会場

埼玉大学 大学院理工学研究科棟5階 数学研究室1 （ このページ の15番の建物）

講演者

M. Humayun Kabir (Meiji University)

タイトル

Mathematical modeling of the Neolithic revolution in Europe

アブストラクト

The Neolithic revolution consists of a demographic shift from hunter-gatherers to farmers, which is one of the most significant single developments in human civilization. Around 10,000 year ago, Neolithic revolution occurred in Europe and its archeological evidence indicates that expanding velocity of farmers is roughly constant [1,2]. To understand such phenomenon, many theoretical attempts have been progressed through mathematical modeling [2]. Existing modeling approaches on Neolithic revolution demonstrates that expanding velocity is faster than the observed one. For understanding of this difference, we propose a three-component reaction-diffusion system by introducing the influence of farming technology as an environmental effect on the spread of farmers into the hunters’ region. Our goal is to study the relation between the expanding velocity and farming technology. In this talk, we focus on the one-dimensional traveling wave solutions with minimal velocity when the expanding pattern of farmers is radially symmetric. Finally our model suggests that the minimal velocity of traveling waves explains the spreading velocity of farmers when expanding pattern exhibits radial symmetry. Numerical result reveals that the minimal velocity of traveling wave solutions becomes slower when farming technology is suitably developed [4]. This is a joint work with Masayasu Mimura (Musashino Univ., Japan), Jan Elias (Univ. of Graz, Austria) and Je-Chiang Tsai (National Tsing Hua Univ., Taiwan).
References:
[1] A. J. Ammerman and L. L. Cavalli-Sforza, Measuring the rate of spread of early farming in Europe, Man, New Series, Vol. 6, No. 4, 674-688 (1971)
[2] A. J. Ammerman and L. L. Cavalli-Sforza, The Neolithic transition and the genetics of populations in Europe, Princeton University Press, Princeton (1984)
[3] J. Eliaˇs, M. H. Kabir and M. Mimura, On the well-posedness of a dispersal model of farmers and hunter-gatherers in the Neolithic transition, Mathematical Models and Methods in Applied Sciences, Vol. 28, No. 2, 195 – 222 (2018).
[4] M. H. Kabir, M. Mimura and J. C. Tsai, Spreading waves in a farmers and hunter-gatherers model of the Neolithic transition in Europe, preprint.

Seminar dinner