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The many faces of synapsid cranial allometry

  • Isaac W. Krone (a1), Christian F. Kammerer (a2) and Kenneth D. Angielczyk (a3)


Previous studies of cranial shape have established a consistent interspecific allometric pattern relating the relative lengths of the face and braincase regions of the skull within multiple families of mammals. In this interspecific allometry, the facial region of the skull is proportionally longer than the braincase in larger species. The regularity and broad taxonomic occurrence of this allometric pattern suggests that it may have an origin near the base of crown Mammalia, or even deeper in the synapsid or amniote forerunners of mammals. To investigate the possible origins of this allometric pattern, we used geometric morphometric techniques to analyze cranial shape in 194 species of nonmammalian synapsids, which constitute a set of successive outgroups to Mammalia. We recovered a much greater diversity of allometric patterns within nonmammalian synapsids than has been observed in mammals, including several instances similar to the mammalian pattern. However, we found no evidence of the mammalian pattern within Therocephalia and nonmammalian Cynodontia, the synapsids most closely related to mammals. This suggests that the mammalian allometric pattern arose somewhere within Mammaliaformes, rather than within nonmammalian synapsids. Further investigation using an ontogenetic series of the anomodont Diictodon feliceps shows that the pattern of interspecific allometry within anomodonts parallels the ontogenetic trajectory of Diictodon. This indicates that in at least some synapsids, allometric patterns associated with ontogeny may provide a “path of least resistance” for interspecific variation, a mechanism that we suggest produces the interspecific allometric pattern observed in mammals.

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This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (, which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.


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Present address: Museum of Vertebrate Zoology, University of California, Berkeley, California 94720-3161, U.S.A.

Data available from the Dryad Digital Repository:



