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Looking forwards and backwards : dynamics and genealogies of locally regulated populations
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Etheridge, Alison M., Kurtz, Thomas G., Letter, Ian, Ralph, Peter L. and Tsui Ho Lung, Terence (2024) Looking forwards and backwards : dynamics and genealogies of locally regulated populations. Electronic Journal of Probability, 29 . 28. doi:10.1214/24-EJP1075 ISSN 1083-6489.
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Official URL: http://doi.org/10.1214/24-EJP1075
Abstract
We introduce a broad class of mechanistic spatial models to describe how spatially heterogeneous populations live, die, and reproduce. Individuals are represented by points of a point measure, whose birth and death rates can depend both on spatial position and local population density, defined at a location to be the convolution of the point measure with a suitable non-negative integrable kernel centred on that location. We pass to three different scaling limits: an interacting superprocess, a nonlocal partial differential equation (PDE), and a classical PDE. The classical PDE is obtained both by a two-step convergence argument, in which we first scale time and population size and pass to the nonlocal PDE, and then scale the kernel that determines local population density; and in the important special case in which the limit is a reaction-diffusion equation, directly by simultaneously scaling the kernel width, timescale and population size in our individual based model.
Item Type: | Journal Article | |||||||||||||||||||||||||||
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Subjects: | H Social Sciences > HA Statistics H Social Sciences > HB Economic Theory Q Science > QA Mathematics Q Science > QH Natural history > QH301 Biology |
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | |||||||||||||||||||||||||||
Library of Congress Subject Headings (LCSH): | Population biology -- Statistical methods, Reaction-diffusion equations, Demography, Population -- Statistics, Genealogy, Percolation (Statistical physics), Stochastic processes -- Mathematical models, Spatial ecology | |||||||||||||||||||||||||||
Journal or Publication Title: | Electronic Journal of Probability | |||||||||||||||||||||||||||
Publisher: | University of Washington. Dept. of Mathematics | |||||||||||||||||||||||||||
ISSN: | 1083-6489 | |||||||||||||||||||||||||||
Official Date: | 13 February 2024 | |||||||||||||||||||||||||||
Dates: |
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Volume: | 29 | |||||||||||||||||||||||||||
Article Number: | 28 | |||||||||||||||||||||||||||
DOI: | 10.1214/24-EJP1075 | |||||||||||||||||||||||||||
Status: | Peer Reviewed | |||||||||||||||||||||||||||
Publication Status: | Published | |||||||||||||||||||||||||||
Access rights to Published version: | Open Access (Creative Commons) | |||||||||||||||||||||||||||
Date of first compliant deposit: | 19 February 2024 | |||||||||||||||||||||||||||
Date of first compliant Open Access: | 19 February 2024 | |||||||||||||||||||||||||||
RIOXX Funder/Project Grant: |
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