Skip to main content

Advertisement

Log in

Structural Constraints in the Evolution of the Tetrapod Skull Complexity: Williston’s Law Revisited Using Network Models

  • Research Article
  • Published:
Evolutionary Biology Aims and scope Submit manuscript

Abstract

Ever since the appearance of the first land vertebrates, the skull has undergone a simplification by loss and fusion of bones in all major groups. This well-documented evolutionary trend is known as “Williston’s Law”. Both loss and fusion of bones are developmental events that generate, at large evolutionary scales, a net reduction in the number of skull bones. We reassess this evolutionary trend by analyzing the patterns of skull organization captured in network models in which nodes represent bones and links represent suture joints. We also evaluate the compensatory process of anisomerism (bone specialization) suggested to occur as a result of this reduction by quantifying the heterogeneity and the ratio of unpaired bones in real skulls. Finally, we perform simulations to test the differential effect of bone losses in skull evolution. We show that the reduction in bone number during evolution is accompanied by a trend toward a more complex organization, rather than toward simplification. Our results indicate that the processes by which bones are lost or fused during development are central to explain the evolution of the morphology of the skull. Our simulations suggest that the evolutionary trend of increasing morphological complexity can be caused as a result of a structural constraint, the systematic loss of less connected bones during development.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

References

  • Albert, R., Jeong, H., & Barabási, A.-L. (2000). Error and attack tolerance of complex networks. Nature, 406, 378–381.

    Article  PubMed  CAS  Google Scholar 

  • Aldridge, K., Marsh, J. L., Govier, D., & Richtsmeier, J. T. (2002). Central nervous system phenotypes in craniosynostosis. Journal of Anatomy, 201, 31–39.

    Article  PubMed  Google Scholar 

  • Benton, M. J. (1990). Reptiles. In K. J. MacNamara (Ed.), Evolutionary trends (pp. 279–300). Tucson: Arizona University Press.

    Google Scholar 

  • Bonner, J. T. (1988). The evolution of complexity. Princeton: Princeton University Press.

    Google Scholar 

  • Boonstra, L. D. (1936). The cranial morpholgy of some titanosuchid deinocephalians. Bulletin of the American Museum of Natural History, 72, 99–116.

    Google Scholar 

  • Cannatella, D. (2008). Living amphibians. Frogs and toads, salamanders and newts, and caecilians. Resource document. http://tolweb.org/Living_Amphibians/14997/2008.11.28. Accessed 23 May 2012.

  • Carroll, R. L. (1988). Vertebrate paleontology and evolution. New York: W. H. Freeman and Company.

    Google Scholar 

  • Carroll, R. L., & Lindsay, W. (1985). Cranial anatomy of the primitive reptile Procolophon. Canadian Journal of Earth Sciences, 22, 1571–1587.

    Article  Google Scholar 

  • Case, E. C. (1904). The osteology of the skull of the pelycosaurian genus, Dimetrodon. Journal of Geology, 12, 304–311.

    Article  Google Scholar 

  • Chernoff, B., & Magwene, P. M. (1999). Afterword. In E. C. Olson & P. L. Miller (Eds.), Morphological integration (pp. 319–353). Chicago: Chicago University Press.

    Google Scholar 

  • Depew, M. J., Compagnucci, C., & Griffin, J. (2008). Suture neontology and paleontology: The bases for where, when, and how boundaries between bones have been established and have evolved. In D. P. Rice (Ed.), Craniofacial sutures. Development, disease, and treatment (pp. 57–78). Basel: Karger.

    Chapter  Google Scholar 

  • Dorogovtsev, S. N., & Mendes, J. F. F. (2003). Evolution of networks: From biological networks to the Internet and WWW. Oxford: Oxford University Press.

    Google Scholar 

  • Dunne, J. A., Williams, R. J., & Martínez, N. D. (2008a). Food-web structure and network theory: The role of connectance and size. Proceedings of the National Academy of Sciences, 99, 12917–12922.

    Article  Google Scholar 

  • Dunne, J. A., Williams, R. J., Martínez, N. D., Wood, R. A., & Erwin, D. H. (2008b). Compilation and network analyses of Cambrian food webs. PLoS Biology, 6, e102.

    Article  PubMed  Google Scholar 

  • Erdos, P., & Renyi, A. (1959). On random graphs. Publicationes mathematicae Debrecen, 6, 290–297.

    Google Scholar 

  • Estes, R. (1961). Cranial anatomy of the cynodont reptile Thrinaxodon liorhinus. Bulletin of the Museum of Comparative Zoology, 125, 165–180.

