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The effect of domain growth on spatial correlations

Author

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  • Ross, Robert J.H.
  • Yates, C.A.
  • Baker, R.E.

Abstract

Mathematical models describing cell movement and proliferation are important tools in developmental biology research. In this work we present methods to include the effects of domain growth on the evolution of spatial correlations between agent locations in a continuum approximation of a one-dimensional lattice-based model of cell motility and proliferation. This is important as the inclusion of spatial correlations in continuum models of cell motility and proliferation without domain growth has previously been shown to be essential for their accuracy in certain scenarios. We include the effect of spatial correlations by deriving a system of ordinary differential equations that describe the expected evolution of individual and pair density functions for agents on a growing domain. We then demonstrate how to simplify this system of ordinary differential equations by using an appropriate approximation. This simplification allows domain growth to be included in models describing the evolution of spatial correlations between agents in a tractable manner.

Suggested Citation

  • Ross, Robert J.H. & Yates, C.A. & Baker, R.E., 2017. "The effect of domain growth on spatial correlations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 466(C), pages 334-345.
    • Handle: RePEc:eee:phsmap:v:466:y:2017:i:c:p:334-345
    DOI: 10.1016/j.physa.2016.09.002
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    References listed on IDEAS

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    5. Richard L. Mort & Robert J. H. Ross & Kirsten J. Hainey & Olivia J. Harrison & Margaret A. Keighren & Gabriel Landini & Ruth E. Baker & Kevin J. Painter & Ian J. Jackson & Christian A. Yates, 2016. "Reconciling diverse mammalian pigmentation patterns with a fundamental mathematical model," Nature Communications, Nature, vol. 7(1), pages 1-13, April.
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