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Title: A reaction–diffusion model for phenotypic evolution

Abstract

We present a reaction–diffusion mathematical model for the evolutionary dynamics of phenotypic evolution. A detailed deduction of the equations is presented for the one-dimensional version, from which a more general model is proposed. Particular cases are studied using analytical approximations and numerical simulations. Results indicate that the approach proposed produces results that are coherent with mainstream models in evolutionary dynamics, suggesting that the reaction–diffusion model could be an alternative tool in the analysis of evolutionary dynamics.

Authors:
 [1];  [2]
  1. UNEMAT, Dep. Matemática (Brazil)
  2. UNICAMP, DMA, IMECC (Brazil)
Publication Date:
OSTI Identifier:
22769386
Resource Type:
Journal Article
Journal Name:
Computational and Applied Mathematics
Additional Journal Information:
Journal Volume: 37; Journal Issue: 1; Other Information: Copyright (c) 2018 SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0101-8205
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; APPROXIMATIONS; COMPUTERIZED SIMULATION; DIFFERENTIAL EQUATIONS; DIFFUSION; MATHEMATICAL MODELS; ONE-DIMENSIONAL CALCULATIONS; PHENOTYPE

Citation Formats

Assis, Raul Abreu de, E-mail: raul@unemat-net.br, and Ferreira, Wilson Castro, E-mail: wilson@unicamp.br. A reaction–diffusion model for phenotypic evolution. United States: N. p., 2018. Web. doi:10.1007/S40314-016-0343-7.
Assis, Raul Abreu de, E-mail: raul@unemat-net.br, & Ferreira, Wilson Castro, E-mail: wilson@unicamp.br. A reaction–diffusion model for phenotypic evolution. United States. doi:10.1007/S40314-016-0343-7.
Assis, Raul Abreu de, E-mail: raul@unemat-net.br, and Ferreira, Wilson Castro, E-mail: wilson@unicamp.br. Thu . "A reaction–diffusion model for phenotypic evolution". United States. doi:10.1007/S40314-016-0343-7.
@article{osti_22769386,
title = {A reaction–diffusion model for phenotypic evolution},
author = {Assis, Raul Abreu de, E-mail: raul@unemat-net.br and Ferreira, Wilson Castro, E-mail: wilson@unicamp.br},
abstractNote = {We present a reaction–diffusion mathematical model for the evolutionary dynamics of phenotypic evolution. A detailed deduction of the equations is presented for the one-dimensional version, from which a more general model is proposed. Particular cases are studied using analytical approximations and numerical simulations. Results indicate that the approach proposed produces results that are coherent with mainstream models in evolutionary dynamics, suggesting that the reaction–diffusion model could be an alternative tool in the analysis of evolutionary dynamics.},
doi = {10.1007/S40314-016-0343-7},
journal = {Computational and Applied Mathematics},
issn = {0101-8205},
number = 1,
volume = 37,
place = {United States},
year = {2018},
month = {3}
}