    Google Scholar 

  • Estes, R., Queiroz, K., & Gauthier, J. (1988). Phylogenetic relationships within Squamata. In R. Estes & G. Pregill (Eds.), Phylogenetic relationships of the lizard families: Essays commemorating Charles L. Camp (pp. 119–281). Stanford: Stanford University Press.

    Google Scholar 

  • Esteve-Altava, B., Marugán-Lobón, J., Botella, H., & Rasskin-Gutman, D. (2011). Network models in anatomical systems. Journal of Anathropological Sciences, 89, 1–10.

    Google Scholar 

  • Felsenstein, J. (1985). Phylogenies and the comparative method. The American Naturalist, 125, 1–15.

    Article  Google Scholar 

  • Gabriel, K. R., & Sokal, R. R. (1969). A new statistical approach to geographic variation analysis. Systematic Zoology, 18, 259–270.

    Article  Google Scholar 

  • Gaffney, E. S. (1979). Comparative cranial morphology of recent and fossil turtles. Bulletin of the American Museum of Natural History, 164, 65–375.

    Google Scholar 

  • Gaffney, E. S. (1990). The comparative osteology of the triassic turtle Proganochelys. Bulletin of the American Museum of Natural History, 194, 2–263.

    Google Scholar 

  • Gardner, N. M., Holliday, C. M., & O’Keefe, F. R. (2010). The Braincase of Youngina capensis (Reptilia, Diapsida): New insights from high-resolution CT scanning of the Holotype. Palaeontologia Electronica, 13, 19A.

    Google Scholar 

  • Giannini, N. P., Wible, J. R., & Simmons, N. B. (2006). On the cranial osteology of Chiroptera. 1, Pteropus (Megachiroptera, Pteropodidae). Bulletin of the American Museum of Natural History, 295, 1–134.

    Article  Google Scholar 

  • Gibbard, L. P., Head, M. J., & Walker, M. J. C. (2010). Formal ratification of the Quaternary System/Period and the Pleistocene Series/Epoch with a base at 2.58 Ma. Journal of Quaternary Science, 25, 96–102.

    Article  Google Scholar 

  • Gilmore, C. W. (1914). Osteology of the armored Dinosauria in the United States National Museum, with special reference to the genus Stegosaurus. Bulletin of the American Museum of Natural History, 89, 2–159.

    Google Scholar 

  • Girgis, F. G., & Pritchard, J. J. (1958). Effects of skull damage on the development of sutural patterns in the rat. Journal of Anatomy, 92, 39–61.

    PubMed  CAS  Google Scholar 

  • Goodrich, E. S. (1958). Studies on the structure and development of vertebrates. New York: Dover Publications.

    Google Scholar 

  • Gradstein, F. M., Agterberg, F. P., Ogg, J. G., Hardenbol, J., Van Veen, P., Thierry, J., et al. (1995). A Triassic, Jurassic, and Cretaceous time scale. SEPM Special: Publication. 54.

    Google Scholar 

  • Gray, H. (1918). Anatomy of the human body. Philadelphia: Lea, & Febiger.

    Google Scholar 

  • Gregory, W. K. (1934). Polysomerism and anisomerism in cranial and dental evolution among vertebrates. Proceedings of the National Academy of Sciences USA, 20, 1–9.

    Article  CAS  Google Scholar 

  • Gregory, W. K., Roigneau, M., Burr, E. R., Evans, G., Hellman, E., Jackson, F. A., et al. (1935). Williston’s law relating to the evolution of skull bones in the vertebrates. American Journal of Physical Anthropology, 20, 123–152.

    Article  Google Scholar 

  • Hall, B. K. (2005). Bones and cartilage. Developmental and evolutionary skeletal biology. San Diego: Elsevier.

    Google Scholar 

  • Hildebrand, M. (1988). Analysis of vertebrate structure (3rd ed.). New York: Wiley.

    Google Scholar 

  • Horvath, S., & Dong, J. (2008). Geometric interpretation of gene coexpression network analysis. PLoS Computational Biology, 4, e1000117.

    Article  PubMed  Google Scholar 

  • Hugall, A. F., Foster, R., & Lee, M. S. (2007). Calibration choice, rate smoothing, and the pattern of tetrapod diversification according to the long nuclear gene RAG-1. Systematic Biology, 56, 543–563.

    Article  PubMed  CAS  Google Scholar 

  • Josse, S., Moreau, T., & Laurin, M. (2006). Stratigraphic tools for mesquite. Available at http://mesquiteproject.org/packages/stratigraphicTools/.

