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Asymptotic expansion approximation for spatial structure arising from directionally biased movement

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  • Plank, Michael J.

Abstract

Spatial structure can arise in spatial point process models via a range of mechanisms, including neighbour-dependent directionally biased movement. This spatial structure is neglected by mean-field models, but can have important effects on population dynamics. Spatial moment dynamics are one way to obtain a deterministic approximation of a dynamic spatial point process that retains some information about spatial structure. However, the applicability of this approach is limited by the computational cost of numerically solving spatial moment dynamic equations at a sufficient resolution. We present an asymptotic expansion for the equilibrium solution to the spatial moment dynamics equations in the presence of neighbour-dependent directional bias. We show that the asymptotic expansion provides a highly efficient scheme for obtaining approximate equilibrium solutions to the spatial moment dynamics equations when bias is weak. This scheme will be particularly useful for performing parameter inference on spatial moment models.

Suggested Citation

  • Plank, Michael J., 2020. "Asymptotic expansion approximation for spatial structure arising from directionally biased movement," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 541(C).
    • Handle: RePEc:eee:phsmap:v:541:y:2020:i:c:s0378437119318448
    DOI: 10.1016/j.physa.2019.123290
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    1. Oliver J Maclaren & Aimée Parker & Carmen Pin & Simon R Carding & Alastair J M Watson & Alexander G Fletcher & Helen M Byrne & Philip K Maini, 2017. "A hierarchical Bayesian model for understanding the spatiotemporal dynamics of the intestinal epithelium," PLOS Computational Biology, Public Library of Science, vol. 13(7), pages 1-23, July.
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