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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.

Original publication

DOI

10.1006/bulm.2002.0283

Type

Journal article

Journal

Bull Math Biol

Publication Date

05/2002

Volume

64

Pages

501 - 530

Keywords

Animals, Computer Simulation, Finite Element Analysis, Ligaments, Microscopy, Electron, Scanning, Models, Biological, Mollusca