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.
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.
|Subjects:||A - C > Biology and other natural sciences|
|Research Groups:||Centre for Mathematical Biology|
|Deposited By:||Philip Maini|
|Deposited On:||20 Nov 2006|
|Last Modified:||29 May 2015 18:21|
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