A unifying theory for 2D spatial redistribution kernels with applications to model-fitting in ecology
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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
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http://purl.org/coar/resource_type/c_6501 http://purl.org/coar/version/c_b1a7d7d4d402bcce http://purl.org/coar/version/c_71e4c1898caa6e32
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en