scientific correspondence

Enquist et al. reply — Energy equivalence, as ecosystems such as adjacent grasslands and influences the acquisition and allocation of originally defined1, was an empirical rela- forests, which have similar rates of resource resources and thereby affects the abun- tionship observed in animals: species differ- supply but are dominated by plants differ- dance, distribution and diversity of sizes. ing in body mass, M, by many orders of ing by many orders of magnitude in mass, Brian J. Enquist*, James H. Brown*, magnitude tend to have almost equal rates typically have similar rates of primary pro- Geoffrey B. West† of energy use per unit area by the popula- duction. This does not seem to have been The Santa Fe Institute, 1399 Hyde Park Road, tion, because of an inverse allometric scal- appreciated, despite work on relationships Santa Fe, New Mexico 87501, USA ing relationship between energy use by the between population density and plant size *Department of Biology, University of New Mexico, individual, or its metabolic rate, B, and the and between individual plant performance Albuquerque, New Mexico 87131, USA maximal population density, Nmax. Because and ecosystem productivity. †Theoretical Division, T-8, MS B285, ʷ 3/4 ʷ ǁ3/4 B M and Nmax M , energy use is We agree with Magnani that transpira- Los Alamos National Laboratory, ʷ 3/4 ǁ3/4ʷ 0 proportional to BNmax M M M . tion and plant metabolism are influenced Los Alamos, New Mexico 87545, USA

We have shown that this also holds for by local environmental conditions, espe- 1. Damuth, J. Nature 290, 699–700 (1981). 2 plants , namely that the allometric scaling cially when comparisons are made between 2. Enquist, B. J., Brown, J. H. & West, G. B. Nature 395, 163–165 8,9 of both B and Nmax appear to be the same as individuals of relatively similar size . This (1998). in animals. Further, we showed that the accounts, for example, for the nearly two 3. Yoda, K., Kira, T., Ogawa, H. & Hozumi, K. J. Biol. Osaka City Univ. 14, 107–129 (1963). scaling of population density, and the orders of magnitude variation in produc- 4. Franco, M. & Kelly, C. K. Proc. Natl Acad. Sci. USA 95, resulting energy equivalence, can be tivity of ecosystems dominated by similarly 7830–7835 (1998). explained by a simple model that assumes sized plants (our Fig. 4 in ref. 2); a good 5. Dewar, R. C. Ann. Bot. 71, 147–159 (1993). that plants grow until the allometric rates of example would be to compare Arctic tun- 6. West, G. B., Brown, J. H. & Enquist, B. J. Science 276, 122–126 (1997). resource use by the population equals the dra with tropical grassland. Organism tran- 7. Enquist, B. J., West, G. B. & Brown, J. H. in Scaling in Biology rate of resource supply. spiration and metabolism, however, are (eds Brown, J. H. & West, G. B.) (Oxford Univ. Press, in the In previous work, this was far from clear. even more strongly influenced by plant size press). The traditional explanation of the thinning (our Fig. 1). Thus, rates of xylem flux vary 8. Kozlowski, T. T. & Pallardy, S. G. Physiology of Woody Plants (Academic, New York, 1997). law was not based on rates of individual by only about two orders of magnitude as 9. Lambers, H., Chapin, F. S. I. & Pons, T. L. Plant Physiological resource use, but was thought to result from plant mass varies by 12 orders of magni- Ecology (Springer, New York, 1998). the geometric packing of canopies3 so that tude from the smallest herbs and seedlings 10.Schulze, E. D., Kelliher, F. M., Korner, C., Lloyd, J. & Leuning, R. ʷ ǁ2/3 Annu. Rev. Ecol. Syst. 25, 629–660 (1994). N M , or to be due to biomechanical to the largest trees. 