Fisher equation for anisotropic diffusion: Simulating South American human dispersals

The Fisher equation is commonly used to model population dynamics. This equation allows describing reaction-diffusion processes, considering both population growth and diffusion mechanism. Some results have been reported about modeling human dispersion, always assuming isotropic diffusion. Neverthel...

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Autores principales: Martino, L.A., Osella, A., Dorso, C., Lanata, J.L.
Formato: JOUR
Materias:
Anisotropy
Approximation theory
Diffusion
Parameter estimation
Population dynamics
Anisotropic diffusion
Fisher equation
Fisher information matrix
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_15393755_v76_n3_p_Martino
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id todo:paper_15393755_v76_n3_p_Martino
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spelling todo:paper_15393755_v76_n3_p_Martino2023-10-03T16:22:16Z Fisher equation for anisotropic diffusion: Simulating South American human dispersals Martino, L.A. Osella, A. Dorso, C. Lanata, J.L. Anisotropy Approximation theory Diffusion Parameter estimation Population dynamics Anisotropic diffusion Fisher equation Fisher information matrix The Fisher equation is commonly used to model population dynamics. This equation allows describing reaction-diffusion processes, considering both population growth and diffusion mechanism. Some results have been reported about modeling human dispersion, always assuming isotropic diffusion. Nevertheless, it is well-known that dispersion depends not only on the characteristics of the habitats where individuals are but also on the properties of the places where they intend to move, then isotropic approaches cannot adequately reproduce the evolution of the wave of advance of populations. Solutions to a Fisher equation are difficult to obtain for complex geometries, moreover, when anisotropy has to be considered and so few studies have been conducted in this direction. With this scope in mind, we present in this paper a solution for a Fisher equation, introducing anisotropy. We apply a finite difference method using the Crank-Nicholson approximation and analyze the results as a function of the characteristic parameters. Finally, this methodology is applied to model South American human dispersal. © 2007 The American Physical Society. Fil:Martino, L.A. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Osella, A. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Dorso, C. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_15393755_v76_n3_p_Martino
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Anisotropy
Approximation theory
Diffusion
Parameter estimation
Population dynamics
Anisotropic diffusion
Fisher equation
Fisher information matrix
spellingShingle Anisotropy
Approximation theory
Diffusion
Parameter estimation
Population dynamics
Anisotropic diffusion
Fisher equation
Fisher information matrix
Martino, L.A.
Osella, A.
Dorso, C.
Lanata, J.L.
Fisher equation for anisotropic diffusion: Simulating South American human dispersals
topic_facet Anisotropy
Approximation theory
Diffusion
Parameter estimation
Population dynamics
Anisotropic diffusion
Fisher equation
Fisher information matrix
description The Fisher equation is commonly used to model population dynamics. This equation allows describing reaction-diffusion processes, considering both population growth and diffusion mechanism. Some results have been reported about modeling human dispersion, always assuming isotropic diffusion. Nevertheless, it is well-known that dispersion depends not only on the characteristics of the habitats where individuals are but also on the properties of the places where they intend to move, then isotropic approaches cannot adequately reproduce the evolution of the wave of advance of populations. Solutions to a Fisher equation are difficult to obtain for complex geometries, moreover, when anisotropy has to be considered and so few studies have been conducted in this direction. With this scope in mind, we present in this paper a solution for a Fisher equation, introducing anisotropy. We apply a finite difference method using the Crank-Nicholson approximation and analyze the results as a function of the characteristic parameters. Finally, this methodology is applied to model South American human dispersal. © 2007 The American Physical Society.
format JOUR
author Martino, L.A.
Osella, A.
Dorso, C.
Lanata, J.L.
author_facet Martino, L.A.
Osella, A.
Dorso, C.
Lanata, J.L.
author_sort Martino, L.A.
title Fisher equation for anisotropic diffusion: Simulating South American human dispersals
title_short Fisher equation for anisotropic diffusion: Simulating South American human dispersals
title_full Fisher equation for anisotropic diffusion: Simulating South American human dispersals
title_fullStr Fisher equation for anisotropic diffusion: Simulating South American human dispersals
title_full_unstemmed Fisher equation for anisotropic diffusion: Simulating South American human dispersals
title_sort fisher equation for anisotropic diffusion: simulating south american human dispersals
url http://hdl.handle.net/20.500.12110/paper_15393755_v76_n3_p_Martino
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AT osellaa fisherequationforanisotropicdiffusionsimulatingsouthamericanhumandispersals
AT dorsoc fisherequationforanisotropicdiffusionsimulatingsouthamericanhumandispersals
AT lanatajl fisherequationforanisotropicdiffusionsimulatingsouthamericanhumandispersals
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