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Adams, D. C., and Nistri, A. 2010. Ontogenetic convergence and evolution of foot morphology in European cave salamanders (Family: Plethodontidae). BMC Evolutionary Biology 10:110.
Adams, D. C., Collyer, M., Kaliontzopoulou, A., and Sherratt, E.. 2016. Geomorph: software for geometric morphometric analyses., accessed September 1, 2017.
Alberch, P., Gould, S. J., Oster, G. F., and Wake, D. B.. 1980. Size and shape in ontogeny and phylogeny. Paleobiology 5:296317.
Angielczyk, K. D., and Kammerer, C. F.. 2017. The cranial morphology, phylogenetic position and biogeography of the Upper Permian dicynodont Compsodon helmoedi van Hoepen (Therapsida, Anomodontia). Papers in Palaeontology 3:513545.
Angielczyk, K. D., and Kammerer, C. F.. 2018. Non-mammalian synapsids: the deep roots of the mammalian family tree. Pp. 117198 in Zachos, F. E. and Asher, R. J., eds. Handbook of zoology: Mammalia: mammalian evolution, diversity and systematics. DeGruyter, Berlin.
Angielczyk, K. D., and Ruta, M.. 2012. The roots of amphibian morphospace: a geometric morphometric analysis of Paleozoic temnospondyls. Fieldiana Life and Earth Sciences 5(October):4058.
Angielczyk, K. D., and Walsh, M. L.. 2008. Patterns in the evolution of nares size and secondary palate length in anomodont therapsids (Synapsida): implications for hypoxia as a cause of end-Permian tetrapod extinctions. Journal of Paleontology 82:528542
Bell, M. A., and Lloyd, G. T.. 2015. strap: an R package for plotting phylogenies against stratigraphy and assessing their stratigraphic congruence. Paleontology 58:379389.
Benoit, J., Abdala, F., Manger, P. R., and Rubidge, B. S.. 2016. The sixth sense in mammalian forerunners: variability of the parietal foramen and the evolution of the pineal eye in South African Permo-Triassic eutheriodont therapsids. Acta Palaeontologica Polonica 61:777789.
Benton, M. J., Donoghue, P. C. J., Asher, R. J., Friedman, M., Near, T. J., and Vinther, J.. 2015. Constraints on the timescale of animal evolutionary history. Palaeontologia Electronica 18.1.1FC:1106.
Bhullar, B-A. S., Marugán-Lobón, J., Racimo, F., Bever, G. S., Rowe, T. B., Norell, M. A., and Abzhanov, A.. 2012. Birds have paedomorphic dinosaur skulls. Nature 487:223226.
Bookstein, F. L. 1991. Morphometric tools for landmark analysis: geometry and biology. Cambridge University Press, New York.
Botha-Brink, J., Codron., D., Huttenlocker, A. K., Angielczyk., K. D., and Ruta, M.. 2016. Breeding young as a survival strategy during Earth's greatest mass extinction. Scientific Reports 6:24053.
Bright, J. A., Marugán-Lobón, J., Cobb, S. N., and Rayfield, E. J.. 2016. The shapes of bird beaks are highly controlled by nondietary factors. Proceedings of the National Academy of Sciences USA 113:53525357.
Brocklehurst, N., Reisz, R. R., Fernandez, V., and Fröbisch, J.. 2016. A re-description of “Mycterosaurus” smithae, an Early Permian eothyridid, and its impact on the phylogeny of pelycosaurian-grade synapsids. PLoS ONE 11:e0156810.
Brusatte, S. L., Benton, M. J., Ruta, M., and Lloyd, G. T.. 2008. Superiority, competition, and opportunism in the evolutionary radiation of dinosaurs. Science 321:14851488.
Brusatte, S. L., Sakamoto, M., Montanari, S., and Harcourt Smith, W. E. H.. 2012. The evolution of cranial form and function in theropod dinosaurs: insights from geometric morphometrics: geometric morphometrics of theropod dinosaurs. Journal of Evolutionary Biology 25:365377.
Cardini, A. 2019. Craniofacial allometry is a rule in evolutionary radiations of placentals. Evolutionary Biology 46:239248
Cardini, A., and Polly, P. D.. 2013. Larger mammals have longer faces because of size-related constraints on skull form. Nature Communications 4:2458.
Cardini, A., Polly, P. D., Dawson, R., and Milne, N.. 2015. Why the long face? Kangaroos and wallabies follow the same “rule” of cranial evolutionary allometry (CREA) as placentals. Evolutionary Biology 42:169176.
Churchill, M., Geisler, J. H., Beatty, B. L., and Goswami, A.. 2018. Evolution of cranial telescoping in echolocating whales (Cetacea: Odontoceti). Evolution 72:10921108.
Claude, J., Pritchard, P. C. H., Tong, H., Paradis, E., and Auffray, J.-C.. 2004. Ecological correlates and evolutionary divergence in the skull of turtles: a geometric morphometric assessment. Systematic Biology 53:933948.
Emerson, S. B., and Bramble, D. M.. 1993. Scaling, allometry, and skull design. Pp. 384421 in Hanken, J. and Hall, B. K., eds. The skull 3. University of Chicago Press, Chicago.
Esteve-Altava, B., Marugán-Lobón, J., Botella, H., and Rasskin-Gutman, D.. 2013. Structural constraints in the evolution of the tetrapod skull complexity: Williston's law revisited using network models. Evolutionary Biology 40:209219.
Ford, D. P., and Benson, R. B. J.. 2018. A redescription of Orovenator mayorum (Sauropsida, Diapsida) using high-resolution μCT, and the consequences for early amniote phylogeny. Papers in Palaeontology 5:197239.
Foth, C., and Rauhut, O. W. M.. 2013. Macroevolutionary and morphofunctional patterns in theropod skulls: a morphometric approach. Acta Palaeontologica Polonica 58:116.
Goswami, A. 2006. Cranial modularity shifts during mammalian evolution. American Naturalist 168:270280.
Goswami, A., and Polly, P. D.. 2010. The influence of modularity on cranial morphological disparity in Carnivora and primates (Mammalia). PLoS ONE 5:e9517.
