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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

American Physical Society

Author: Fort, Joaquim
Pérez Losada, Joaquim
Isern Sardó, Neus
Abstract: 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
Document access: http://hdl.handle.net/2072/25837
Language: eng
Publisher: American Physical Society
Rights: Tots els drets reservats
Subject: Física -- Ecologia
Neolític -- Models matemàtics
Neolithic period -- Mathematical models
Physics -- Ecology
Equacions de reacció-difusió
Reaction-diffusion equations
Title: Fronts from integrodifference equations and persistence effects on the Neolithic transition
Type: info:eu-repo/semantics/article
Repository: Recercat

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