Bulletin of Mathematical Biology

, Volume 64, Issue 3, pp 501–530 | Cite as

A numerical approach to the study of spatial pattern formation in the ligaments of arcoid bivalves

  • Anotida Madzvamuse
  • Roger D. K. Thomas
  • Philip K. Maini
  • Andrew J. Wathen


In this paper, we employ the novel application of a reaction-diffusion model on a growing domain to examine growth patterns of the ligaments of arcoid bivalves (marine molluscs) using realistic growth functions. Solving the equations via a novel use of the finite element method on a moving mesh, we show how a reaction-diffusion model can mimic a number of different ligament growth patterns with modest changes in the parameters. Our results imply the existence of a common mode of ligament pattern formation throughout the Arcoida. Consequently, arcoids that share a particular pattern cannot be assumed, on this basis alone, to share an immediate common ancestry. Strikingly different patterns within the set can easily be generated by the same developmental program. We further show how the model can be used to make quantitatively testable predictions with biological implications.


Mixed Boundary Condition Vertical Strip Domain Growth Attachment Area Homogeneous Neumann Boundary Condition 
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Copyright information

© Society for Mathematical Biology 2002

Authors and Affiliations

  • Anotida Madzvamuse
    • 1
  • Roger D. K. Thomas
    • 2
  • Philip K. Maini
    • 3
  • Andrew J. Wathen
    • 1
  1. 1.Oxford University Computing Laboratory, Wolfson BuildingOxfordUK
  2. 2.Department of GeosciencesFranklin & Marshall CollegeLancasterUSA
  3. 3.Centre for Mathematical Biology, Mathematical InstituteUniversity of OxfordOxfordUK

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