We evaluate the effect of a power-law-distributed social popularity on the origin and change of language, based on three artificial life models meticulously tracing the evolution of linguistic conventions including lexical items, categories, and simple syntax. A cross-model analysis reveals an optimal social popularity, in which the λ value of the power law distribution is around 1.0. Under this scaling, linguistic conventions can efficiently emerge and widely diffuse among individuals, thus maintaining a useful level of mutual understandability even in a big population. From an evolutionary perspective, we regard this social optimality as a tradeoff among social scaling, mutual understandability, and population growth. Empirical evidence confirms that such optimal power laws exist in many large-scale social systems that are constructed primarily via language-related interactions. This study contributes to the empirical explorations and theoretical discussions of the evolutionary relations between ubiquitous power laws in social systems and relevant individual behaviors.

This article adopts the category game model, which simulates the origins and evolution of linguistic categories in a group of artificial agents, to evaluate the effect of social structure on linguistic categorization. Based on the simulation results in a number of typical networks, we examine the isolating and collective effects of some structural features, including average degree, shortcuts, and level of centrality, on the categorization process. This study extends the previous simulations mainly on lexical evolution, and illustrates a general framework to systematically explore the effect of social structure on language evolution.