Open AccessEnhanced (hydrodynamic) transport induced by population growth in reaction–diffusion systems with application to population genetics
Author(s) -
Marcel Ovidiu Vlad,
L. L. Cavalli-Sforza,
John Ross
Publication year - 2004
Publication title -
proceedings of the national academy of sciences of the united states of america
Language(s) - English
Resource type - Journals
eISSN - 1091-6490
pISSN - 0027-8424
DOI - 10.1073/pnas.0403419101
Subject(s) - diffusion , mutation , population , statistical physics , position (finance) , transformation (genetics) , replication (statistics) , distribution (mathematics) , diffusion process , transport system , biological system , physics , biology , genetics , computer science , mathematics , thermodynamics , statistics , innovation diffusion , economics , engineering , mathematical analysis , knowledge management , demography , finance , sociology , gene , transport engineering
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.