AB 12:205-214 (2011)  -  DOI: https://doi.org/10.3354/ab00331

Temporal kernels of larval connectivity: a generalised random-walk approach

Stephen M. Chiswell*

National Institute of Water and Atmospheric Research, PO Box 14-901, Kilbirnie, Wellington, New Zealand

ABSTRACT: For many sessile subtidal and intertidal organisms, the connection between isolated adult populations occurs through oceanic dispersal of the larval stage. We define the ‘temporal ­kernel’ as  the normalised frequency histogram of oceanic dispersal times between ­otherwise isolated populations, and suggest minimum dispersal times are best defined in terms of a percentile of the temporal kernel. Under certain assumptions, larval dispersal in the ocean can be treated as Gaussian-distributed random-walk motion in the presence of a mean flow. If this is so, the dispersal time is analogous to the ‘first-passage time’ as described by Schrödinger (1915: Phys Z 16:289–295), and the temporal kernels are described by the inverse Gaussian function. Here, solutions for the temporal kernel are derived for such a model. The solutions for the percentiles of the temporal kernel are exact, but solutions for mean and standard deviation values exist only in the limit of large island ­separation. The exact and approximate solutions are compared for random walks ­representative of realistic oceans, and the sensitivity of the temporal kernel to uncertainty in the eddy diffusivity is evaluated.

KEY WORDS: Larval dispersal · Connectivity · Modelling · Dispersal times

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Cite this article as: Chiswell SM (2011) Temporal kernels of larval connectivity: a generalised random-walk approach. Aquat Biol 12:205-214. https://doi.org/10.3354/ab00331

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