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Fronts from integrodifference equations and persistence effects on the Neolithic transition

We extend a previous model of the Neolithic transition in Europe [J. Fort and V. Méndez, Phys. Rev. Lett. 82, 867 (1999)] by taking two effects into account: (i) we do not use the diffusion approximation (which corresponds to second-order Taylor expansions), and (ii) we take proper care of the fact that parents do not migrate away from their children (we refer to this as a time-order effect, in the sense that it implies that children grow up with their parents, before they become adults and can survive and migrate). We also derive a time-ordered, second-order equation, which we call the sequential reaction-diffusion equation, and use it to show that effect (ii) is the most important one, and that both of them should in general be taken into account to derive accurate results. As an example, we consider the Neolithic transition: the model predictions agree with the observed front speed, and the corrections relative to previous models are important (up to 70%)

Funded by the European Commission Grant No. NEST-28192-FEPRE, the MEC-FEDER Grant No. FIS-2006-12296-C02-02, and the Generalitat de Catalunya Grant No.SGR-2005-00087

© Physical Review E: (Statistical, Nonlinear, and Soft Matter Physics), 2007, vol. 76, núm. 3, p. 031913(10)

American Physical Society

Autor: Fort, Joaquim
Pérez Losada, Joaquim
Isern Sardó, Neus
Data: setembre 2007
Resum: We extend a previous model of the Neolithic transition in Europe [J. Fort and V. Méndez, Phys. Rev. Lett. 82, 867 (1999)] by taking two effects into account: (i) we do not use the diffusion approximation (which corresponds to second-order Taylor expansions), and (ii) we take proper care of the fact that parents do not migrate away from their children (we refer to this as a time-order effect, in the sense that it implies that children grow up with their parents, before they become adults and can survive and migrate). We also derive a time-ordered, second-order equation, which we call the sequential reaction-diffusion equation, and use it to show that effect (ii) is the most important one, and that both of them should in general be taken into account to derive accurate results. As an example, we consider the Neolithic transition: the model predictions agree with the observed front speed, and the corrections relative to previous models are important (up to 70%)
Funded by the European Commission Grant No. NEST-28192-FEPRE, the MEC-FEDER Grant No. FIS-2006-12296-C02-02, and the Generalitat de Catalunya Grant No.SGR-2005-00087
Format: application/pdf
Cita: Fort, J., Pérez-Losada, J., i Isern, N. (2007). Fronts from integrodifference equations and persistence effects on the Neolithic transition. Physical Review E: (Statistical, Nonlinear, and Soft Matter Physics), 76(3), 031913(10). Recuperat 24 de setembre de 2008, a http://dx.doi.org/10.1103/PhysRevE.76.031913
ISSN: 1539-3755 (versió paper)
1550-2376 (versió electrònica)
Accés al document: http://hdl.handle.net/10256/1011
Llenguatge: eng
Editor: American Physical Society
Col·lecció: MICYT/PN 2007-2009/FIS-2006-12296-C02-02
AGAUR/2005-2008/2005-SGR-00087
Reproducció digital del document publicat a: http://dx.doi.org/10.1103/PhysRevE.76.031913
Articles publicats (D-F)
És part de: © Physical Review E: (Statistical, Nonlinear, and Soft Matter Physics), 2007, vol. 76, núm. 3, p. 031913(10)
Drets: Tots els drets reservats
Matèria: Física -- Ecologia
Neolític -- Models matemàtics
Neolithic period -- Mathematical models
Physics -- Ecology
Equacions de reacció-difusió
Reaction-diffusion equations
Títol: Fronts from integrodifference equations and persistence effects on the Neolithic transition
Tipus: info:eu-repo/semantics/article
Repositori: DUGiDocs

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