Seascape origin of Richards growth
Name
PhysRevE.105.014417.pdf
Description
Published version
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869.02 KB
Format
Adobe PDF
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Author(s)
Swartz, Daniel W
Ottino-Löffler, Bertrand
Kardar, Mehran
Date Issued
January 2022
Journal
Physical Review E
Publisher
American Physical Society (APS)
Citation
Swartz, Daniel W, Ottino-Löffler, Bertrand and Kardar, Mehran. 2022. "Seascape origin of Richards growth." Physical Review E, 105 (1).
Version
Final published version
Abstract
First proposed as an empirical rule over half a century ago, the Richards
growth equation has been frequently invoked in population modeling and pandemic
forecasting. Central to this model is the advent of a fractional exponent
$\gamma$, typically fitted to the data. While various motivations for this
non-analytical form have been proposed, it is still considered foremost an
empirical fitting procedure. Here, we find that Richards-like growth laws
emerge naturally from generic analytical growth rules in a distributed
population, upon inclusion of {\bf (i)} migration (spatial diffusion) amongst
different locales, and {\bf (ii)} stochasticity in the growth rate, also known
as "seascape noise." The latter leads to a wide (power-law) distribution in
local population number that, while smoothened through the former, can still
result in a fractional growth law for the overall population. This
justification of the Richards growth law thus provides a testable connection to
the distribution of constituents of the population.
MIT Department
Massachusetts Institute of Technology. Department of Physics
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DOI of Published Version
https://doi.org/10.1103/physreve.105.014417
