Fisher equation for anisotropic diffusion: Simulating South American human dispersals

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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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Detalles Bibliográficos
Autores principales:	Martino, Luis Angel, Osella, Ana María, Dorso, Claudio Oscar
Publicado:	2007
Materias:	Anisotropy Approximation theory Diffusion Parameter estimation Population dynamics Anisotropic diffusion Fisher equation Fisher information matrix
Acceso en línea:	https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_15393755_v76_n3_p_Martino http://hdl.handle.net/20.500.12110/paper_15393755_v76_n3_p_Martino
Aporte de:	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires

id	paper:paper_15393755_v76_n3_p_Martino
record_format	dspace
spelling	paper:paper_15393755_v76_n3_p_Martino2023-06-08T16:20:34Z Fisher equation for anisotropic diffusion: Simulating South American human dispersals Martino, Luis Angel Osella, Ana María Dorso, Claudio Oscar 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. 2007 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_15393755_v76_n3_p_Martino 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, Luis Angel Osella, Ana María Dorso, Claudio Oscar 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.
author	Martino, Luis Angel Osella, Ana María Dorso, Claudio Oscar
author_facet	Martino, Luis Angel Osella, Ana María Dorso, Claudio Oscar
author_sort	Martino, Luis Angel
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
publishDate	2007
url	https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_15393755_v76_n3_p_Martino http://hdl.handle.net/20.500.12110/paper_15393755_v76_n3_p_Martino
work_keys_str_mv	AT martinoluisangel fisherequationforanisotropicdiffusionsimulatingsouthamericanhumandispersals AT osellaanamaria fisherequationforanisotropicdiffusionsimulatingsouthamericanhumandispersals AT dorsoclaudiooscar fisherequationforanisotropicdiffusionsimulatingsouthamericanhumandispersals
_version_	1768544929731051520

Fisher equation for anisotropic diffusion: Simulating South American human dispersals

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