Evolutionary Biology

, Volume 40, Issue 2, pp 209–219 | Cite as

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

  • Borja Esteve-Altava
  • Jesús Marugán-Lobón
  • Héctor Botella
  • Diego Rasskin-GutmanEmail author
Research Article


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.


Morphological complexity Constraints Network theory Tetrapod skull 



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.

Supplementary material

11692_2012_9200_MOESM1_ESM.pdf (905 kb)
Supplementary material 1 (PDF 905 kb)


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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  • Borja Esteve-Altava
    • 1
  • Jesús Marugán-Lobón
    • 2
  • Héctor Botella
    • 3
  • Diego Rasskin-Gutman
    • 1
    Email author
  1. 1.Theoretical Biology Research Group, Institute Cavanilles for Biodiversity and Evolutionary BiologyUniversity of ValenciaValenciaSpain
  2. 2.Unidad de Paleontología, Dpto. BiologíaUniversidad Autónoma de MadridCantoblancoSpain
  3. 3.Area de Paleontología, Dpto. GeologíaUniversity of ValenciaValenciaSpain

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