Journal of Mammalian Evolution

, Volume 23, Issue 1, pp 17–31 | Cite as

Body Weight and Relative Brain Size (Encephalization) in Eocene Archaeoceti (Cetacea)

  • Philip D. Gingerich
Original Paper


Calibration of the Brownian diffusion model of Felsenstein indicates that phylogeny may have an influence on body length and other phenotypic measures in Cetacea for as many as 10,000 generations or about 180,000 years, which is negligible in the 35 million year history of extant Cetacea. Observations of phenotypic traits in cetacean species living today are independent of phylogeny and independent statistically. Four methods for estimating body weight in fossil cetaceans are compared: (1) median serial regression involving a set of multiple regressions of log body weight on log centrum length, width, and height for core vertebrae; (2) regression of log whole body weight on log body length for individuals; (3) regression of log whole body weight on log body length for species means; and (4) regression of log lean body weight on log body length for individuals. These yield body weight estimates for the Eocene archaeocete Dorudon atrox of 1126, 1118, 1132, and 847 kg, respectively, with consistency and applicability to partial skeletons favoring the first approach. The whole-body weight expected, Pe (in kg), for a given body length, Li (in cm), is given by log10 Pe = 2.784 • log10 Li − 4.429. Negative allometry of body weight and body length (slope 2.784 < 3.000) means that small cetaceans are shorter and more maneuverable than expected for their weight, while large cetaceans are longer and more efficient energetically than expected for their weight. Encephalization is necessarily quantified relative to a reference sample, most mammals are terrestrial, and terrestrial mammals provide a logical baseline. The encephalization residual for living terrestrial mammals as a class (ERTC), is the difference between observed log2 brain weight (Ei in g) and expected log2 brain weight (Ee in g), where the latter is estimated from body weight (Pi in g), as log2 Ee = 0.740 • log2 Pi − 4.004. ERTC is positive for brains that are larger than expected for a given body size, and negative for brains that are smaller than expected. Base-2 logarithms make the ERTC scale intuitive, in uniform units of halving or doubling. Encephalization quotients (EQ) are unsuitable for comparison because they are proportions on a non-uniform scale. Middle Eocene archaeocetes have ERTC values close to −2 (two halvings compared to expectation), while late Eocene archaeocetes have ERTC values close to −1 (one halving compared to expectation). ERTC is not known for fossil mysticetes, but living mysticetes have ERTC values averaging about −2. Oligocene-Recent odontocetes appear to have ERTC values averaging about +1 (one doubling compared to expectation) through their temporal range. Definitive interpretation of the evolution of encephalization in Cetacea will require better documentation for Oligocene–Recent mysticetes and odontocetes.


Allometry Archaeoceti Encephalization residual ER Remingtonocetidae Protocetidae Basilosauridae 



Publication was prompted by Marino et al. (2003), who noted that the computer program of Gingerich (1998) for estimating body weight in fossil cetaceans was still unpublished. This was rewritten in R to carry out the analyses presented here (Online Resource 2). I thank Bruce D. Patterson, Field Museum of Natural History, and Philip Myers, University of Michigan Museum of Zoology, for access to mammal specimens in their care. John L. Gittleman checked several questionable published measurements, and Graham A. J. Worthy supplied important marine mammal references. Michael Foote, Gregg Gunnell, Serge Legendre, and Philip Myers read early versions of the manuscript. Two anonymous reviewers made suggestions and raised questions that improved the text substantially.

Supplementary material

10914_2015_9304_MOESM1_ESM.xlsx (20 kb)
Online Resource 1 Measurements of vertebral centra for eleven extant marine mammals used to predict body weight from centrum length, centrum width, and centrum height. (XLSX 19 kb)
10914_2015_9304_MOESM2_ESM.pdf (18 kb)
Online Resource 2 R script used to predict body weight in Eocene Archaeoceti from vertebral centrum length, centrum width, and centrum height. (PDF 18 kb)
10914_2015_9304_MOESM3_ESM.xlsx (12 kb)
Online Resource 3 Measurements of vertebral centrum length, centrum width, and centrum height used to predict body weight for the Eocene basilosaurid archaeocete Dorudon atrox. (XLSX 11 kb)
10914_2015_9304_MOESM4_ESM.xlsx (116 kb)
Online Resource 4 Measurements of body length (meters) and body weight (metric tonnes) for 1711 individuals representing all 12 or 13 families, 32 genera, and 59 species of extant cetaceans. When available , weights of blubber, meat, bone, and viscera (metric tonnes) are included. (XLSX 116 kb)