11.Ehleringer, J. R. & Field, C. B. Scaling Physiological Processes: constraints and the accumulation of non- The rates of evaporation for ecosystems Leaf to Globe (Academic, New York, 1993). living material4 so that NʷMǁ3/4. None of (our Fig. 4) are near-maximal short-term these studies, including that of Dewar5, has rates measured for individuals of known predicted the scaling of individual resource size of different plant species under near- use. We not only make this explicit predic- optimal conditions. A few of these values Biostratigraphy of new tion, but also derive it from a model of are indeed higher than rates reported for resource distribution in plants with fractal- ecosystems averaged over longer periods of pterosaurs from China like branching structures6. months to years. Given this caveat, it is Dewar implies that energy equivalence impressive that our estimates obtained by Pterosaurs are represented in China by five reflects the fact that essentially all of the scaling up from individual plants (max, genera and some isolated bones ranging in light is intercepted by closed canopies, and 82.4 l mǁ2 per day; min, 1.0 l mǁ2 per day; age from the Middle Jurassic to the Late that growth rates of plants per unit of radia- mean, 16.3 l mǁ2 per day, s.d. 16.44) are Cretaceous period1,2. Four of these genera tion are invariant. We agree, and in fact this within an order of magnitude of the maxi- belong to the derived monophyletic sub- is a special case of our general argument. mum reported values. Most values fall group Pterodactyloidea; only the Middle Furthermore, we now have a detailed quan- within the range obtained using different Jurassic Angustinaripterus from Dashanpu, titative whole-plant model of resource dis- sampling techniques, including remote Sichuan, is a non-pterodactyloid (tradition- tribution from which the general derivation sensing, for estimating the productivity of ally ‘rhamphorhynchoids’, a paraphyletic of energy equivalence follows7. This model entire ecosystems10. taxon). Two further pterosaurs1,2 (Fig. 1) assumes that the size and photosynthetic We therefore disagree with Magnani’s from the Chaomidianzi Formation of the rate of leaves are independent of plant mass. objection to our extrapolation of the conse- Beipiao area, western Liaoning Province, It predicts the number of leaves to be pro- quences of allometric scaling at the level of occur in the Liaoning beds, several metres portional to B, which is proportional to individual plants to processes that operate higher than the compsognathid coelurosaur M3/4. This is exactly the condition needed to at the level of populations and ecosystems11. Sinosauropteryx and the basal bird Confu- give the density–mass relationship and Allometric relationships are not useful for ciusornis. Our analysis of these two fossils therefore energy equivalence. But our understanding small differences in perfor- and other components of the fauna suggest model is much more general because it also mance among similarly sized plants, such as a Late Jurassic biostratigraphic age for the applies to populations in which canopies forest trees following canopy closure. Liaoning beds, which are important in the are not closed and where water or nutrients, Allometry is invaluable, however, for study of avian origins. as well as light (as claimed by Dewar), are understanding the pervasive effects of plant One new pterosaur, Dendrorhynchus the critical limiting resources. size on such diverse phenomena as the curvidentatus1, is morphometrically most Dewar correctly observes that there may structure of single- and mixed-species similar to the Late Jurassic (Tithonian) be a slight decrease in production or growth stands, or on the productivity of ecosystems Solnhofen form Rhamphorhynchus but does following canopy closure during second- dominated by plants of contrasting size, not fit within that taxon. Principal compo- ary succession. But this is a point of detail. such as adjacent agricultural fields, grass- nents analysis (by K. I. Warheit and K. P.) The hundred-fold variation in resource use, lands and forests. Understanding quarter- (Fig. 2) of the long bones of various including any possible decline in produc- power allometric scaling relations at pterosaurs indicates that Dendrorhynchus tion associated with age, is very small different levels of biological organization clusters most closely with Rhampho- compared with the trillion-fold variation (in both plants and animals) will contribute rhynchus and has no obvious unique fea- in vascular plant size. We emphasized that to a common explanation of how body size tures, but its proportions differ from those

