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A unifying theory for 2D spatial redistribution kernels with applications to model-fitting in ecology

  • Author(s) / Creator(s)
  • When building models to explain the dispersal patterns of organisms, ecologists
    often use an isotropic redistribution kernel to represent the distribution of
    movement distances based on phenomenological observations or biological
    considerations of the underlying physical movement mechanism. The
    Gaussian, two-dimensional (2D) Laplace and Bessel kernels are common
    choices for 2D space. All three are special (or limiting) cases of a kernel
    family, the Whittle–Matérn–Yasuda (WMY), first derived by Yasuda from an
    assumption of 2D Fickian diffusion with gamma-distributed settling times.
    We provide a novel derivation of this kernel family, using the simpler assumption of constant settling hazard, by means of a non-Fickian 2D diffusion
    equation representing movements through heterogeneous 2D media having a
    fractal structure. Our derivation reveals connections among a number of established redistribution kernels, unifying them under a single, flexible modelling
    framework. We demonstrate improvements in predictive performance in an
    established model for the spread of the mountain pine beetle upon replacing
    the Gaussian kernel by the Whittle–Matérn–Yasuda, and report similar
    results for a novel approximation, the product-Whittle–Matérn–Yasuda, that
    substantially speeds computations in applications to large datasets

  • Date created
    2020-01-01
  • Subjects / Keywords
  • Type of Item
    Article (Draft / Submitted)
  • DOI
    https://doi.org/10.7939/r3-fbye-5b90
  • License
    Attribution-NonCommercial 4.0 International