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Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA


Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania


Who Replaces Whom? Local versus Non-local Replacement in Social and Evolutionary Dynamics

Discontinuity, Nonlinearity, and Complexity 2(1) (2012) 57--73 | DOI:10.5890/DNC.2012.12.002

Sven Banisch$^{1}$; Tanya Araújo$^{2}$

$^{1}$ Mathematical Physics, Bielefeld University, Germany

$^{2}$ ISEG - Technical University of Lisbon (TULisbon) and Research Unit on Complexity in Economics(UECE), Portugal

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In this paper, we inspect well–known population genetics and social dynamics models. In these models, interacting individuals, while participating in a self-organizing process, give rise to the emergence of complex behaviors and patterns. While one main focus in population genetics is on the adaptive behavior of a population, social dynamics is more often concerned with the splitting of a connected array of individuals into a state of global polarization, that is, the emergence of speciation. Applying computational and mathematical tools we show that the way the mechanisms of selection, interaction and replacement are constrained and combined in the modeling have an important bearing on both adaptation and the emergence of speciation. Differently (un)constraining the mechanism of individual replacement provides the conditions required for either speciation or adaptation, since these features appear as two opposing phenomena, not achieved by one and the same model. Even though natural selection, operating as an external, environmental mechanism, is neither necessary nor sufficient for the creation of speciation, our modeling exercises highlight the important role played by natural selection in the interplay of the evolutionary and the self–organization modeling methodologies.


Financial support of the German Federal Ministry of Education and Research (BMBF) through the project Linguistic Networks is gratefully acknowledged ( This work has also benefited from financial support from the Fundação para a Ciência e a Tecnologia (FCT), under the 13 Multi-annual Funding Project of UECE, ISEG, Technical University of Lisbon.


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