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Seceder Model

The seceder model shows how the local tendency to be different gives rise to the formation of groups. The model consists of a population of simple entities which reproduce and die. In a single reproduction event three individuals are chosen randomly and the individual which possesses the largest distance to their center is reproduced by creating a mutated offspring. The offspring replaces a randomly chosen individual of the population. This simple algorithm generates a complex group formation behavior as for example shown in the figure on the left-hand side.

The following paper demonstrates the behavior of the basic model and the dependency of the group formation on the population size.

Peter Dittrich, Fredrik Liljeros, Arne Soulier, Wolfgang Banzhaf (2000)
Spontaneous Group Formation in the Seceder Model
Phys. Rev. Lett., 84:3205-3208
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New phenomena appear if the genotype space is bounded. The following paper demonstrates these phenomena for two variants of a boundary: (1) cyclic space (periodic boundary condition) and (2) open space where the death rate increases with distance to the center of the space.

Peter Dittrich (2000)
The Seceder Effect in Bounded Space
InterJournal Complex Systems, 363
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The investigation of the (effective) fitness landscape revealed an on the first view counterintuitive phenomena: The individuals of the basic seceder model are always located in the "worst" regions of the fitness landscape where the replication rate is relatively low. (Fitness is measured as reproductive success.)

Peter Dittrich, Wolfgang Banzhaf (2001)
Survival of the Unfittest? - The Seceder Model and its Fitness Landscape
J. Kelemen and P. Sosik (Eds.), Advances in Artificial Life (Proc. 6th European Conference on Artificial Life), LNCS 2159, pp. 100-109, Prague, September 10-14, 2001. Springer, Berlin

The seceder model can be simulated very nicely by using Mathcad:

Fredrik Liljeros (2002) 
The Seceder Model
Mathcad Advisor Newslatter, 4/3/2002

The following work explores a generalized, stochastic seceder model. with variable size polling groups and higher-dimensional opinion vectors, revealing its essential modes of self-organized segregation. It pins down the upper critical size of the sampling group and analytically uncovers a self-similar hierarchy of dynamically stable, multiple-branch fixed points.

A. Soulier and T. Halpin-Healy (2003)
The dynamics of multidimensional secession: Fixed points and ideological condensation
Phys. Rev. Lett. 90(25): art. no. 258103

People Involved in Research on the Seceder Model