  • Kardong, K. V. (2005). Vertebrates. Comparative anatomy, function, evolution. New York: Mcgraw Hill.

    Google Scholar 

  • Knight, C. G., & Pinney, J. W. (2009). Making the right connections: Biological networks in the light of evolution. BioEssays, 31, 1080–1090.

    Article  PubMed  Google Scholar 

  • Koyabu, D., Maier, W., & Sánchez-Villagra, M. R. (2012). Paleontological and developmental evidence resolve the homology and dual embryonic origin of a mammalian skull bone, the interparietal. Proceedings of the Natinal Academy of Science USA,. doi:10.1073/pnas.1208693109.

    Google Scholar 

  • Laurin, M. (1996). A redescription of the cranial anatomy of Seymouria baylorensis, the best known Seymouriamorph (Veretebrata: Seymouriamorpha). PaleoBios, 17, 1–16.

    Google Scholar 

  • Laurin, M. (2004). The evolution of body size, Cope’s rule and the origin of amniotes. Systematic Biology, 53, 594–622.

    Article  PubMed  Google Scholar 

  • Laurin, M. (2010). Assessment of the relative merits of a few methods to detect evolutionary trends. Systematic Biology, 59, 689–704.

    Article  PubMed  Google Scholar 

  • Laurin, M. (2011). Terrestrial vertebrates. Stegocephalians: Tetrapods and other digit-bearing vertebrates. Resource document. http://tolweb.org/Terrestrial_Vertebrates/14952/2011.04.21. Accessed 23 May 2012.

  • Laurin, M., & Gauthier, J. A. (2011). Diapsida. Lizards, Sphenodon, crocodylians, birds, and their extinct relatives. Resource document. http://tolweb.org/Diapsida/14866/2011.04.20. Accessed 23 May 2012.

  • Laurin, M., & Gauthier, J. A. (2012). Amniota. Mammals, reptiles (turtles, lizards, Sphenodon, crocodiles, birds) and their extinct relatives. Resource document. http://tolweb.org/Amniota/14990/2012.01.30. Accessed 23 May 2012.

  • Laurin, M., & Reisz, R. R. (2011). Synapsida. Mammals and their extinct relatives. Resource document. http://tolweb.org/Synapsida/14845/2011.08.14. Accessed 23 May 2012.

  • Le Guyader, H. (2004). Geoffroy Saint-Hilaire: A visionary naturalist. Chicago: Chicago University Press.

    Google Scholar 

  • Louys, J., Aplin, K., Beck, R. M. D., & Archer, M. (2009). Cranial anatomy of Oligo-Miocene koalas (Diprotodontia: Phascolarctidae): Stages in the evolution of an extreme leaf-eating specialization. Journal of Vertebrate Paleontology, 29, 981–992.

    Article  Google Scholar 

  • Mabbutt, L. W., & Kokich, V. G. (1979). Calvarial and sutural re-development following craniectomy in the neonatal rabbit. Journal of Anatomy, 129, 413–422.

    PubMed  CAS  Google Scholar 

  • Maddin, H. C., Sidor, C. A., & Reisz, R. R. (2008). Cranial anatomy of Ennatosaurus tecton (Synapsida: Caseidae) from the Middle Permian of Russia and the evolutionary relationships of Caseidae. Journal of Vertebrate Paleontology, 28, 160–180.

    Article  Google Scholar 

  • Maddison, D. R., & Schulz, K. S. (2007) The tree of life web project. Internet address: http://tolweb.org.

  • Maddison, W. P., & Maddison, D. R. (2011). Mesquite: A modular system for evolutionary analysis. Version 2.75. Available at http://mesquiteproject.org.

  • Magwene, P. M. (2008). Using correlation proximity graphs to study phenotypic integration. Evolutionary Biology, 35, 191–198.

    Article  Google Scholar 

  • Maisano, J. A., Kearney, M., & Rowe, T. (2006). Cranial anatomy of the spade-headed amphisbaenian Diplometopon zarudnyi (Squamata: Amphisbaenia) based on high-resolution X-ray computed tomography. Journal of Morphology, 267, 70–102.

    Article  PubMed  Google Scholar 

  • Mason, O., & Verwoerd, M. (2007). Graph theory and networks in biology. IET Systems Biology, 1, 89–119.

    Article  PubMed  CAS  Google Scholar 

  • MATLAB version 7.10. (2010). The MathWorks Inc., Natick, Massachusetts.

  • McShea, D. W. (1991). Complexity and evolution: What everybody knows. Biology and Philosophy, 6, 303–324.

