| Abstract: |
| The Neolithic transition, 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 transition 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 transition 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. From the viewpoint of transient behaviors of farmers and hunter-gatherers, we investigate the occurrence of traveling wave solutions with minimal and non-minimal velocities of the model. In this talk, we discuss the traveling wave solutions with minimal velocity depending on the development of farming technology. 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) 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. Elia\v{s}, 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. |
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