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 people 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 $q_c = q_c (F)$ and $F \geq 3$. 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 $C = q^F$ 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.
Local Convergence and Global Diversity: The Robustness of Cultural Homophily
最近对文化传播的阿克塞尔罗德模型（Klemm et al 2003）的扩展表明，全球多样性是极其脆弱的，只有少量的文化突变。这似乎破坏了原来的阿克塞尔罗德理论，同质性保护多样性。我们表明，文化多样性是令人惊讶的强大，如果我们增加的倾向，同质性如下。首先，我们提高了相似性的门槛，低于这个门槛就排除了影响。其次，我们允许代理同时受到所有邻居的影响，而不是像原始模型中假设的那样只有一个邻居。计算实验表明，这两种修改强烈增加的多样性对突变的鲁棒性。我们还发现，我们的扩展可能会扭转Axelrod的主要结果之一。虽然阿克塞尔罗德预测，更多的文化维度（功能）减少多样性，我们发现，更多的功能可能会带来更高水平的多样性。