    Article  Google Scholar 

  • McShea, D. W. (1996). Metazoan complexity and evolution: Is there a trend? Evolution, 50, 477–492.

    Article  Google Scholar 

  • McShea, D. W. (1998). Possible largest-scale trends in organismal evolution: Eight “live hypotheses”. Annual Review of Ecology Evolution and Systematics, 29, 293–318.

    Article  Google Scholar 

  • Mead, J. G., & Fordyce, R. E. (2009). The therian skull: A lexicon with emphasis on the odontocetes. Smithsonian Contributions to Zoology, 627, 1–248.

    Article  Google Scholar 

  • Meylan, P. A. (2001). Testudines. Turtles, tortoises and terrapins. Resource document. http://tolweb.org/Testudines/14861/2001.05.31. Accessed 23 May 2012.

  • Midford, P., Garland, T. J., & Maddison, W. P. (2008). PDAP Package for Mesquite. http://mesquiteproject.org/pdap_mesquite/index.html.

  • Moazen, M., Curtis, N., O’Higgins, P., Jones, M. E. H., Evans, S. E., & Fagan, M. J. (2009). Assessment of the role of sutures in a lizard skull: A computer modelling study. Proceedings of the Royal Society B: Biological Sciences, 276, 39–46.

    Article  PubMed  Google Scholar 

  • Newman, M. E. J. (2003). The structure and function of complex networks. SIAM Reviews, 45, 167–256.

    Article  Google Scholar 

  • Newman, M. E. J., Barabási, A.-L., & Watts, D. J. (2006). The structure and dynamics of networks. Princeton: Princeton University Press.

    Google Scholar 

  • Newman, S. A., & Forgacs, G. (2005). Complexity and self-organization in biological development and evolution. In D. Bonchev & D. H. Rouvray (Eds.), Complexity in chemistry, biology, and ecology (pp. 49–190). New York: Springer Science.

    Chapter  Google Scholar 

  • Nussbaum, R. A. (1977). Rhinatrematidae: A new family of caecilians (Amphibia: Gymnophiona). Occasional Papers of the Museum of Zoology of the University of Michigan, 682, 1–30.

    Google Scholar 

  • Okajima, Y., & Kumazawa, Y. (2010). Mitochondrial genomes of acrodont lizards: Timing of gene rearrangements and phylogenetic and biogeographic implications. BMC Evolutionary Biology, 10, 141e.

    Article  Google Scholar 

  • Olson, E. C., & Miller, R. L. (1958). Morphological Integration. Chicago: University of Chicago Press.

    Google Scholar 

  • Ostrom, J. H. (1961). Cranial morphology of the hadrosaurian dinosaurs of North America. Bulletin of the American Museum of Natural History, 122, 33–195.

    Google Scholar 

  • Pace, J. K., Gilbert, C., Clark, M. S., & Feschotte, C. (2008). Repeated horizontal transfer of a DNA transposon in mammals and other tetrapods. Proceedings of the Natinal Academy of Science USA, 105, 17023–17028.

    Article  CAS  Google Scholar 

  • Padian, K. (1984). Pterosaur remains from the Kayenta Formation (? Early Jurassic) of Arizona. Paleobiology, 27, 407–413.

    Google Scholar 

  • Payne, S. L., Holliday, C. M., & Vickaryous, M. K. (2011). An osteological and histological investigation of cranial joints in Geckos. Anatomical Records, 294, 399–405.

    Article  Google Scholar 

  • Phillips, M. J., Bennett, T., & Lee, M. S. Y. (2009). Molecules and morphology suggest a recent, amphibious ancestry for echidnas. Proceedings of the National Academy of Sciences USA, 106, 17089–17094.

    Article  CAS  Google Scholar 

  • Proulx, S. R., Promislow, D. E., & Phillips, P. C. (2005). Network thinking in ecology and evolution. Trends in Ecology & Evolution, 20, 345–353.

    Article  Google Scholar 

  • Rasskin-Gutman, D. (2003). Boundary constraints for the emergence of form. In G. Müller & S. Newman (Eds.), Origination of organismal form (pp. 305–322). Cambridge: MIT Press.

    Google Scholar 

  • Reisz, R. (1981). A diapsid reptile from the Pennsylvanian of Kansas. University of Kansas Museum of Natural History Special Publications, 7, 1–74.

    Google Scholar 

  • Rice, D. P. (2008). Developmental anatomy of craniofacial sutures. In D. P. Rice (Ed.), Craniofacial sutures. Development, disease, and treatment (pp. 1–21). Basel: Karger.