NATURE | VOL 398 | 15 APRIL 1999 | www.nature.com © 1999 Macmillan Magazines Ltd 573 scientific correspondence

Figure 1 The new Liaoning pterosaurs. a, Dendrorhyn- choides (“Dendrorhynchus”) curvidentatus n. g. (Ji & Ji, 1998) (holotype, National Geo- logical Museum of China GMV2128). Scale bar, 20 mm. b, Detail of D. curvidentatus skull. Scale bar, 20 mm. c, Pterodactylus (“Eosipterus”) yangi Ji & Ji, 1997 (holotype, GMV2117). Scale bar, 50 mm.

of the ontogenetic trajectories of Rhampho- through the entire section of the Yixian and Archaeopteryx, and the Liaoning form rhynchus. Instead, like Scaphognathus, it is Chaomidianzi formations is ambiguous. At Caudipteryx has been linked basally to these distinct at the generic level. The generic Sihetun (in the Beipiao area), fish, frogs, taxa3. Confuciusornis is the next most basal name Dendrorhynchus is preoccupied by a turtles, lizards and mammals have been bird known after Archaeopteryx. The nemertine3, so we propose replacing it with found, as well as theropod and sauropod coelurosaurian lineages therefore provide a the name Dendrorhynchoides. (saurischian) and psittacosaurid (ornith- biostratigraphic signal of sister-taxa rooted The second new fossil, Eosipterus yangi 2 ischian) dinosaurs6,7. Among the theropods, in the Late Jurassic. None of these specific (Fig. 1c), is a large pterodactylid with a Sinosauropteryx, Protarchaeopteryx, Caudi- genera is known from the Early Cretaceous, wingspan of about 1.25 metres. The incom- pteryx and Confuciusornis8–10 are of primary although related lineages persisted. plete fusion of the carpals and tarsals indi- importance to studies of the origins of birds The two new Liaoning pterosaurs pro- cates that this specimen, although large for and avian features. vide a similar signal by clustering with a pterodactylid, was not fully adult. A plot When exact faunal equivalents are not Late Jurassic relatives. Pterodactyloids are of the second and third principal compo- available, next-of-kin taxa can provide at known from both the Late Jurassic and the nents (the first was size) of the preserved least minimal divergence times. Psittaco- Cretaceous, but non-pterodactyloid ptero- long bones of Eosipterus (Fig. 2) groups saurid dinosaurs have so far been known saurs are not reliably known from any Cre- Eosipterus with the Late Jurassic Solnhofen only from the Early Cretaceous7, but the taceous deposits12. The Jurassic–Cretaceous pterodactylids Pterodactylus kochi, P. separation of these marginocephalians from transition among pterosaurs may therefore antiquus and Germanodactylus, which have other ornithischian dinosaurs was no later be sharper than in some other tetrapod fau- been viewed as part of a single ontogenetic than Early Jurassic, perhaps much earlier11. nal components, and the available data series4 of P. antiquus, with which Eosipterus Sinosauropteryx is the most closely related of from coelurosaurs and particularly ptero- may be synonymous. the Liaoning coelurosaurs to the Late Juras- saurs suggest a Late Jurassic age for the beds The age of the Liaoning beds has been sic basal coelurosaur Compsognathus from in which they are found. In contrast, the argued to be Late Jurassic or Early Creta- the Solnhofen limestones of Germany8. earliest Cretaceous faunas, such as that of ceous, and radiometric dates give conflict- Protarchaeopteryx3 is a basal maniraptoran, the Wealden, bear little resemblance to the ing results5. The biostratigraphy of the fauna as are avians such as the Solnhofen form Liaoning and Solnhofen faunas13. But the most basal Cretaceous faunas must be better 0.20 known before any biostratigraphic hypoth- esis can be considered iron-clad. 0.15 Campylognathoides S.-A. Ji, Q. Ji, K. Padian* 0.10 Ctenochasma National Geological Museum of China, Dendrorhynchoides Xisi, Beijing 100034, China 0.05 Dorygnathus *Department of Integrative Biology and Museum of Eosipterus 0 Gallodactylus Paleontology, University of California, Berkeley, PCA3 Germanodactylus California 94720-3140, USA —0.05 Pterodactylus e-mail: [email protected] Rhamphorhynchus —0.10 Scaphognathus 1. Ji, S.-A. & Ji, Q. Jiangsu Geol. 22, 199–206 (1998). 2. Ji, S.-A. & Ji, Q. Acta Geol. Sin. 71, 115–121 (1997). —0.15 3. Yin, Z. & Zeng, F. Oceanol. Limnol. Sin. 16, 323–335 (1995). 4. Bennett, S. C. J. Vert. Paleontol. 16, 432–444 (1996). —0.20 5. Ji, Q. et al. Prof. Pap. Stratigr. Paleontol. (in the press). —0.4 —0.3 —0.2 —0.10 0.1 0.2 0.3 0.4 0.5 0.6 6. Wang, X.-L. et al. Vert. PalAsiat. 36, 81–101 (1998). 7. Xu, X. & Wang, Y. Vert. PalAsiat. 36, 147–158 (1998). PCA2 8. Chen, P.-J., Dong, Z.-M. & Zhen, S.-N. Nature 391, 147–152 (1998). 9. Ji, Q., Currie, P. J., Norell, M. A. & Ji, S.-A. Nature 393, 753–761 Figure 2 Principal components analysis (PCA). PCA plot of second and third major axes, comparing radius, (1998). wing metacarpal, first two wing phalanges, and tibia in Campylognathoides, Ctenochasma, Dendrorhyn- 10.Hou, L.-H., Martin, L. D., Zhou, Z.-H. & Feduccia, A. Science choides1, Dorygnathus, “Eosipterus”2, Gallodactylus, Germanodactylus, Pterodactylus, Rhamphorhynchus 274, 1164–1167 (1996). and Scaphognathus. Dendrorhynchoides differs significantly from Rhamphorhynchus along the third major 11.Padian, K. in Encyclopedia of Dinosaurs (eds Currie, P. J. & Padian, K.) 549 (Academic, San Diego, 1997). axis; “Eosipterus” falls within the cluster of points of the congenerics Pterodactylus, Germanodactylus and 12.Padian, K. Modern Geol. 23, 57–68 (1998). 4 Ctenochasma for pairwise comparisons of PCAs 1–3, and so is probably a large specimen of Pterodactylus 13.Norman, D. B. in Encyclopedia of Dinosaurs (eds Currie, P. J. & (including Germanodactylus). Padian, K.) 783–785 (Academic, San Diego, 1997).

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