the Evolution and Adaptive Significance of Postnatal Growth Rates in the Terrestrial Ver- [6] J. M. Grady, B. J. Enquist, E. Dettweiler-Robinson, N. A. Wright, F. A. Smith. 2014. Evidence for Mesothermy I conclude that an organism’s growth tebrates. The Quarterly Review of Biology, 53(3): 243–282. in Dinosaurs. Science, 344: 1268–1272. doi: 10.1126/science.1253143. ments without checking whether other functional forms produce even [2] G. M. Erickson, T. A. Tumanova. 2000. Growth Curve of Psittacosaurus mongoliensisOsborn (Ceratopsia: Psit- [7] J. Werner, E. M. Griebeler. 2014. Allometries of Maximum Growth Rate Versus Body Mass at Maximum rate is not solely determined by its met- better fits. In many cases, they do—and the best-fitting functions are- com tacosauridae) Inferred from Long-Bone Histology. Zoological Journal of the Linnean Society, 130(4): 551–566. Growth Indicate That Non-avian Dinosaurs Had Growth Rates Typical of Fast-Growing Ectothermic Saurop- doi:10.1111/j.1096-3642.2000.tb02201. sids. PLoS ONE, 9(2): e88834. doi:10.1371/journal.pone.0088834. abolic rate, although the evolutionary plex curves such as cubics, not simple exponentials. It is a statistical error to Figure 4. A reanalysis of growth and metabolic data presented by Werner and Griebeler [7] (left) and (B) by Grady et al. [6] (right) finds that the best fit for altricial birds, eutherians, and other groups BMR (w) BMR (w) [3] G. M. Erickson, K. C. Rogers, S. A. Yerby. 2001. Dinosaurian Growth Patterns and Rapid Avian Growth Rates. [8] N. P. Myhrvold. 2015. Comment on “Evidence for Mesothermy in Dinosaurs.” Science, 348: 982–983. fit data and claim a best fit has been found when only a subset of plausible Nature, 412: 429–433. doi:10.1038/35086558. doi:10.1126/science.1260061 achievement of endothermy seems to is not a simple power law but instead a cubic or some other complex curve [9]. Figures from ref. [9] functional forms have been tested. [4] G. M. Erickson, P. J. Makovicky, P. J. Currie, M. A. Norell, S. A. Yerby, C. A. Brochu. 2004. Gigantism and [9] N. P. Myhrvold. 2015. Dinosaur Metabolism and the Allometry of Maximum Growth Rate. In press. Comparative Life-History Parameters of Tyrannosaurid Dinosaurs. Nature, 430: 772–775. doi:10.1038/na- have resulted in lifting the physiological [10] K. P. Burnham, D. R. Anderson. 2002. Model Selection and Inference: A Practical Information-Theoretic Approach. restraints upon growth rate enough to ture02699. Springer-Verlag, New York. [5] G. M. Erickson, O. W. M. Rauhut, Z. Zhou, A. H. Turner, B. D. Inouye, D. Hu, M. A. Norell. 2009. [11] B. G. Lovegrove. 2009. Age at First Reproduction and Growth Rate are Independent of Basal Metabolic Rate Was Dinosaurian Physiology Inherited by Birds? Reconciling Slow Growth in . produce nearly a ten-fold increase over Archaeopteryx PLoS ONE, in Mammals. Journal of Comparative Physiology B, 179(4): 391–401. doi:10.1007/s00360-008-0322-4. 4 The ecological fallacy: averages can mislead. 4(10): e7390. doi:10.1371/journal.pone.0007390.

ectothermic growth rates. BMR and Gmax are both properties of individual species; if they are cor- when, as in the case of metabolism, characteristics are not actually shared k/e (1/y) k/e (1/y) Figure 5. Correlation is nontransitive among growth rate (k /e), metabolic rate (BMR), and maximum mass The author would like to acknowledge the assistance of J. Grady for providing data, and of W. Gibbs, A. Modoran, —Ted J. Case, 1978 [1] related, then that should occur at the single-taxon level—it applies only to among all members of the group. Such overgeneralization is an example (M). The dramatic differences in results that occur when one performs pairwise regression of these variables and D. Sivam in the creation of this report. No funding was sought for this research. individual species. Performing regressions on averages taken across wide of a famous problem in statistical inference known as the ecological fallacy M (g) M (g) is illustrated here. The correlations are moderately strong for BMR versus M (B) and k /e versus M (C), but groups of biologically distinct species can produce highly misleading results [10]. there is little correlation between BMR and k /e (D). Figure from ref. [8]

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