    Chapter  Google Scholar 

  • Richtsmeier, J. T., Aldridge, K., DeLeon, V. B., Panchal, J., Kane, A. A., Marsh, J. L., et al. (2006). Phenotypic integration of neurocranium and brain. Journal of Experimental Zoology B, 306, 360–378.

    Google Scholar 

  • Riedl, R. (1978). Order in living organisms: A systems analysis of evolution. New York: Wiley.

    Google Scholar 

  • Rieppel, O. (1993). Patterns of diversity in the reptilian skull. In J. Hanken & B. K. Hall (Eds.), The Skull (Vol. 2, pp. 344–390). Chicago: Chicago University Press.

    Google Scholar 

  • Roscher, M., & Schneider, J. W. (2006). Permo-Carboniferous climate: Early Pennsylvanian to Late Permian climate development of central Europe in a regional and global context. In G. Lucas, G. Cassinis, & J. W. Schneider (Eds.), Non-Marine Permian biostratigraphy and biochronology (pp. 95–136). London: Geological Society Special Publications.

    Google Scholar 

  • Schoch, R. R. (2010). Riedl’s burden and the body plan: Selection, constraint, and deep time. Journal of Experimental Zoology B, 314, 1–10.

    Google Scholar 

  • Sereno, P. C. (1997). The origin and evolution of dinosaurs. Annual Reviews of Earth and Planetary Sciences, 25, 435–489.

    Article  CAS  Google Scholar 

  • Sidor, C. A. (2001). Simplification as a trend in synapsid cranial evolution. Evolution, 55, 1419–1442.

    PubMed  CAS  Google Scholar 

  • Sporns, O. (2002). Network analysis, complexity, and brain function. Complexity, 8, 56–60.

    Article  Google Scholar 

  • Springer, M. S., Murphy, W. J., Eizirik, E., & O’Brien, J. (2003). Placental mammal diversification and the Cretaceous-Tertiary boundary. Proceedings of the National Academy of Sciences USA, 100, 1056–1061.

    Article  CAS  Google Scholar 

  • Sterli, J., & Joyce, W. G. (2007). The cranial anatomy of the Early Jurassic turtle Kayentachelys aprix. Acta Palaeontologica Polonica, 52, 675–694.

    Google Scholar 

  • Torres-Carvajal, O. (2003). Cranial osteology of the andean lizard Stenocercus guentheri (Squamata: Tropiduridae) and its postembryonic development. Journal of Morphology, 255, 94–113.

    Article  PubMed  Google Scholar 

  • Trueb, L. (1993). Patterns of cranial diversity among the Lissamphibia. In J. Hanken & B. K. Hall (Eds.), The skull (Vol. 2, pp. 255–343). Chicago: Chicago University Press.

    Google Scholar 

  • Valentine, J. W., Collins, A. G., & Meyer, C. P. (1994). Morphological complexity increase in metazoans. Paleobiology, 20, 131–142.

    Google Scholar 

  • Weishampel, D. B., Dodson, P., & Osmólska, H. (1993). The Dinosauria. Los Angeles: California University Press.

    Google Scholar 

  • Williams, G. C. (1966). Adaptation and natural selection. Princeton: Princeton University Press.

    Google Scholar 

  • Williston, S. W. (1914). Water reptiles of the past and present. Chicago: Chicago University Press.

    Book  Google Scholar 

  • Xu, K., Bezakova, I., Bunimovich, L., & Yi, S. V. (2011). Path lengths in protein–protein interaction networks and biological complexity. Proteomics, 11, 1857–1867.

    Article  PubMed  CAS  Google Scholar 

Download references

Acknowledgments

We thank Angela D. Buscalioni for constructive comments. We thank Michel Laurin for suggestions about the phylogenetic analysis and comments in a previous version of this manuscript. We thank the Konrad Lorenz Institute for Evolution and Cognition Research were the final manuscript was completed. This research project was supported by grant (BFU2008-00643) from the Spanish Ministerio de Ciencia e Innovación.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Diego Rasskin-Gutman.

Electronic supplementary material

Below is the link to the electronic supplementary material.

Supplementary material 1 (PDF 905 kb)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Esteve-Altava, B., Marugán-Lobón, J., Botella, H. et al. Structural Constraints in the Evolution of the Tetrapod Skull Complexity: Williston’s Law Revisited Using Network Models. Evol Biol 40, 209–219 (2013). https://doi.org/10.1007/s11692-012-9200-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11692-012-9200-9

Keywords

Navigation