  1. André JM, Ribeyre F, Boudou A (1990) Relation entre l’âge, la longueur totale, le poids total et le poids des organes chez trois espèces de dauphins de la zone torpicale est de l’océan Pacifique. Mammalia 54:479–488. doi: 10.1515/mamm.1990.54.3.479 CrossRefGoogle Scholar
  2. Barnes LG, Mitchell ED (1978) Cetacea. In: Maglio VJ, Cooke HBS (eds) Evolution of African Mammals. Harvard University Press, Cambridge, pp 582–602Google Scholar
  3. Bauchot R (1978) Encephalization in vertebrates: a new mode of calculation for allometry coefficients and isoponderal indices. Brain Behav Evol 15:1–18. doi: 10.1159/000123769 CrossRefPubMedGoogle Scholar
  4. Bigg MA, Wolman AA (1975) Live-capture killer whale (Orcinus orca) fishery, British Columbia and Washington, 1962–73. J Fish Res Bd Can 32:1213–1221. doi: 10.1139/f75-140 CrossRefGoogle Scholar
  5. Brownell RL, Findley LT, Vidal O, Robles A, Silvia Manzanilla N (1987) External morphology and pigmentation of the vaquita, Phocoena sinus (Cetacea: Mammalia). Mar Mammal Sci 3:22–30. doi: 10.1111/j.1748-7692.1987.tb00149.x CrossRefGoogle Scholar
  6. Buchholtz EA (2001) Vertebral osteology and swimming style in living and fossil whales (Order: Cetacea). J Zool 253:175–190. doi: 10.1017/S0952836901000164 CrossRefGoogle Scholar
  7. Camphuysen CJ, Smeenk C, Addink M, Grouw Hv, Jansen OE (2008) Cetaceans stranded in the Netherlands from 1998 to 2007. Lutra 51:87–122Google Scholar
  8. Cockcroft VG, Ross GJB (1990) Age growth and reproduction of bottlenose dolphins Tursiops truncatus from the east coast of southern Africa. Fish Bull 88:289–302Google Scholar
  9. Enders RK (1942) Notes on a stranded pigmy sperm whale (Kogia breviceps). Not Nat Acad Nat Sci Phila 111:1–6Google Scholar
  10. Felsenstein J (1985) Phylogenies and the comparative method. Am Nat 125:1–15. CrossRefGoogle Scholar
  11. Fordyce RE (2002) Simocetus rayi (Odontoceti: Simocetidae, new family): a bizarre new archaic Oligocene dolphin from the eastern North Pacific. In: Emry RJ (ed), Cenozoic Mammals of Land and Sea: Tributes to the Career of Clayton E. Ray. Smithsonian Contrib Paleobiol, 93: 185–222
  12. Fordyce RE, Muizon C de (2001) Evolutionary history of cetaceans: a review. In: Mazin J-M, Buffrénil V de (eds) Secondary Adaptation of Tetrapods to Life in Water. Verlag Friedrich Pfeil, Munich, pp 169–233Google Scholar
  13. Forrester DJ, Odell DK, Thompson NP, White JR (1980) Morphometrics, parasites, and chlorinated hydrocarbon residues of pygmy killer whales from Florida. J Mammal 61:356–360. CrossRefGoogle Scholar
  14. Gihr M, Pilleri GE (1969a) On the anatomy and biometry of Stenella styx Gray and Delphinus delphis L. (Cetacea, Delphinidae) of the western Mediterranean. Investigations on Cetacea, Berne 1:15–65.Google Scholar
  15. Gihr M, Pilleri GE (1969b) Hirn-Körpergewichts-Beziehungen bei Cetaceen. Investigations on Cetacea, Berne 1:109–126.Google Scholar
  16. Gingerich PD (1998) Paleobiological perspectives on Mesonychia, Archaeoceti, and the origin of whales. In: Thewissen JGM (ed) Emergence of Whales: Evolutionary Patterns in the Origin of Cetacea. Plenum Press, New York, pp 423–449CrossRefGoogle Scholar
  17. Gingerich PD (2000) Arithmetic or geometric normality of biological variation: an empirical test of theory. J Theor Biol 204:201–221. doi: 10.1006/jtbi.2000.2008 CrossRefPubMedGoogle Scholar
  18. Gingerich PD (2001) Rates of evolution on the time scale of the evolutionary process. Genetica 112/113:127–144. doi: 10.1023/A:1013311015886
  19. Gingerich PD (2015) New partial skeleton and relative brain size in late Eocene Zygorhiza kochii (Mammalia, Cetacea) from the Pachuta Marl of Alabama. Contrib Mus Paleontol Univ Mich 32: 161–188Google Scholar
