The Mathematical Institute, University of Oxford, Eprints Archive

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

Madzvamuse, A. and Thomas, R. D. K. and Maini, P. K. and Wathen, A. J. (2002) A numerical approach to the study of spatial pattern formation in the ligaments of arcoid bivalves. Bulletin of Mathematical Biology, 64 (3). pp. 501-530.

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Abstract

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.

Item Type:Article
Uncontrolled Keywords:n/a
Subjects:A - C > Biology and other natural sciences
Research Groups:Centre for Mathematical Biology
ID Code:393
Deposited By:Philip Maini
Deposited On:20 Nov 2006
Last Modified:20 Jul 2009 14:20

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