Culture-area relation in Axelrod's model for culture dissemination.
Axelrod's model for culture dissemination offers a nontrivial answer to the question of why there is cultural diversity given that people's beliefs have a tendency to become more similar to each other's as they interact repeatedly. The answer depends on the two control parameters of the model, namely, the number F of cultural features that characterize each agent, and the number q of traits that each feature can take on, as well as on the size A of the territory or, equivalently, on the number of interacting agents. Here, we investigate the dependence of the number C of distinct coexisting cultures on the area A in Axelrod's model, the culture-area relationship, through extensive Monte Carlo simulations. We find a non-monotonous culture-area relation, for which the number of cultures decreases when the area grows beyond a certain size, provided that q is smaller than a threshold value qc = qc (F) and F > or = 3. In the limit of infinite area, this threshold value signals the onset of a discontinuous transition between a globalized regime marked by a uniform culture (C = 1), and a completely polarized regime where all C = qF possible cultures coexist. Otherwise, the culture- area relation exhibits the typical behavior of the species- area relation, i.e., a monotonically increasing curve the slope of which is steep at first and steadily levels off at some maximum diversity value.
Instituto de Física de São Carlos, Universidade de São Paulo, Caixa Postal 369, São Carlos, SP 13560-970, Brazil.
Lauro A
LA
Barbosa
José F
JF
Fontanari
D000465:Algorithms; D003198:Computer Simulation; D003466:Cultural Characteristics; D018864:Cultural Diversity; D003468:Cultural Evolution; D003469:Culture; D006801:Humans; D007398:Interpersonal Relations; D008962:Models, Theoretical; D009010:Monte Carlo Method; D011156:Population Density