  20. Harrison RJ, Brownell RL (1971) The gonads of the South American dolphins, Inia goeffrensis, Pontoporia blainvillei, and Sotalia fluviatilis. J Mammal 52:413–419. CrossRefPubMedGoogle Scholar
  21. Harvey PH, Bennett PM ( 1983) Brain size, energetics, ecology and life history patterns. Nature 306:314–316. doi: 10.1038/306314a0 CrossRefPubMedGoogle Scholar
  22. Hofman MA (1982) Encephalization in mammals in relation to the size of the cerebral cortex. Brain Behav Evol 20:84–96. doi: 10.1159/000121583 CrossRefPubMedGoogle Scholar
  23. Houck WJ (1961) Notes on the Pacific striped porpoise. J Mammal 42:107.  10.2307/1377264 CrossRefGoogle Scholar
  24. Jerison HJ (1955) Brain to body ratios and the evolution of intelligence. Science 121:447–449. doi: 10.1126/science.121.3144.447 CrossRefPubMedGoogle Scholar
  25. Jerison HJ (1961) Quantitative analysis of evolution of the brain in mammals. Science 133:1012–1014. doi: 10.1126/science.133.3457.1012 CrossRefPubMedGoogle Scholar
  26. Jerison HJ (1973) Evolution of the Brain and Intelligence. Academic Press, New YorkGoogle Scholar
  27. Jerison HJ (1978) Brain and intelligence in whales. In: Frost S (ed), Whales and Whaling: Report of the Independent Inquiry Conducted by Sir Sydney Frost. Australian Government Publishing Service, Canberra, 2:159–197Google Scholar
  28. Kamiya T, Yamasaki F (1974) Organ weights of Pontoporia blainvillei and Platanista gangetica (Platanistidae). Sci Rep Whales Res Inst 26:265–270Google Scholar
  29. Kasuya T (1972) Some information on the growth of the Ganges dolphin with a comment on the Indus dolphin. Sci Rep Whales Res Inst 24:87–108Google Scholar
  30. Kenyon KW (1961) Cuvier beaked whales stranded in the Aleutian Islands. J Mammal 42:71–76. CrossRefGoogle Scholar
  31. Laurie AH (1933) Some aspects of respiration in blue and fin whales. Discovery Reports 7:363–406Google Scholar
  32. Lockyer C (1976) Body weights of some species of large whales. J Conseil Internatl Explor Mer 36:259–273. doi: 10.1093/icesjms/36.3.259 CrossRefGoogle Scholar
  33. Manger PR (2006) An examination of cetacean brain structure with a novel hypothesis correlating thermogenesis to the evolution of a big brain. Biol Rev 81:1–46. doi: 10.1017/S1464793106007019 CrossRefGoogle Scholar
  34. Marino L, McShea DW, Uhen MD (2004) The origin and evolution of large brains in toothed whales. Anat Rec 281A:1247–1255. doi: 10.1002/ar.a.20128 CrossRefGoogle Scholar
  35. Marino L, Uhen MD, Frohlich B, Aldag JM, Blane C, Bohaska D, Whitmore FC (2000) Endocranial volume of mid-late Eocene archaeocetes (order Cetacea) revealed by computed tomography: implications for cetacean brain evolution. J Mammal Evol 7:81–94. doi: 10.1023/A:1009417831601 CrossRefGoogle Scholar
  36. Marino L, Uhen MD, Pyenson ND, Frohlich B (2003) Reconstructing cetacean brain evolution using computed tomography. Anat Rec 272B:107–117. doi: 10.1002/ar.b.10018 CrossRefGoogle Scholar
  37. Martin RD (1981) Relative brain size and basal metabolic rate in terrestrial vertebrates. Nature 293:57–60. doi: 10.1038/293057a0 CrossRefPubMedGoogle Scholar
  38. May-Collado LJ, Agnarsson I (2006) Cytochrome b and Bayesian inference of whale phylogeny. Mol Phylogenet Evol 38:344–354. doi: 10.1016/j.ympev.2005.09.019 CrossRefPubMedGoogle Scholar
  39. Mikhalev YA, Budylenko GA (2012) Dwarf whale Caperea marginata Gray, 1846, from the South Atlantic. Ukrainian Antarctic Journal 10–11:144–160Google Scholar
  40. Miyazaki N, Fujise Y, Fujiyama T (1981) Body and organ weight of striped and spotted dolphins off the Pacific coast of Japan. Sci Rep Whales Res Inst 33:27–67Google Scholar
