Enhanced (hydrodynamic) transport induced by population growth in reaction-diffusion systems with application to population genetics

Proceedings of the National Academy of Sciences of the United States of America
Marcel O VladJohn Ross

Abstract

We consider a system made up of different physical, chemical, or biological species undergoing replication, transformation, and disappearance processes, as well as slow diffusive motion. We show that for systems with net growth the balance between kinetics and the diffusion process may lead to fast, enhanced hydrodynamic transport. Solitary waves in the system, if they exist, stabilize the enhanced transport, leading to constant transport speeds. We apply our theory to the problem of determining the original mutation position from the current geographic distribution of a given mutation. We show that our theory is in good agreement with a simulation study of the mutation problem presented in the literature. It is possible to evaluate migratory trajectories from measured data related to the current distribution of mutations in human populations.

References

Apr 1, 1995·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·M O Vlad, M C Mackey
Aug 22, 2002·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Marcel Ovidiu VladJohn Ross
Oct 3, 2002·Nature Cell Biology·Masayoshi NishiyamaToshio Yanagida
Jan 21, 2004·Proceedings of the National Academy of Sciences of the United States of America·Christopher A EdmondsL Luca Cavalli-Sforza

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Citations

Oct 14, 2009·Nature Reviews. Genetics·John Novembre, Anna Di Rienzo
May 23, 2012·Proceedings of the National Academy of Sciences of the United States of America·Lionel RoquesEtienne K Klein
Feb 9, 2012·Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences·John Novembre, Eunjung Han
Apr 5, 2013·PLoS Computational Biology·Kirill S Korolev
Mar 1, 2012·Genetics·Montgomery Slatkin, Laurent Excoffier
Mar 16, 2007·Proceedings of the National Academy of Sciences of the United States of America·Marcel O VladJohn Ross
Jul 5, 2005·Proceedings of the National Academy of Sciences of the United States of America·Marcel O VladJohn Ross
Jan 10, 2013·Theoretical Population Biology·S PigolottiD R Nelson
Oct 30, 2007·Theoretical Population Biology·Oskar Hallatschek, David R Nelson
Jan 14, 2010·Journal of Evolutionary Biology·J FayardF Lefèvre
Sep 7, 2014·Journal of Mathematical Biology·L RoquesT Boivin
Sep 2, 2016·Current Opinion in Genetics & Development·Stephan PeischlLaurent Excoffier
Oct 13, 2007·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Joaquim FortNeus Isern
May 1, 2012·Physical Review Letters·Simone PigolottiDavid R Nelson
Apr 4, 2018·Proceedings of the National Academy of Sciences of the United States of America·Gabriel BirzuKirill S Korolev
Jan 22, 2020·Theoretical Population Biology·Marcus W Feldman
Feb 21, 2007·The Journal of Physical Chemistry. a·F MoránJ Ross

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