Gould, S. J. 1967. Evolutionary patterns in pelycosaurian reptiles: a factor-analytic study. Evolution 21:385401.
Gunz, P., Mitteroecker, P., Neubauer, S., Weber, G. W., and Bookstein, F. L.. 2009. Principles for the virtual reconstruction of hominin crania. Journal of Human Evolution 57:4862.
Griffin, C. T., and Angielczyk, K. D.. 2019. The evolution of the dicynodont sacrum: constraint and innovation in the synapsid axial column. Paleobiology 45:201220.
Hoffman, E. A., and Rowe, T. B.. 2018. Jurassic stem-mammal perinates and the origin of mammalian reproduction and growth. Nature 561:104108.
Hopson, J. A. 1991. Systematics of the nonmammalian Synapsida and implications for patterns of evolution in synapsids. Pp. 635693 in Schultze, H.-P. and Trueb, L., eds. Origins of the higher groups of tetrapods: controversy and consensus. Cornell University Press, Ithaca, N.Y.
Howland, H. C., Merola, S., and Basarab, J. R.. 2004. The allometry and scaling of the size of vertebrate eyes. Vision Research 44:20432065.
Huttenlocker, A. K., and Abdala, F.. 2016. Revision of the first therocephalian, Theriognathus Owen (Therapsida: Whaitsiidae), and implications for cranial ontogeny and allometry in nonmammaliaform eutheriodonts. Journal of Paleontology 89:645664.
Kammerer, C. F. 2011. Systematics of the Anteosauria (Therapsida: Dinocephalia). Journal of Systematic Palaeontology 9:261304.
Kammerer, C. F., and Masyutin, V.. 2018. Gorgonopsian therapsids (Nochnitsa gen. nov. and Viatkogorgon) from the Permian Kotelnich locality of Russia. PeerJ 6:e4954.
Kemp, T. S. 1982. Mammal-like reptiles and the origin of mammals. Academic Press, New York.
Kemp, T. S. 2005. The origin and evolution of mammals. Oxford University Press, Oxford.
Kruger, A., Rubidge, B. S., Abdala, F., Chindebvu, E. G., and Jacobs, L. L.. 2015. Lende chiweta, a new therapsid from Malawi, and its influence on burnetiamorph phylogeny and biogeography. Journal of Vertebrate Paleontology 35:e1008698.
Linde-Medina, M. 2016. Testing the cranial evolutionary allometric “rule” in Galliformes. Journal of Evolutionary Biology 29:18731878.
Martin, R. D., Genoud, M., and Hemelrijk, C.K.. 2005. Problems of allometric scaling analysis: examples from mammalian reproductive biology. Journal of Experimental Biology 208:17311747.
Metzger, K. A., and Herrel, A.. 2005. Correlations between lizard cranial shape and diet: a quantitative, phylogenetically informed analysis. Biological Journal of the Linnean Society 86:433466.
Mitchell, D. R., Sherratt, E., Ledogar, J. A., and Wroe, S.. 2018. The biomechanics of foraging determines face length among kangaroos and their relatives. Proceedings of the Royal Society of London B 285:20180845.
R Core Team. 2017. A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria., accessed September 1, 2017.
Radinsky, L. B. (1985) Approaches in evolutionary morphology: a search for patterns. Annual Review of Ecology and Systematics 16:114.
Revell, L. J. (2012) phytools: an R package for phylogenetic comparative biology (and other things). Methods in Ecology and Evolution 3:217223.
Rohlf, F. J. 2016. TpsDig, Version 2.26 (Tps_Digitize)., accessed September 1, 2017.
Ruta, M., Botha-Brink, J., Mitchell, S. A., and Benton, M. J.. 2013. The radiation of cynodonts and the ground plan of mammalian morphological diversity. Proceedings of the Royal Society of London B 28:20131865.
Sakamoto, M. 2010. Jaw biomechanics and the evolution of biting performance in theropod dinosaurs. Proceedings of the Royal Society of London B 277:33273333.
Sherratt, E., Gower, D. J., Klingenberg, C. P., and Wilkinson, M.. 2014. Evolution of cranial shape in caecilians (Amphibia: Gymnophiona). Evolutionary Biology 41:528545.
Sidor, C. A. 2001. Simplification as a trend in synapsid cranial evolution. Evolution 55:14191442.
Sidor, C. A., and Hopson, J. A.. 1998. Ghost lineages and “mammalness”: assessing the temporal pattern of character acquisition in the Synapsida. Paleobiology 24:5473.
Sigurdsen, T., Huttenlocker, A. K., Modesto, S. P., Rowe, T. B., and Damiani, R.. 2012. Reassessment of the morphology and paleobiology of the therocephalian Tetracynodon darti (Therapsida), and the phylogenetic relationships of Baurioidea. Journal of Vertebrate Paleontology 32:11131134.
Stayton, C. T. 2005. Morphological evolution of the lizard skull: a geometric morphometrics survey. Journal of Morphology 263:4759.
Stayton, C. T. 2006. Testing hypotheses of convergence with multivariate data: morphological and functional convergence among herbivorous lizards. Evolution 60:824841.
Stovall, J. W., Price, L. I., and Romer, A. S.. 1966. The postcranial skeleton of the giant Permian pelycosaur Cotylorhynchus romeri. Bulletin of the Museum of Comparative Zoology 135(1). Harvard University, Cambridge, Mass.
Tamagnini, D., Meloro, C., and Cardini, A., 2017. Anyone with a long-face? Craniofacial evolutionary allometry (CREA) in a family of short-faced mammals, the Felidae. Evolutionary Biology 44:476495.
Zelditch, M. L., Sheets, H. D., and Fink, W. L.. 2003. The ontogenetic dynamics of shape disparity. Paleobiology 29:139156.
Zelditch, M. L., Calamari, Z. T., and Swiderski, D. L.. 2016. Disparate postnatal ontogenies do not add to the shape disparity of infants. Evolutionary Biology 43:188207.

The many faces of synapsid cranial allometry

  • Isaac W. Krone (a1), Christian F. Kammerer (a2) and Kenneth D. Angielczyk (a3)


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