  41. Montgomery SH, Geisler JH, McGowen MR, Fox C, Marino L, Gatesy J (2013) The evolutionary history of cetacean brain and body size. Evolution 67:3339–3353.  10.1111/evo.12197 CrossRefPubMedGoogle Scholar
  42. Nagorsen DW, Stewart GE (1983) A dwarf sperm whale (Kogia simus) from the Pacific Coast of Canada. J Mammal 64:505–506. CrossRefGoogle Scholar
  43. Omura H, Shirakihara M, Ito H (1984) A pygmy sperm whale accidentally taken by drift net in the North Pacific. Sci Rep Whales Res Inst 35:183–193Google Scholar
  44. Pagel MD, Harvey PH (1988) The taxon-level problem in the evolution of mammalian brain size: facts and artifacts. Am Nat 132:344–359. CrossRefGoogle Scholar
  45. Pilleri GE, Gihr M (1971) Brain-body weight ratio in Pontoporia blainvillei. Investigations on Cetacea 3:69–73Google Scholar
  46. Purvis A, Harvey PH (1997) The right size for a mammal. Nature 386:332–333. doi: 10.1038/386332b0 CrossRefPubMedGoogle Scholar
  47. Pyenson ND, Sponberg SN (2011) Reconstructing body size in extinct crown Cetacea (Neoceti) using allometry, phylogenetic methods and tests from the fossil record. J Mammal Evol 18:269–288. doi: 10.1007/s10914-011-9170-1 CrossRefGoogle Scholar
  48. R Development Core Team (2008) R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, ViennaGoogle Scholar
  49. Robineau D, Buffrenil Vd (1985) Données ostéologiques et ostéométriques sur le dauphin de Commerson, Cephalorhynchus commersonii (Lacépède, 1804), en particulier celui des îles Kerguelen. Mammalia 49:109–124. doi: 10.1515/mamm.1985.49.1.109 CrossRefGoogle Scholar
  50. Silva M, Downing JA (1995) Mammalian Body Masses. CRC Press, Boca RatonGoogle Scholar
  51. Taylor BL, Chivers SJ, Larese J, Perrin WF (2007) Generation length and percent mature estimates for IUCN assessments of cetaceans. Administrative Report LJ-07-01, Southwest Fisheries Science Center, La JollaGoogle Scholar
  52. Teixeira AM (1979) Marine mammals of the Portuguese coast. Z Säugetierk 44:221–238Google Scholar
  53. Thewissen JGM, George J, Rosa C, Kishida T (2011) Olfaction and brain size in the bowhead whale (Balaena mysticetus). Mar Mammal Sci 27:282–294. doi: 10.1111/j.1748-7692.2010.00406.x CrossRefGoogle Scholar
  54. Thompson DW (1912) Whales, seals, and sea-serpents. In: Fowler GH (ed) Science of the Sea: An Elementary Handbook of Practical Oceanography for Travellers, Sailors, and Yachtsmen. John Murray, London, pp 383–414Google Scholar
  55. Uhen MD (1996) Dorudon atrox (Mammalia, Cetacea): form, function, and phylogenetic relationships of an archaeocete from the late middle Eocene of Egypt. PhD Dissertation, University of Michigan, Ann ArborGoogle Scholar
  56. Uhen MD (2004) Form, function, and anatomy of Dorudon atrox (Mammalia, Cetacea): an archaeocete from the middle to late Eocene of Egypt. Univ Mich Papers Paleontol 34:1–222. Google Scholar
  57. USNM (2014) Division of mammals whale collection. Smithsonian Institution NMNH Search
  58. Vandenberghe N, Hilgen FJ, Speijer RP, Ogg JG, Gradstein FM, Hammer O, Hollis CJ, Hooker JJ (2012) The Paleogene period. In: Gradstein FM, Ogg JG, Schmitz MD, Ogg GM (eds) The Geological Time Scale 2012. Elsevier, Amsterdam, pp 855–921CrossRefGoogle Scholar
  59. Víkingsson G, Sigurjónsson J, Gunnlaugsson T (1988) On the relationship between weight, length and girth dimensions in fin and sei whales caught off Iceland. Rep Internatl Whal Commn 38:323–326Google Scholar
  60. Wilke F, Taniwaki T, Kuroda N (1953) Phocoenoides and Labenorhynchus in Japan, with notes on hunting. J Mammal 34:488–497. CrossRefGoogle Scholar
  61. Worthy GAJ, Hickie JP ( 1986) Relative brain size in marine mammals. Am Nat 128:445–459. CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Museum of PaleontologyUniversity of MichiganAnn ArborUSA

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