Spreading Waves in a Farmers and Hunter-Gatherers Model of the Neolithic Transition in Europe

M. H. Kabir*, M. Mimura, J. C. Tsai

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)


The Neolithic transition began the spread of early agriculture throughout Europe through interactions between farmers and hunter-gatherers about 10,000 years ago. Archeological evidence produced by radiocarbon dating indicates that the expanding velocity of farming is roughly constant all over Europe. Theoretical understanding of such evidence has been performed from mathematical modeling viewpoint. However, the expanding velocity determined by existing modeling approaches is faster than the observed velocity. For understanding this difference, we propose a three-component reaction–diffusion system which consists of two different types of farmers (sedentary and migratory) and hunter-gatherers from the viewpoint of the influence of farming technology. Our purpose is to study the relation between the expanding velocity of farmers and the farming technology parameter (say, γ). In this paper, we mainly focus on the one-dimensional traveling wave solution with minimal velocity and show that the minimal velocity decreases, as γ increases. This can be compatible with the observed velocity when farming technology is developed. Our results suggest that the reason for the slowdown of the Neolithic transition might be related to the increase in the development of farming technology.

Original languageEnglish
Pages (from-to)2452-2480
Number of pages29
JournalBulletin of Mathematical Biology
Issue number9
Publication statusPublished - 2018 Sept 1


  • Neolithic transition
  • Reaction–diffusion model of farmers and hunter-gatherers interaction
  • Traveling wave solutions

ASJC Scopus subject areas

  • General Neuroscience
  • Immunology
  • General Mathematics
  • General Biochemistry,Genetics and Molecular Biology
  • General Environmental Science
  • Pharmacology
  • General Agricultural and Biological Sciences
  • Computational Theory and Mathematics


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