Spreading speed in a farmers and hunter-gatherers model arising from Neolithic transition in Europe

Xinfu Chen; Je Chiang Tsai

doi:10.1016/j.matpur.2020.03.007

Spreading speed in a farmers and hunter-gatherers model arising from Neolithic transition in Europe

Xinfu Chen, Je Chiang Tsai^*

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

18 Citations (Scopus)

Abstract

We study spreading phenomena in a two-component reaction-diffusion system, modeling the Neolithic transition from hunter-gatherer societies to agricultural societies in Europe. When farmer populations were introduced into the region inhabited by hunter-gatherer populations, farmer populations spread as an expanding wave through Europe. The speed of the wave is observed to tend to be a constant. We analytically compute the spreading velocity of the model, and characterize the longtime behavior of solutions of the model. Without comparison principle, we introduce a new technique that can locate the spreading front in reaction-diffusion systems.

Original language	English
Pages (from-to)	192-207
Number of pages	16
Journal	Journal des Mathematiques Pures et Appliquees
Volume	143
DOIs	https://doi.org/10.1016/j.matpur.2020.03.007
Publication status	Published - 2020 Nov

Keywords

Farmers and Hunter-gatherers model
Spreading speed
Traveling waves

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.1016/j.matpur.2020.03.007

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abstract = "We study spreading phenomena in a two-component reaction-diffusion system, modeling the Neolithic transition from hunter-gatherer societies to agricultural societies in Europe. When farmer populations were introduced into the region inhabited by hunter-gatherer populations, farmer populations spread as an expanding wave through Europe. The speed of the wave is observed to tend to be a constant. We analytically compute the spreading velocity of the model, and characterize the longtime behavior of solutions of the model. Without comparison principle, we introduce a new technique that can locate the spreading front in reaction-diffusion systems.",

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AB - We study spreading phenomena in a two-component reaction-diffusion system, modeling the Neolithic transition from hunter-gatherer societies to agricultural societies in Europe. When farmer populations were introduced into the region inhabited by hunter-gatherer populations, farmer populations spread as an expanding wave through Europe. The speed of the wave is observed to tend to be a constant. We analytically compute the spreading velocity of the model, and characterize the longtime behavior of solutions of the model. Without comparison principle, we introduce a new technique that can locate the spreading front in reaction-diffusion systems.

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ER -

Spreading speed in a farmers and hunter-gatherers model arising from Neolithic transition in Europe

Abstract

Keywords

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